pax_global_header00006660000000000000000000000064131771533470014525gustar00rootroot0000000000000052 comment=146793bf1dd26ab6d31e62e09b1d8781a4b8ece4 sasmodels/000077500000000000000000000000001317715334700130635ustar00rootroot00000000000000sasmodels/.gitattributes000066400000000000000000000001251317715334700157540ustar00rootroot00000000000000*.py text eol=lf *.c text eol=lf *.h text eol=lf *.cpp text eol=lf *.rst text eol=lf sasmodels/.gitignore000066400000000000000000000004051317715334700150520ustar00rootroot00000000000000/build/ /dist/ /logs/ /*.csv *.pyc *.cl *.def *.so *.obj /doc/_build/ /doc/api/ /doc/model/ /doc/guide/models .mplconfig /pylint_violations.txt /coverage.xml /.coverage /.project /.pydevproject /.idea /sasmodels.egg-info/ /example/Fit_*/ /example/batch_fit.csv sasmodels/.travis.yml000066400000000000000000000030421317715334700151730ustar00rootroot00000000000000language: python sudo: false matrix: include: - os: linux env: - PY=2.7 - os: linux env: - PY=3.6 - os: osx language: generic env: - PY=2.7 - os: osx language: generic env: - PY=3.5 branches: only: - master addons: apt: packages: opencl-headers before_install: - if [[ $encrypted_cb04388797b6_iv ]]; then openssl aes-256-cbc -K $encrypted_cb04388797b6_key -iv $encrypted_cb04388797b6_iv -in .travis/travis_rsa.enc -out .travis/travis_rsa -d; fi; - echo $TRAVIS_OS_NAME - if [[ "$TRAVIS_OS_NAME" == "linux" ]]; then wget https://repo.continuum.io/miniconda/Miniconda3-latest-Linux-x86_64.sh -O miniconda.sh; fi; - if [[ "$TRAVIS_OS_NAME" == "osx" ]]; then wget https://repo.continuum.io/miniconda/Miniconda3-latest-MacOSX-x86_64.sh -O miniconda.sh; fi; - bash miniconda.sh -b -p $HOME/miniconda - export PATH="$HOME/miniconda/bin:$PATH" - hash -r - conda update --yes conda - conda info -a - conda install --yes python=$PY numpy scipy cython mako cffi install: - pip install bumps - pip install unittest-xml-reporting script: - python --version - python -m sasmodels.model_test -v dll all before_deploy: - echo -e "Host danse.chem.utk.edu\n\tStrictHostKeyChecking no\n" >> ~/.ssh/config deploy: skip_cleanup: true provider: script script: "/bin/sh -ex ./deploy.sh" on: branch: master notifications: slack: secure: xNAUeSu1/it/x9Q2CSg79aw1LLc7d6mLpcqSCTeKROp71RhkFf8VjJnJm/lEbKHNC8yj5H9UHrz5DmzwJzI+6oMt4NdEeS6WvGhwGY/wCt2IcJKxw0vj1DAU04qFMS041Khwclo6jIqm76DloinXvmvsS+K/nSyQkF7q4egSlwA= sasmodels/.travis/000077500000000000000000000000001317715334700144515ustar00rootroot00000000000000sasmodels/.travis/travis_rsa.enc000066400000000000000000000032201317715334700173120ustar00rootroot00000000000000gϡiIDҍm] r7wDd >;Yܣ0xT% wX1I.5xԻܽDm+#$C]vB|{i ?"wO-˦h޿"{5̳ 3`1Q2Ya7ciY'H^fiwFCNp 6>0XMzB{g/v&%ul-`ǸpH2 VYeSϭ|K̵%;GD98&g*ma(P*c=GRg,OPtDfݮNJkcjsN3ey 0LbP!КQe7 \xKH0 5r?&-8<_Aw] #hCzE9keVkqaKs2;I5_ayok'/ndEBoʇ}K)C}Lc⮲aj˅Rs:Vf}ğ QoEJboRV*/%"hG s JDokNX@0YX mnh4Istd`5z5Bq'XʎCMvI* FPO[ &"bo9/=Q%uwk^v`IccKD'K1,.8~z5"# rc&JLZ-' Mzp:}Y3smDcHWg^,9x)cHwҠAC9>Oy:Rr\K&#.l֨!+eΡ#l s p ֖reh]YNGY0οR҂rFF[4b$]v  )+&vDb>+de9Hk7wdg Ip:NCǡNau9+ݤzcII8&]Owc3Iwϗxmxz 3ay(x@-zpgZՁ47~ /ttck]LJnd%?hOv+XtBlQl~IExzZG`3RPyx!RuDEpfCYg:X7"c+H(#qa{[iBy EUX$PanE Gǰ?H W ;;Ymse.BpL5zq=22;SlE v- 5`)</[%ykLgAFW>*8VfF;K\M &0T^l{:i_πPJ8{C~R }BbL Տ, ڢxm:,l#aUa-޻S<Зμ `,ζzYSRه5AL=ѲgcL5>&ݰVA |+(EG>[3XWػ^po6'biFİ+^wcRet/c;|ovFy?L[#Lѹ~œGܻwS ̿-FkHo_Aѷ˟‰+1>&\/}c]8hsasmodels/LICENSE.txt000077500000000000000000000027261317715334700147200ustar00rootroot00000000000000Copyright (c) 2009-2017, SasView Developers All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. 3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. sasmodels/MANIFEST.in000066400000000000000000000001731317715334700146220ustar00rootroot00000000000000include LICENSE.txt include README.rst include setup.py recursive-include sasmodels *.py *.c *.cl *.json *.gif *.jpg *.png sasmodels/README.rst000066400000000000000000000034401317715334700145530ustar00rootroot00000000000000Sasmodels ========= Theory models for small angle scattering. The models provided are usable directly in the bumps fitting package and in the sasview analysis package. If OpenCL is available, the models will run much faster. If not, then precompiled versions will be included with the distributed package. New models can be added if OpenCL or a C compiler is available. Example ------- The example directory contains a radial+tangential data set for an oriented rod-like shape. The data is loaded by sas.dataloader from the sasview package, so sasview is needed to run the example. To run the example, you need sasview, sasmodels and bumps. Assuming these repositories are installed side by side, change to the sasmodels/example directory and enter:: PYTHONPATH=..:../../sasview/src ../../bumps/run.py fit.py \ cylinder --preview See bumps documentation for instructions on running the fit. With the python packages installed, e.g., into a virtual environment, then the python path need not be set, and the command would be:: bumps fit.py cylinder --preview The fit.py model accepts up to two arguments. The first argument is the model type, which has been defined for cylinder, capped_cylinder, core_shell_cylinder, ellipsoid, triaxial_ellipsoid and lamellar. The second argument is view, which can be radial or tangential. To fit both radial and tangential simultaneously, use the word "both". Notes ----- cylinder.c + cylinder.py is the cylinder model with renamed variables and sld scaled by 1e6 so the numbers are nicer. The model name is "cylinder" lamellar.py is an example of a single file model with embedded C code. |TravisStatus|_ .. |TravisStatus| image:: https://travis-ci.org/SasView/sasmodels.svg?branch=master .. _TravisStatus: https://travis-ci.org/SasView/sasmodels sasmodels/TESTS.txt000066400000000000000000000011011317715334700145170ustar00rootroot00000000000000REM CHECK IF SASMODELS AND SASVIEW GIVE THE SAME ANSWER compare-local poly_gauss_coil -1d multi_compare-local.sh poly_gauss_coil 200 1d100 0 double > poly_gauss_coil-1d.csv REM CHECK IF THE UNIT TEST PASSES python -m sasmodels.model_test poly_gauss_coil REM IF YOU ARE REALLY FEELING KEEN... python -m pylint --rcfile=extra/pylint.rc sasmodels/models/poly_gauss_coil.py REM CHECK THE DOCUMENTATION RENDERED cd to \sasmodels\doc make html cd to \sasmodels\doc\_build\html open index.html and navigate to poly_gauss_coil sasmodels/appveyor.yml000066400000000000000000000057121317715334700154600ustar00rootroot00000000000000environment: # SDK v7.0 MSVC Express 2008's SetEnv.cmd script will fail if the # /E:ON and /V:ON options are not enabled in the batch script interpreter # See: http://stackoverflow.com/a/13751649/163740 CMD_IN_ENV: "cmd /E:ON /V:ON /C obvci_appveyor_python_build_env.cmd" # Workaround for https://github.com/conda/conda-build/issues/636 PYTHONIOENCODING: "UTF-8" matrix: # Note: Because we have to separate the py2 and py3 components due to compiler version, we have a race condition for non-python packages. # Not sure how to resolve this, but maybe we should be tracking the VS version in the build string anyway? - TARGET_ARCH: "x86" CONDA_PY: "27" PY_CONDITION: "python >=2.7,<3" CONDA_INSTALL_LOCN: "C:\\Miniconda" # - TARGET_ARCH: "x86" # CONDA_PY: "34" # PY_CONDITION: "python >=3.4,<3.5" # CONDA_INSTALL_LOCN: "C:\\Miniconda3" - TARGET_ARCH: "x86" CONDA_PY: "35" PY_CONDITION: "python >=3.5" CONDA_INSTALL_LOCN: "C:\\Miniconda35" - TARGET_ARCH: "x64" CONDA_PY: "27" PY_CONDITION: "python >=2.7,<3" CONDA_INSTALL_LOCN: "C:\\Miniconda-x64" # - TARGET_ARCH: "x64" # CONDA_PY: "34" # PY_CONDITION: "python >=3.4,<3.5" # CONDA_INSTALL_LOCN: "C:\\Miniconda3-x64" - TARGET_ARCH: "x64" CONDA_PY: "35" PY_CONDITION: "python >=3.5" CONDA_INSTALL_LOCN: "C:\\Miniconda35-x64" # We always use a 64-bit machine, but can build x86 distributions # with the TARGET_ARCH variable (which is used by CMD_IN_ENV). platform: - x64 install: # Set the CONDA_NPY, although it has no impact on the actual build. We need this because of a test within conda-build. - cmd: set CONDA_NPY=19 # Remove cygwin (and therefore the git that comes with it). - cmd: rmdir C:\cygwin /s /q # Use the pre-installed Miniconda for the desired arch # # However, it is really old. So, we need to update some # things before we proceed. That seems to require it being # on the path. So, we temporarily put conda on the path # so that we can update it. Then we remove it so that # we can do a proper activation. - cmd: set "OLDPATH=%PATH%" - cmd: set "PATH=%CONDA_INSTALL_LOCN%\\Scripts;%CONDA_INSTALL_LOCN%\\Library\\bin;%PATH%" - cmd: conda update --yes --quiet conda python - cmd: set "PATH=%OLDPATH%" - cmd: call %CONDA_INSTALL_LOCN%\Scripts\activate.bat - cmd: conda config --add channels conda-forge - cmd: conda config --set show_channel_urls true - cmd: conda update --yes --quiet conda - cmd: conda install --yes --quiet obvious-ci - cmd: conda install --yes --quiet numpy toolchain scipy cython cffi - cmd: conda install --yes --channel conda-forge pyopencl - cmd: pip install bumps unittest-xml-reporting tinycc build_script: # Build the project - "%CMD_IN_ENV% python setup.py build" test_script: # Run the project tests - "%CMD_IN_ENV% python -m sasmodels.model_test dll all" sasmodels/compare.bat000066400000000000000000000005761317715334700152110ustar00rootroot00000000000000@echo off rem === Set the python path to include sasview for /D %%i in (..\sasview\build\lib*) do set SASVIEW=%%i set PYTHONPATH=..\bumps;../periodictable;%SASVIEW% rem echo PYTHONPATH=%PYTHONPATH% rem === Set the pyopencl control parameters rem set PYOPENCL_COMPILER_OUTPUT=1 rem set PYOPENCL_CTX=0 rem === Set OpenMP or not rem set SAS_OPENMP=1 python -m sasmodels.compare %* sasmodels/compare.sh000077500000000000000000000005761317715334700150600ustar00rootroot00000000000000#!/bin/bash sasview=( ../sasview/build/lib.* ) sep=$(python -c "import os;print(os.pathsep)") PYTHONPATH=../bumps${sep}../periodictable${sep}$sasview export PYTHONPATH #echo PYTHONPATH=$PYTHONPATH #PYOPENCL_COMPILER_OUTPUT=1; export PYOPENCL_COMPILER_OUTPUT #PYOPENCL_CTX=${CTX:-1}; export PYOPENCL_CTX #SAS_OPENMP=1; export SAS_OPENMP ${PYTHON:-python} -m sasmodels.compare $* sasmodels/deploy.sh000066400000000000000000000003461317715334700147160ustar00rootroot00000000000000if [ "$encrypted_cb04388797b6_iv" ] then eval "$(ssh-agent -s)" chmod 600 .travis/travis_rsa ssh-add .travis/travis_rsa git remote add deploy git@danse.chem.utk.edu:/home/git/sasmodels git push deploy master fisasmodels/doc/000077500000000000000000000000001317715334700136305ustar00rootroot00000000000000sasmodels/doc/Makefile000066400000000000000000000107611317715334700152750ustar00rootroot00000000000000# Makefile for Sphinx documentation # # You can set these variables from the command line. PYTHON ?= python SPHINXOPTS = SPHINXBUILD = $(PYTHON) -m sphinx.__init__ PAPER ?= letter BUILDDIR = _build ifdef ComSpec RMDIR = rmdir /s/q CPDIR = xcopy /q/e/i MKDIR = mkdir PATHSEP = $(strip \) COPY = copy else RMDIR = rm -rf CPDIR = cp -rp MKDIR = mkdir -p PATHSEP = $(strip /) COPY = cp endif # Internal variables. PAPEROPT_a4 = -D latex_paper_size=a4 PAPEROPT_letter = -D latex_paper_size=letter ALLSPHINXOPTS = -d _build/doctrees $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) . IMG_SOURCE = $(wildcard ../sasmodels/models/img/*) IMG_DEST = $(patsubst ../sasmodels/models/img/%,model/img/%,$(IMG_SOURCE)) MODELS_PY = $(wildcard ../sasmodels/models/[a-z]*.py) MODELS_RST = $(patsubst ../sasmodels/models/%.py,model/%.rst,$(MODELS_PY)) help: @echo "Please use \`make ' where is one of" @echo " html to make standalone HTML files" @echo " dirhtml to make HTML files named index.html in directories" @echo " pickle to make pickle files" @echo " json to make JSON files" @echo " htmlhelp to make HTML files and a HTML help project" @echo " qthelp to make HTML files and a qthelp project" @echo " latex to make LaTeX files, you can set PAPER=a4 or PAPER=letter" @echo " changes to make an overview of all changed/added/deprecated items" @echo " linkcheck to check all external links for integrity" @echo " doctest to run all doctests embedded in the documentation (if enabled)" model/img/%: ../sasmodels/models/img/% ifdef ComSpec $(COPY) $(subst /,\,$<) $(subst /,\,$@) else $(COPY) $< $@ endif model/%.rst: ../sasmodels/models/%.py $(PYTHON) genmodel.py $< $@ ref/models/index.rst: gentoc.py $(MODELS_PY) $(PYTHON) gentoc.py $(MODELS_PY) .PHONY: help clean html dirhtml pickle json htmlhelp qthelp latex changes linkcheck doctest build api: genapi.py -$(RMDIR) api $(PYTHON) genapi.py model: $(MKDIR) model ifdef ComSpec $(MKDIR) model\img else $(MKDIR) model/img endif build: model $(MODELS_RST) $(IMG_DEST) api ref/models/index.rst ifdef ComSpec rem cd ..\.. rem python setup.py build else #cd ../.. && python setup.py build endif upload: scp -r _build/html/* reflectometry.org:web/danse/docs/sasmodels scp _build/latex/SASModels.pdf reflectometry.org:web/danse/download clean: -$(RMDIR) _build model api ref$(PATHSEP)models html: build $(SPHINXBUILD) -b html $(ALLSPHINXOPTS) _build/html @echo @echo "Build finished. The HTML pages are in _build/html." dirhtml: $(SPHINXBUILD) -b dirhtml $(ALLSPHINXOPTS) _build/dirhtml @echo @echo "Build finished. The HTML pages are in _build/dirhtml." pickle: $(SPHINXBUILD) -b pickle $(ALLSPHINXOPTS) _build/pickle @echo @echo "Build finished; now you can process the pickle files." json: $(SPHINXBUILD) -b json $(ALLSPHINXOPTS) _build/json @echo @echo "Build finished; now you can process the JSON files." htmlhelp: $(SPHINXBUILD) -b htmlhelp $(ALLSPHINXOPTS) _build/htmlhelp @echo @echo "Build finished; now you can run HTML Help Workshop with the" \ ".hhp project file in _build/htmlhelp." qthelp: $(SPHINXBUILD) -b qthelp $(ALLSPHINXOPTS) _build/qthelp @echo @echo "Build finished; now you can run "qcollectiongenerator" with the" \ ".qhcp project file in _build/qthelp, like this:" @echo "# qcollectiongenerator _build/qthelp/Periodic Table.qhcp" @echo "To view the help file:" @echo "# assistant -collectionFile _build/qthelp/Periodic Table.qhc" latex: build $(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) _build/latex @echo @echo "Build finished; the LaTeX files are in _build/latex." @echo "Run \`make all-pdf' or \`make all-ps' in that directory to" \ "run these through (pdf)latex." pdf: latex $(MAKE) -C _build/latex all-pdf $(COPY) _build/latex/SASModels.pdf _build/html changes: $(SPHINXBUILD) -b changes $(ALLSPHINXOPTS) _build/changes @echo @echo "The overview file is in _build/changes." linkcheck: $(SPHINXBUILD) -b linkcheck $(ALLSPHINXOPTS) _build/linkcheck @echo @echo "Link check complete; look for any errors in the above output " \ "or in _build/linkcheck/output.txt." doctest: $(SPHINXBUILD) -b doctest $(ALLSPHINXOPTS) _build/doctest @echo "Testing of doctests in the sources finished, look at the " \ "results in _build/doctest/output.txt." sasmodels/doc/README.txt000066400000000000000000000015261317715334700153320ustar00rootroot00000000000000This is the top level build direcgtory for the periodictable documentation. All of the documentation is written using sphinx, a python documentation system using restructured text. See the User Guide section "Contributing Changes" for details on how to build the documentation. Manifest: Makefile use "make clean html pdf" to build the docs guide user documentation api auto-generated interface documentation plots programs to generate figures index.rst top level include document genmods.py creates the module index files conf.py sphinx configuration rst_prolog restructured text macros (for units) discoverer, shelltable sample extensions _static images and style sheets _templates page layouts _extensions sphinx extensions _build output directory sasmodels/doc/_extensions/000077500000000000000000000000001317715334700161665ustar00rootroot00000000000000sasmodels/doc/_extensions/dollarmath.py000066400000000000000000000050521317715334700206710ustar00rootroot00000000000000# This program is public domain # Author: Paul Kienzle r""" Allow $math$ markup in text and docstrings, ignoring \$. The $math$ markup should be separated from the surrounding text by spaces. To embed markup within a word, place backslash-space before and after. For convenience, the final $ can be followed by punctuation (period, comma or semicolon). """ import re _dollar = re.compile(r"(?:^|(?<=\s|[(]))[$]([^\n]*?)(? not converted\n") # sys.stdout.write(content) # sys.stdout.write("\n") #elif '$' in original: # import sys # sys.stdout.write("\n========> converted\n") # sys.stdout.write(content) # sys.stdout.write("\n") return content def rewrite_rst(app, docname, source): source[0] = replace_dollar(source[0]) def rewrite_autodoc(app, what, name, obj, options, lines): lines[:] = [replace_dollar(L) for L in lines] def setup(app): app.connect('source-read', rewrite_rst) app.connect('autodoc-process-docstring', rewrite_autodoc) def test_dollar(): assert replace_dollar(u"no dollar")==u"no dollar" assert replace_dollar(u"$only$")==u":math:`only`" assert replace_dollar(u"$first$ is good")==u":math:`first` is good" assert replace_dollar(u"so is $last$")==u"so is :math:`last`" assert replace_dollar(u"and $mid$ too")==u"and :math:`mid` too" assert replace_dollar(u"$first$, $mid$, $last$")==u":math:`first`, :math:`mid`, :math:`last`" assert replace_dollar(u"dollar\$ escape")==u"dollar$ escape" assert replace_dollar(u"dollar \$escape\$ too")==u"dollar $escape$ too" assert replace_dollar(u"spaces $in the$ math")==u"spaces :math:`in the` math" assert replace_dollar(u"emb\ $ed$\ ed")==u"emb\ :math:`ed`\ ed" assert replace_dollar(u"$first$a")==u"$first$a" assert replace_dollar(u"a$last$")==u"a$last$" assert replace_dollar(u"$37")==u"$37" assert replace_dollar(u"($37)")==u"($37)" assert replace_dollar(u"$37 - $43")==u"$37 - $43" assert replace_dollar(u"($37, $38)")==u"($37, $38)" assert replace_dollar(u"a $mid$dle a")==u"a $mid$dle a" assert replace_dollar(u"a ($in parens$) a")==u"a (:math:`in parens`) a" assert replace_dollar(u"a (again $in parens$) a")==u"a (again :math:`in parens`) a" if __name__ == "__main__": test_dollar() sasmodels/doc/_extensions/numfig.py000066400000000000000000000064501317715334700200320ustar00rootroot00000000000000from docutils.nodes import figure, caption, Text, reference, raw, SkipNode, Element from sphinx.roles import XRefRole # Element classes class page_ref(reference): pass class num_ref(reference): pass # Visit/depart functions def skip_num_ref(self, node): raise SkipNode def skip_page_ref(self, node): raise SkipNode def latex_visit_page_ref(self, node): self.body.append("\\pageref{%s:%s}" % (node['refdoc'], node['reftarget'])) raise SkipNode def latex_visit_num_ref(self, node): fields = node['reftarget'].split('#') if len(fields) > 1: label, target = fields ref_link = '%s:%s' % (node['refdoc'], target) latex = "\\hyperref[%s]{%s \\ref*{%s}}" % (ref_link, label, ref_link) self.body.append(latex) else: self.body.append('\\ref{%s:%s}' % (node['refdoc'], fields[0])) raise SkipNode def doctree_read(app, doctree): # first generate figure numbers for each figure env = app.builder.env figid_docname_map = getattr(env, 'figid_docname_map', {}) for figure_info in doctree.traverse(figure): for id in figure_info['ids']: figid_docname_map[id] = env.docname env.figid_docname_map = figid_docname_map def doctree_resolved(app, doctree, docname): i = 1 figids = {} for figure_info in doctree.traverse(figure): if app.builder.name != 'latex' and app.config.number_figures: for cap in figure_info.traverse(caption): cap[0] = Text("%s %d: %s" % (app.config.figure_caption_prefix, i, cap[0])) for id in figure_info['ids']: figids[id] = i i += 1 # replace numfig nodes with links if app.builder.name != 'latex': for ref_info in doctree.traverse(num_ref): if '#' in ref_info['reftarget']: label, target = ref_info['reftarget'].split('#') labelfmt = label + " %d" else: labelfmt = '%d' target = ref_info['reftarget'] if target not in figids: continue if app.builder.name == 'html': target_doc = app.builder.env.figid_docname_map[target] link = "%s#%s" % (app.builder.get_relative_uri(docname, target_doc), target) html = '%s' % (link, labelfmt %(figids[target])) ref_info.replace_self(raw(html, html, format='html')) else: ref_info.replace_self(Text(labelfmt % (figids[target]))) def clean_env(app): app.builder.env.i=1 app.builder.env.figid_docname_map = {} def setup(app): app.add_config_value('number_figures', True, True) app.add_config_value('figure_caption_prefix', "Figure", True) app.add_node(page_ref, text=(skip_page_ref, None), html=(skip_page_ref, None), latex=(latex_visit_page_ref, None)) app.add_role('page', XRefRole(nodeclass=page_ref)) app.add_node(num_ref, latex=(latex_visit_num_ref, None), html=(skip_num_ref, None)) app.add_role('num', XRefRole(nodeclass=num_ref)) app.connect("builder-inited", clean_env) app.connect('doctree-read', doctree_read) app.connect('doctree-resolved', doctree_resolved) sasmodels/doc/_static/000077500000000000000000000000001317715334700152565ustar00rootroot00000000000000sasmodels/doc/_static/haiku-site.css000066400000000000000000000004251317715334700200340ustar00rootroot00000000000000@import url("haiku.css"); div.contents { float: right; background: Cornsilk; margin: 0.5em 0.5em; } div.contents p.topic-title { display: none; } div.contents ul { padding: 0em; } div.contents ul > li { background: none; padding: 0 0 0 1em; } sasmodels/doc/_templates/000077500000000000000000000000001317715334700157655ustar00rootroot00000000000000sasmodels/doc/_templates/layout.html000066400000000000000000000003321317715334700201660ustar00rootroot00000000000000{% extends "!layout.html" %} {%- block extrahead %} {% endblock %}sasmodels/doc/conf.py000066400000000000000000000175611317715334700151410ustar00rootroot00000000000000# -*- coding: utf-8 -*- # # Periodic Table documentation build configuration file, created by # sphinx-quickstart on Tue Jun 2 11:16:08 2009. # # This file is execfile()d with the current directory set to its containing dir. # # Note that not all possible configuration values are present in this # autogenerated file. # # All configuration values have a default; values that are commented out # serve to show the default. import sys, os # If extensions (or modules to document with autodoc) are in another directory, # add these directories to sys.path here. If the directory is relative to the # documentation root, use os.path.abspath to make it absolute, like shown here. #sys.path.append(os.path.abspath('_extensions'+(os.path.dirname('../../periodictable')))) sys.path.insert(0, os.path.abspath('..')) sys.path.insert(0, os.path.abspath('_extensions')) sys.path.insert(0, os.path.abspath('.')) # needed for extension tests print("\n".join(sys.path)) import sasmodels # -- General configuration ----------------------------------------------------- # Add any Sphinx extension module names here, as strings. 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List of tuples # (source start file, target name, title, author, documentclass [howto/manual]). latex_documents = [ ('index', 'SASModels.tex', 'SAS Models Documentation', 'sasview team', 'manual'), ] # The name of an image file (relative to this directory) to place at the top of # the title page. #latex_logo = None # For "manual" documents, if this is true, then toplevel headings are parts, # not chapters. #latex_use_parts = False # Additional stuff for the LaTeX preamble. #latex_preamble = '' LATEX_PREAMBLE=r""" \newcommand{\lt}{<} \newcommand{\gt}{>} \renewcommand{\AA}{\text{\r{A}}} % Allow \AA in math mode \usepackage[utf8]{inputenc} % Allow unicode symbols in text \DeclareUnicodeCharacter {00B7} {\ensuremath{\cdot}} % cdot \DeclareUnicodeCharacter {00B0} {\ensuremath{^\circ}} % degrees \DeclareUnicodeCharacter {212B} {\AA} % Angstrom """ latex_elements = {'preamble' : LATEX_PREAMBLE} # Documents to append as an appendix to all manuals. #latex_appendices = [] # If false, no module index is generated. #latex_use_modindex = True # Which class/__init__ docstring to use: class, init, or both autoclass_content = 'both' # Autodoc member sort order: by class or by type autodoc_member_order = 'groupwise' if os.path.exists('rst_prolog'): with open('rst_prolog') as fid: rst_prolog = fid.read() numfig = True #numfig_format = {"figure": "Fig. %s", "table": "Table %s", "code-block": "Program %s"} sasmodels/doc/developer/000077500000000000000000000000001317715334700156155ustar00rootroot00000000000000sasmodels/doc/developer/calculator.rst000066400000000000000000000327701317715334700205110ustar00rootroot00000000000000.. currentmodule:: sasmodels .. _Calculator_Interface: Calculator Interface ==================== This document describes the layer between the form factor kernels and the model calculator which implements the polydispersity and magnetic SLD calculations. There are three separate implementations of this layer, :mod:`kernelcl` for OpenCL, which operates on a single Q value at a time, :mod:`kerneldll` for the DLL, which loops over a vector of Q values, and :mod:`kernelpy` for python models which operates on vector Q values. Each implementation provides three different calls *Iq*, *Iqxy* and *Imagnetic* for 1-D, 2-D and 2-D magnetic kernels respectively. The C code is defined in *kernel_iq.c* and *kernel_iq.cl* for DLL and OpenCL respectively. The kernel call looks as follows:: kernel void KERNEL_NAME( int nq, // Number of q values in the q vector int pd_start, // Starting position in the polydispersity loop int pd_stop, // Ending position in the polydispersity loop ProblemDetails *details, // Polydispersity info double *values, // Value and weights vector double *q, // q or (qx,qy) vector double *result, // returned I(q), with result[nq] = pd_weight double cutoff) // polydispersity weight cutoff The details for OpenCL and the python loop are slightly different, but these data structures are common. *nq* indicates the number of q values that will be calculated. The *pd_start* and *pd_stop* parameters set the range of the polydispersity loop to compute for the current kernel call. Give a polydispersity calculation with 30 weights for length and 30 weights for radius for example, there are a total of 900 calls to the form factor required to compute the kernel. These might be done in chunks of 100, so the first call would start at zero and stop after 100 iterations. The second call would then have to set the length index to 3 and the radius index to 10 for a position of 3*30+10=100, and could then proceed to position 200. This allows us to interrupt the calculation in the middle of a long polydispersity loop without having to do special tricks with the C code. More importantly, it stops the OpenCL kernel in a reasonable time; because the GPU is used by the operating system to show its windows, if a GPU kernel runs too long then it will be automatically killed and no results will be returned to the caller. The *ProblemDetails* structure is a direct map of the :class:`details.CallDetails` buffer. This indicates which parameters are polydisperse, and where in the values vector the values and weights can be found. For each polydisperse parameter there is a parameter id, the length of the polydispersity loop for that parameter, the offset of the parameter values in the pd value and pd weight vectors and the 'stride' from one index to the next, which is used to translate between the position in the polydispersity loop and the particular parameter indices. The *num_eval* field is the total size of the polydispersity loop. *num_weights* is the number of elements in the pd value and pd weight vectors. *num_active* is the number of non-trivial pd loops (polydisperse parameters should be ordered by decreasing pd vector length, with a length of 1 meaning no polydispersity). Oriented objects in 2-D need a cos(theta) spherical correction on the angular variation in order to preserve the 'surface area' of the weight distribution. *theta_par* is the id of the polar coordinate parameter if there is one. The *values* vector consists of the fixed values for the model plus pd value and pd weight vectors. There are *NUM_VALUES* fixed values for the model, which includes the initial two slots for scale and background, the NUM_PARS values for the kernel parameters, three slots for the applied magnetism, and three slots for each of the SLD parameters for the sample magnetiziation *(Mx, My, Mz)*. Sample magnetization is translated from *(M, theta, phi)* to *(Mx, My, Mz)* before the kernel is called. After the fixed values comes the pd value vector, with the polydispersity values for each parameter stacked one after the other. The order isn't important since the location for each parameter is stored in the *pd_offset* field of the *ProblemDetails* structure, but the values do need to be contiguous. After *num_weights* values, the pd weight vector is stored, with the same configuration as the pd value vector. Note that the pd vectors can contain values that are not in the polydispersity loop; this is used by :class:`mixture.MixtureKernel` to make it easier to call the various component kernels. The *q* vector contains one value for each q for *Iq* kernels, or a pair of *(qx,qy)* values for each q for *Iqxy* and *Imagnetic* kernels. OpenCL pads all vectors to 32 value boundaries just to be safe, including the *values* vector and the the *results* vector. The *results* vector contains one slot for each of the *nq* values, plus one extra slot at the end for the current polydisperse normalization. This is required when the polydispersity loop is broken across several kernel calls. *cutoff* is a importance cutoff so that points which contribute negligibly to the total scattering can be skipped without calculating them. :func:`generate.make_source` defines the following C macros: - USE_OPENCL is defined if running in opencl - MAX_PD is the maximum depth of the polydispersity loop [model specific] - NUM_PARS is the number of parameter values in the kernel. This may be more than the number of parameters if some of the parameters are vector values. - NUM_VALUES is the number of fixed values, which defines the offset in the value list to the polydisperse value and weight vectors. - NUM_MAGNETIC is the number of magnetic SLDs - MAGNETIC_PARS is a comma separated list of the magnetic SLDs, indicating their locations in the values vector. - MAGNETIC_PAR0 to MAGNETIC_PAR2 are the first three magnetic parameter ids so we can hard code the setting of magnetic values if there are only a few of them. - KERNEL_NAME is the name of the function being declared - PARAMETER_TABLE is the declaration of the parameters to the kernel: Cylinder:: #define PARAMETER_TABLE \ double length; \ double radius; \ double sld; \ double sld_solvent; Note: scale and background are never included Multi-shell cylinder (10 shell max):: #define PARAMETER_TABLE \ double num_shells; \ double length; \ double radius[10]; \ double sld[10]; \ double sld_solvent; - CALL_IQ(q, i, var) is the declaration of a call to the kernel: Cylinder:: #define CALL_IQ(q, i, var) Iq(q[i], \ var.length, \ var.radius, \ var.sld, \ var.sld_solvent) Multi-shell cylinder:: #define CALL_IQ(q, i, var) Iq(q[i], \ var.num_shells, \ var.length, \ var.radius, \ var.sld, \ var.sld_solvent) Cylinder2D:: #define CALL_IQ(q, i, var) Iqxy(q[2*i], q[2*i+1], \ var.length, \ var.radius, \ var.sld, \ var.sld_solvent, \ var.theta, \ var.phi) - CALL_VOLUME(var) is similar, but for calling the form volume:: #define CALL_VOLUME(var) \ form_volume(var.length, var.radius) There is an additional macro that can be defined within the model.c file: - INVALID(var) is a test for model parameters in the correct range: Cylinder:: #define INVALID(var) 0 BarBell:: #define INVALID(var) (var.bell_radius < var.radius) Model with complicated constraints:: inline bool constrained(p1, p2, p3) { return expression; } #define INVALID(var) constrained(var.p1, var.p2, var.p3) Our design supports a limited number of polydispersity loops, wherein we need to cycle through the values of the polydispersity, calculate the I(q, p) for each combination of parameters, and perform a normalized weighted sum across all the weights. Parameters may be passed to the underlying calculation engine as scalars or vectors, but the polydispersity calculator treats the parameter set as one long vector. Let's assume we have 8 parameters in the model, with two polydisperse. Since this is a 1-D model the orientation parameters won't be used:: 0: scale {scl = constant} 1: background {bkg = constant} 2: radius {r = vector of 10pts} 3: length {l = vector of 30pts} 4: sld {s = constant/(radius**2*length)} 5: sld_solvent {s2 = constant} 6: theta {not used} 7: phi {not used} This generates the following call to the kernel. Note that parameters 4 and 5 are treated as polydisperse even though they are not --- this is because it is harmless to do so and simplifies the looping code:: MAX_PD = 4 NUM_PARS = 6 // kernel parameters only NUM_VALUES = 17 // all values, including scale and background NUM_MAGNETIC = 2 // two parameters might be magnetic MAGNETIC_PARS = 4, 5 // they are sld and sld_solvent MAGNETIC_PAR0 = 4 // sld index MAGNETIC_PAR1 = 5 // solvent index details { pd_par = {3, 2, 4, 5} // parameters *radius* and *length* vary pd_length = {30, 10, 1, 1} // *length* has more, so it is first pd_offset = {10, 0, 31, 32} // *length* starts at index 10 in weights pd_stride = {1, 30, 300, 300} // cumulative product of pd length num_eval = 300 // 300 values in the polydispersity loop num_weights = 42 // 42 values in the pd vector num_active = 2 // only the first two pd are active theta_var = 6 // spherical correction } values = { scl, bkg, // universal r, l, s, s2, theta, phi, // kernel pars in spin, out spin, spin angle, // applied magnetism mx s, my s, mz s, mx s2, my s2, mz s2, // magnetic slds r0, .., r9, l0, .., l29, s, s2, // pd values r0, .., r9, l0, .., l29, s, s2} // pd weights nq = 130 q = { q0, q1, ..., q130, x, x } # pad to 8 element boundary result = {r1, ..., r130, pd_norm, x } The polydisperse parameters are stored in as an array of parameter indices, one for each polydisperse parameter, stored in pd_par[n]. Non-polydisperse parameters do not appear in this array. Each polydisperse parameter has a weight vector whose length is stored in pd_length[n]. The weights are stored in a contiguous vector of weights for all parameters, with the starting position for the each parameter stored in pd_offset[n]. The values corresponding to the weights are stored together in a separate weights[] vector, with offset stored in par_offset[pd_par[n]]. Polydisperse parameters should be stored in decreasing order of length for highest efficiency. We limit the number of polydisperse dimensions to MAX_PD (currently 4), though some models may have fewer if they have fewer polydisperse parameters. The main reason for the limit is to reduce code size. Each additional polydisperse parameter requires a separate polydispersity loop. If more than 4 levels of polydispersity are needed, then kernel_iq.c and kernel_iq.cl will need to be extended. Constraints between parameters are not supported. Instead users will have to define a new model with the constraints built in by making a copy of the existing model. Mac provides OpenCL and we are supplying the tinycc compiler for Windows so this won't be a complete limitation, but it is rather inconvenient. The process could perhaps be automated so that there is no code copying required, just an alternate CALL_IQ macro that implements the constraints. Think carefully about constraining theta since the polar coordinates normalization is tied to this parameter. If there is no polydispersity we pretend that it is polydisperisty with one parameter, pd_start=0 and pd_stop=1. We may or may not short circuit the calculation in this case, depending on how much time it saves. The problem details structure could be allocated and sent in as an integer array using the read-only flag. This would allow us to copy it once per fit along with the weights vector, since features such as the number of polydisperity elements per pd parameter or the coordinated won't change between function evaluations. A new parameter vector must be sent for each I(q) evaluation. This is not currently implemented, and would require some resturcturing of the :class:`sasview_model.SasviewModel` interface. The results array will be initialized to zero for polydispersity loop entry zero, and preserved between calls to [start, stop] so that the results accumulate by the time the loop has completed. Background and scale will be applied when the loop reaches the end. This does require that the results array be allocated read-write, which is less efficient for the GPU, but it makes the calling sequence much more manageable. For accuracy we may want to introduce Kahan summation into the integration:: double accumulated_error = 0.0; ... #if USE_KAHAN_SUMMATION const double y = next - accumulated_error; const double t = ret + y; accumulated_error = (t - ret) - y; ret = t; #else ret += next; #endif This will require accumulated error for each I(q) value to be preserved between kernel calls to implement this fully. The kernel_iq.c code, which loops over q for each parameter set in the polydispersity loop, will need also need the accumalation vector. sasmodels/doc/developer/index.rst000066400000000000000000000002441317715334700174560ustar00rootroot00000000000000*************************** Sasmodels Developers Guide *************************** .. toctree:: :numbered: 4 :maxdepth: 4 overview.rst calculator.rst sasmodels/doc/developer/overview.rst000066400000000000000000000251311317715334700202170ustar00rootroot00000000000000.. py:currentmodule:: sasmodels *************************** Code Overview *************************** Computational kernels --------------------- * :mod:`core` * :mod:`modelinfo` * :mod:`kernel` * :mod:`product` * :mod:`mixture` At the heart of *sasmodels* are the individual computational kernels. These functions take a particular $q$ value and a set of parameter values and return the expected scattering for that $q$. The instructions for writing a kernel are documented in :ref:`Writing_a_Plugin`. The source code for the kernels is stored in :mod:`models`. The primary interface to the models is through :mod:`core`, which provides functions for listing available models, loading the model definition and compiling the model. Use :func:`core.load_model` to load in a model definition and compile it. This makes use of :func:`core.load_model_info` to load the model definition and :func:`core.build_model` to turn it into a computational kernel model :class:`kernel.KernelModel`. The :class:`modelinfo.ModelInfo` class defines the properties of the model including the available model parameters :class:`modelinfo.ParameterTable` with individual parameter attributes such as units and hard limits defined in :class:`modelinfo.Parameter`. The :class:`product.ProductModel` and :class:`mixture.MixtureModel` classes are derived models, created automatically for models with names like "hardsphere*sphere" and "cylinder+sphere". Data loaders ------------ * :mod:`data` In order to test models a minimal set of data management routines is provided in :mod:`data`. In particular, it provides mock :class:`data.Data1D` and :class:`data.Data2D` classes which mimic those classes in *SasView*. The functions :func:`data.empty_data1D` and :func:`data.empty_data2D` are handy for creating containers with a particular set of $q$, $\Delta q$ points which can later be evaluated, and :func:`data.plot_theory` to show the result. If *SasView* is available on the path then :func:`data.load_data` can be used to load any data type defined in *SasView*. The function :func:`data.plot_data` can plot that data alone without the theory value. Kernel execution ---------------- * :mod:`resolution` * :mod:`resolution2d` * :mod:`sesans` * :mod:`weights` * :mod:`details` * :mod:`direct_model` * :mod:`bumps_model` * :mod:`sasview_model` To execute a computational kernel at a particular set of $q$ values, the use :meth:`kernel.KernelModel.make_kernel`, which returns a callable :class:`kernel.Kernel` for that $q$ vector (or a pair of $q_x$, $q_y$ for 2-D datasets). The calculated $q$ values should include the measured data points as well as additional $q$ values required to properly compute the $q$ resolution function. The *Resolution* subclasses in :mod:`resolution` define the *q_calc* attribute for this purpose. These are :class:`resolution.Perfect1D` for perfect resolution, :class:`resolution.Pinhole1D` for the usual SANS pinhole aperture, :class:`resolution.Slit1D` for the usual USANS slit aperture and :class:`resolution2d.Pinhole2D` for 2-D pinhole data. In addition, :class:`resolution2d.Slit2D` defines 1-D slit smeared data for oriented samples, which require calculation at particular $q_x$ and $q_y$ values instead of $|q|$ as is the case for orientationally averaged USANS. The :class:`sesans.SesansTransform` class acts like a 1-D resolution, having a *q_calc* attribute that defines the calculated $q$ values for the SANS models that get converted to spin-echo values by the :meth:`sesnas.SesansTransform.apply` method. Polydispersity is defined by :class:`weights.Dispersion` classes, :class:`weights.RectangleDispersion`, :class:`weights.ArrayDispersion`, :class:`weights.LogNormalDispersion`, :class:`weights.GaussianDispersion`, :class:`weights.SchulzDispersion`. The :func:`weights.get_weights` function creates a dispersion object of the class matching :attr:`weights.Dispersion.type`, and calls it with the current value of the parameter. This returns a vector of values and weights for a weighted average polydispersity. In order to call the :class:`kernel.Kernel`, the values and weights for all parameters must be composed into a :class:`details.CallDetails` object. This is a compact vector representation of the entire polydispersity loop that can be passed easily to the kernel. Additionally, the magnetic parameters must be converted from polar to cartesian coordinates. This work is done by the :func:`details.make_kernel_args` function, which returns values that can be sent directly to the kernel. It uses :func:`details.make_details` to set the details object and :func:`details.convert_magnetism` for the coordinate transform. In the end, making a simple theory function evaluation requires a lot of setup. To make calling them a little easier, the *DirectModel* and *BumpsModel* interfaces are provided. See :ref:`Scripting_Interface` for an example. The :class:`direct_model.DirectModel` interface accepts a data object and a kernel model. Within the class, the :meth:`direct_model.DataMixin._interpret_data` method is called to query the data and set the resolution. The :meth:`direct_model.DataMixin._calc_theory` takes a set of parameter values, builds the kernel arguments, calls the kernel, and applies the resolution function, returning the predicted value for the data $q$ values. The :class:`bumps_model.Experiment` class is like the DirectModel class, but it defines a Fitness class that can be handed directly to the bumps optimization and uncertainty analysis program. The :class:`sasview_model.SasviewModel` class defines a SasView 4.x compatible interface to the sasmodels definitions, allowing sasmodels to be used directly from SasView. Over time the SasView shim should disappear as SasView access the :class:`modelinfo.ModelInfo` and computational kernels directly. Kernel execution ---------------- * :mod:`kernelcl` * :mod:`kerneldll` * :mod:`kernelpy` * :mod:`generate` The kernel functions for the most part do not define polydispersity, resolution or magnetism directly. Instead sasmodels automatically applies these, calling the computation kernel as needed. The outermost loop is the resolution calculation. For the 1-D case this computes a single vector of $I(q)$ values and applies the convolution to the resulting set. Since the same $I(q)$ vector is used to compute the convolution at each point, it can be precomputed before the convolution, and so the convolution is reasonably efficient. The 2-D case is not that efficient, and instead recomputes the entire shifted/scaled set of $q_x$, $q_y$ values many times, or very many times depending on the accuracy requested. Polydispersity is handled as a mesh over the polydisperse parameters. This is the next level of the loop. For C kernels run in a DLL or using OpenCL, the polydisperisty loop is generated separately for each model as C code. Inside the polydispersity loop there is a loop over the magnetic cross sections for magnetic models, updating the SLD parameters with the effective magnetic SLD for that particular $q$ value. For OpenCL, each $q$ value loops over the polydispersity mesh on a separate processor. For DLL, the outer loop cycles through polydispersity, and the inner loop distributes q values amongst the processors. Like the DLL, the Python kernel execution cycles over the polydisperse parameters and the magnetic cross sections, calling the computation kernel with a vector of $q$ values. Assuming the kernel code accepts vectors, this can be fast enough (though it is painfully slow if not vectorized). Further details are provided in the next section, :ref:`Calculator_Interface` Testing ------- * :mod:`model_test` * :mod:`compare` * :mod:`compare_many` * :mod:`rst2html` * :mod:`list_pars` Individual models should all have test values to make sure that the evaluation is correct. This is particularly important in the context of OpenCL since sasmodels doesn't control the compiler or the hardware, and since GPUs are notorious for preferring speed over precision. The tests can be run as a group using :mod:`model_test` as main:: $ python -m sasmodels.model_test all Individual models can be listed instead of *all*, which is convenient when adding new models. The :mod:`compare` module, usually invoked using *./sascomp* provides a rich interface for exploring model accuracy, execution speed and parameter ranges. It also allows different models to be compared. The :mod:`compare_many` module does batch comparisons, keeping a list of the particular random seeds which lead to large differences in output between different computing platforms. The :mod:`rst2html` module provides tools for converting model docs to html and viewing the html. This is used by :mod:`compare` to display the model description, such as:: $ ./sascomp -html sphere This makes debugging the latex much faster, though this may require Qt in order for mathjax to work correctly. When run as main, it can display arbitrary ReStructuredText files. E.g., :: $ python -m sasmodels.rst2html doc/developer/overview.rst This is handy for sorting out rst and latex syntax. With some work the results could be improved so that it recognizes sphinx roles such as *mod*, *class* and *func*, and so that it uses the style sheets from the sasmodels docs. The :mod:`list_pars` module lists all instances of parameters across all models. This helps to make sure that similar parameters have similar names across the different models. With the verbose flag, the particular models which use each named parameter are listed. Model conversion ---------------- * :mod:`convert` * :mod:`conversion_table` Model definitions are not static. As needs change or problems are found, models may be updated with new model names or may be reparameterized with new parameter definitions. For example, in translating the Teubner-Strey model from SasView 3.x to sasmodels, the definition in terms of *drho*, *k*, *c1*, *c2*, *a2* and prefactor was replaced by the defintion in terms of *volfraction_a*, *xi*, *d*, *sld_a* and *sld_b*. Within :mod:`convert`, the *_hand_convert_3_1_2_to_4_1* function must be called when loading a 3.x model definition to update it to 4.1, and then the model should be further updated to 4.2, 5.0, and so on. The :func:`convert.convert_model` function does this, using the conversion table in :mod:`conversion_table` (which handled the major renaming from SasView 3.x to sasmodels), and using the internal *_hand_convert* function for the more complicated cases. Other ----- * :mod:`exception` * :mod:`alignment` The :func:`exception.annotate_exception` function annotates the current exception with a context string, such as "while opening myfile.dat" without adjusting the traceback. The :mod:`alignment` module is unused.sasmodels/doc/genapi.py000066400000000000000000000052201317715334700154440ustar00rootroot00000000000000from __future__ import with_statement import os.path MODULE_TEMPLATE = """.. Autogenerated by genmods.py ****************************************************************************** %(name)s ****************************************************************************** :mod:`%(package)s.%(module)s` ============================================================================== .. automodule:: %(package)s.%(module)s :members: :undoc-members: :inherited-members: :show-inheritance: """ INDEX_TEMPLATE = """.. Autogenerated by genmods.py .. _api-index: ############################################################################## %(package_name)s ############################################################################## .. only:: html :Release: |version| :Date: |today| .. toctree:: :titlesonly: :numbered: 1 :maxdepth: 2 %(rsts)s """ def genfiles(package, package_name, modules, dir='api'): if not os.path.exists(dir): os.makedirs(dir) for module, name in modules: with open(os.path.join(dir, module+'.rst'), 'w') as f: f.write(MODULE_TEMPLATE%locals()) rsts = "\n ".join(module+'.rst' for module, name in modules) with open(os.path.join(dir, 'index.rst'), 'w') as f: f.write(INDEX_TEMPLATE%locals()) modules = [ ('__init__', 'Sasmodels package'), #('alignment', 'GPU data alignment [unused]'), ('bumps_model', 'Bumps interface'), ('compare_many', 'Batch compare models on different compute engines'), ('compare', 'Compare models on different compute engines'), ('convert', 'Sasview to sasmodel converter'), ('core', 'Model access'), ('data', 'Data layout and plotting routines'), ('details', 'Parameter packing for kernel calls'), ('direct_model', 'Simple interface'), ('exception', 'Annotate exceptions'), ('generate', 'Model parser'), ('kernel', 'Evaluator type definitions'), ('kernelcl', 'OpenCL model evaluator'), ('kerneldll', 'Ctypes model evaluator'), ('kernelpy', 'Python model evaluator'), ('list_pars', 'Identify all parameters in all models'), ('mixture', 'Mixture model evaluator'), ('model_test', 'Unit test support'), ('modelinfo', 'Parameter and model definitions'), ('product', 'Product model evaluator'), ('resolution', '1-D resolution functions'), ('resolution2d', '2-D resolution functions'), ('rst2html', 'Convert doc strings the web pages'), ('sasview_model', 'Sasview interface'), ('sesans', 'SESANS calculation routines'), ('weights', 'Distribution functions'), ] package = 'sasmodels' package_name = 'Reference' genfiles(package, package_name, modules) sasmodels/doc/genmodel.py000066400000000000000000000150141317715334700157750ustar00rootroot00000000000000from __future__ import print_function import sys, os, math, re import numpy as np import matplotlib matplotlib.use('Agg') import matplotlib.pyplot as plt sys.path.insert(0, os.path.abspath('..')) from sasmodels import generate, core from sasmodels.direct_model import DirectModel, call_profile from sasmodels.data import empty_data1D, empty_data2D try: from typing import Dict, Any except ImportError: pass else: from matplotlib.axes import Axes from sasmodels.kernel import KernelModel from sasmodels.modelinfo import ModelInfo def plot_1d(model, opts, ax): # type: (KernelModel, Dict[str, Any], Axes) -> None """ Create a 1-D image. """ q_min, q_max, nq = opts['q_min'], opts['q_max'], opts['nq'] q_min = math.log10(q_min) q_max = math.log10(q_max) q = np.logspace(q_min, q_max, nq) data = empty_data1D(q) calculator = DirectModel(data, model) Iq1D = calculator() ax.plot(q, Iq1D, color='blue', lw=2, label=model.info.name) ax.set_xlabel(r'$Q \/(\AA^{-1})$') ax.set_ylabel(r'$I(Q) \/(\mathrm{cm}^{-1})$') ax.set_xscale(opts['xscale']) ax.set_yscale(opts['yscale']) #ax.legend(loc='best') def plot_2d(model, opts, ax): # type: (KernelModel, Dict[str, Any], Axes) -> None """ Create a 2-D image. """ qx_max, nq2d = opts['qx_max'], opts['nq2d'] q = np.linspace(-qx_max, qx_max, nq2d) # type: np.ndarray data2d = empty_data2D(q, resolution=0.0) calculator = DirectModel(data2d, model) Iq2D = calculator() #background=0) Iq2D = Iq2D.reshape(nq2d, nq2d) if opts['zscale'] == 'log': Iq2D = np.log(np.clip(Iq2D, opts['vmin'], np.inf)) ax.imshow(Iq2D, interpolation='nearest', aspect=1, origin='lower', extent=[-qx_max, qx_max, -qx_max, qx_max], cmap=opts['colormap']) ax.set_xlabel(r'$Q_x \/(\AA^{-1})$') ax.set_ylabel(r'$Q_y \/(\AA^{-1})$') def plot_profile_inset(model_info, ax): p = ax.get_position() width, height = 0.4*(p.x1-p.x0), 0.4*(p.y1-p.y0) left, bottom = p.x1-width, p.y1-height inset = plt.gcf().add_axes([left, bottom, width, height]) x, y, labels = call_profile(model_info) inset.plot(x, y, '-') inset.locator_params(nbins=4) #inset.set_xlabel(labels[0]) #inset.set_ylabel(labels[1]) inset.text(0.99, 0.99, "profile", horizontalalignment="right", verticalalignment="top", transform=inset.transAxes) def figfile(model_info): # type: (ModelInfo) -> str return model_info.id + '_autogenfig.png' def make_figure(model_info, opts): # type: (ModelInfo, Dict[str, Any]) -> None """ Generate the figure file to include in the docs. """ model = core.build_model(model_info) fig_height = 3.0 # in fig_left = 0.6 # in fig_right = 0.5 # in fig_top = 0.6*0.25 # in fig_bottom = 0.6*0.75 if model_info.parameters.has_2d: plot_height = fig_height - (fig_top+fig_bottom) plot_width = plot_height fig_width = 2*(plot_width + fig_left + fig_right) aspect = (fig_width, fig_height) ratio = aspect[0]/aspect[1] ax_left = fig_left/fig_width ax_bottom = fig_bottom/fig_height ax_height = plot_height/fig_height ax_width = ax_height/ratio # square axes fig = plt.figure(figsize=aspect) ax2d = fig.add_axes([0.5+ax_left, ax_bottom, ax_width, ax_height]) plot_2d(model, opts, ax2d) ax1d = fig.add_axes([ax_left, ax_bottom, ax_width, ax_height]) plot_1d(model, opts, ax1d) #ax.set_aspect('square') else: plot_height = fig_height - (fig_top+fig_bottom) plot_width = (1+np.sqrt(5))/2*fig_height fig_width = plot_width + fig_left + fig_right ax_left = fig_left/fig_width ax_bottom = fig_bottom/fig_height ax_width = plot_width/fig_width ax_height = plot_height/fig_height aspect = (fig_width, fig_height) fig = plt.figure(figsize=aspect) ax1d = fig.add_axes([ax_left, ax_bottom, ax_width, ax_height]) plot_1d(model, opts, ax1d) if model_info.profile: plot_profile_inset(model_info, ax1d) # Save image in model/img path = os.path.join('model', 'img', figfile(model_info)) plt.savefig(path, bbox_inches='tight') #print("figure saved in",path) def gen_docs(model_info): # type: (ModelInfo) -> None """ Generate the doc string with the figure inserted before the references. """ # Load the doc string from the module definition file and store it in rst docstr = generate.make_doc(model_info) # Auto caption for figure captionstr = '\n' captionstr += '.. figure:: img/' + figfile(model_info) + '\n' captionstr += '\n' if model_info.parameters.has_2d: captionstr += ' 1D and 2D plots corresponding to the default parameters of the model.\n' else: captionstr += ' 1D plot corresponding to the default parameters of the model.\n' captionstr += '\n' # Add figure reference and caption to documentation (at end, before References) pattern = '\*\*REFERENCE' match = re.search(pattern, docstr.upper()) if match: docstr1 = docstr[:match.start()] docstr2 = docstr[match.start():] docstr = docstr1 + captionstr + docstr2 else: print('------------------------------------------------------------------') print('References NOT FOUND for model: ', model_info.id) print('------------------------------------------------------------------') docstr += captionstr open(sys.argv[2],'w').write(docstr) def process_model(path): # type: (str) -> None """ Generate doc file and image file for the given model definition file. """ # Load the model file model_name = os.path.basename(path)[:-3] model_info = core.load_model_info(model_name) # Plotting ranges and options opts = { 'xscale' : 'log', 'yscale' : 'log' if not model_info.structure_factor else 'linear', 'zscale' : 'log' if not model_info.structure_factor else 'linear', 'q_min' : 0.001, 'q_max' : 1.0, 'nq' : 1000, 'nq2d' : 1000, 'vmin' : 1e-3, # floor for the 2D data results 'qx_max' : 0.5, #'colormap' : 'gist_ncar', 'colormap' : 'nipy_spectral', #'colormap' : 'jet', } # Generate the RST file and the figure. Order doesn't matter. gen_docs(model_info) make_figure(model_info, opts) if __name__ == "__main__": process_model(sys.argv[1]) sasmodels/doc/gentoc.py000066400000000000000000000112361317715334700154640ustar00rootroot00000000000000from __future__ import print_function import sys # make sure sasmodels is on the path sys.path.append('..') from os import mkdir from os.path import basename, exists, join as joinpath from sasmodels.core import load_model_info try: from typing import Optional, BinaryIO, List, Dict except ImportError: pass else: from sasmodels.modelinfo import ModelInfo TEMPLATE = """\ .. Generated from doc/gentoc.py -- DO NOT EDIT -- .. _%(label)s: %(bar)s %(title)s %(bar)s .. toctree:: """ MODEL_TOC_PATH = "guide/models" def _make_category(category_name, label, title, parent=None): # type: (str, str, str, Optional[BinaryIO]) -> BinaryIO file = open(joinpath(MODEL_TOC_PATH, category_name+".rst"), "w") file.write(TEMPLATE%{'label':label, 'title':title, 'bar':'*'*len(title)}) if parent: _add_subcategory(category_name, parent) return file def _add_subcategory(category_name, parent): # type: (str, BinaryIO) -> None parent.write(" %s.rst\n"%category_name) def _add_model(file, model_name): # type: (IO[str], str) -> None file.write(" ../../model/%s.rst\n"%model_name) def _maybe_make_category(category, models, cat_files, model_toc): # type: (str, List[str], Dict[str, BinaryIO], BinaryIO) -> None if category not in cat_files: print("Unexpected category %s containing"%category, models, file=sys.stderr) title = category.capitalize()+" Functions" cat_files[category] = _make_category(category, category, title, model_toc) def generate_toc(model_files): # type: (List[str]) -> None if not model_files: print("gentoc needs a list of model files", file=sys.stderr) # find all categories category = {} # type: Dict[str, List[str]] for item in model_files: # assume model is in sasmodels/models/name.py, and ignore the full path model_name = basename(item)[:-3] if model_name.startswith('_'): continue model_info = load_model_info(model_name) if model_info.category is None: print("Missing category for", item, file=sys.stderr) else: category.setdefault(model_info.category, []).append(model_name) # Check category names for k, v in category.items(): if len(v) == 1: print("Category %s contains only %s"%(k, v[0]), file=sys.stderr) # Generate category files for the table of contents. # Initially we had "shape functions" as an additional TOC level, but we # have revised it so that the individual shape categories now go at # the top level. Judicious rearrangement of comments will make the # "shape functions" level reappear. # We are forcing shape-independent, structure-factor and custom-models # to come at the end of the TOC. All other categories will come in # alphabetical order before them. if not exists(MODEL_TOC_PATH): mkdir(MODEL_TOC_PATH) model_toc = _make_category( 'index', 'Models', 'Model Functions') #shape_toc = _make_category( # 'shape', 'Shapes', 'Shape Functions', model_toc) free_toc = _make_category( 'shape-independent', 'Shape-independent', 'Shape-Independent Functions') struct_toc = _make_category( 'structure-factor', 'Structure-factor', 'Structure Factors') #custom_toc = _make_category( # 'custom-models', 'Custom-models', 'Custom Models') # remember to top level categories cat_files = { #'shape':shape_toc, 'shape':model_toc, 'shape-independent':free_toc, 'structure-factor': struct_toc, #'custom': custom_toc, } # Process the model lists for k, v in sorted(category.items()): if ':' in k: cat, subcat = k.split(':') _maybe_make_category(cat, v, cat_files, model_toc) cat_file = cat_files[cat] label = "-".join((cat, subcat)) filename = label title = subcat.capitalize() + " Functions" sub_toc = _make_category(filename, label, title, cat_file) for model in sorted(v): _add_model(sub_toc, model) sub_toc.close() else: _maybe_make_category(k, v, cat_files, model_toc) cat_file = cat_files[k] for model in sorted(v): _add_model(cat_file, model) #_add_subcategory('shape', model_toc) _add_subcategory('shape-independent', model_toc) _add_subcategory('structure-factor', model_toc) #_add_subcategory('custom-models', model_toc) # Close the top-level category files #model_toc.close() for f in cat_files.values(): f.close() if __name__ == "__main__": generate_toc(sys.argv[1:]) sasmodels/doc/guide/000077500000000000000000000000001317715334700147255ustar00rootroot00000000000000sasmodels/doc/guide/gpu_setup.rst000066400000000000000000000131761317715334700175020ustar00rootroot00000000000000.. _gpu-setup: ******************** GPU Setup ******************** SAS model evaluations can run on your graphics card (GPU) or they can run on the processor (CPU). In general, calculations performed on the GPU will run faster. OpenCL Installation ******************* *Warning! GPU devices do not in general offer the same level of memory protection as CPU devices. If your code attempts to write outside allocated memory buffers unpredicatable behaviour may result (eg, your video display may freeze, or your system may crash, etc). Do not install OpenCL drivers without first checking for known issues (eg, some computer manufacturers install modified graphics drivers so replacing these may not be a good idea!). If in doubt, seek advice from an IT professional before proceeding further.* Check if you have OpenCL already installed ========================================== **Windows** The following instructions are based on http://web.engr.oregonstate.edu/~mjb/cs475/DoIHaveOpenCL.pdf * Go to: Start -> Control Panel -> System & Security -> Administrative Tools * Double Click on Computer Managment * Click on Device Manager * Click open Display Adapters * Right-click on available adapter and select Properties * Click on Driver * Go to Driver Details * Scroll down and see if OpenCL is installed (look for OpenCL*.dll files) **Mac OSX** For OS X operating systems higher than 10.6 OpenCL is shipped along with the system. However, OpenCL has had a rocky history on Macs. Apple provide a useful compatibility table at https://support.apple.com/en-us/HT202823 Installation ============ **Windows** Depending on the graphic card in your system, drivers can be obtained from different sources: * NVIDIA: https://developer.nvidia.com/opencl * AMD: http://developer.amd.com/tools-and-sdks/opencl-zone/ **Mac OSX** N/A You cannot download OpenCL driver updates for your Mac. They are packaged with the normal quarterly OS X updates from Apple. .. note:: Intel provides OpenCL drivers for Intel processors at https://software.intel.com/en-us/articles/opencl-drivers These can sometimes make use of special vector instructions across multiple processors, so it is worth installing if the GPU does not support double precision. You can install this driver alongside the GPU driver for NVIDIA or AMD. GPU Selection ************* The logic for choosing the compute platform is a little bit complicated. If the model has the line *single=False* then it requires double precision. If the GPU is single precision only, then it will try running via OpenCL on the CPU. If the OpenCL driver is not available for the CPU then it will run as a normal program on the CPU. For models with a large number of parameters or with a lot of code, the GPU may be too small to run the program effectively. In this case, you should try simplifying the model, maybe breaking it into several different models so that you don't need *IF* statements in your code. If it is still too big, you can set *opencl=False* in the model file and the model will only run as a normal program on the CPU. This will not usually be necessary. Device Selection ================ If you have multiple GPU devices you can tell the program which device to use. By default, the program looks for one GPU and one CPU device from available OpenCL platforms. It prefers AMD or NVIDIA drivers for GPU, and prefers Intel or Apple drivers for CPU. Both GPU and CPU are included on the assumption that CPU is always available and supports double precision. The device order is important: GPU is checked before CPU on the assumption that it will be faster. By examining ~/sasview.log you can see which device was used to run the model. **If you don't want to use OpenCL, you can set** *SAS_OPENCL=None* **in your environment settings, and it will only use normal programs.** If you want to use one of the other devices, you can run the following from the python console:: import pyopencl as cl cl.create_some_context() This will provide a menu of different OpenCL drivers available. When one is selected, it will say "set PYOPENCL_CTX=..." Use that value as the value of *SAS_OPENCL*. Device Testing ============== Unfortunately, not all vendors provide working OpenCL implementations for their GPU devices. For example, the HD 6000 Intel GPUs with double precision support fail for some of the double precision models. The SasView user interface provides a Fitting OpenCL Options dialog for selecting amongst and testing the available devices. After a few minutes of seeming to freeze, the application will return a list of model tests which have passed. The same tests can be run directly from the python console using:: from sasmodels.model_tests import main as model_tests model_tests("-v", "opencl", "all") Compiler Selection ================== For models run as normal programs, you may need to specify a compiler. This is done using the *SAS_COMPILER* environment variable, and the *SAS_OPENMP* environment variable if OpenMP support is available for the compiler. On Windows, set *SASCOMPILER=tinycc* for the tinycc compiler, *SASCOMPILER=msvc* for the Microsoft Visual C compiler, or *SASCOMPILER=mingw* for the MinGW compiler. If TinyCC is available on the python path (it is provided with SasView), that will be the default. If you want one of the other compilers, be sure to have it available in your *PATH* so we can find it! On Mac OS/X and Linux, set *SAS_COMPILER=unix* for the compiler. This will use the unix cc command to compile the model, with gcc style command line options. For OS/X you will need to install the Xcode package to make the compiler available. *Document History* | 2017-09-27 Paul Kienzlesasmodels/doc/guide/index.rst000066400000000000000000000004721317715334700165710ustar00rootroot00000000000000**************** SAS Models Guide **************** .. toctree:: :numbered: 4 :maxdepth: 4 intro.rst install.rst gpu_setup.rst pd/polydispersity.rst resolution.rst magnetism/magnetism.rst sesans/sans_to_sesans.rst sesans/sesans_fitting.rst plugin.rst scripting.rst refs.rst sasmodels/doc/guide/install.rst000066400000000000000000000030541317715334700171270ustar00rootroot00000000000000******************** sasmodels Setup ******************** sasmodels Installation ********************** Sasmodels can be installed using a simple pip installation:: # Won't work yet! For now follow the developer instructions below. $ pip install sasmodels There are a number of dependent python packages which need to be installed separately:: numpy scipy opencl (for speed if your system has OpenCL drivers) tinycc (windows only, if no C compiler and no OpenCL) When using sasmodels to fit data:: sasview (for loading data) bumps (for fitting) matplotlib (for displaying results) For development and testing it is handy to have some additional packages:: nose (for testing) xmlrunner (for testing) matplotlib (for showing models) docutils (for showing model docs) sphinx (for building docs) wx ([optional] for adjusting parameters interactively) **Developer Installation** Developers will need to clone the sasmodels reposistory from github:: $ git clone https://github.com/sasview/sasmodels.git or if you have a github account:: $ git clone git@github.com:sasview/sasmodels.git Sasmodels can be run in-place by including the sasmodels directory on the python path. There are numerous ways to do this which will not be outlined here. It will be easiest to install the package in "develop" mode using:: $ cd sasmodels $ python setup.py develop This will allow you to edit the files in the package and have the changes show up immediately in python the next time you load your program. sasmodels/doc/guide/intro.rst000066400000000000000000000041131317715334700166110ustar00rootroot00000000000000 .. _models-intro: ************ Introduction ************ This software provides form factors for various particle shapes and computes resolution, polydispersity and angular dispersion. After giving a mathematical definition of each model, we show the list of parameters available to the user. Validation plots for each model are also presented. To easily compare to the scattering intensity measured in experiments, we normalize the form factors by the volume of the particle .. math:: P(\vec q) = \frac{P_o(\vec q)}{V} = \frac{1}{V} F(\vec q) F^*(\vec q) with .. math:: F(\vec q) = \int\int\int dV\rho(\vec r) e^{-i\vec q \cdot \vec r} where $P_0(\vec q)$ is the un-normalized form factor, $\rho(\vec r)$ is the scattering length density at a given point in space and the integration is done over the volume $V$ of the scatterer. For systems without inter-particle interference, the form factors we provide can be related to the scattering intensity by the particle volume fraction .. math:: I(\vec q) = \Phi P(\vec q) Our so-called 1D scattering intensity functions provide $P(Q)$ for the case where the scatterer is randomly oriented. In that case, the scattering intensity only depends on the length of $Q$ . The intensity measured on the plane of the SAS detector will have an azimuthal symmetry around $Q=0$. Our so-called 2D scattering intensity functions provide $P(Q,\phi)$ for an oriented system as a function of a $q$ vector in the plane of the detector. We define the angle $\phi$ as the angle between the $q$ vector and the horizontal ($x$) axis of the plane of the detector. For information about polarised and magnetic scattering, see :ref:`magnetism`. The models are used within the SasView package. Instructions on how to use SasView itself are available separately. Many of our models use the form factor calculations as implemented in the C-library provided by the NIST Center for Neutron Research and thus some content and figures in this document are originated from or shared with the NIST SANS Igor-based analysis package. *Document History* | 2017-05-07 Paul Kienzlesasmodels/doc/guide/magnetism/000077500000000000000000000000001317715334700167115ustar00rootroot00000000000000sasmodels/doc/guide/magnetism/mag_img/000077500000000000000000000000001317715334700203115ustar00rootroot00000000000000sasmodels/doc/guide/magnetism/mag_img/M_angles_pic.png000066400000000000000000003442741317715334700234150ustar00rootroot00000000000000PNG  IHDR.dIsRGB@IDATxi$uYuUgUոII`Iy`0 8fiWH~ڙ1IIHk3Dۘ͐\(rv8(R$軻YYWxGG===Y\XXG @<y#z{{Kగ^zi``U誊/w.@<y1(|C',vtV^-#G @hա5tR5ldO<yler۞TBfhh]!UG@ZFCu<@>8[<yRD5Ukj4h9&>4hN+V!j@>Bg#G``zlA[6@YarV6iK֏R҈UZ9DC;ǫܓ<y4{mVN-(f&% Y8Z T2P&SΥ#G`[#Ђ9UlkÕLeafn߭K]BnI#o#:vi׷`ߥim84Ձmu+ Tۯi5=9'@S#˦77(hL)ܤNlLbA".678Asktc%ղZ<"Dʅ؁h< -] 1G'`v ׽lq>T*rXrȻ{tbބ<y&MM2ۼ8mt6qV`6k6:*~rڞ7@<+-QE3l&FJ) VIafE&(V+#";-3l*I#--J374!W ډddQK 4!lm@>,1 V]li[@72BN#FhoVvNkq5(wyiF`~3oxk%g݈?)瘝: >@>0țG`OF -sn31.zՈe1҈u)Z"BԪ:׏43F r҈yHδTũhSWvWmMJzl6ëbTtn56oQ<yvEZ63gXQZG嶎Fܫ6X(khFٌ6%;ኒ/v"O21.`b!:j܇:Q"ӈuj_X(KTG B19'OY++;7h<[TΤ3+t58 vZ+ӠۮH:bGw{#P'NqYYN1Md]u!;%r5.V|<(82#wJy4il&F݉qC+1N]Hz`6n͵v]o$X/Ɖ@DZ#G @Lgbd{ZLjz:]ޠz(t] lj6b~:7G sMsk-H4/8A:!Ma9Q$>3ۈ.aiP=2kW BʰU|$v7t0Ǟ,s[F [(@VQmN4?N-)Gl" :DZH kb6b6)Te3W=s?LUԱY,>2O)5-[]{/9]x[Fǿ}Ї7ѢKHխ1ܞ M5nXy׷t C,M1P$Ɛd0P*kr"D`nxiڎu=U+R&-fݒ-Kq]]".UO>s'po_=<vO>3U _^/5EC`3Ӆ2%,̵٭NMb ]r֔g*lI@m6-NJ> 8w =uTz]T0Oxa"A:X=80CUP)GEH fl yUMkH쪚$Xkߤ5jvec쑟~OȪop[|3~Yap:ȝ=rqGa"v`0J}_V(\AeziZ@LnI@-"U0?43C*>N}і]Mcpn`p]>6W fӑ k=l|a5}L~G]u뫘|be9@BQ{y;[$VWWv? 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SdRHr 7L|Iꂘ,keyFt22.C e@@@8|#]   `J +zBK *J쳂r   SQAE9{p@@@QTPQ<   Tge@@@<%?E3   R CQAEIwvTT'c   JPRj.\ԩ_   QTPQo   **(%mxT(M; *JqD   $帢ooWQAEysZx2@@@WSTPQ/    FbECC=M    &7o\*R}IOAEi|` v/" IENDB`sasmodels/doc/guide/magnetism/magnetism.rst000066400000000000000000000056271317715334700214410ustar00rootroot00000000000000.. _magnetism: Polarisation/Magnetic Scattering ================================ Models which define a scattering length density parameter can be evaluated as magnetic models. In general, the scattering length density (SLD = $\beta$) in each region where the SLD is uniform, is a combination of the nuclear and magnetic SLDs and, for polarised neutrons, also depends on the spin states of the neutrons. For magnetic scattering, only the magnetization component $\mathbf{M_\perp}$ perpendicular to the scattering vector $\mathbf{Q}$ contributes to the magnetic scattering length. .. figure:: mag_img/mag_vector.png The magnetic scattering length density is then .. math:: \beta_M = \dfrac{\gamma r_0}{2\mu_B}\sigma \cdot \mathbf{M_\perp} = D_M\sigma \cdot \mathbf{M_\perp} where $\gamma = -1.913$ is the gyromagnetic ratio, $\mu_B$ is the Bohr magneton, $r_0$ is the classical radius of electron, and $\sigma$ is the Pauli spin. Assuming that incident neutrons are polarized parallel (+) and anti-parallel (-) to the $x'$ axis, the possible spin states after the sample are then No spin-flips (+ +) and (- -) Spin-flips (+ -) and (- +) .. figure:: mag_img/M_angles_pic.png If the angles of the $Q$ vector and the spin-axis $x'$ to the $x$ - axis are $\phi$ and $\theta_{up}$, respectively, then, depending on the spin state of the neutrons, the scattering length densities, including the nuclear scattering length density ($\beta{_N}$) are .. math:: \beta_{\pm\pm} = \beta_N \mp D_M M_{\perp x'} \text{ when there are no spin-flips} and .. math:: \beta_{\pm\mp} = -D_M (M_{\perp y'} \pm iM_{\perp z'}) \text{ when there are} where .. math:: M_{\perp x'} = M_{0q_x}\cos(\theta_{up})+M_{0q_y}\sin(\theta_{up}) \\ M_{\perp y'} = M_{0q_y}\cos(\theta_{up})-M_{0q_x}\sin(\theta_{up}) \\ M_{\perp z'} = M_{0z} \\ M_{0q_x} = (M_{0x}\cos\phi - M_{0y}\sin\phi)\cos\phi \\ M_{0q_y} = (M_{0y}\sin\phi - M_{0x}\cos\phi)\sin\phi Here, $M_{0x}$, $M_{0x}$, $M_{0z}$ are the x, y and z components of the magnetization vector given in the laboratory xyz frame given by .. math:: M_{0x} = M_0\cos\theta_M\cos\phi_M \\ M_{0y} = M_0\sin\theta_M \\ M_{0z} = -M_0\cos\theta_M\sin\phi_M and the magnetization angles $\theta_M$ and $\phi_M$ are defined in the figure above. The user input parameters are: =========== ================================================================ M0_sld = $D_M M_0$ Up_theta = $\theta_\mathrm{up}$ M_theta = $\theta_M$ M_phi = $\phi_M$ Up_frac_i = (spin up)/(spin up + spin down) neutrons *before* the sample Up_frac_f = (spin up)/(spin up + spin down) neutrons *after* the sample =========== ================================================================ .. note:: The values of the 'Up_frac_i' and 'Up_frac_f' must be in the range 0 to 1. *Document History* | 2015-05-02 Steve King | 2017-05-08 Paul Kienzlesasmodels/doc/guide/pd/000077500000000000000000000000001317715334700153305ustar00rootroot00000000000000sasmodels/doc/guide/pd/pd_gaussian.jpg000066400000000000000000000407341317715334700203370ustar00rootroot00000000000000JFIF``C    $.' 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Fzꨣ"Mf m?[((((((:|c.%O=ūn'͹ H3&Y霏஖O[K| 󟓁<:ϱjAE`,+fhc8VĚ6iz%Ĺ)2(A$^w(,6y/r며oD?w!##Ͽ]Vf+aCI@`>w ?*d((d%FT;AӴD0H` 9êAaݹ?1ZTPEPEPEPEPEPF2 *0c^D8N1qE*en>%[q4OQ@Wr]k\0,`;BOASySF w \end{cases} where $\bar x$ is the mean of the distribution, $w$ is the half-width, and *Norm* is a normalization factor which is determined during the numerical calculation. Note that the standard deviation and the half width $w$ are different! The standard deviation is .. math:: \sigma = w / \sqrt{3} whilst the polydispersity is .. math:: \text{PD} = \sigma / \bar x .. figure:: pd_rectangular.jpg Rectangular distribution. .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ Gaussian Distribution ^^^^^^^^^^^^^^^^^^^^^ The Gaussian Distribution is defined as .. math:: f(x) = \frac{1}{\text{Norm}} \exp\left(-\frac{(x - \bar x)^2}{2\sigma^2}\right) where $\bar x$ is the mean of the distribution and *Norm* is a normalization factor which is determined during the numerical calculation. The polydispersity is .. math:: \text{PD} = \sigma / \bar x .. figure:: pd_gaussian.jpg Normal distribution. .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ Lognormal Distribution ^^^^^^^^^^^^^^^^^^^^^^ The Lognormal Distribution is defined as .. math:: f(x) = \frac{1}{\text{Norm}} \frac{1}{xp}\exp\left(-\frac{(\ln(x) - \mu)^2}{2p^2}\right) where $\mu=\ln(x_\text{med})$ when $x_\text{med}$ is the median value of the distribution, and *Norm* is a normalization factor which will be determined during the numerical calculation. The median value for the distribution will be the value given for the respective size parameter, for example, *radius=60*. The polydispersity is given by $\sigma$ .. math:: \text{PD} = p For the angular distribution .. math:: p = \sigma / x_\text{med} The mean value is given by $\bar x = \exp(\mu+ p^2/2)$. The peak value is given by $\max x = \exp(\mu - p^2)$. .. figure:: pd_lognormal.jpg Lognormal distribution. This distribution function spreads more, and the peak shifts to the left, as $p$ increases, so it requires higher values of $N_\sigma$ and more points in the distribution. .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ Schulz Distribution ^^^^^^^^^^^^^^^^^^^ The Schulz distribution is defined as .. math:: f(x) = \frac{1}{\text{Norm}} (z+1)^{z+1}(x/\bar x)^z\frac{\exp[-(z+1)x/\bar x]}{\bar x\Gamma(z+1)} where $\bar x$ is the mean of the distribution and *Norm* is a normalization factor which is determined during the numerical calculation, and $z$ is a measure of the width of the distribution such that .. math:: z = (1-p^2) / p^2 The polydispersity is .. math:: p = \sigma / \bar x Note that larger values of PD might need larger number of points and $N_\sigma$. For example, at PD=0.7 and radius=60 |Ang|, Npts>=160 and Nsigmas>=15 at least. .. figure:: pd_schulz.jpg Schulz distribution. For further information on the Schulz distribution see: M Kotlarchyk & S-H Chen, *J Chem Phys*, (1983), 79, 2461. .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ Array Distribution ^^^^^^^^^^^^^^^^^^ This user-definable distribution should be given as as a simple ASCII text file where the array is defined by two columns of numbers: $x$ and $f(x)$. The $f(x)$ will be normalized to 1 during the computation. Example of what an array distribution file should look like: ==== ===== 30 0.1 32 0.3 35 0.4 36 0.5 37 0.6 39 0.7 41 0.9 ==== ===== Only these array values are used computation, therefore the parameter value given for the model will have no affect, and will be ignored when computing the average. This means that any parameter with an array distribution will not be fittable. .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ Note about DLS polydispersity ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Many commercial Dynamic Light Scattering (DLS) instruments produce a size polydispersity parameter, sometimes even given the symbol $p$\ ! This parameter is defined as the relative standard deviation coefficient of variation of the size distribution and is NOT the same as the polydispersity parameters in the Lognormal and Schulz distributions above (though they all related) except when the DLS polydispersity parameter is <0.13. For more information see: S King, C Washington & R Heenan, *Phys Chem Chem Phys*, (2005), 7, 143 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ *Document History* | 2015-05-01 Steve King | 2017-05-08 Paul Kienzle sasmodels/doc/guide/plugin.rst000066400000000000000000001215651317715334700167670ustar00rootroot00000000000000.. _Writing_a_Plugin: Writing a Plugin Model ====================== Overview ^^^^^^^^ In addition to the models provided with the sasmodels package, you are free to create your own models. Models can be of three types: - A pure python model : Example - `broadpeak.py `_ - A python model with embedded C : Example - `sphere.py `_ - A python wrapper with separate C code : Example - `cylinder.py `_, `cylinder.c `_ When using SasView, plugin models should be saved to the SasView *plugin_models* folder *C:\\Users\\{username}\\.sasview\\plugin_models* (on Windows) or */Users/{username}/.sasview\\plugin_models* (on Mac). The next time SasView is started it will compile the plugin and add it to the list of *Plugin Models* in a FitPage. Scripts can load the models from anywhere. The built-in modules are available in the *models* subdirectory of the sasmodels package. For SasView on Windows, these will be found in *C:\\Program Files (x86)\\SasView\\sasmodels-data\\models*. On Mac OSX, these will be within the application bundle as */Applications/SasView 4.0.app/Contents/Resources/sasmodels-data/models*. Other models are available for download from the `Model Marketplace `_. You can contribute your own models to the Marketplace as well. Create New Model Files ^^^^^^^^^^^^^^^^^^^^^^ Copy the appropriate files to your plugin models directory (we recommend using the examples above as templates) as mymodel.py (and mymodel.c, etc) as required, where "mymodel" is the name for the model you are creating. *Please follow these naming rules:* - No capitalization and thus no CamelCase - If necessary use underscore to separate words (i.e. barbell not BarBell or broad_peak not BroadPeak) - Do not include "model" in the name (i.e. barbell not BarBellModel) Edit New Model Files ^^^^^^^^^^^^^^^^^^^^ Model Contents .............. The model interface definition is in the .py file. This file contains: - a **model name**: - this is the **name** string in the *.py* file - titles should be: - all in *lower* case - without spaces (use underscores to separate words instead) - without any capitalization or CamelCase - without incorporating the word "model" - examples: *barbell* **not** *BarBell*; *broad_peak* **not** *BroadPeak*; *barbell* **not** *BarBellModel* - a **model title**: - this is the **title** string in the *.py* file - this is a one or two line description of the model, which will appear at the start of the model documentation and as a tooltip in the SasView GUI - a **short description**: - this is the **description** string in the *.py* file - this is a medium length description which appears when you click *Description* on the model FitPage - a **parameter table**: - this will be auto-generated from the *parameters* in the *.py* file - a **long description**: - this is ReStructuredText enclosed between the r""" and """ delimiters at the top of the *.py* file - what you write here is abstracted into the SasView help documentation - this is what other users will refer to when they want to know what your model does; so please be helpful! - a **definition** of the model: - as part of the **long description** - a **formula** defining the function the model calculates: - as part of the **long description** - an **explanation of the parameters**: - as part of the **long description** - explaining how the symbols in the formula map to the model parameters - a **plot** of the function, with a **figure caption**: - this is automatically generated from your default parameters - at least one **reference**: - as part of the **long description** - specifying where the reader can obtain more information about the model - the **name of the author** - as part of the **long description** - the *.py* file should also contain a comment identifying *who* converted/created the model file Models that do not conform to these requirements will *never* be incorporated into the built-in library. Model Documentation ................... The *.py* file starts with an r (for raw) and three sets of quotes to start the doc string and ends with a second set of three quotes. For example:: r""" Definition ---------- The 1D scattering intensity of the sphere is calculated in the following way (Guinier, 1955) .. math:: I(q) = \frac{\text{scale}}{V} \cdot \left[ 3V(\Delta\rho) \cdot \frac{\sin(qr) - qr\cos(qr))}{(qr)^3} \right]^2 + \text{background} where *scale* is a volume fraction, $V$ is the volume of the scatterer, $r$ is the radius of the sphere and *background* is the background level. *sld* and *sld_solvent* are the scattering length densities (SLDs) of the scatterer and the solvent respectively, whose difference is $\Delta\rho$. You can included figures in your documentation, as in the following figure for the cylinder model. .. figure:: img/cylinder_angle_definition.jpg Definition of the angles for oriented cylinders. References ---------- A Guinier, G Fournet, *Small-Angle Scattering of X-Rays*, John Wiley and Sons, New York, (1955) """ This is where the FULL documentation for the model goes (to be picked up by the automatic documentation system). Although it feels odd, you should start the documentation immediately with the **definition**---the model name, a brief description and the parameter table are automatically inserted above the definition, and the a plot of the model is automatically inserted before the **reference**. Figures can be included using the *figure* command, with the name of the *.png* file containing the figure and a caption to appear below the figure. Figure numbers will be added automatically. See this `Sphinx cheat sheet `_ for a quick guide to the documentation layout commands, or the `Sphinx Documentation `_ for complete details. The model should include a **formula** written using LaTeX markup. The example above uses the *math* command to make a displayed equation. You can also use *\$formula\$* for an inline formula. This is handy for defining the relationship between the model parameters and formula variables, such as the phrase "\$r\$ is the radius" used above. The live demo MathJax page ``_ is handy for checking that the equations will look like you intend. Math layout uses the `amsmath `_ package for aligning equations (see amsldoc.pdf on that page for complete documentation). You will automatically be in an aligned environment, with blank lines separating the lines of the equation. Place an ampersand before the operator on which to align. For example:: .. math:: x + y &= 1 \\ y &= x - 1 produces .. math:: x + y &= 1 \\ y &= x - 1 If you need more control, use:: .. math:: :nowrap: Model Definition ................ Following the documentation string, there are a series of definitions:: name = "sphere" # optional: defaults to the filename without .py title = "Spheres with uniform scattering length density" description = """\ P(q)=(scale/V)*[3V(sld-sld_solvent)*(sin(qr)-qr cos(qr)) /(qr)^3]^2 + background r: radius of sphere V: The volume of the scatter sld: the SLD of the sphere sld_solvent: the SLD of the solvent """ category = "shape:sphere" single = True # optional: defaults to True opencl = False # optional: defaults to False structure_factor = False # optional: defaults to False **name = "mymodel"** defines the name of the model that is shown to the user. If it is not provided it will use the name of the model file. The name must be a valid variable name, starting with a letter and contains only letters, numbers or underscore. Spaces, dashes, and other symbols are not permitted. **title = "short description"** is short description of the model which is included after the model name in the automatically generated documentation. The title can also be used for a tooltip. **description = """doc string"""** is a longer description of the model. It shows up when you press the "Description" button of the SasView FitPage. It should give a brief description of the equation and the parameters without the need to read the entire model documentation. The triple quotes allow you to write the description over multiple lines. Keep the lines short since the GUI will wrap each one separately if they are too long. **Make sure the parameter names in the description match the model definition!** **category = "shape:sphere"** defines where the model will appear in the model documentation. In this example, the model will appear alphabetically in the list of spheroid models in the *Shape* category. **single = True** indicates that the model can be run using single precision floating point values. Set it to False if the numerical calculation for the model is unstable, which is the case for about 20 of the built in models. It is worthwhile modifying the calculation to support single precision, allowing models to run up to 10 times faster. The section `Test_Your_New_Model`_ describes how to compare model values for single vs. double precision so you can decide if you need to set single to False. **opencl = False** indicates that the model should not be run using OpenCL. This may be because the model definition includes code that cannot be compiled for the GPU (for example, goto statements). It can also be used for large models which can't run on most GPUs. This flag has not been used on any of the built in models; models which were failing were streamlined so this flag was not necessary. **structure_factor = True** indicates that the model can be used as a structure factor to account for interactions between particles. See `Form_Factors`_ for more details. Model Parameters ................ Next comes the parameter table. For example:: # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [min, max], "type", "description"], parameters = [ ["sld", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Layer scattering length density"], ["sld_solvent", "1e-6/Ang^2", 6, [-inf, inf], "sld", "Solvent scattering length density"], ["radius", "Ang", 50, [0, inf], "volume", "Sphere radius"], ] # pylint: enable=bad-whitespace, line-too-long **parameters = [["name", "units", default, [min,max], "type", "tooltip"],...]** defines the parameters that form the model. **Note: The order of the parameters in the definition will be the order of the parameters in the user interface and the order of the parameters in Iq(), Iqxy() and form_volume(). And** *scale* **and** *background* **parameters are implicit to all models, so they do not need to be included in the parameter table.** - **"name"** is the name of the parameter shown on the FitPage. - the name must be a valid variable name, starting with a letter and containing only letters, numbers and underscore. - parameter names should follow the mathematical convention; e.g., *radius_core* not *core_radius*, or *sld_solvent* not *solvent_sld*. - model parameter names should be consistent between different models, so *sld_solvent*, for example, should have exactly the same name in every model. - to see all the parameter names currently in use, type the following in the python shell/editor under the Tools menu:: import sasmodels.list_pars sasmodels.list_pars.list_pars() *re-use* as many as possible!!! - use "name[n]" for multiplicity parameters, where *n* is the name of the parameter defining the number of shells/layers/segments, etc. - **"units"** are displayed along with the parameter name - every parameter should have units; use "None" if there are no units. - **sld's should be given in units of 1e-6/Ang^2, and not simply 1/Ang^2 to be consistent with the builtin models. Adjust your formulas appropriately.** - fancy units markup is available for some units, including:: Ang, 1/Ang, 1/Ang^2, 1e-6/Ang^2, degrees, 1/cm, Ang/cm, g/cm^3, mg/m^2 - the list of units is defined in the variable *RST_UNITS* within `sasmodels/generate.py `_ - new units can be added using the macros defined in *doc/rst_prolog* in the sasmodels source. - units should be properly formatted using sub-/super-scripts and using negative exponents instead of the / operator, though the unit name should use the / operator for consistency. - please post a message to the SasView developers mailing list with your changes. - **default** is the initial value for the parameter. - **the parameter default values are used to auto-generate a plot of the model function in the documentation.** - **[min, max]** are the lower and upper limits on the parameter. - lower and upper limits can be any number, or *-inf* or *inf*. - the limits will show up as the default limits for the fit making it easy, for example, to force the radius to always be greater than zero. - these are hard limits defining the valid range of parameter values; polydisperity distributions will be truncated at the limits. - **"type"** can be one of: "", "sld", "volume", or "orientation". - "sld" parameters can have magnetic moments when fitting magnetic models; depending on the spin polarization of the beam and the $q$ value being examined, the effective sld for that material will be used to compute the scattered intensity. - "volume" parameters are passed to Iq(), Iqxy(), and form_volume(), and have polydispersity loops generated automatically. - "orientation" parameters are only passed to Iqxy(), and have angular dispersion. Some models will have integer parameters, such as number of pearls in the pearl necklace model, or number of shells in the multi-layer vesicle model. The optimizers in BUMPS treat all parameters as floating point numbers which can take arbitrary values, even for integer parameters, so your model should round the incoming parameter value to the nearest integer inside your model you should round to the nearest integer. In C code, you can do this using:: static double Iq(double q, ..., double fp_n, ...) { int n = (int)(fp_n + 0.5); ... } in python:: def Iq(q, ..., n, ...): n = int(n+0.5) ... Derivative based optimizers such as Levenberg-Marquardt will not work for integer parameters since the partial derivative is always zero, but the remaining optimizers (DREAM, differential evolution, Nelder-Mead simplex) will still function. Model Computation ................. Models can be defined as pure python models, or they can be a mixture of python and C models. C models are run on the GPU if it is available, otherwise they are compiled and run on the CPU. Models are defined by the scattering kernel, which takes a set of parameter values defining the shape, orientation and material, and returns the expected scattering. Polydispersity and angular dispersion are defined by the computational infrastructure. Any parameters defined as "volume" parameters are polydisperse, with polydispersity defined in proportion to their value. "orientation" parameters use angular dispersion defined in degrees, and are not relative to the current angle. Based on a weighting function $G(x)$ and a number of points $n$, the computed value is .. math:: \hat I(q) = \frac{\int G(x) I(q, x)\,dx}{\int G(x) V(x)\,dx} \approx \frac{\sum_{i=1}^n G(x_i) I(q,x_i)}{\sum_{i=1}^n G(x_i) V(x_i)} That is, the individual models do not need to include polydispersity calculations, but instead rely on numerical integration to compute the appropriately smeared pattern. Angular dispersion values over polar angle $\theta$ requires an additional $\cos \theta$ weighting due to decreased arc length for the equatorial angle $\phi$ with increasing latitude. Python Models ............. For pure python models, define the *Iq* function:: import numpy as np from numpy import cos, sin, ... def Iq(q, par1, par2, ...): return I(q, par1, par2, ...) Iq.vectorized = True The parameters *par1, par2, ...* are the list of non-orientation parameters to the model in the order that they appear in the parameter table. **Note that the auto-generated model file uses** *x* **rather than** *q*. The *.py* file should import trigonometric and exponential functions from numpy rather than from math. This lets us evaluate the model for the whole range of $q$ values at once rather than looping over each $q$ separately in python. With $q$ as a vector, you cannot use if statements, but must instead do tricks like :: a = x*q*(q>0) + y*q*(q<=0) or :: a = np.empty_like(q) index = q>0 a[index] = x*q[index] a[~index] = y*q[~index] which sets $a$ to $q \cdot x$ if $q$ is positive or $q \cdot y$ if $q$ is zero or negative. If you have not converted your function to use $q$ vectors, you can set the following and it will only receive one $q$ value at a time:: Iq.vectorized = False Return np.NaN if the parameters are not valid (e.g., cap_radius < radius in barbell). If I(q; pars) is NaN for any $q$, then those parameters will be ignored, and not included in the calculation of the weighted polydispersity. Similar to *Iq*, you can define *Iqxy(qx, qy, par1, par2, ...)* where the parameter list includes any orientation parameters. If *Iqxy* is not defined, then it will default to *Iqxy = Iq(sqrt(qx**2+qy**2), par1, par2, ...)*. Models should define *form_volume(par1, par2, ...)* where the parameter list includes the *volume* parameters in order. This is used for a weighted volume normalization so that scattering is on an absolute scale. If *form_volume* is not defined, then the default *form_volume = 1.0* will be used. Embedded C Models ................. Like pure python models, inline C models need to define an *Iq* function:: Iq = """ return I(q, par1, par2, ...); """ This expands into the equivalent C code:: #include double Iq(double q, double par1, double par2, ...); double Iq(double q, double par1, double par2, ...) { return I(q, par1, par2, ...); } *Iqxy* is similar to *Iq*, except it uses parameters *qx, qy* instead of *q*, and it includes orientation parameters. *form_volume* defines the volume of the shape. As in python models, it includes only the volume parameters. *Iqxy* will default to *Iq(sqrt(qx**2 + qy**2), par1, ...)* and *form_volume* will default to 1.0. **source=['fn.c', ...]** includes the listed C source files in the program before *Iq* and *Iqxy* are defined. This allows you to extend the library of C functions available to your model. Models are defined using double precision declarations for the parameters and return values. When a model is run using single precision or long double precision, each variable is converted to the target type, depending on the precision requested. **Floating point constants must include the decimal point.** This allows us to convert values such as 1.0 (double precision) to 1.0f (single precision) so that expressions that use these values are not promoted to double precision expressions. Some graphics card drivers are confused when functions that expect floating point values are passed integers, such as 4*atan(1); it is safest to not use integers in floating point expressions. Even better, use the builtin constant M_PI rather than 4*atan(1); it is faster and smaller! The C model operates on a single $q$ value at a time. The code will be run in parallel across different $q$ values, either on the graphics card or the processor. Rather than returning NAN from Iq, you must define the *INVALID(v)*. The *v* parameter lets you access all the parameters in the model using *v.par1*, *v.par2*, etc. For example:: #define INVALID(v) (v.bell_radius < v.radius) Special Functions ................. The C code follows the C99 standard, with the usual math functions, as defined in `OpenCL `_. This includes the following: M_PI, M_PI_2, M_PI_4, M_SQRT1_2, M_E: $\pi$, $\pi/2$, $\pi/4$, $1/\sqrt{2}$ and Euler's constant $e$ exp, log, pow(x,y), expm1, sqrt: Power functions $e^x$, $\ln x$, $x^y$, $e^x - 1$, $\sqrt{x}$. The function expm1(x) is accurate across all $x$, including $x$ very close to zero. sin, cos, tan, asin, acos, atan: Trigonometry functions and inverses, operating on radians. sinh, cosh, tanh, asinh, acosh, atanh: Hyperbolic trigonometry functions. atan2(y,x): Angle from the $x$\ -axis to the point $(x,y)$, which is equal to $\tan^{-1}(y/x)$ corrected for quadrant. That is, if $x$ and $y$ are both negative, then atan2(y,x) returns a value in quadrant III where atan(y/x) would return a value in quadrant I. Similarly for quadrants II and IV when $x$ and $y$ have opposite sign. fmin(x,y), fmax(x,y), trunc, rint: Floating point functions. rint(x) returns the nearest integer. NAN: NaN, Not a Number, $0/0$. Use isnan(x) to test for NaN. Note that you cannot use :code:`x == NAN` to test for NaN values since that will always return false. NAN does not equal NAN! INFINITY: $\infty, 1/0$. Use isinf(x) to test for infinity, or isfinite(x) to test for finite and not NaN. erf, erfc, tgamma, lgamma: **do not use** Special functions that should be part of the standard, but are missing or inaccurate on some platforms. Use sas_erf, sas_erfc and sas_gamma instead (see below). Note: lgamma(x) has not yet been tested. Some non-standard constants and functions are also provided: M_PI_180, M_4PI_3: $\frac{\pi}{180}$, $\frac{4\pi}{3}$ SINCOS(x, s, c): Macro which sets s=sin(x) and c=cos(x). The variables *c* and *s* must be declared first. square(x): $x^2$ cube(x): $x^3$ sas_sinx_x(x): $\sin(x)/x$, with limit $\sin(0)/0 = 1$. powr(x, y): $x^y$ for $x \ge 0$; this is faster than general $x^y$ on some GPUs. pown(x, n): $x^n$ for $n$ integer; this is faster than general $x^n$ on some GPUs. FLOAT_SIZE: The number of bytes in a floating point value. Even though all variables are declared double, they may be converted to single precision float before running. If your algorithm depends on precision (which is not uncommon for numerical algorithms), use the following:: #if FLOAT_SIZE>4 ... code for double precision ... #else ... code for single precision ... #endif SAS_DOUBLE: A replacement for :code:`double` so that the declared variable will stay double precision; this should generally not be used since some graphics cards do not support double precision. There is no provision for forcing a constant to stay double precision. The following special functions and scattering calculations are defined in `sasmodels/models/lib `_. These functions have been tuned to be fast and numerically stable down to $q=0$ even in single precision. In some cases they work around bugs which appear on some platforms but not others, so use them where needed. Add the files listed in :code:`source = ["lib/file.c", ...]` to your *model.py* file in the order given, otherwise these functions will not be available. polevl(x, c, n): Polynomial evaluation $p(x) = \sum_{i=0}^n c_i x^i$ using Horner's method so it is faster and more accurate. $c = \{c_n, c_{n-1}, \ldots, c_0 \}$ is the table of coefficients, sorted from highest to lowest. :code:`source = ["lib/polevl.c", ...]` (`link to code `_) p1evl(x, c, n): Evaluation of normalized polynomial $p(x) = x^n + \sum_{i=0}^{n-1} c_i x^i$ using Horner's method so it is faster and more accurate. $c = \{c_{n-1}, c_{n-2} \ldots, c_0 \}$ is the table of coefficients, sorted from highest to lowest. :code:`source = ["lib/polevl.c", ...]` (`polevl.c `_) sas_gamma(x): Gamma function sas_gamma\ $(x) = \Gamma(x)$. The standard math function, tgamma(x) is unstable for $x < 1$ on some platforms. :code:`source = ["lib/sas_gamma.c", ...]` (`sas_gamma.c `_) sas_erf(x), sas_erfc(x): Error function sas_erf\ $(x) = \frac{2}{\sqrt\pi}\int_0^x e^{-t^2}\,dt$ and complementary error function sas_erfc\ $(x) = \frac{2}{\sqrt\pi}\int_x^{\infty} e^{-t^2}\,dt$. The standard math functions erf(x) and erfc(x) are slower and broken on some platforms. :code:`source = ["lib/polevl.c", "lib/sas_erf.c", ...]` (`sas_erf.c `_) sas_J0(x): Bessel function of the first kind sas_J0\ $(x)=J_0(x)$ where $J_0(x) = \frac{1}{\pi}\int_0^\pi \cos(x\sin(\tau))\,d\tau$. The standard math function j0(x) is not available on all platforms. :code:`source = ["lib/polevl.c", "lib/sas_J0.c", ...]` (`sas_J0.c `_) sas_J1(x): Bessel function of the first kind sas_J1\ $(x)=J_1(x)$ where $J_1(x) = \frac{1}{\pi}\int_0^\pi \cos(\tau - x\sin(\tau))\,d\tau$. The standard math function j1(x) is not available on all platforms. :code:`source = ["lib/polevl.c", "lib/sas_J1.c", ...]` (`sas_J1.c `_) sas_JN(n, x): Bessel function of the first kind and integer order $n$, sas_JN\ $(n, x) =J_n(x)$ where $J_n(x) = \frac{1}{\pi}\int_0^\pi \cos(n\tau - x\sin(\tau))\,d\tau$. If $n$ = 0 or 1, it uses sas_J0($x$) or sas_J1($x$), respectively. The standard math function jn(n, x) is not available on all platforms. :code:`source = ["lib/polevl.c", "lib/sas_J0.c", "lib/sas_J1.c", "lib/sas_JN.c", ...]` (`sas_JN.c `_) sas_Si(x): Sine integral Si\ $(x) = \int_0^x \tfrac{\sin t}{t}\,dt$. This function uses Taylor series for small and large arguments: For large arguments, .. math:: \text{Si}(x) \sim \frac{\pi}{2} - \frac{\cos(x)}{x}\left(1 - \frac{2!}{x^2} + \frac{4!}{x^4} - \frac{6!}{x^6} \right) - \frac{\sin(x)}{x}\left(\frac{1}{x} - \frac{3!}{x^3} + \frac{5!}{x^5} - \frac{7!}{x^7}\right) For small arguments, .. math:: \text{Si}(x) \sim x - \frac{x^3}{3\times 3!} + \frac{x^5}{5 \times 5!} - \frac{x^7}{7 \times 7!} + \frac{x^9}{9\times 9!} - \frac{x^{11}}{11\times 11!} :code:`source = ["lib/Si.c", ...]` (`Si.c `_) sas_3j1x_x(x): Spherical Bessel form sph_j1c\ $(x) = 3 j_1(x)/x = 3 (\sin(x) - x \cos(x))/x^3$, with a limiting value of 1 at $x=0$, where $j_1(x)$ is the spherical Bessel function of the first kind and first order. This function uses a Taylor series for small $x$ for numerical accuracy. :code:`source = ["lib/sas_3j1x_x.c", ...]` (`sas_3j1x_x.c `_) sas_2J1x_x(x): Bessel form sas_J1c\ $(x) = 2 J_1(x)/x$, with a limiting value of 1 at $x=0$, where $J_1(x)$ is the Bessel function of first kind and first order. :code:`source = ["lib/polevl.c", "lib/sas_J1.c", ...]` (`sas_J1.c `_) Gauss76Z[i], Gauss76Wt[i]: Points $z_i$ and weights $w_i$ for 76-point Gaussian quadrature, respectively, computing $\int_{-1}^1 f(z)\,dz \approx \sum_{i=1}^{76} w_i\,f(z_i)$. Similar arrays are available in :code:`gauss20.c` for 20-point quadrature and in :code:`gauss150.c` for 150-point quadrature. :code:`source = ["lib/gauss76.c", ...]` (`gauss76.c `_) Problems with C models ...................... The graphics processor (GPU) in your computer is a specialized computer tuned for certain kinds of problems. This leads to strange restrictions that you need to be aware of. Your code may work fine on some platforms or for some models, but then return bad values on other platforms. Some examples of particular problems: **(1) Code is too complex, or uses too much memory.** GPU devices only have a limited amount of memory available for each processor. If you run programs which take too much memory, then rather than running multiple values in parallel as it usually does, the GPU may only run a single version of the code at a time, making it slower than running on the CPU. It may fail to run on some platforms, or worse, cause the screen to go blank or the system to reboot. **(2) Code takes too long.** Because GPU devices are used for the computer display, the OpenCL drivers are very careful about the amount of time they will allow any code to run. For example, on OS X, the model will stop running after 5 seconds regardless of whether the computation is complete. You may end up with only some of your 2D array defined, with the rest containing random data. Or it may cause the screen to go blank or the system to reboot. **(3) Memory is not aligned**. The GPU hardware is specialized to operate on multiple values simultaneously. To keep the GPU simple the values in memory must be aligned with the different GPU compute engines. Not following these rules can lead to unexpected values being loaded into memory, and wrong answers computed. The conclusion from a very long and strange debugging session was that any arrays that you declare in your model should be a multiple of four. For example:: double Iq(q, p1, p2, ...) { double vector[8]; // Only going to use seven slots, but declare 8 ... } The first step when your model is behaving strangely is to set **single=False**. This automatically restricts the model to only run on the CPU, or on high-end GPU cards. There can still be problems even on high-end cards, so you can force the model off the GPU by setting **opencl=False**. This runs the model as a normal C program without any GPU restrictions so you know that strange results are probably from your code rather than the environment. Once the code is debugged, you can compare your output to the output on the GPU. Although it can be difficult to get your model to work on the GPU, the reward can be a model that runs 1000x faster on a good card. Even your laptop may show a 50x improvement or more over the equivalent pure python model. External C Models ................. External C models are very much like embedded C models, except that *Iq*, *Iqxy* and *form_volume* are defined in an external source file loaded using the *source=[...]* statement. You need to supply the function declarations for each of these that you need instead of building them automatically from the parameter table. .. _Form_Factors: Form Factors ............ Away from the dilute limit you can estimate scattering including particle-particle interactions using $I(q) = P(q)*S(q)$ where $P(q)$ is the form factor and $S(q)$ is the structure factor. The simplest structure factor is the *hardsphere* interaction, which uses the effective radius of the form factor as an input to the structure factor model. The effective radius is the average radius of the form averaged over all the polydispersity values. :: def ER(radius, thickness): """Effective radius of a core-shell sphere.""" return radius + thickness Now consider the *core_shell_sphere*, which has a simple effective radius equal to the radius of the core plus the thickness of the shell, as shown above. Given polydispersity over *(r1, r2, ..., rm)* in radius and *(t1, t2, ..., tn)* in thickness, *ER* is called with a mesh grid covering all possible combinations of radius and thickness. That is, *radius* is *(r1, r2, ..., rm, r1, r2, ..., rm, ...)* and *thickness* is *(t1, t1, ... t1, t2, t2, ..., t2, ...)*. The *ER* function returns one effective radius for each combination. The effective radius calculator weights each of these according to the polydispersity distributions and calls the structure factor with the average *ER*. :: def VR(radius, thickness): """Sphere and shell volumes for a core-shell sphere.""" whole = 4.0/3.0 * pi * (radius + thickness)**3 core = 4.0/3.0 * pi * radius**3 return whole, whole - core Core-shell type models have an additional volume ratio which scales the structure factor. The *VR* function returns the volume of the whole sphere and the volume of the shell. Like *ER*, there is one return value for each point in the mesh grid. *NOTE: we may be removing or modifying this feature soon. As of the time of writing, core-shell sphere returns (1., 1.) for VR, giving a volume ratio of 1.0.* Unit Tests .......... THESE ARE VERY IMPORTANT. Include at least one test for each model and PLEASE make sure that the answer value is correct (i.e. not a random number). :: tests = [ [{}, 0.2, 0.726362], [{"scale": 1., "background": 0., "sld": 6., "sld_solvent": 1., "radius": 120., "radius_pd": 0.2, "radius_pd_n":45}, 0.2, 0.228843], [{"radius": 120., "radius_pd": 0.2, "radius_pd_n":45}, "ER", 120.], [{"radius": 120., "radius_pd": 0.2, "radius_pd_n":45}, "VR", 1.], ] **tests=[[{parameters}, q, result], ...]** is a list of lists. Each list is one test and contains, in order: - a dictionary of parameter values. This can be *{}* using the default parameters, or filled with some parameters that will be different from the default, such as *{"radius":10.0, "sld":4}*. Unlisted parameters will be given the default values. - the input $q$ value or tuple of $(q_x, q_y)$ values. - the output $I(q)$ or $I(q_x,q_y)$ expected of the model for the parameters and input value given. - input and output values can themselves be lists if you have several $q$ values to test for the same model parameters. - for testing *ER* and *VR*, give the inputs as "ER" and "VR" respectively; the output for *VR* should be the sphere/shell ratio, not the individual sphere and shell values. .. _Test_Your_New_Model: Test Your New Model ^^^^^^^^^^^^^^^^^^^ Minimal Testing ............... From SasView either open the Python shell (*Tools* > *Python Shell/Editor*) or the plugin editor (*Fitting* > *Plugin Model Operations* > *Advanced Plugin Editor*), load your model, and then select *Run > Check Model* from the menu bar. An *Info* box will appear with the results of the compilation and a check that the model runs. If you are not using sasmodels from SasView, skip this step. Recommended Testing ................... If the model compiles and runs, you can next run the unit tests that you have added using the **test =** values. From SasView, switch to the *Shell* tab and type the following:: from sasmodels.model_test import run_one run_one("~/.sasview/plugin_models/model.py") This should print:: test_model_python (sasmodels.model_test.ModelTestCase) ... ok To check whether single precision is good enough, type the following:: from sasmodels.compare import main as compare compare("~/.sasview/plugin_models/model.py") This will pop up a plot showing the difference between single precision and double precision on a range of $q$ values. :: demo = dict(scale=1, background=0, sld=6, sld_solvent=1, radius=120, radius_pd=.2, radius_pd_n=45) **demo={'par': value, ...}** in the model file sets the default values for the comparison. You can include polydispersity parameters such as *radius_pd=0.2, radius_pd_n=45* which would otherwise be zero. These commands can also be run directly in the python interpreter: $ python -m sasmodels.model_test -v ~/.sasview/plugin_models/model.py $ python -m sasmodels.compare ~/.sasview/plugin_models/model.py The options to compare are quite extensive; type the following for help:: compare() Options will need to be passed as separate strings. For example to run your model with a random set of parameters:: compare("-random", "-pars", "~/.sasview/plugin_models/model.py") For the random models, - *sld* will be in the range (-0.5,10.5), - angles (*theta, phi, psi*) will be in the range (-180,180), - angular dispersion will be in the range (0,45), - polydispersity will be in the range (0,1) - other values will be in the range (0, 2\ *v*), where *v* is the value of the parameter in demo. Dispersion parameters *n*\, *sigma* and *type* will be unchanged from demo so that run times are more predictable (polydispersity calculated across multiple parameters can be very slow). If your model has 2D orientation calculation, then you should also test with:: compare("-2d", "~/.sasview/plugin_models/model.py") Check The Docs ^^^^^^^^^^^^^^ You can get a rough idea of how the documentation will look using the following:: compare("-help", "~/.sasview/plugin_models/model.py") This does not use the same styling as the rest of the docs, but it will allow you to check that your ReStructuredText and LaTeX formatting. Here are some tools to help with the inevitable syntax errors: - `Sphinx cheat sheet `_ - `Sphinx Documentation `_ - `MathJax `_ - `amsmath `_ There is also a neat online WYSIWYG ReStructuredText editor at http://rst.ninjs.org\ . Clean Lint - (Developer Version Only) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ **NB: For now we are not providing pylint with the installer version of SasView; so unless you have a SasView build environment available, you can ignore this section!** Run the lint check with:: python -m pylint --rcfile=extra/pylint.rc ~/.sasview/plugin_models/model.py We are not aiming for zero lint just yet, only keeping it to a minimum. For now, don't worry too much about *invalid-name*. If you really want a variable name *Rg* for example because $R_g$ is the right name for the model parameter then ignore the lint errors. Also, ignore *missing-docstring* for standard model functions *Iq*, *Iqxy*, etc. We will have delinting sessions at the SasView Code Camps, where we can decide on standards for model files, parameter names, etc. For now, you can tell pylint to ignore things. For example, to align your parameters in blocks:: # pylint: disable=bad-whitespace,line-too-long # ["name", "units", default, [lower, upper], "type", "description"], parameters = [ ["contrast_factor", "barns", 10.0, [-inf, inf], "", "Contrast factor of the polymer"], ["bjerrum_length", "Ang", 7.1, [0, inf], "", "Bjerrum length"], ["virial_param", "1/Ang^2", 12.0, [-inf, inf], "", "Virial parameter"], ["monomer_length", "Ang", 10.0, [0, inf], "", "Monomer length"], ["salt_concentration", "mol/L", 0.0, [-inf, inf], "", "Concentration of monovalent salt"], ["ionization_degree", "", 0.05, [0, inf], "", "Degree of ionization"], ["polymer_concentration", "mol/L", 0.7, [0, inf], "", "Polymer molar concentration"], ] # pylint: enable=bad-whitespace,line-too-long Don't put in too many pylint statements, though, since they make the code ugly. Share Your Model! ^^^^^^^^^^^^^^^^^ Once compare and the unit test(s) pass properly and everything is done, consider adding your model to the `Model Marketplace `_ so that others may use it! .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ *Document History* | 2016-10-25 Steve King | 2017-05-07 Paul Kienzle - Moved from sasview to sasmodels docssasmodels/doc/guide/refs.rst000066400000000000000000000014141317715334700164160ustar00rootroot00000000000000.. _models-refs: ********** References ********** *Small-Angle Scattering of X-Rays* A Guinier and G Fournet John Wiley & Sons, New York (1955) P Stckel, R May, I Strell, Z Cejka, W Hoppe, H Heumann, W Zillig and H Crespi *Eur. J. Biochem.*, 112, (1980), 411-417 G Porod in *Small Angle X-ray Scattering* (editors) O Glatter and O Kratky Academic Press (1982) *Structure Analysis by Small-Angle X-Ray and Neutron Scattering* L.A Feigin and D I Svergun Plenum Press, New York (1987) S Hansen *J. Appl. Cryst.* 23, (1990), 344-346 S J Henderson *Biophys. J.* 70, (1996), 1618-1627 B C McAlister and B P Grady *J. Appl. Cryst.* 31, (1998), 594-599 S R Kline *J Appl. Cryst.* 39(6), (2006), 895 **Also see the references at the end of the each model function descriptions.**sasmodels/doc/guide/resolution.rst000066400000000000000000000217771317715334700177000ustar00rootroot00000000000000.. sm_help.rst .. This is a port of the original SasView html help file to ReSTructured text .. by S King, ISIS, during SasView CodeCamp-III in Feb 2015. .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ Resolution Functions ==================== Sometimes the instrumental geometry used to acquire the experimental data has an impact on the clarity of features in the reduced scattering curve. For example, peaks or fringes might be slightly broadened. This is known as *Q resolution smearing*. To compensate for this effect one can either try and remove the resolution contribution - a process called *desmearing* - or add the resolution contribution into a model calculation/simulation (which by definition will be exact) to make it more representative of what has been measured experimentally - a process called *smearing*. Sasmodels does the latter. Both smearing and desmearing rely on functions to describe the resolution effect. Sasmodels provides three smearing algorithms: * *Slit Smearing* * *Pinhole Smearing* * *2D Smearing* The $Q$ resolution values should be determined by the data reduction software for the instrument and stored with the data file. If not, they will need to be set manually before fitting. .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ Slit Smearing ------------- **This type of smearing is normally only encountered with data from X-ray Kratky** **cameras or X-ray/neutron Bonse-Hart USAXS/USANS instruments.** The slit-smeared scattering intensity is defined by .. math:: I_s = \frac{1}{\text{Norm}} \int_{-\infty}^{\infty} dv\, W_v(v) \int_{-\infty}^{\infty} du\, W_u(u)\, I\left(\sqrt{(q+v)^2 + |u|^2}\right) where *Norm* is given by .. math:: \int_{-\infty}^{\infty} dv\, W_v(v) \int_{-\infty}^{\infty} du\, W_u(u) **[Equation 1]** The functions $W_v(v)$ and $W_u(u)$ refer to the slit width weighting function and the slit height weighting determined at the given $q$ point, respectively. It is assumed that the weighting function is described by a rectangular function, such that .. math:: W_v(v) = \delta(|v| \leq \Delta q_v) **[Equation 2]** and .. math:: W_u(u) = \delta(|u| \leq \Delta q_u) **[Equation 3]** so that $\Delta q_\alpha = \int_0^\infty d\alpha\, W_\alpha(\alpha)$ for $\alpha$ as $v$ and $u$. Here $\Delta q_u$ and $\Delta q_v$ stand for the the slit height (FWHM/2) and the slit width (FWHM/2) in $q$ space. This simplifies the integral in Equation 1 to .. math:: I_s(q) = \frac{2}{\text{Norm}} \int_{-\Delta q_v}^{\Delta q_v} dv \int_{0}^{\Delta q_u} du\, I\left(\sqrt{(q+v)^2 + u^2}\right) **[Equation 4]** which may be solved numerically, depending on the nature of $\Delta q_u$ and $\Delta q_v$. Solution 1 ^^^^^^^^^^ **For** $\Delta q_v = 0$ **and** $\Delta q_u = \text{constant}$ .. math:: I_s(q) \approx \int_0^{\Delta q_u} du\, I\left(\sqrt{q^2+u^2}\right) = \int_0^{\Delta q_u} d\left(\sqrt{q'^2-q^2}\right)\, I(q') For discrete $q$ values, at the $q$ values of the data points and at the $q$ values extended up to $q_N = q_i + \Delta q_u$ the smeared intensity can be approximately calculated as .. math:: I_s(q_i) \approx \sum_{j=i}^{N-1} \left[\sqrt{q_{j+1}^2 - q_i^2} - \sqrt{q_j^2 - q_i^2}\right]\, I(q_j) \sum_{j=1}^{N-1} W_{ij}\, I(q_j) **[Equation 5]** where $W_{ij} = 0$ for $I_s$ when $j < i$ or $j > N-1$. Solution 2 ^^^^^^^^^^ **For** $\Delta q_v = \text{constant}$ **and** $\Delta q_u = 0$ Similar to Case 1 .. math:: I_s(q_i) \approx \sum_{j=p}^{N-1} [q_{j+1} - q_i]\, I(q_j) \approx \sum_{j=p}^{N-1} W_{ij}\, I(q_j) for $q_p = q_i - \Delta q_v$ and $q_N = q_i + \Delta q_v$ **[Equation 6]** where $W_{ij} = 0$ for $I_s$ when $j < p$ or $j > N-1$. Solution 3 ^^^^^^^^^^ **For** $\Delta q_v = \text{constant}$ **and** $\Delta q_u = \text{constant}$ In this case, the best way is to perform the integration of Equation 1 numerically for both slit height and slit width. However, the numerical integration is imperfect unless a large number of iterations, say, at least 10000 by 10000 for each element of the matrix $W$, is performed. This is usually too slow for routine use. An alternative approach is used in sasmodels which assumes slit width << slit height. This method combines Solution 1 with the numerical integration for the slit width. Then .. math:: I_s(q_i) &\approx \sum_{j=p}^{N-1} \sum_{k=-L}^L \left[\sqrt{q_{j+1}^2 - (q_i + (k\Delta q_v/L))^2} - \sqrt{q_j^2 - (q_i + (k\Delta q_v/L))^2}\right] (\Delta q_v/L)\, I(q_j) \\ &\approx \sum_{j=p}^{N-1} W_{ij}\,I(q_j) **[Equation 7]** for $q_p = q_i - \Delta q_v$ and $q_N = q_i + \Delta q_v$ where $W_{ij} = 0$ for $I_s$ when $j < p$ or $j > N-1$. .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ Pinhole Smearing ---------------- **This is the type of smearing normally encountered with data from synchrotron** **SAXS cameras and SANS instruments.** The pinhole smearing computation is performed in a similar fashion to the slit-smeared case above except that the weight function used is a Gaussian. Thus Equation 6 becomes .. math:: I_s(q_i) &\approx \sum_{j=0}^{N-1}[\operatorname{erf}(q_{j+1}) - \operatorname{erf}(q_j)]\, I(q_j) \\ &\approx \sum_{j=0}^{N-1} W_{ij}\, I(q_j) **[Equation 8]** .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 2D Smearing ----------- The 2D smearing computation is performed in a similar fashion to the 1D pinhole smearing above except that the weight function used is a 2D elliptical Gaussian. Thus .. math:: I_s(x_0,\, y_0) &= A\iint dx'dy'\, \exp \left[ -\left(\frac{(x'-x_0')^2}{2\sigma_{x_0'}^2} + \frac{(y'-y_0')^2}{2\sigma_{y_0'}}\right)\right] I(x',\, y') \\ &= A\sigma_{x_0'}\sigma_{y_0'}\iint dX dY\, \exp\left[-\frac{(X^2+Y^2)}{2}\right] I(\sigma_{x_0'}X x_0',\, \sigma_{y_0'} Y + y_0') \\ &= A\sigma_{x_0'}\sigma_{y_0'}\iint dR d\Theta\, R\exp\left(-\frac{R^2}{2}\right) I(\sigma_{x_0'}R\cos\Theta + x_0',\, \sigma_{y_0'}R\sin\Theta+y_0') **[Equation 9]** In Equation 9, $x_0 = q \cos(\theta)$, $y_0 = q \sin(\theta)$, and the primed axes are all in the coordinate rotated by an angle $\theta$ about the $z$\ -axis (see the figure below) so that $x'_0 = x_0 \cos(\theta) + y_0 \sin(\theta)$ and $y'_0 = -x_0 \sin(\theta) + y_0 \cos(\theta)$. Note that the rotation angle is zero for a $x$\ -\ $y$ symmetric elliptical Gaussian distribution. The $A$ is a normalization factor. .. figure:: resolution_2d_rotation.png Coordinate axis rotation for 2D resolution calculation. Now we consider a numerical integration where each of the bins in $\theta$ and $R$ are *evenly* (this is to simplify the equation below) distributed by $\Delta \theta$ and $\Delta R$ respectively, and it is further assumed that $I(x',y')$ is constant within the bins. Then .. math:: I_s(x_0,\, y_0) &\approx A \sigma_{x'_0}\sigma_{y'_0}\sum_i^n \Delta\Theta\left[\exp\left(\frac{(R_i-\Delta R/2)^2}{2}\right) - \exp\left(\frac{(R_i + \Delta R/2)^2}{2}\right)\right] I(\sigma_{x'_0} R_i\cos\Theta_i+x'_0,\, \sigma_{y'_0}R_i\sin\Theta_i + y'_0) \\ &\approx \sum_i^n W_i\, I(\sigma_{x'_0} R_i \cos\Theta_i + x'_0,\, \sigma_{y'_0}R_i\sin\Theta_i + y'_0) **[Equation 10]** Since the weighting factor on each of the bins is known, it is convenient to transform $x'$\ -\ $y'$ back to $x$\ -\ $y$ coordinates (by rotating it by $-\theta$ around the $z$\ -axis). Then, for a polar symmetric smear .. math:: I_s(x_0,\, y_0) \approx \sum_i^n W_i\, I(x'\cos\theta - y'\sin\theta,\, x'sin\theta + y'\cos\theta) **[Equation 11]** where .. math:: x' &= \sigma_{x'_0} R_i \cos\Theta_i + x'_0 \\ y' &= \sigma_{y'_0} R_i \sin\Theta_i + y'_0 \\ x'_0 &= q = \sqrt{x_0^2 + y_0^2} \\ y'_0 &= 0 while for a $x$\ -\ $y$ symmetric smear .. math:: I_s(x_0,\, y_0) \approx \sum_i^n W_i\, I(x',\, y') **[Equation 12]** where .. math:: x' &= \sigma_{x'_0} R_i \cos\Theta_i + x'_0 \\ y' &= \sigma_{y'_0} R_i \sin\Theta_i + y'_0 \\ x'_0 &= x_0 = q_x \\ y'_0 &= y_0 = q_y The current version of sasmodels uses Equation 11 for 2D smearing, assuming that all the Gaussian weighting functions are aligned in the polar coordinate. .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ Weighting & Normalization ------------------------- In all the cases above, the weighting matrix $W$ is calculated on the first call to a smearing function, and includes ~60 $q$ values (finely and evenly binned) below (>0) and above the $q$ range of data in order to smear all data points for a given model and slit/pinhole size. The *Norm* factor is found numerically with the weighting matrix and applied on the computation of $I_s$. .. 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The key functions are :func:`sasmodels.core.load_model` for loading the model definition and compiling the kernel and :func:`sasmodels.data.load_data` for calling sasview to load the data. Need the data because that defines the resolution function and the q values to evaluate. If there is no data, then use :func:`sasmodels.data.empty_data1D` or :func:`sasmodels.data.empty_data2D` to create some data with a given $q$. Using sasmodels through bumps ============================= With the data and the model, you can wrap it in a *bumps* model with class:`sasmodels.bumps_model.Model` and create an class:`sasmodels.bump_model.Experiment` that you can fit with the *bumps* interface. Here is an example from the *example* directory such as *example/model.py*:: import sys from bumps.names import * from sasmodels.core import load_model from sasmodels.bumps_model import Model, Experiment from sasmodels.data import load_data, set_beam_stop, set_top """ IMPORT THE DATA USED """ radial_data = load_data('DEC07267.DAT') set_beam_stop(radial_data, 0.00669, outer=0.025) set_top(radial_data, -.0185) kernel = load_model("ellipsoid") model = Model(kernel, scale=0.08, radius_polar=15, radius_equatorial=800, sld=.291, sld_solvent=7.105, background=0, theta=90, phi=0, theta_pd=15, theta_pd_n=40, theta_pd_nsigma=3, radius_polar_pd=0.222296, radius_polar_pd_n=1, radius_polar_pd_nsigma=0, radius_equatorial_pd=.000128, radius_equatorial_pd_n=1, radius_equatorial_pd_nsigma=0, phi_pd=0, phi_pd_n=20, phi_pd_nsigma=3, ) # SET THE FITTING PARAMETERS model.radius_polar.range(15, 1000) model.radius_equatorial.range(15, 1000) model.theta_pd.range(0, 360) model.background.range(0,1000) model.scale.range(0, 10) #cutoff = 0 # no cutoff on polydisperisity loops #cutoff = 1e-5 # default cutoff cutoff = 1e-3 # low precision cutoff M = Experiment(data=radial_data, model=model, cutoff=cutoff) problem = FitProblem(M) Assume that bumps has been installed and the bumps command is available. Maybe need to set the path to sasmodels/sasview using *PYTHONPATH=path/to/sasmodels:path/to/sasview/src*. To run the model use the *bumps* program:: $ bumps example/model.py --preview Note that bumps and sasmodels are included as part of the SasView distribution. On windows, bumps can be called from the cmd prompt as follows:: SasViewCom bumps.cli example/model.py --preview Using sasmodels directly ======================== Bumps has a notion of parameter boxes in which you can set and retrieve values. Instead of using bumps, you can create a directly callable function with :class:`sasmodels.direct_model.DirectModel`. The resulting object *f* will be callable as *f(par=value, ...)*, returning the $I(q)$ for the $q$ values in the data. Polydisperse parameters use the same naming conventions as in the bumps model, with e.g., radius_pd being the polydispersity associated with radius. Getting a simple function that you can call on a set of q values and return a result is not so simple. Since the time critical use case (fitting) involves calling the function over and over with identical $q$ values, we chose to optimize the call by only transfering the $q$ values to the GPU once at the start of the fit. We do this by creating a :class:`sasmodels.kernel.Kernel` object from the :class:`sasmodels.kernel.KernelModel` returned from :func:`sasmodels.core.load_model` using the :meth:`sasmodels.kernel.KernelModel.make_kernel` method. What it actual does depends on whether it is running as a DLL, as OpenCL or as a pure python kernel. Once the kernel is in hand, we can then marshal a set of parameters into a :class:`sasmodels.details.CallDetails` object and ship it to the kernel using the :func:`sansmodels.direct_model.call_kernel` function. An example should help, *example/cylinder_eval.py*:: from numpy import logspace from matplotlib import pyplot as plt from sasmodels.core import load_model from sasmodels.direct_model import call_kernel model = load_model('cylinder') q = logspace(-3, -1, 200) kernel = model.make_kernel([q]) Iq = call_kernel(kernel, dict(radius=200.)) plt.loglog(q, Iq) plt.show() On windows, this can be called from the cmd prompt using sasview as:: SasViewCom example/cylinder_eval.py sasmodels/doc/guide/sesans/000077500000000000000000000000001317715334700162215ustar00rootroot00000000000000sasmodels/doc/guide/sesans/SESANSinSASVIEW.pdf000066400000000000000000022356051317715334700213160ustar00rootroot00000000000000%PDF-1.5 % 3 0 obj << /Length 1573 /Filter /FlateDecode >> stream xuWKs6WHT,8uZg S((*/v we"=lg(cQVRqJgh|%idaH˨7}ǫv:Wo\3N{x?˫{T+Qd x]Y{Fw;ҰVqQ bqJՑQ?"SR$*R |!{&@چ3f"Ő",q=y.#eF[x3qCڭ6ؘ-JXx=qc72:^S juY-+:HtT8\J&OuO@rpCB+TB~8}\]C0Jm ,/)R \iJB+E'P"j1QEIo:sD(^zש)JH*kYj霢n%#F :]@ձ3kыlWxklOȝck6 *ٰ쨗{ʡKVڂA LGP?jh+xPN"~c3K촞 Q"ڱCmGc&ˎLjrFvvۛ\\YrMg7ְ;2_4 ᅼq#m^ ׯ@y`0K!Ѽ\Fmodz P6`Uu{뿫AǕ#abݝXɱS\hBa,3b9!hYNsٲ# p},a `3^ |eH^uPDdU{^9=X]ڰF沛!Ep՗Pjz[A;( $AB+{"a,b]c0 O[|IJo,L4*dse ~܁fNPUt5\-z)@?C2]cT;)Qn}a촾><[GJ4'A{SsotG/$<IYnx}x)&BȐBƏq' a[?^7݅?,g4 G4ul"6ޕvOL ۇ{CD4nnN(6 endstream endobj 2 0 obj << /Type /Page /Contents 3 0 R /Resources 1 0 R /MediaBox [0 0 612 792] /Parent 8 0 R >> endobj 1 0 obj << /Font << /F15 4 0 R /F16 5 0 R /F26 6 0 R /F8 7 0 R >> /ProcSet [ /PDF /Text ] >> endobj 11 0 obj << /Length 2305 /Filter /FlateDecode >> stream xڵYK6ϯ-T!|*Vx)#A+% Oƿ~Mfhkzs{u}Sʸd6̄.\YTv=#BY)s?h;b{rEd2>e?lCsVP[o׼_-M{ KEPb6M Q-KWeʚ6onS&7 [}ߣǪ+aSZw;Ү|64(#Hf^l&t:xaRFU]%I N2~>xu4cב;OU|wܣWyLgayEoYhk ,LPjK\ @ w Ֆ(IbRnw}wD%M*'rS%JB 1F @ GQ67Xz\xk0qqq𡐢w+vUhuFZWͪ> T,j74~p02 >WAXeJc(җ5]y;Oeo& 4rU*@*A罈 `ZF;kBB?Xg1fry֪ՇG[bn[vJ߀Jtdut[l6{WncV6 h JJ;%SO) g >OXٴȹ2 \uWՕdF!wѯٷa֎W aj.JX2:K*(_Tѧ%&bo;vvϠ+Cp% ٤O -y^LŔAvG1JP8#u{J{xir%ûWĺ;4!M/sɅ } %\D@8~澗&,mX(E\H1nؘǮ@_j'y0`>bgFi\/!M@oWCQ] }՘yۭu8! vϣ"x-ޙ ҈ri.},a*' å.L # y%5q~H@, 5&}plmc;S!?OΑ*@?C #%Xp90٣@9Tz ibڃDx$!8*){  H >~`<[`ɉ~S8 ;(njKΜ! 6#/Cmx< ?A*r#O˟ R R;T]^;vsmm81(fb$'/c-u/ʞc8S^F-Xʄ1RǢd$bBX qg$%ťA V ]X >0 ^~/cTR݆yR+x̸螤fd=ԡ{)o<6eN2 y\W_,Ek/%,Lw`f3\abgb]jLՏg)cSy@gl+gQ_r.BwhrGuwLJŔKNG- I;s,!%/RN~J DPmibpJ|ӋٵY:dwePT zI @޻]B 74?=9|]RW%"4~n7u>ܣD Th>6=XtYOh` jEg")O Ia-&'H g6 SA!I7cܘ/磉JN)%Rjr{*KE@5˦ T)|'#Ɏ /kʙd fMB$lJ_XS*$si~2`*B rn`I&үehқ"M_p۫^!'31e rf&5=&Ve133?WoΟY(xNRLy+Ûf_Y<09Q:ΠrғJKjs9tQ@}I}t^o|xZ-D(&<;-woM>ܧⰹA*fq2FeTyG.~* ]mW-> O`U&L~NZK];\QhZ u*OOֺ<v/̺킟  p G_zrƞf!W0| RޒƕBYC ?㟷 endstream endobj 10 0 obj << /Type /Page /Contents 11 0 R /Resources 9 0 R /MediaBox [0 0 612 792] /Parent 8 0 R >> endobj 9 0 obj << /Font << /F8 7 0 R /F26 6 0 R /F14 12 0 R /F11 13 0 R /F7 14 0 R >> /ProcSet [ /PDF /Text ] >> endobj 17 0 obj << /Length 1806 /Filter /FlateDecode >> stream xXKo6WR@F\)EN(&:h4--UVp}Ei(E ?΋3}rs6:J6RLVRE7u,?q.Tt[Ɯdr,iu]<*Xhs&P.E3!x\\q۷sG@Pt5ichcmVz̚u9Yg4[;qc,2~eny~@k5di]I6 io__/ i-Iz4v]V ݒd!J+P`~*P,,.jXmJ;J)?L/*yRjribT= v)}*6g lkp%8 $G[o0( Үrx^G~i<#Z~A&|<}ǦgSɯhxI3O'1gIWx,mNѕ71=$0Ay=z՟5lUvc#4-.٤eS?oh35)PE*'}>yX0!3Ԟ^ЅS07zmxD1%re2mÖ%j5/]B͡MvdUOtwXnPTUP90x'ޗͧj[u}()˲HAKXUSXLL$A\/UXoYMx GaƟ2!z"7*|˂(x.~w.? 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%%EOF sasmodels/doc/guide/sesans/sans_to_sesans.rst000066400000000000000000000037611317715334700220040ustar00rootroot00000000000000.. currentmodule:: sasmodels .. Wim Bouwman, DUT, written at codecamp-V, Oct2016 .. _SESANS: SANS to SESANS conversion ========================= The conversion from SANS into SESANS in absolute units is a simple Hankel transformation when all the small-angle scattered neutrons are detected. First we calculate the Hankel transform including the absolute intensities by .. math:: G(\delta) = 2 \pi \int_0^{\infty} J_0(Q \delta) \frac{d \Sigma}{d \Omega} (Q) Q dQ \!, in which :math:`J_0` is the zeroth order Bessel function, :math:`\delta` the spin-echo length, :math:`Q` the wave vector transfer and :math:`\frac{d \Sigma}{d \Omega} (Q)` the scattering cross section in absolute units. Out of necessity, a 1-dimensional numerical integral approximates the exact Hankel transform. The upper bound of the numerical integral is :math:`Q_{max}`, which is calculated from the wavelength and the instrument's maximum acceptance angle, both of which are included in the file. While the true Hankel transform has a lower bound of zero, most scattering models are undefined at :math: `Q=0`, so the integral requires an effective lower bound. The lower bound of the integral is :math:`Q_{min} = 0.1 \times 2 \pi / R_{max}`, in which :math:`R_{max}` is the maximum length scale probed by the instrument multiplied by the number of data points. This lower bound is the minimum expected Q value for the given length scale multiplied by a constant. The constant, 0.1, was chosen empirically by integrating multiple curves and finding where the value at which the integral was stable. A constant value of 0.3 gave numerical stability to the integral, so a factor of three safety margin was included to give the final value of 0.1. From the equation above we can calculate the polarisation that we measure in a SESANS experiment: .. math:: P(\delta) = e^{t \left( \frac{ \lambda}{2 \pi} \right)^2 \left(G(\delta) - G(0) \right)} \!, in which :math:`t` is the thickness of the sample and :math:`\lambda` is the wavelength of the neutrons. sasmodels/doc/guide/sesans/sesans_fitting.rst000066400000000000000000000102311317715334700217700ustar00rootroot00000000000000.. currentmodule:: sasmodels .. Wim Bouwman, DUT, written at codecamp-V, Oct2016 .. _sesans_fitting: Fitting SESANS Data =================== .. note:: A proper installation of the developers setup of SasView (http://trac.sasview.org/wiki/AnacondaSetup) is a prerequisite for using these instructions. It is possible to fit SESANS measurements from the command line in Python. Simple Fits ........... In the folder sasmodels/example the file sesans_sphere_2micron.py gives an example of how to fit a shape to a measurement. The command:: >python fit_sesans.py sesans_sphere_2micron.py then results in a GUI from which you can control the fit. .. image:: sesans_img/SphereLineFitSasView.png All the parameters and names in sesans_sphere_2micron.py (shown below) can be adjusted to fit your own problem:: """ This is a data file used to load in sesans data and fit it using the bumps engine """ from bumps.names import * import sesansfit # Enter the model name to use model_name = "sphere" # DO NOT MODIFY THIS LINE model = sesansfit.get_bumps_model(model_name) # Enter any custom parameters # name = Parameter(initial_value, name='name') phi = Parameter(0.0855, name='phi') # Add the parameters to this list that should be displayed in the fitting window custom_params = {"phi" : phi} # SESANS data file name sesans_file = "spheres2micron.ses" # Initial parameter values (if other than defaults) # "model_parameter_name" : value initial_vals = { "sld" : 1.41, "radius" : 10000, "sld_solvent" : 2.70, } # Ranges for parameters if other than default # "model_parameter_name" : [min, max] param_range = { "phi" : [0.001, 0.5], "radius" : [100, 100000] } # Constraints # model.param_name = f(other params) # EXAMPLE: model.scale = model.radius*model.radius*(1 - phi) - where radius # and scale are model functions and phi is a custom parameter model.scale = phi*(1-phi) # Send to the fitting engine # DO NOT MODIFY THIS LINE problem = sesansfit.sesans_fit(sesans_file, model, initial_vals, custom_params, param_range) Incorporating a Structure Factor ................................ An example of how to also include a structure factor can be seen in the following example taken from Washington et al., *Soft Matter*\, (2014), 10, 3016 (dx.doi.org/10.1039/C3SM53027B). These are time-of-flight measurements, which is the reason that not the polarisation is plotted, but the :math:`\frac{log(P/P_0)}{\lambda^2}` . The sample is a dispersion of core-shell colloids at a high volume fraction with hard sphere interactions. The fit can be started by:: >python fit_sesans.py sesans_parameters_css-hs.py This yields after the fitting: .. image:: sesans_img/HardSphereLineFitSasView.png The code sesans_parameters_css-hs.py can then be used as a template for a fitting problem with a structure factor:: """ This is a data file used to load in sesans data and fit it using the bumps engine """ from bumps.names import * import sesansfit # Enter the model name to use model_name = "core_shell_sphere*hardsphere" # DO NOT MODIFY THIS LINE model = sesansfit.get_bumps_model(model_name) # Enter any custom parameters phi = Parameter(0.45, name='phi') pen = Parameter(0.95, name='solvent penetration') custom_params = {"phi" : phi, "pen" : pen} # SESANS data file sesans_file = "core_shell.ses" # Initial parameter values (if other than defaults) initial_vals = { "sld_core" : 1.05, "sld_shell" : 2.88*pen-0.05*(1-pen), "sld_solvent" : 2.88, "radius" : 730, "thickness" : 20, "volfraction" : phi, "scale" : (1-phi) } # Ranges for parameters if other than default param_range = { "phi" : [0.2, 0.5], "pen" : [0,1], "radius" : [500, 3000], "thickness" : [0,200] } # Constraints # model.param_name = f(other params) # EXAMPLE: model.scale = model.radius*model.radius*(1 - phi) - where radius # and scale are model functions and phi is a custom parameter model.scale = phi*(1-phi) model.volfraction = phi model.shell_sld = pen*2.88 # Send to the fitting engine problem = sesansfit.sesans_fit(sesans_file, model_name, initial_vals, custom_params, param_range) sasmodels/doc/guide/sesans/sesans_img/000077500000000000000000000000001317715334700203515ustar00rootroot00000000000000sasmodels/doc/guide/sesans/sesans_img/HardSphereLineFitSasView.png000066400000000000000000003411341317715334700256670ustar00rootroot00000000000000PNG  IHDR>_sRGBgAMA a pHYsttfxIDATx^|\Օ/lMM6CKH $!!ݰ؀cqwKdKd{S5"i4E3j3%sHbsy3}u/۷E̊ةfTG S*j?5A|9|T "8>s  轷`F4Q'j>)y{G!?.̌*]ŧI왥t%SgOqx쪄|Qh9x( ~ji-C8˥gS3<ӳسw+ϰs$^t,*Á#_y{ul;#}u6@GЪviyM^]O_:\1hrOi=:;h:\X]HMPm TZ*A K/1a<;љUߑQ۞^ݚVeKrsbiKBIs|qsBqs|I$hI(5'Y,ԪִZ{V3Gw{ &#& ^$REz|#O/+r}/ N|^377 aH>`-9 ɖD(FtPT^"E SHD$(HhGO6"q  w/7'XUʮި $.<\ʈ(qqN#^5]gB;$Q@\|zVCc_0`ՇUJC1/1ZNSc$a 2x$ِp <&R[+dq"~6f>Q J/H5{>V 7<:"> %bbDP#0$p.q`'cpphppH 䊥NLKӋe ع)+4dY&I2O;${b:I넭y`െW烷*{$WDY·4Ip~5$'EDHU" 08 @ A H8>ega`@t~f:x臇Y:bݏ <6FVH% @;{>ĆmǦ=#@p3:}{_kRgz+dx^/#9$d$f$áȁ)~H#BpOWzJGZJVFk;F CǿI0w6?h{R EO!DBC]w!L4|ց6±F k'vN68kۆ[*b聶!_f6`+|;љ]בYkϬi2 +m@J5̜Tڒ\jd?3`R%RiKnˬiti"9@D )>ȗJst m00|*-y0\hfCd0\@!Z(a ,ij1\QWm$@"? 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The scattering is computed as a function of reciprocal space $q$, which arises from a combination of beam wavelength and scattering angles. Each pixel on the detector corresponds to a different scattering angle, and has a distinct $q_x$ and $q_y$. If the sample is unoriented, the scattering pattern will appear as rings on the detector. In this case, a circular average can be taken with 1-dimension data at $q = \surd (q_x^2 + q_y^2)$ compared to the orientationally averaged SAS scattering pattern. The sasmodels package provides theory functions for small angle scattering calculations for different shapes, including the effects of resolution, polydispersity and orientational dispersion. .. htmlonly:: :Release: |version| :Date: |today| Download pdf version `here `_ .. toctree:: :numbered: :maxdepth: 4 guide/index.rst guide/models/index.rst developer/index.rst api/index.rst Indices and Tables ================== * :ref:`genindex` * :ref:`modindex` .. htmlonly:: * :ref:`search` sasmodels/doc/rst_prolog000066400000000000000000000015341317715334700157500ustar00rootroot00000000000000.. Set up some substitutions to make life easier... .. |Ang| unicode:: U+212B .. |Ang^-1| replace:: |Ang|\ :sup:`-1` .. |Ang^2| replace:: |Ang|\ :sup:`2` .. |Ang^-2| replace:: |Ang|\ :sup:`-2` .. |1e-6Ang^-2| replace:: 10\ :sup:`-6`\ |Ang|\ :sup:`-2` .. |Ang^3| replace:: |Ang|\ :sup:`3` .. |Ang^-3| replace:: |Ang|\ :sup:`-3` .. |Ang^-4| replace:: |Ang|\ :sup:`-4` .. |cm^-1| replace:: cm\ :sup:`-1` .. |cm^2| replace:: cm\ :sup:`2` .. |cm^-2| replace:: cm\ :sup:`-2` .. |cm^3| replace:: cm\ :sup:`3` .. |1e15cm^3| replace:: 10\ :sup:`15`\ cm\ :sup:`3` .. |cm^-3| replace:: cm\ :sup:`-3` .. |sr^-1| replace:: sr\ :sup:`-1` .. |cdot| unicode:: U+00B7 .. |deg| unicode:: U+00B0 .. |g/cm^3| replace:: g\ |cdot|\ cm\ :sup:`-3` .. |mg/m^2| replace:: mg\ |cdot|\ m\ :sup:`-2` .. |fm^2| replace:: fm\ :sup:`2` .. |Ang*cm^-1| replace:: |Ang|\ |cdot|\ cm\ :sup:`-1` sasmodels/example/000077500000000000000000000000001317715334700145165ustar00rootroot00000000000000sasmodels/example/093191_201.dat000066400000000000000000000124331317715334700163430ustar00rootroot00000000000000GRASP V.7.11CD Instrument: ILL_d22 ***** Sample, Backgrounds and Transmissions Data: ***** Subtitle: CM 10% SDS Start: 01-Sep-16 12:23:13 End: 01-Sep-16 12:23:18 Foreground: 93191 , Loaded: 92991:93230 Background: 91098 , Loaded: 91098 Cadmium: 90990 , Loaded: 90990 Det: 1 : Applying Deadtime Correction per (vertical) Tube: 1/[1-tau/detector_rate], tau = 1e-06 (seconds) Data Normalisation: Standard Monitor (10000000) counts Attenuator: 0 is In. Attenuation factor 1 Attenuator: 0 is In. Up-scaling data by 1 Attenuator2: is Out Attenuator2: Up-scaling data by 1 Beam Centre1 : Cx = 27.1492 Cy = 127.3257 Cm Translation : Tx = 0 Ty = 0 [mm] Transmissions: Ts = 0.97203 +/- 0.010336 Te = 1 +/- 0.0013531 Transmissions Thickness Correction is: on Applying standard SANS data reduction: I_corr = 1/[Ts Te] [I_s - I_cd] - 1/[Te] [I_bck - I_cd] ***** Calibrations: ***** Data: Corrected for D22 Detector Paralax Data: Corrected for Detector Efficiency (doesn't change magnitude but contains curvature correction) Data: Divided by Volume 0.025 cm3 Solid Angle Correction: Divide data by empty beam flux, I0, from worksheet: I0 Beam Intensity 1 202 Applying Default Instrument Mask Applying User Defined Mask Applying NanInf Mask Intensity units are: cm-1 \\ \Delta\Omega ***** Analysis ***** Averaging I vs. Q. Bin size: 1 [Pixel(s)] Mod_Q I Err_I Sigma_Q 0.0399306 0.455087 0.0263041 0.00471442 0.0461801 0.594146 0.0176702 0.00480794 0.0519658 0.721063 0.0154168 0.00490303 0.0578791 0.975489 0.0151415 0.00500984 0.0639094 1.32481 0.01666 0.00512844 0.0698138 1.91231 0.0190375 0.00525617 0.0757907 2.70255 0.0212271 0.00539353 0.0818611 3.45201 0.022998 0.00553989 0.0878521 3.84812 0.0236703 0.00569104 0.0937984 3.67201 0.0223657 0.00584668 0.0997329 3.08463 0.0199299 0.00603593 0.105788 2.44287 0.0169271 0.00623212 0.111814 1.8944 0.0149048 0.00640109 0.117765 1.48387 0.0128443 0.00662702 0.123807 1.19565 0.0112736 0.00668684 0.129841 1.0071 0.0102806 0.00680967 0.135846 0.836246 0.00923172 0.00712461 0.141859 0.716454 0.00849073 0.00743994 0.14784 0.628444 0.00788484 0.00755558 0.153823 0.534797 0.00722617 0.0076497 0.159753 0.456498 0.00677101 0.00780975 0.165751 0.378987 0.00646111 0.00810292 0.171732 0.33881 0.00616212 0.00839535 0.177739 0.289236 0.00584175 0.00868898 0.18374 0.238016 0.00546703 0.00866381 0.189736 0.203079 0.00520056 0.00894656 0.195698 0.171069 0.00495042 0.00899438 0.201668 0.153949 0.00475784 0.0092688 0.207677 0.131067 0.00454288 0.00954494 0.213601 0.118889 0.00446381 0.00981725 0.219565 0.110022 0.00427412 0.0100913 0.225593 0.10747 0.00424177 0.0103684 0.231541 0.100865 0.00417778 0.0106418 0.237547 0.093447 0.00402577 0.0107734 0.243603 0.0937223 0.00400622 0.0108222 0.249624 0.0948064 0.00399285 0.0110897 0.255615 0.0949532 0.00397902 0.0111138 0.26162 0.0915976 0.00390164 0.0113749 0.267619 0.0927151 0.00391519 0.0116357 0.27357 0.0966561 0.00392083 0.0118944 0.279514 0.0896038 0.00382976 0.0121528 0.285494 0.0909465 0.00379672 0.0124129 0.291495 0.090641 0.00376077 0.0126738 0.297457 0.0845533 0.00370577 0.012933 0.303394 0.0834418 0.00366612 0.0131911 0.309405 0.0815794 0.00358735 0.0134525 0.315461 0.086537 0.00360475 0.0137158 0.321501 0.0814197 0.00354806 0.0139784 0.32749 0.0811975 0.00354551 0.0142388 0.333458 0.0788328 0.0035047 0.0144983 0.339368 0.0757621 0.00352639 0.0146465 0.345351 0.0783668 0.00365607 0.0149047 0.351315 0.074696 0.00367733 0.0151621 0.357265 0.0746856 0.00376074 0.0154189 0.363299 0.0723696 0.00397781 0.015444 0.369344 0.077648 0.00413299 0.015701 0.375347 0.0715659 0.00424208 0.0159562 0.381274 0.0715309 0.00430186 0.0159573 0.387269 0.0752993 0.00438052 0.0162082 0.393257 0.0707649 0.00435293 0.0164588 0.399251 0.0695322 0.00433681 0.0167097 0.405282 0.0735785 0.00439895 0.0169621 0.411261 0.0783315 0.00450466 0.0172124 0.417164 0.0625388 0.00439646 0.0174594 0.423179 0.0749592 0.00443032 0.0177111 0.429234 0.0774125 0.0045065 0.0179645 0.435236 0.0671526 0.00443888 0.0182158 0.441167 0.0664527 0.0044592 0.018464 0.447074 0.0670769 0.0044726 0.0187112 0.453098 0.067893 0.00436489 0.0189633 0.459189 0.0706633 0.00447217 0.0192182 0.465129 0.072765 0.00456344 0.019312 0.471073 0.0676428 0.00447517 0.0195588 0.477118 0.0679994 0.0043968 0.0198098 0.483165 0.0744563 0.00455855 0.0200609 0.489079 0.0696971 0.00455032 0.0203064 0.495076 0.0666634 0.00441788 0.0205555 0.50109 0.0650749 0.00446766 0.0208051 0.507012 0.0716745 0.00456643 0.021051 0.513065 0.0612866 0.00433361 0.0213024 0.519078 0.0751487 0.0046292 0.021552 0.52495 0.0708117 0.00459551 0.0217958 0.53097 0.0665376 0.00439133 0.0220457 0.536987 0.0647267 0.00448903 0.0222956 0.54287 0.0680348 0.0045584 0.0225398 0.54886 0.0682137 0.00516347 0.0227885 0.554866 0.0600309 0.00549151 0.0230379 0.560915 0.0708694 0.00609187 0.023289 0.566896 0.0802486 0.00686271 0.0235374 0.572844 0.0586832 0.00697213 0.0237843 0.578801 0.0556705 0.00770313 0.0240317 0.584749 0.0647072 0.00866416 0.0242786 0.590751 0.0690938 0.0100902 0.0245279 0.596726 0.0968634 0.0126976 0.0247759 0.602559 0.0547113 0.0150671 0.0250181 0.608118 0.0874406 0.0258455 0.0252489 0.612818 0.0787903 0.0650848 0.025444 sasmodels/example/093192_202.dat000066400000000000000000000124171317715334700163470ustar00rootroot00000000000000GRASP V.7.11CD Instrument: ILL_d22 ***** Sample, Backgrounds and Transmissions Data: ***** Subtitle: CM 10% SDS Start: 01-Sep-16 12:23:18 End: 01-Sep-16 12:23:23 Foreground: 93192 , Loaded: 92991:93230 Background: 91098 , Loaded: 91098 Cadmium: 90990 , Loaded: 90990 Det: 1 : Applying Deadtime Correction per (vertical) Tube: 1/[1-tau/detector_rate], tau = 1e-06 (seconds) Data Normalisation: Standard Monitor (10000000) counts Attenuator: 0 is In. Attenuation factor 1 Attenuator: 0 is In. Up-scaling data by 1 Attenuator2: is Out Attenuator2: Up-scaling data by 1 Beam Centre1 : Cx = 27.1492 Cy = 127.3257 Cm Translation : Tx = 0 Ty = 0 [mm] Transmissions: Ts = 0.95963 +/- 0.010298 Te = 1 +/- 0.0013531 Transmissions Thickness Correction is: on Applying standard SANS data reduction: I_corr = 1/[Ts Te] [I_s - I_cd] - 1/[Te] [I_bck - I_cd] ***** Calibrations: ***** Data: Corrected for D22 Detector Paralax Data: Corrected for Detector Efficiency (doesn't change magnitude but contains curvature correction) Data: Divided by Volume 0.025 cm3 Solid Angle Correction: Divide data by empty beam flux, I0, from worksheet: I0 Beam Intensity 1 203 Applying Default Instrument Mask Applying User Defined Mask Applying NanInf Mask Intensity units are: cm-1 \\ \Delta\Omega ***** Analysis ***** Averaging I vs. Q. 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Attenuation factor 1 Attenuator: 0 is In. Up-scaling data by 1 Attenuator2: is Out Attenuator2: Up-scaling data by 1 Beam Centre1 : Cx = 27.1492 Cy = 127.3257 Cm Translation : Tx = 0 Ty = 0 [mm] Transmissions: Ts = 0.95103 +/- 0.010242 Te = 1 +/- 0.0013531 Transmissions Thickness Correction is: on Applying standard SANS data reduction: I_corr = 1/[Ts Te] [I_s - I_cd] - 1/[Te] [I_bck - I_cd] ***** Calibrations: ***** Data: Corrected for D22 Detector Paralax Data: Corrected for Detector Efficiency (doesn't change magnitude but contains curvature correction) Data: Divided by Volume 0.025 cm3 Solid Angle Correction: Divide data by empty beam flux, I0, from worksheet: I0 Beam Intensity 1 204 Applying Default Instrument Mask Applying User Defined Mask Applying NanInf Mask Intensity units are: cm-1 \\ \Delta\Omega ***** Analysis ***** Averaging I vs. Q. 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Attenuation factor 1 Attenuator: 0 is In. Up-scaling data by 1 Attenuator2: is Out Attenuator2: Up-scaling data by 1 Beam Centre1 : Cx = 27.1492 Cy = 127.3257 Cm Translation : Tx = 0 Ty = 0 [mm] Transmissions: Ts = 0.96022 +/- 0.010227 Te = 1 +/- 0.0013531 Transmissions Thickness Correction is: on Applying standard SANS data reduction: I_corr = 1/[Ts Te] [I_s - I_cd] - 1/[Te] [I_bck - I_cd] ***** Calibrations: ***** Data: Corrected for D22 Detector Paralax Data: Corrected for Detector Efficiency (doesn't change magnitude but contains curvature correction) Data: Divided by Volume 0.025 cm3 Solid Angle Correction: Divide data by empty beam flux, I0, from worksheet: I0 Beam Intensity 1 205 Applying Default Instrument Mask Applying User Defined Mask Applying NanInf Mask Intensity units are: cm-1 \\ \Delta\Omega ***** Analysis ***** Averaging I vs. Q. 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Attenuation factor 1 Attenuator: 0 is In. Up-scaling data by 1 Attenuator2: is Out Attenuator2: Up-scaling data by 1 Beam Centre1 : Cx = 27.1492 Cy = 127.3257 Cm Translation : Tx = 0 Ty = 0 [mm] Transmissions: Ts = 0.96543 +/- 0.010298 Te = 1 +/- 0.0013531 Transmissions Thickness Correction is: on Applying standard SANS data reduction: I_corr = 1/[Ts Te] [I_s - I_cd] - 1/[Te] [I_bck - I_cd] ***** Calibrations: ***** Data: Corrected for D22 Detector Paralax Data: Corrected for Detector Efficiency (doesn't change magnitude but contains curvature correction) Data: Divided by Volume 0.025 cm3 Solid Angle Correction: Divide data by empty beam flux, I0, from worksheet: I0 Beam Intensity 1 206 Applying Default Instrument Mask Applying User Defined Mask Applying NanInf Mask Intensity units are: cm-1 \\ \Delta\Omega ***** Analysis ***** Averaging I vs. Q. 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CREATED: Thu, Jul 24, 2014 9:15:11 AM LABEL: 2350Hz Tan Scatt 14m mixed sample MON CNT LAMBDA (A) DET_OFF(cm) DET_DIST(m) TRANS THICK(cm) 1e+08 6 15 14.547 0.22305 1 BCENT(X,Y) A1(mm) A2(mm) A1A2DIST(m) DL/L BSTOP(mm) DET_TYP 94.7 63.04 38 12.7 15.727 0.124 76.2 ORNL SAM: Dec07266.SA2_LP _P557 BGD: DEC07039.SA2_LP_P330, EMP: DEC07135.SA2_LP_P426, DIV: PLEX_02NOV2007_NG7.DIV, MASK: DEFAULT_NOV2007.MASK, ABS Parameters (3-6): TSTAND=1;DSTAND=1;IZERO=1.8617;XSECT=1;SDEV=0.005291 Average Choices: AVTYPE=QxQy_ASCII;SAVE=Yes;NAME=Auto;PLOT=Yes; *** Data written from ABS folder and may not be a fully corrected data file *** Data columns are Qx - Qy - I(Qx,Qy) - err(I) - Qz - SigmaQ_parall - SigmaQ_perp - fSubS(beam stop shadow) Error wave is properly propagated through all reduction steps 8/2011 ASCII data created Thu, Jul 24, 2014 9:15:11 AM -0.033700924 -0.022313826 22.236408 40.49147 0.00078030553 0.002224667 0.00078542152 1 -0.033341624 -0.022314072 40.098385 44.758091 0.00076880085 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0.00077696267 1 -0.0031306529 0.023375548 125.58292 61.050289 0.00026560787 0.0013619798 0.0007771682 1 -0.0027708104 0.023375573 90.595734 54.583012 0.00026459419 0.0013601121 0.00077737641 1 -0.0024109667 0.023375591 88.249939 54.945312 0.0002637041 0.001358486 0.000777587 1 -0.0020511223 0.023375608 125.45565 61.047592 0.00026293765 0.0013571022 0.00077779969 1 -0.0016912771 0.023375623 119.63757 59.514389 0.00026229481 0.0013559612 0.00077801413 1 -0.0013314313 0.023375634 128.35284 62.530224 0.0002617756 0.0013550635 0.00077823002 1 -0.0009715851 0.023375643 109.25729 57.927261 0.00026138002 0.0013544093 0.00077844708 1 -0.00061173853 0.023375649 137.43791 62.531624 0.00026110804 0.0013539989 0.00077866495 1 -0.00025189173 0.023375653 156.14124 66.744446 0.0002609597 0.0013538323 0.00077888335 1 0.00010795517 0.023375655 97.591751 56.406258 0.00026093496 0.0013539094 0.00077910192 1 0.00046780202 0.023375651 96.389923 54.577412 0.00026103386 0.0013542299 0.00077932031 1 0.00082764868 0.023375647 159.76562 69.374352 0.00026125638 0.0013547934 0.00077953824 1 0.0011874951 0.02337564 116.5265 59.623837 0.00026160254 0.0013555996 0.0007797553 1 0.001547341 0.023375629 99.923737 59.833904 0.00026207231 0.0013566477 0.00077997125 1 0.0019071865 0.023375615 134.14552 62.523746 0.00026266568 0.001357937 0.00078018574 1 0.0022670312 0.023375599 160.76814 68.070374 0.00026338271 0.0013594668 0.00078039849 1 0.0026268752 0.02337558 144.07501 65.366814 0.00026422332 0.0013612359 0.00078060915 1 0.0029867182 0.02337556 142.76852 66.835045 0.00026518758 0.0013632433 0.00078081747 1 0.0033465601 0.023375534 79.984573 52.79076 0.00026627543 0.0013654877 0.00078102312 1 0.003706401 0.023375507 77.207291 52.789215 0.00026748693 0.0013679679 0.00078122586 1 0.0040662405 0.023375478 124.30733 61.031288 0.00026882201 0.0013706825 0.00078142545 1 0.0044260784 0.023375444 101.03631 57.911266 0.00027028073 0.0013736298 0.00078162161 1 0.0047859149 0.023375411 146.29063 65.361382 0.00027186307 0.0013768083 0.00078181422 1 0.0051457495 0.023375371 95.871674 56.268982 0.00027356899 0.0013802162 0.00078200293 1 0.0055055823 0.02337533 213.54063 76.630928 0.00027539855 0.0013838519 0.00078218762 1 0.0058654132 0.023375288 140.74808 65.356117 0.0002773517 0.0013877132 0.00078236812 1 0.0062252423 0.023375241 78.867424 53.290966 0.00027942847 0.0013917984 0.00078254432 1 0.006585069 0.023375191 35.093887 42.808369 0.00028162883 0.0013961053 0.00078271597 1 0.0069448934 0.023375141 78.621521 52.914322 0.0002839528 0.0014006317 0.00078288297 1 0.0073047155 0.023375085 111.91664 61.343498 0.00028640035 0.0014053758 0.00078304525 1 0.0076645347 0.023375027 88.529625 56.919132 0.0002889715 0.001410335 0.0007832027 1 0.0080243507 0.023374967 100.3662 57.901466 0.00029166625 0.0014155069 0.00078335532 1 0.0083841654 0.023374904 153.32121 68.048538 0.00029448461 0.0014208895 0.00078350288 1 0.0087439753 0.023374839 118.57809 61.016174 0.00029742654 0.0014264802 0.00078364549 1 0.0091037834 0.02337477 89.579628 56.609428 0.00030049204 0.0014322767 0.00078378309 1 0.0094635878 0.023374699 114.30727 61.012688 0.00030368112 0.0014382763 0.00078391563 1 0.0098233894 0.023374625 87.315742 54.551655 0.00030699381 0.0014444764 0.00078404311 1 0.010183186 0.023374548 90.070229 56.378349 0.00031043004 0.0014508747 0.00078416558 1 0.01054298 0.02337447 64.210358 48.959934 0.00031398988 0.0014574684 0.00078428298 1 0.010902771 0.023374386 60.081902 49.362862 0.00031767326 0.001464255 0.0007843955 1 0.011262557 0.023374302 104.88199 59.474903 0.00032148018 0.0014712318 0.000784503 1 0.011622339 0.023374215 96.720932 56.376217 0.00032541069 0.0014783962 0.00078460568 1 0.011982118 0.023374123 96.807014 48.965504 0.00032946476 0.0014857454 0.00078470353 1 sasmodels/example/DEC07267.DAT000066400000000000000000054274721317715334700160760ustar00rootroot00000000000000FILE: Dec07267.SA2_LP _P558 CREATED: Thu, Jul 24, 2014 9:11:19 AM LABEL: 2350Hz Rad Scatt 14m mixed sample MON CNT LAMBDA (A) DET_OFF(cm) DET_DIST(m) TRANS THICK(cm) 1e+08 6 15 14.547 0.87239 0.1 BCENT(X,Y) A1(mm) A2(mm) A1A2DIST(m) DL/L BSTOP(mm) DET_TYP 94.7 63.04 38 12.7 15.727 0.124 76.2 ORNL SAM: Dec07267.SA2_LP _P558 BGD: DEC07039.SA2_LP_P330, EMP: DEC07138.SA2_LP_P429, DIV: PLEX_02NOV2007_NG7.DIV, MASK: DEFAULT_NOV2007.MASK, ABS Parameters (3-6): TSTAND=1;DSTAND=1;IZERO=51.25;XSECT=1;SDEV=0.30265 Average Choices: AVTYPE=QxQy_ASCII;SAVE=Yes;NAME=Auto;PLOT=Yes; *** Data written from ABS folder and may not be a fully corrected data file *** Data columns are Qx - Qy - I(Qx,Qy) - err(I) - Qz - SigmaQ_parall - SigmaQ_perp - fSubS(beam stop shadow) Error wave is properly propagated through all reduction steps 8/2011 ASCII data created Thu, Jul 24, 2014 9:11:19 AM -0.033700924 -0.022313826 20.209991 15.485017 0.00078030553 0.002224667 0.00078542152 1 -0.033341624 -0.022314072 8.2847929 12.409316 0.00076880085 0.0022108187 0.00078544609 1 -0.032982308 -0.022314314 9.3082075 12.761409 0.00075741921 0.0021970333 0.0007854703 1 -0.032622986 -0.022314554 10.999227 13.639123 0.00074616069 0.0021833114 0.00078549422 1 -0.032263648 -0.022314792 15.730721 14.478785 0.00073502521 0.0021696547 0.0007855178 1 -0.031904299 -0.022315027 11.505077 13.367644 0.00072401285 0.0021560644 0.00078554096 1 -0.031544939 -0.022315258 10.073761 12.761391 0.00071312359 0.0021425416 0.00078556372 1 -0.031185569 -0.022315489 16.98354 14.992325 0.0007023575 0.0021290877 0.00078558613 1 -0.030826189 -0.022315716 11.878708 13.367614 0.00069171452 0.0021157037 0.00078560802 1 -0.030466795 -0.02231594 15.818889 15.234119 0.00068119471 0.0021023913 0.00078562938 1 -0.030107392 -0.022316162 2.3744738 10.112365 0.00067079801 0.0020891516 0.00078565028 1 -0.029747978 -0.022316381 4.1815782 10.965107 0.00066052453 0.0020759862 0.00078567059 1 -0.029388554 -0.022316597 13.142879 14.197605 0.00065037422 0.0020628965 0.00078569027 1 -0.02902912 -0.022316812 4.0161366 10.965068 0.00064034708 0.0020498836 0.0007857093 1 -0.028669674 -0.022317022 8.5936546 12.111058 0.00063044316 0.0020369494 0.00078572769 1 -0.028310219 -0.022317231 22.554335 16.411215 0.00062066247 0.002024095 0.00078574533 1 -0.027950753 -0.022317436 12.971427 13.937695 0.000611005 0.002011322 0.00078576221 1 -0.027591279 -0.02231764 25.000893 17.275417 0.00060147076 0.0019986322 0.00078577828 1 -0.027231792 -0.02231784 19.684427 15.956261 0.00059205975 0.001986027 0.00078579347 1 -0.026872298 -0.022318039 8.6190367 12.111814 0.00058277202 0.0019735079 0.00078580779 1 -0.026512794 -0.022318235 12.172689 13.368109 0.00057360757 0.0019610769 0.00078582106 1 -0.026153281 -0.022318427 12.358036 14.19729 0.00056456635 0.0019487351 0.00078583334 1 -0.025793757 -0.022318617 21.466293 16.410896 0.00055564841 0.0019364845 0.00078584458 1 -0.025434226 -0.022318805 23.152374 16.850031 0.00054685381 0.0019243269 0.00078585465 1 -0.025074685 -0.022318989 13.177037 14.197146 0.0005381825 0.0019122639 0.00078586355 1 -0.024715135 -0.022319172 10.3923 12.762448 0.00052963448 0.0019002974 0.00078587118 1 -0.024355577 -0.02231935 22.266352 16.411325 0.00052120979 0.001888429 0.00078587746 1 -0.02399601 -0.022319529 26.160576 17.274849 0.00051290845 0.0018766609 0.00078588235 1 -0.023636434 -0.022319702 17.214048 15.919385 0.00050473039 0.0018649945 0.00078588579 1 -0.023276851 -0.022319874 10.252022 12.76063 0.00049667573 0.0018534319 0.00078588765 1 -0.022917258 -0.022320043 19.402708 16.182968 0.00048874441 0.0018419751 0.00078588794 1 -0.022557657 -0.022320211 22.131245 16.631487 0.00048093646 0.0018306262 0.00078588654 1 -0.022198049 -0.022320375 16.675692 14.991235 0.00047325189 0.0018193867 0.00078588334 1 -0.021838434 -0.022320535 27.174757 18.288019 0.00046569071 0.0018082591 0.00078587834 1 -0.021478809 -0.022320693 26.646177 17.892527 0.00045825291 0.0017972451 0.00078587135 1 -0.021119177 -0.02232085 18.376431 15.482908 0.00045093847 0.0017863469 0.00078586239 1 -0.02075954 -0.022321003 33.102055 18.856354 0.00044374747 0.0017755666 0.00078585127 1 -0.020399893 -0.022321153 35.095673 19.588837 0.0004366799 0.0017649063 0.00078583794 1 -0.020040238 -0.022321302 28.290335 18.287516 0.00042973572 0.0017543682 0.00078582234 1 -0.019680578 -0.022321448 30.83131 18.672945 0.00042291498 0.0017439544 0.00078580435 1 -0.019320911 -0.022321589 27.947542 17.685898 0.00041621766 0.001733667 0.00078578386 1 -0.018961236 -0.022321731 31.806927 18.476595 0.00040964378 0.0017235085 0.00078576076 1 -0.018601555 -0.022321869 21.543226 16.630442 0.00040319335 0.0017134808 0.00078573497 1 -0.018241867 -0.022322003 29.686916 18.086039 0.00039686641 0.0017035864 0.00078570633 1 -0.017882174 -0.022322135 37.050728 19.587975 0.0003906629 0.0016938277 0.00078567484 1 -0.017522473 -0.022322265 37.095592 19.94183 0.00038458285 0.0016842067 0.00078564032 1 -0.017162766 -0.022322392 44.035931 20.960548 0.00037862631 0.0016747258 0.00078560272 1 -0.016803052 -0.022322517 34.526234 19.22613 0.00037279323 0.0016653875 0.00078556186 1 -0.016443335 -0.022322638 38.901115 20.287893 0.00036708364 0.001656194 0.00078551762 1 -0.016083609 -0.022322757 44.556625 20.960079 0.00036149754 0.0016471478 0.00078547001 1 -0.01572388 -0.022322873 41.993423 20.627586 0.00035603493 0.0016382511 0.00078541879 1 -0.015364144 -0.022322988 53.982048 22.537243 0.00035069586 0.0016295066 0.00078536395 1 -0.015004402 -0.022323098 43.906013 20.959572 0.00034548028 0.0016209164 0.00078530534 1 -0.014644655 -0.022323208 40.072617 20.287088 0.00034038821 0.0016124832 0.00078524282 1 -0.014284904 -0.022323312 36.732822 19.586456 0.00033541967 0.0016042091 0.00078517635 1 -0.013925147 -0.022323417 49.278877 22.087454 0.00033057464 0.0015960968 0.0007851058 1 -0.013565386 -0.022323517 43.935619 21.604507 0.00032585318 0.0015881485 0.00078503106 1 -0.013205619 -0.022323616 47.56818 21.605953 0.00032125521 0.001580367 0.00078495208 1 -0.012845848 -0.022323711 43.687172 20.958473 0.00031678082 0.0015727544 0.00078486872 1 -0.012486072 -0.022323804 50.866516 22.230927 0.00031242997 0.0015653131 0.00078478095 1 -0.012126291 -0.022323893 53.79287 22.534969 0.00030820267 0.0015580456 0.00078468863 1 -0.011766507 -0.022323981 57.365795 23.576406 0.00030409891 0.0015509545 0.00078459171 1 -0.011406719 -0.022324067 52.507088 22.229801 0.00030011873 0.001544042 0.00078449008 1 -0.011046926 -0.022324149 54.960926 23.286924 0.00029626212 0.0015373104 0.0007843838 1 -0.010687129 -0.022324227 62.916794 23.989788 0.00029252906 0.0015307623 0.00078427268 1 -0.010327329 -0.022324305 64.419205 24.268433 0.00028891957 0.0015243998 0.00078415679 1 -0.0099675246 -0.02232438 85.831032 27.362009 0.00028543369 0.0015182255 0.00078403606 1 -0.0096077165 -0.02232445 73.603363 25.610085 0.00028207136 0.0015122414 0.00078391039 1 -0.0092479056 -0.022324519 96.579941 28.538008 0.00027883262 0.00150645 0.00078377989 1 -0.0088880919 -0.022324586 79.194611 26.626493 0.00027571747 0.0015008533 0.0007836445 1 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250.65875 32.583935 6.2137369e-05 0.0010134918 0.00078384671 1 -0.0042110132 -0.010451953 178.53604 27.84276 6.062831e-05 0.0010092977 0.00078356708 1 -0.0038511024 -0.010451967 297.09839 34.869034 5.9242939e-05 0.001005398 0.00078326685 1 -0.0034911905 -0.01045198 334.98593 36.925819 5.7981255e-05 0.0010017967 0.0007829463 1 -0.0031312772 -0.010451991 259.27762 32.975479 5.6843262e-05 0.00099849736 0.00078260613 1 -0.0027713629 -0.010452001 364.03839 38.105495 5.5828961e-05 0.00099550374 0.00078224723 1 -0.0024114475 -0.01045201 408.74625 40.275826 5.4938351e-05 0.00099281967 0.00078187085 1 -0.0020515313 -0.010452018 417.6973 41.291561 5.4171436e-05 0.00099044875 0.00078147848 1 -0.0016916144 -0.010452025 422.14883 40.431217 5.3528216e-05 0.00098839472 0.00078107184 1 -0.0013316969 -0.010452029 574.99115 46.486187 5.3008691e-05 0.00098666106 0.00078065298 1 -0.00097177882 -0.010452033 562.72742 46.498333 5.2612864e-05 0.00098525151 0.00078022416 1 -0.00061186048 -0.010452036 457.49365 42.417252 5.2340733e-05 0.00098416919 0.00077978784 1 -0.00025194194 -0.010452038 514.28821 44.982899 5.2192296e-05 0.00098341738 0.00077934668 1 0.0001079767 -0.010452038 576.44293 47.293121 5.2167557e-05 0.00098299899 0.00077890325 1 0.0004678953 -0.010452037 508.82547 44.645054 5.2266514e-05 0.00098291656 0.00077846047 1 0.00082781375 -0.010452035 498.52759 43.854969 5.2489169e-05 0.00098317245 0.000778021 1 0.0011877319 -0.010452031 452.47757 42.633987 5.2835519e-05 0.00098376838 0.00077758753 1 0.0015476496 -0.010452027 473.22403 43.436024 5.3305568e-05 0.00098470587 0.00077716261 1 0.0019075668 -0.010452021 392.09158 40.437656 5.3899308e-05 0.00098598562 0.00077674864 1 0.0022674832 -0.010452013 325.87167 36.470669 5.4616747e-05 0.00098760822 0.00077634776 1 0.0026273991 -0.010452005 312.9845 35.866196 5.545788e-05 0.00098957343 0.0007759619 1 0.0029873138 -0.010451996 275.68536 34.035152 5.6422705e-05 0.00099188031 0.00077559281 1 0.0033472273 -0.010451985 223.01767 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0.0069449465 0.023015477 64.355873 19.210835 0.00027598449 0.00138635 0.00078293402 1 0.0073047709 0.023015423 108.89644 23.692183 0.00027843213 0.0013911433 0.00078309741 1 0.0076645929 0.023015365 93.737549 22.214951 0.00028100333 0.0013961535 0.00078325573 1 0.0080244122 0.023015307 81.449883 21.904669 0.00028369814 0.0014013783 0.00078340899 1 0.0083842287 0.023015244 68.966637 19.924795 0.00028651656 0.0014068153 0.00078355713 1 0.0087440424 0.023015181 89.108727 21.904112 0.00028945855 0.0014124619 0.00078370009 1 0.0091038523 0.023015112 86.477173 21.903667 0.00029252411 0.0014183156 0.00078383781 1 0.0094636595 0.023015043 81.525078 21.588875 0.00029571328 0.0014243739 0.00078397035 1 0.0098234639 0.02301497 73.31813 20.26947 0.00029902603 0.0014306343 0.00078409771 1 0.010183265 0.023014894 64.256531 19.56974 0.00030246237 0.0014370941 0.00078421982 1 0.01054306 0.023014816 69.496422 19.922476 0.00030602227 0.0014437505 0.00078433682 1 0.010902854 0.023014735 51.853436 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0.0002637041 0.001358486 0.000777587 1 -0.0020511223 0.023375608 145.3237 30.521793 0.00026293765 0.0013571022 0.00077779969 1 -0.0016912771 0.023375623 126.92915 28.532518 0.00026229481 0.0013559612 0.00077801413 1 -0.0013314313 0.023375634 159.62097 32.373207 0.0002617756 0.0013550635 0.00077823002 1 -0.0009715851 0.023375643 110.7009 27.113039 0.00026138002 0.0013544093 0.00077844708 1 -0.00061173853 0.023375649 117.95842 27.594807 0.00026110804 0.0013539989 0.00077866495 1 -0.00025189173 0.023375653 147.39757 30.941948 0.0002609597 0.0013538323 0.00077888335 1 0.00010795517 0.023375655 156.58757 31.882074 0.00026093496 0.0013539094 0.00077910192 1 0.00046780202 0.023375651 132.61084 28.758705 0.00026103386 0.0013542299 0.00077932031 1 0.00082764868 0.023375647 151.38005 32.370201 0.00026125638 0.0013547934 0.00077953824 1 0.0011874951 0.02337564 149.33688 30.729729 0.00026160254 0.0013555996 0.0007797553 1 0.001547341 0.023375629 143.9521 32.169579 0.00026207231 0.0013566477 0.00077997125 1 0.0019071865 0.023375615 145.67793 30.516741 0.00026266568 0.001357937 0.00078018574 1 0.0022670312 0.023375599 139.67136 30.516184 0.00026338271 0.0013594668 0.00078039849 1 0.0026268752 0.02337558 150.29218 31.559662 0.00026422332 0.0013612359 0.00078060915 1 0.0029867182 0.02337556 155.55423 32.762764 0.00026518758 0.0013632433 0.00078081747 1 0.0033465601 0.023375534 134.49382 30.085642 0.00026627543 0.0013654877 0.00078102312 1 0.003706401 0.023375507 121.16882 29.205599 0.00026748693 0.0013679679 0.00078122586 1 0.0040662405 0.023375478 144.97984 30.844193 0.00026882201 0.0013706825 0.00078142545 1 0.0044260784 0.023375444 130.686 30.084078 0.00027028073 0.0013736298 0.00078162161 1 0.0047859149 0.023375411 118.43787 28.293587 0.00027186307 0.0013768083 0.00078181422 1 0.0051457495 0.023375371 95.9403 26.621471 0.00027356899 0.0013802162 0.00078200293 1 0.0055055823 0.02337533 95.307587 26.110321 0.00027539855 0.0013838519 0.00078218762 1 0.0058654132 0.023375288 107.37613 27.586609 0.0002773517 0.0013877132 0.00078236812 1 0.0062252423 0.023375241 115.28579 27.586586 0.00027942847 0.0013917984 0.00078254432 1 0.006585069 0.023375191 123.44139 29.645245 0.00028162883 0.0013961053 0.00078271597 1 0.0069448934 0.023375141 86.597046 25.213034 0.0002839528 0.0014006317 0.00078288297 1 0.0073047155 0.023375085 103.01654 27.345226 0.00028640035 0.0014053758 0.00078304525 1 0.0076645347 0.023375027 77.34549 23.974611 0.0002889715 0.001410335 0.0007832027 1 0.0080243507 0.023374967 93.035835 26.106976 0.00029166625 0.0014155069 0.00078335532 1 0.0083841654 0.023374904 86.847687 25.734493 0.00029448461 0.0014208895 0.00078350288 1 0.0087439753 0.023374839 113.92599 28.416513 0.00029742654 0.0014264802 0.00078364549 1 0.0091037834 0.02337477 72.25779 23.843287 0.00030049204 0.0014322767 0.00078378309 1 0.0094635878 0.023374699 57.660793 21.587975 0.00030368112 0.0014382763 0.00078391563 1 0.0098233894 0.023374625 100.10268 26.607122 0.00030699381 0.0014444764 0.00078404311 1 0.010183186 0.023374548 62.156818 22.211485 0.00031043004 0.0014508747 0.00078416558 1 0.01054298 0.02337447 79.681091 24.398642 0.00031398988 0.0014574684 0.00078428298 1 0.010902771 0.023374386 56.222897 21.437147 0.00031767326 0.001464255 0.0007843955 1 0.011262557 0.023374302 71.065475 24.252308 0.00032148018 0.0014712318 0.000784503 1 0.011622339 0.023374215 65.422165 22.373276 0.00032541069 0.0014783962 0.00078460568 1 0.011982118 0.023374123 48.916698 17.464722 0.00032946476 0.0014857454 0.00078470353 1 sasmodels/example/SiO2_100pc_H2O_0pc_D2O.ses000066400000000000000000000042741317715334700205760ustar00rootroot00000000000000name SiO2 stober sample SiO2 100pcH2O collimation unknown ID CPD Date di 27 jan 2015 18:17:50 Method Offspec Thickness [mm] 1 z-acceptance [nm^-1] 0.3 y-acceptance [nm^-1] 0.3 spin echo length [nm] error spin-echo length wavelength [nm] error wavelength Sample P Sample P -error 244.098 5 0.220907401 0.006627222 0.96321 0.0113507 0.029882023 29.882023 340.136 5 0.260768096 0.007823043 0.973305 0.0034846 0.085257531 85.257531 452.181 5 0.300665994 0.00901998 0.951588 0.00287498 0.140798634 140.798634 580.232 5 0.340587727 0.010217632 0.911935 0.00310965 0.196560502 196.560502 724.29 5 0.380526057 0.011415782 0.856129 0.00356166 0.252528125 252.528125 884.354 5 0.420476016 0.01261428 0.78817 0.0036651 0.308729274 308.729274 1060.42 5 0.460433709 0.013813011 0.719608 0.00386121 0.365037117 365.037117 1252.5 5 0.50039968 0.01501199 0.653424 0.00418035 0.421684677 421.684677 1460.58 5 0.540369504 0.016211085 0.603456 0.00472218 0.478564852 478.564852 1684.67 5 0.580344105 0.017410323 0.558174 0.00537231 0.535715521 535.715521 1924.77 5 0.620322561 0.018609677 0.532672 0.00617699 0.59324408 593.24408 2180.87 5 0.660302658 0.01980908 0.505018 0.00707792 0.650985498 650.985498 2452.98 5 0.700285542 0.021008566 0.475536 0.00829962 0.709203958 709.203958 2741.1 5 0.740270761 0.022208123 0.440819 0.00957178 0.767809943 767.809943 3045.22 5 0.780256676 0.0234077 0.397642 0.0111225 0.826762925 826.762925 3365.35 5 0.820244402 0.024607332 0.363717 0.0132055 0.886302296 886.302296 3701.48 5 0.860232527 0.025806976 0.302206 0.0158338 0.946236366 946.236366 4053.62 5 0.900222106 0.027006663 0.302188 0.0204351 1.006784115 1006.784115 4421.77 5 0.940212955 0.028206389 0.263252 0.0264158 1.067891213 1067.891213 4805.92 5 0.980203897 0.029406117 0.230149 0.0339972 1.129598722 1129.598722 5206.08 5 1.020195903 0.030605877 0.268749 0.0480167 1.192022694 1192.022694 5622.25 5 1.060188851 0.031805666 0.340439 0.0701945 1.255271282 1255.271282 6054.42 5 1.10018173 0.033005452 0.238197 0.0986631 1.319307134 1319.307134 6502.6 5 1.140175425 0.034205263 0.0985987 0.170273 1.384197821 1384.197821 6966.79 5 1.180169852 0.035405096 0.0814573 0.256765 1.448518618 1448.518618sasmodels/example/batch_fit.py000077500000000000000000000106301317715334700170160ustar00rootroot00000000000000#!/usr/bin/env python """ Script to run a batch fit in a series of files and plot the fitted parameters. Usage syntax:: python batch_fit.py model.py sample1.dat sample2.dat ... other_sample.dat (files named sample1.dat, sample2.dat, ..., other_sample.dat) or if the file names are numbers (and the extension is .dat):: python batch_fit.py model.py 93190 93210 (files named 093190.dat, 093191.dat, ..., 093210.dat) or for Grasp-like naming:: python batch_fit.py model.py 93190 93210 200 (files named 093190_200.dat, 093191_201.dat, ..., 093210_220.dat) The script reads a series of files and fits the model defined by model.py. For example model_ellipsoid_hayter_msa.py fits a model consisting in an ellipsoid form factor multiplied by a Hayter MSA structure factor. The file *model.py* must load the data using:: data = load_data(sys.argv[1]) Include options to bumps (minimizer, steps, etc.) as desired. For example:: python batch_fit.py model.py 93190 93210 200 --fit=lm --steps=200 --ftol=1.5e-8 --xtol=1.5e-8 Fit options can come before or after the model and files. For each file a directory named Fit_filename is created. There the file model.par contains the fitted parameters. These are gathered together into batch_fit.csv in the current directory. Finally the fitted parameters are plotted for the full series. Example:: python batch_fit.py model_ellipsoid_hayter_msa.py 93191 93195 201 Note: If sasmodels, sasview or bumps are not in the path, use the PYTHONPATH environment variable to set them. """ from __future__ import print_function import sys import os import numpy as np import matplotlib.pyplot as plt from bumps.dream.views import tile_axes # make a grid of plots # GET INPUT AND ENSURE MODEL AND DATA FILES ARE DEFINED fit_opts = [v for v in sys.argv[1:] if v.startswith('--')] args = [v for v in sys.argv[1:] if not v.startswith('--')] nargs = len(args) if nargs < 2: print ("Error in the list of arguments! \n") sys.exit() model_file = args[0] if not model_file.endswith('.py'): print("Expected model.py as the first argument") sys.exit(1) if '.' in args[1]: data_files = args[1:] else: first = int(args[1]) last = int(args[2]) count = last-first+1 data_files = [] if nargs == 3: data_files = ['%06d.dat'%(first+i) for i in range(count)] elif nargs == 4: ext = int(args[3]) data_files = ['%06d_%d.dat'%(first+i, ext+i) for i in range(count)] else: print("Unexpected arguments: " + " ".join(args[4:])) sys.exit(1) # CHECK THAT DATA FILES EXIST missing = [filename for filename in data_files if not os.path.isfile(filename)] if missing: print("Missing data files: %s" % ", ".join(missing)) sys.exit(1) # STORE DIRECTORY FOR BUMPS FITS def fit_dir(filename): "Return the store directory name for the given file" return "Fit_" + os.path.splitext(filename)[0] # LOOP OVER FILES AND CALL TO BUMPS FOR EACH OF THEM bumps_cmd = "python -m bumps.cli --batch" fit_opts = " ".join(fit_opts) for data_file in data_files: store_opts = "--store=" + fit_dir(data_file) cmd = " ".join((bumps_cmd, fit_opts, store_opts, model_file, data_file)) os.system(cmd) # GATHER RESULTS results = {} par_file = os.path.splitext(model_file)[0] + '.par' for data_file in data_files: with open(os.path.join(fit_dir(data_file), par_file), 'r') as fid: for line in fid: parameter, value = line.split() results.setdefault(parameter, []).append(float(value)) # SAVE RESULTS INTO FILE with open('batch_fit.csv', 'w') as fid: parameters = list(sorted(results.keys())) values_by_file = zip(*(v for k, v in sorted(results.items()))) fid.write(','.join(['filename'] + parameters) + '\n') for filename, values in zip(data_files, values_by_file): fid.write(','.join([filename] + [str(v) for v in values]) + '\n') # SHOW FITTED PARAMETERS nh, nw = tile_axes(len(results)) ticks = np.arange(1, len(data_files)+1) labels = [os.path.splitext(filename)[0] for filename in data_files] for k, (parameter, values) in enumerate(sorted(results.items())): plt.subplot(nh, nw, k+1) plt.plot(ticks, values) plt.xlim(ticks[0]-0.5, ticks[-1]+0.5) if k%nh == nh-1: #plt.xlabel('Dataset #') plt.xticks(ticks, labels, rotation=30) else: plt.xticks(ticks, [' ']*len(labels)) plt.ylabel(parameter) plt.suptitle("Fit " + args[0]) plt.show() sasmodels/example/core_shell.ses000066400000000000000000000074141317715334700173570ustar00rootroot00000000000000name se009051.dat sample "SiO2 pH=6 & NiO pH=10, nanosized, in D2O, Sine ++ only." collimation "D1=D2=20x8 mm,Ds = 16x10 mm (WxH), GF1 =scanning, GF2 = 2.5 A. " ID CPD Date di 27 jan 2015 18:17:50 Method sine one element scan Thickness [mm] 2 z-acceptance [nm^-1] 0.3 y-acceptance [nm^-1] 0.3 spin echo length [um] error spin-echo length wavelength [nm] error wavelength Sample 5 Sample 5 -error 26 5 0.161245 0.01 0.996315 0.00528445 0.161245 26 28.08 5 0.167571 0.01 0.995937 0.00522962 0.167571 28.08 30.3264 5 0.174145 0.01 0.995039 0.00371164 0.174145 30.3264 32.7525 5 0.180977 0.01 0.99448 0.00381089 0.180977 32.7525 35.3727 5 0.188076 0.01 0.992143 0.00319011 0.188076 35.3727 38.2025 5 0.195455 0.01 0.991403 0.0032496 0.195455 38.2025 41.2587 5 0.203122 0.01 0.990106 0.002978 0.203122 41.2587 44.5594 5 0.211091 0.01 0.98857 0.00297338 0.211091 44.5594 48.1242 5 0.219372 0.01 0.986236 0.00286669 0.219372 48.1242 51.9741 5 0.227978 0.01 0.982739 0.00283988 0.227978 51.9741 56.132 5 0.236922 0.01 0.979995 0.00287147 0.236922 56.132 60.6226 5 0.246217 0.01 0.976516 0.00290667 0.246217 60.6226 65.4724 5 0.255876 0.01 0.971858 0.00300969 0.255876 65.4724 70.7102 5 0.265914 0.01 0.967518 0.00310597 0.265914 70.7102 76.367 5 0.276346 0.01 0.963198 0.00310409 0.276346 76.367 82.4764 5 0.287187 0.01 0.957071 0.00306271 0.287187 82.4764 89.0745 5 0.298454 0.01 0.952784 0.00299587 0.298454 89.0745 96.2005 5 0.310162 0.01 0.947462 0.0029896 0.310162 96.2005 103.897 5 0.322331 0.01 0.941226 0.00300217 0.322331 103.897 112.208 5 0.334975 0.01 0.936151 0.00305677 0.334975 112.208 121.185 5 0.348116 0.01 0.930884 0.00307969 0.348116 121.185 130.88 5 0.361773 0.01 0.927992 0.00316999 0.361773 130.88 141.35 5 0.375965 0.01 0.926511 0.00326096 0.375965 141.35 152.658 5 0.390715 0.01 0.925098 0.00340349 0.390715 152.658 164.871 5 0.406043 0.01 0.924369 0.0035662 0.406043 164.871 178.06 5 0.421972 0.01 0.925632 0.00372489 0.421972 178.06 192.305 5 0.438526 0.01 0.922762 0.00390394 0.438526 192.305 207.69 5 0.45573 0.01 0.918753 0.00412162 0.45573 207.69 224.305 5 0.473608 0.01 0.90663 0.0043316 0.473608 224.305 242.249 5 0.492188 0.01 0.893251 0.00454417 0.492188 242.249 261.629 5 0.511497 0.01 0.878299 0.00473364 0.511497 261.629 282.559 5 0.531563 0.01 0.867266 0.00497459 0.531563 282.559 305.164 5 0.552417 0.01 0.859537 0.00521977 0.552417 305.164 329.577 5 0.574088 0.01 0.855935 0.0055573 0.574088 329.577 355.943 5 0.59661 0.01 0.851389 0.00581848 0.59661 355.943 384.419 5 0.620015 0.01 0.836311 0.00620483 0.620015 384.419 415.172 5 0.644338 0.01 0.821362 0.00668373 0.644338 415.172 448.386 5 0.669616 0.01 0.803833 0.0071725 0.669616 448.386 484.257 5 0.695886 0.01 0.792211 0.00786449 0.695886 484.257 522.998 5 0.723186 0.01 0.787407 0.00860688 0.723186 522.998 564.838 5 0.751557 0.01 0.765977 0.00938856 0.751557 564.838 610.025 5 0.781041 0.01 0.746618 0.0101567 0.781041 610.025 658.827 5 0.811682 0.01 0.734672 0.0110357 0.811682 658.827 711.533 5 0.843524 0.01 0.720351 0.0118912 0.843524 711.533 768.455 5 0.876616 0.01 0.692587 0.0130927 0.876616 768.455 829.932 5 0.911006 0.01 0.674767 0.0137763 0.911006 829.932 896.326 5 0.946745 0.01 0.664497 0.0148902 0.946745 896.326 968.032 5 0.983886 0.01 0.634464 0.0158459 0.983886 968.032 1045.47 5 1.02248 0.01 0.604792 0.0166925 1.02248 1045.47 1129.11 5 1.0626 0.01 0.591534 0.0179667 1.0626 1129.11 1219.44 5 1.10428 0.01 0.582625 0.0198223 1.10428 1219.44 1317 5 1.14761 0.01 0.549232 0.0217725 1.14761 1317 1422.36 5 1.19263 0.01 0.53863 0.024516 1.19263 1422.36 1536.15 5 1.23942 0.01 0.521353 0.0281108 1.23942 1536.15 1659.04 5 1.28804 0.01 0.460045 0.0314452 1.28804 1659.04 1791.76 5 1.33857 0.01 0.411185 0.0366899 1.33857 1791.76 1930.34 5 1.38937 0.01 0.414685 0.0478689 1.38937 1930.34 sasmodels/example/cylinder_eval.py000066400000000000000000000007251317715334700177140ustar00rootroot00000000000000""" Minimal example of calling a kernel for a specific set of q values. """ from numpy import logspace from matplotlib import pyplot as plt from sasmodels.core import load_model from sasmodels.direct_model import call_kernel model = load_model('cylinder') q = logspace(-3, -1, 200) kernel = model.make_kernel([q]) Iq = call_kernel(kernel, dict(radius=200.)) plt.loglog(q, Iq) plt.xlabel('q (1/A)') plt.ylabel('I(q)') plt.title('Cylinder with radius 200.') plt.show() sasmodels/example/fit.py000066400000000000000000000144371317715334700156630ustar00rootroot00000000000000#!/usr/bin/env python # -*- coding: utf-8 -*- import sys from bumps.names import * from sasmodels.core import load_model from sasmodels.bumps_model import Model, Experiment from sasmodels.data import load_data, set_beam_stop, set_top """ IMPORT THE DATA USED """ radial_data = load_data('DEC07267.DAT') set_beam_stop(radial_data, 0.00669, outer=0.025) set_top(radial_data, -.0185) tan_data = load_data('DEC07266.DAT') set_beam_stop(tan_data, 0.00669, outer=0.025) set_top(tan_data, -.0185) #sas.set_half(tan_data, 'right') name = "ellipsoid" if len(sys.argv) < 2 else sys.argv[1] section = "radial" if len(sys.argv) < 3 else sys.argv[2] if section not in ("radial","tangential","both"): raise ValueError("section %r should be 'radial', 'tangential' or 'both'" % section) data = radial_data if section != "tangential" else tan_data theta = 89.9 if section != "tangential" else 0 phi = 90 kernel = load_model(name, dtype="single") cutoff = 1e-3 if name == "ellipsoid": model = Model(kernel, scale=0.08, background=35, radius_polar=15, radius_equatorial=800, sld=.291, sld_solvent=7.105, theta=theta, phi=phi, theta_pd=0, theta_pd_n=0, theta_pd_nsigma=3, phi_pd=0, phi_pd_n=20, phi_pd_nsigma=3, radius_polar_pd=0.222296, radius_polar_pd_n=1, radius_polar_pd_nsigma=0, radius_equatorial_pd=.000128, radius_equatorial_pd_n=1, radius_equatorial_pd_nsigma=0, ) # SET THE FITTING PARAMETERS model.radius_polar.range(15, 1000) model.radius_equatorial.range(15, 1000) #model.theta.range(0, 90) #model.theta_pd.range(0,10) model.phi_pd.range(0,20) model.phi.range(0, 180) model.background.range(0,1000) model.scale.range(0, 10) elif name == "lamellar": model = Model(kernel, scale=0.08, background=0.003, thickness=19.2946, sld=5.38,sld_sol=7.105, thickness_pd= 0.37765, thickness_pd_n=10, thickness_pd_nsigma=3, ) # SET THE FITTING PARAMETERS #model.thickness.range(0, 1000) #model.scale.range(0, 1) #model.thickness_pd.range(0, 1000) #model.background.range(0, 1000) model.sld.range(0, 1) elif name == "cylinder": """ pars = dict(scale=0.0023, radius=92.5, length=798.3, sld=.29, solvent_sld=7.105, background=5, theta=0, phi=phi, theta_pd=22.11, theta_pd_n=5, theta_pd_nsigma=3, radius_pd=.0084, radius_pd_n=10, radius_pd_nsigma=3, length_pd=0.493, length_pd_n=10, length_pd_nsigma=3, phi_pd=0, phi_pd_n=5 phi_pd_nsigma=3,) """ pars = dict( scale=.01, background=35, sld=.291, sld_solvent=5.77, radius=250, length=178, radius_pd=0.1, radius_pd_n=5, radius_pd_nsigma=3, length_pd=0.1,length_pd_n=5, length_pd_nsigma=3, theta=theta, phi=phi, theta_pd=0, theta_pd_n=0, theta_pd_nsigma=3, phi_pd=10, phi_pd_n=20, phi_pd_nsigma=3) model = Model(kernel, **pars) # SET THE FITTING PARAMETERS model.radius.range(1, 500) model.length.range(1, 5000) #model.theta.range(0, 90) model.phi.range(0, 180) model.phi_pd.range(0, 30) model.radius_pd.range(0, 1) model.length_pd.range(0, 1) model.scale.range(0, 10) model.background.range(0, 100) elif name == "core_shell_cylinder": model = Model(kernel, scale= .031, background=0, radius=19.5, thickness=30, length=22, sld_core=7.105, sld_shell=.291, sld_solvent=7.105, radius_pd=0.26, radius_pd_n=10, radius_pd_nsigma=3, length_pd=0.26, length_pd_n=10, length_pd_nsigma=3, thickness_pd=1, thickness_pd_n=1, thickness_pd_nsigma=1, theta=theta, phi=phi, theta_pd=1, theta_pd_n=1, theta_pd_nsigma=3, phi_pd=0, phi_pd_n=20, phi_pd_nsigma=3, ) # SET THE FITTING PARAMETERS model.radius.range(115, 1000) model.length.range(0, 2500) #model.thickness.range(18, 38) #model.thickness_pd.range(0, 1) #model.phi.range(0, 90) model.phi_pd.range(0,20) #model.radius_pd.range(0, 1) #model.length_pd.range(0, 1) #model.theta_pd.range(0, 360) #model.background.range(0,5) model.scale.range(0, 1) elif name == "capped_cylinder": model = Model(kernel, scale=.08, background=35, radius=20, cap_radius=40, length=400, sld=1, sld_solvent=6.3, radius_pd=.1, radius_pd_n=5, radius_pd_nsigma=3, cap_radius_pd=.1, cap_radius_pd_n=5, cap_radius_pd_nsigma=3, length_pd=.1, length_pd_n=1, length_pd_nsigma=0, theta=theta, phi=phi, theta_pd=0, theta_pd_n=1, theta_pd_nsigma=0, phi_pd=10, phi_pd_n=20, phi_pd_nsigma=0, ) model.radius.range(115, 1000) model.length.range(0, 2500) #model.thickness.range(18, 38) #model.thickness_pd.range(0, 1) #model.phi.range(0, 90) model.phi_pd.range(0,20) #model.radius_pd.range(0, 1) #model.length_pd.range(0, 1) #model.theta_pd.range(0, 360) #model.background.range(0,5) model.scale.range(0, 1) elif name == "triaxial_ellipsoid": model = Model(kernel, scale=0.08, background=35, radius_equat_minor=15, radius_equat_major=20, radius_polar=500, sld=7.105, solvent_sld=.291, radius_equat_minor_pd=.1, radius_equat_minor_pd_n=1, radius_equat_minor_pd_nsigma=0, radius_equat_major_pd=.1, radius_equat_major_pd_n=1, radius_equat_major_pd_nsigma=0, radius_polar_pd=.1, radius_polar_pd_n=1, radius_polar_pd_nsigma=0, theta=theta, phi=phi, psi=0, theta_pd=20, theta_pd_n=40, theta_pd_nsigma=3, phi_pd=.1, phi_pd_n=1, phi_pd_nsigma=0, psi_pd=30, psi_pd_n=1, psi_pd_nsigma=0, ) # SET THE FITTING PARAMETERS model.radius_equat_minor.range(15, 1000) model.radius_equat_major.range(15, 1000) #model.radius_polar.range(15, 1000) #model.background.range(0,1000) #model.theta_pd.range(0, 360) #model.phi_pd.range(0, 360) #model.psi_pd.range(0, 360) else: print "No parameters for %s"%name sys.exit(1) model.cutoff = cutoff M = Experiment(data=data, model=model) if section == "both": tan_model = Model(model.sasmodel, **model.parameters()) tan_model.phi = model.phi - 90 tan_model.cutoff = cutoff tan_M = Experiment(data=tan_data, model=tan_model) problem = FitProblem([M, tan_M]) else: problem = FitProblem(M) sasmodels/example/fit_sesans.py000077500000000000000000000011001317715334700172210ustar00rootroot00000000000000#!/usr/bin/env python import os import sys # Need to fix the paths to sasmodels and sasview if no eggs present ONEUP=os.path.dirname(os.path.dirname(os.path.abspath(__file__))) PROJECTS=os.path.dirname(ONEUP) SASMODELS=os.path.join(PROJECTS, 'sasmodels') SASVIEW=os.path.join(PROJECTS, 'sasview', 'src') BUMPS=os.path.join(PROJECTS, 'bumps') sys.path.insert(0, BUMPS) sys.path.insert(0, SASVIEW) sys.path.insert(0, SASMODELS) if sys.argv[-1].startswith('-'): from bumps.cli import main as run_bumps else: from bumps.gui.gui_app import main as run_bumps run_bumps() sasmodels/example/model.py000066400000000000000000000023301317715334700161660ustar00rootroot00000000000000#!/usr/bin/env python # -*- coding: utf-8 -*- import sys from bumps.names import * from sasmodels.core import load_model from sasmodels.bumps_model import Model, Experiment from sasmodels.data import load_data, set_beam_stop, set_top """ IMPORT THE DATA USED """ radial_data = load_data('DEC07267.DAT') set_beam_stop(radial_data, 0.00669, outer=0.025) set_top(radial_data, -.0185) kernel = load_model("ellipsoid") model = Model(kernel, scale=0.08, radius_polar=15, radius_equatorial=800, sld=.291, sld_solvent=7.105, background=0, theta=90, phi=0, theta_pd=15, theta_pd_n=40, theta_pd_nsigma=3, radius_polar_pd=0.222296, radius_polar_pd_n=1, radius_polar_pd_nsigma=0, radius_equatorial_pd=.000128, radius_equatorial_pd_n=1, radius_equatorial_pd_nsigma=0, phi_pd=0, phi_pd_n=20, phi_pd_nsigma=3, ) # SET THE FITTING PARAMETERS model.radius_polar.range(15, 1000) model.radius_equatorial.range(15, 1000) model.theta_pd.range(0, 360) model.background.range(0,1000) model.scale.range(0, 10) #cutoff = 0 # no cutoff on polydisperisity loops #cutoff = 1e-5 # default cutoff cutoff = 1e-3 # low precision cutoff M = Experiment(data=radial_data, model=model, cutoff=cutoff) problem = FitProblem(M)sasmodels/example/model_ellipsoid_hayter_msa.py000066400000000000000000000022041317715334700224460ustar00rootroot00000000000000import sys #sys.path.append('path_to_sasmodels') import numpy as np from bumps.names import * from sasmodels.core import load_model from sasmodels.bumps_model import Model, Experiment from sasmodels.data import load_data, plot_data # IMPORT THE DATA USED data = load_data(sys.argv[1]) #setattr(data, 'qmin', 0.0) #setattr(data, 'qmax', 10.0) # DEFINE THE MODEL kernel = load_model('ellipsoid*hayter_msa') pars = dict(scale=6.4, background=0.06, sld=0.33, sld_solvent=2.15, radius_polar=14.0, radius_equatorial=24.0, volfraction=0.075, charge=66.373, temperature=298.0, concentration_salt=0.001, dielectconst=71.0) model = Model(kernel, **pars) # PARAMETER RANGES (ONLY THOSE PARAMETERS ARE FITTED) model.scale.range(0, inf) model.background.range(-inf, inf) #model.sld.range(-inf, inf) model.sld_solvent.range(-inf, inf) #model.radius_polar.range(0, inf) #model.radius_equatorial.range(0, inf) #model.volfraction.range(0,0.74) #model.charge.range(0, inf) #model.temperature.range(0,1000) #model.concentration_salt.range(0, 1) #model.dielectconst.range(0,inf) M = Experiment(data=data, model=model) problem = FitProblem(M) sasmodels/example/oriented_usans.py000066400000000000000000000022771317715334700201220ustar00rootroot00000000000000from bumps.names import * from sasmodels.data import load_data from sasmodels.core import load_model from sasmodels.bumps_model import Model, Experiment # Spherical particle data, not ellipsoids sans, usans = load_data('latex_smeared.xml', index='all') usans.qmin, usans.qmax = np.min(usans.x), np.max(usans.x) usans.mask = (usans.x < 0.0) usans.oriented = True #print sans.dxl, usans.dxl #import pprint; pprint.pprint(sans.__dict__) kernel = load_model("ellipsoid") model = Model( kernel, scale=0.08, background=0, sld=.291, sld_solvent=7.105, radius_polar=1800, radius_polar_pd=0.222296, radius_polar_pd_n=0, radius_equatorial=2600, radius_equatorial_pd=0.28, radius_equatorial_pd_n=0, theta=60, theta_pd=0, theta_pd_n=0, phi=60, phi_pd=0, phi_pd_n=0, ) # SET THE FITTING PARAMETERS model.radius_polar.range(1000, 10000) model.radius_equatorial.range(1000, 10000) model.theta.range(0, 360) model.phi.range(0, 360) model.background.range(0,1000) model.scale.range(0, 10) #cutoff = 0 # no cutoff on polydisperisity loops #cutoff = 1e-5 # default cutoff cutoff = 1e-3 # low precision cutoff M = Experiment(data=usans, model=model, cutoff=cutoff) problem = FitProblem(M) sasmodels/example/polynomial.py000066400000000000000000000005151317715334700172540ustar00rootroot00000000000000from numpy import inf parameters = [ ["n", "", 1, [1,5], "", "number of coefficients (or degree+1)"], ["c[n]", "", 0, [-inf, inf], "", "coefficients to c_n x^n"], ] Iq = r""" int int_n = (int)n; double result = c[int_n-1]; for (int k=int_n-2; k >= 0; k--) { result = result*q + c[k]; } return result; """sasmodels/example/se008724_01.ses000066400000000000000000000135071317715334700166340ustar00rootroot00000000000000DataFileTitle Polystyrene of Markus Strobl, Full Sine, ++ only Sample Polystyrene 2 um in 53% H2O, 47% D2O Settings D1=D2=20x8 mm,Ds = 16x10 mm (WxH), GF1 =scanning, GF2 = 2.5 A. 2 um polystyrene in 53% H2O, 47% D2O; 8.55% contrast Operator CPD Date ma 7 jul 2014 18:54:43 ScanType sine one element scan Thickness [mm] 2 Q_zmax [\AA^-1] 0.05 Q_ymax [\AA^-1] 0.05 spin echo length [nm] error SEL wavelength [nm] error wavelength polarisation error pol 49.778 2.4889 0.211 0.01055 0.99782 0.0044367 63.041 3.152 0.211 0.01055 1.0026 0.0047862 76.487 3.8244 0.211 0.01055 0.99601 0.0060598 89.847 4.4924 0.211 0.01055 0.99175 0.0058257 103.41 5.1705 0.211 0.01055 0.99543 0.0060966 116.95 5.8475 0.211 0.01055 0.99512 0.0048106 130.61 6.5303 0.211 0.01055 0.9975 0.0062594 144.37 7.2184 0.211 0.01055 0.99473 0.005293 158.2 7.9102 0.211 0.01055 0.9927 0.0053389 172.12 8.6062 0.211 0.01055 0.99453 0.0064548 186.17 9.3087 0.211 0.01055 0.98641 0.0073259 200.28 10.014 0.211 0.01055 0.98879 0.0078682 214.46 10.723 0.211 0.01055 0.9895 0.0068058 228.73 11.436 0.211 0.01055 0.99204 0.0082509 243.12 12.156 0.211 0.01055 0.99406 0.0051381 257.55 12.878 0.211 0.01055 0.97965 0.0055447 272.22 13.611 0.211 0.01055 0.97982 0.0065843 286.9 14.345 0.211 0.01055 0.97793 0.0071814 301.73 15.087 0.211 0.01055 0.97835 0.0066197 316.75 15.838 0.211 0.01055 0.98125 0.0069484 331.82 16.591 0.211 0.01055 0.97828 0.0068737 347.16 17.358 0.211 0.01055 0.97682 0.006744 362.45 18.122 0.211 0.01055 0.98155 0.0059865 378.09 18.904 0.211 0.01055 0.96446 0.0066788 393.74 19.687 0.211 0.01055 0.97276 0.0073781 409.61 20.481 0.211 0.01055 0.97101 0.0071053 425.55 21.278 0.211 0.01055 0.97501 0.0068244 441.91 22.096 0.211 0.01055 0.96958 0.0072272 458.12 22.906 0.211 0.01055 0.95991 0.0064035 474.77 23.739 0.211 0.01055 0.96219 0.0059227 491.52 24.576 0.211 0.01055 0.96016 0.0058606 508.51 25.426 0.211 0.01055 0.9509 0.0049836 525.68 26.284 0.211 0.01055 0.95558 0.0055218 543.08 27.154 0.211 0.01055 0.95079 0.0058258 560.74 28.037 0.211 0.01055 0.9514 0.0043921 578.69 28.935 0.211 0.01055 0.94562 0.0046962 596.75 29.838 0.211 0.01055 0.94588 0.0047341 615.17 30.758 0.211 0.01055 0.93958 0.0045821 633.77 31.688 0.211 0.01055 0.93731 0.0043108 652.82 32.641 0.211 0.01055 0.93664 0.0052044 672.04 33.602 0.211 0.01055 0.93209 0.0035563 691.57 34.578 0.211 0.01055 0.93385 0.0046002 711.48 35.574 0.211 0.01055 0.93028 0.0051136 731.67 36.583 0.211 0.01055 0.93012 0.0035279 752.17 37.608 0.211 0.01055 0.92594 0.0039458 773.1 38.655 0.211 0.01055 0.92352 0.0027613 794.42 39.721 0.211 0.01055 0.91823 0.0034587 816.14 40.807 0.211 0.01055 0.90862 0.0034262 838.19 41.91 0.211 0.01055 0.91909 0.003498 860.69 43.034 0.211 0.01055 0.91013 0.0030537 883.74 44.187 0.211 0.01055 0.90449 0.0035391 907.04 45.352 0.211 0.01055 0.90057 0.0029672 930.95 46.547 0.211 0.01055 0.90316 0.0031245 955.38 47.769 0.211 0.01055 0.89492 0.0030981 980.25 49.013 0.211 0.01055 0.89636 0.0036625 1005.7 50.284 0.211 0.01055 0.88808 0.0022652 1031.7 51.586 0.211 0.01055 0.88665 0.0044622 1058.3 52.914 0.211 0.01055 0.88205 0.0030275 1085.5 54.276 0.211 0.01055 0.88257 0.0028637 1113.4 55.669 0.211 0.01055 0.87629 0.0030312 1141.9 57.093 0.211 0.01055 0.87732 0.0026539 1171 58.55 0.211 0.01055 0.87361 0.0034591 1201 60.052 0.211 0.01055 0.86595 0.0028129 1231.6 61.582 0.211 0.01055 0.86804 0.0043311 1263 63.151 0.211 0.01055 0.86676 0.0028806 1295.2 64.762 0.211 0.01055 0.85655 0.0028657 1328.4 66.419 0.211 0.01055 0.85794 0.0034773 1362.3 68.113 0.211 0.01055 0.85521 0.0032798 1397.1 69.854 0.211 0.01055 0.84974 0.0044537 1432.9 71.644 0.211 0.01055 0.84149 0.0032738 1469.7 73.487 0.211 0.01055 0.84801 0.0037874 1507.5 75.376 0.211 0.01055 0.84334 0.003206 1546.4 77.318 0.211 0.01055 0.83749 0.0040707 1586.4 79.322 0.211 0.01055 0.83921 0.0049938 1627.6 81.381 0.211 0.01055 0.83434 0.0057337 1669.9 83.497 0.211 0.01055 0.82878 0.0062417 1713.6 85.678 0.211 0.01055 0.82309 0.0080179 1758.5 87.927 0.211 0.01055 0.82433 0.0074191 1804.8 90.239 0.211 0.01055 0.82023 0.0076431 1852.5 92.627 0.211 0.01055 0.82756 0.0063064 1901.7 95.087 0.211 0.01055 0.82584 0.0052944 1952.4 97.622 0.211 0.01055 0.82799 0.0050662 2004.8 100.24 0.211 0.01055 0.82345 0.0043127 2058.8 102.94 0.211 0.01055 0.82296 0.0038 2114.5 105.72 0.211 0.01055 0.81987 0.0034072 2172 108.6 0.211 0.01055 0.82021 0.0036752 2231.4 111.57 0.211 0.01055 0.82765 0.0028851 2292.8 114.64 0.211 0.01055 0.82664 0.0038942 2356.2 117.81 0.211 0.01055 0.82702 0.0047371 2421.8 121.09 0.211 0.01055 0.81593 0.0043772 2489.6 124.48 0.211 0.01055 0.8251 0.0028026 2559.5 127.98 0.211 0.01055 0.8292 0.0024574 2631.9 131.59 0.211 0.01055 0.82626 0.0036198 2706.8 135.34 0.211 0.01055 0.8208 0.0032314 2784.3 139.22 0.211 0.01055 0.81959 0.0042731 2864.5 143.23 0.211 0.01055 0.82653 0.002699 2947.5 147.38 0.211 0.01055 0.82401 0.0036726 3033.5 151.67 0.211 0.01055 0.82361 0.0048224 3122.4 156.12 0.211 0.01055 0.82358 0.0041221 3214.5 160.73 0.211 0.01055 0.82187 0.0028807 3310.1 165.5 0.211 0.01055 0.82644 0.003516 3409 170.45 0.211 0.01055 0.82355 0.0021166 3511.4 175.57 0.211 0.01055 0.82513 0.0033911 3617.6 180.88 0.211 0.01055 0.82802 0.0015342 3727.6 186.38 0.211 0.01055 0.82663 0.0029222 3841.7 192.08 0.211 0.01055 0.82026 0.0020755 3960 198 0.211 0.01055 0.83079 0.0026394 4082.7 204.13 0.211 0.01055 0.82665 0.0027466 4209.9 210.5 0.211 0.01055 0.82774 0.0025199 4341.9 217.09 0.211 0.01055 0.83489 0.0030619 4478.7 223.94 0.211 0.01055 0.81987 0.0020988 4620.8 231.04 0.211 0.01055 0.8253 0.0023899 4768.2 238.41 0.211 0.01055 0.82653 0.0022851 4921.1 246.06 0.211 0.01055 0.82442 0.003383 5079.8 253.99 0.211 0.01055 0.82827 0.0015979 5244.7 262.23 0.211 0.01055 0.82494 0.0031129 5415.7 270.79 0.211 0.01055 0.82183 0.0030149 5593.3 279.67 0.211 0.01055 0.83217 0.0046976 5777.8 288.89 0.211 0.01055 0.82227 0.005574 5969.3 298.46 0.211 0.01055 0.82338 0.0025569 sasmodels/example/se008731_01_40pcorr.ses000066400000000000000000000057711317715334700202070ustar00rootroot00000000000000DataFileTitle "Polystyrene of Markus Strobl, Full Sine, ++ only " Sample "Polystyrene 2 um in 53% H2O, 47% D2O " Settings "D1=D2=20x8 mm,Ds = 16x10 mm (WxH), GF1 =scanning, GF2 = 2.5 A. 2 um polystyrene in 53% H2O, 47% D2O; 8.55% contrast " Operator CPD Date do 10 jul 2014 16:37:30 ScanType sine one element scan Thickness [cm] 2.00E-01 Q_zmax [\A^-1] 0.05 Q_ymax [\A^-1] 0.05 spin echo length [A] Depolarisation [A-2 cm-1] error depol [A-2 cm-1] error SEL [A] wavelength [A] error wavelength [A] polarisation error pol 391.56 0.0041929 0.0036894 19.578 2.11 0.1055 1.0037 0.0032974 1564 -0.0046571 0.0038185 78.2 2.11 0.1055 0.99586 0.003386 2735.6 -0.017007 0.0038132 136.78 2.11 0.1055 0.98497 0.0033444 3907.9 -0.033462 0.0035068 195.39 2.11 0.1055 0.97064 0.0030309 5080.2 -0.047483 0.0038208 254.01 2.11 0.1055 0.9586 0.0032613 6251.8 -0.070375 0.00376 312.59 2.11 0.1055 0.93926 0.0031446 7423.2 -0.092217 0.0037927 371.16 2.11 0.1055 0.92117 0.0031108 8595.5 -0.10238 0.004006 429.77 2.11 0.1055 0.91287 0.0032562 9767.7 -0.12672 0.0038534 488.39 2.11 0.1055 0.8933 0.0030651 10940 -0.1374 0.004243 546.98 2.11 0.1055 0.88484 0.003343 12112 -0.16072 0.0045837 605.58 2.11 0.1055 0.86666 0.0035372 13284 -0.16623 0.0045613 664.2 2.11 0.1055 0.86242 0.0035027 14456 -0.18468 0.0044918 722.79 2.11 0.1055 0.84837 0.0033931 15628 -0.19143 0.0048967 781.38 2.11 0.1055 0.84328 0.0036768 16800 -0.20029 0.0045421 840.02 2.11 0.1055 0.83666 0.0033837 17971 -0.19798 0.0046642 898.56 2.11 0.1055 0.83838 0.0034819 19143 -0.21442 0.0047052 957.17 2.11 0.1055 0.82619 0.0034614 20316 -0.20885 0.0044931 1015.8 2.11 0.1055 0.8303 0.0033218 21488 -0.21393 0.0049186 1074.4 2.11 0.1055 0.82655 0.00362 22660 -0.20685 0.004423 1133 2.11 0.1055 0.83179 0.0032758 23832 -0.20802 0.0046979 1191.6 2.11 0.1055 0.83092 0.0034758 25003 -0.19848 0.0045953 1250.2 2.11 0.1055 0.838 0.0034289 26175 -0.21117 0.0044567 1308.8 2.11 0.1055 0.82859 0.0032881 27347 -0.21283 0.004137 1367.4 2.11 0.1055 0.82736 0.0030477 28520 -0.2042 0.0044587 1426 2.11 0.1055 0.83375 0.0033101 29692 -0.2112 0.0042852 1484.6 2.11 0.1055 0.82857 0.0031615 30864 -0.20319 0.0043483 1543.2 2.11 0.1055 0.8345 0.003231 32036 -0.20752 0.0044297 1601.8 2.11 0.1055 0.83129 0.0032788 33207 -0.20654 0.0043188 1660.4 2.11 0.1055 0.83201 0.0031995 34380 -0.20126 0.0046375 1719 2.11 0.1055 0.83593 0.0034518 35551 -0.20924 0.0042871 1777.6 2.11 0.1055 0.83001 0.0031684 36724 -0.21323 0.0045471 1836.2 2.11 0.1055 0.82707 0.0033487 37895 -0.21324 0.0045354 1894.7 2.11 0.1055 0.82706 0.00334 39067 -0.19905 0.0044141 1953.4 2.11 0.1055 0.83758 0.003292 40239 -0.1991 0.0047441 2012 2.11 0.1055 0.83754 0.003538 41411 -0.20359 0.0050136 2070.5 2.11 0.1055 0.8342 0.003724 42583 -0.21032 0.0049474 2129.1 2.11 0.1055 0.82922 0.0036529 43755 -0.20689 0.0048203 2187.8 2.11 0.1055 0.83176 0.00357 44927 -0.21075 0.0052337 2246.4 2.11 0.1055 0.8289 0.0038628 46099 -0.19956 0.0047827 2304.9 2.11 0.1055 0.8372 0.0035653 sasmodels/example/sesans_parameters_css-hs.py000066400000000000000000000024241317715334700220710ustar00rootroot00000000000000""" This is a data file used to load in sesans data and fit it using the bumps engine """ from bumps.names import * import sesansfit # Enter the model name to use model_name = "core_shell_sphere*hardsphere" # DO NOT MODIFY THIS LINE model = sesansfit.get_bumps_model(model_name) # Enter any custom parameters phi = Parameter(0.45, name='phi') pen = Parameter(0.95, name='solvent penetration') custom_params = {"phi" : phi, "pen" : pen} # SESANS data file sesans_file = "core_shell.ses" # Initial parameter values (if other than defaults) initial_vals = { "sld_core" : 1.05, "sld_shell" : 2.88*pen-0.05*(1-pen), "sld_solvent" : 2.88, "radius" : 730, "thickness" : 20, "volfraction" : phi, "scale" : (1-phi) } # Ranges for parameters if other than default param_range = { "phi" : [0.2, 0.5], "pen" : [0,1], "radius" : [500, 3000], "thickness" : [0,200] } # Constraints # model.param_name = f(other params) # EXAMPLE: model.scale = model.radius*model.radius*(1 - phi) - where radius and scale are model functions and phi is # a custom parameter model.scale = phi*(1-phi) model.volfraction = phi model.shell_sld = pen*2.88 # Send to the fitting engine problem = sesansfit.sesans_fit(sesans_file, model_name, initial_vals, custom_params, param_range) sasmodels/example/sesans_parameters_sphere.py000066400000000000000000000023451317715334700221610ustar00rootroot00000000000000""" This is a data file used to load in sesans data and fit it using the bumps engine """ from bumps.names import * import sesansfit # Enter the model name to use model_name = "sphere" # DO NOT MODIFY THIS LINE model = sesansfit.get_bumps_model(model_name) model.radius.range(1,10000) # Enter any custom parameters # name = Parameter(initial_value, name='name') phi = Parameter(0.10, name='phi') # Add the parameters to this list that should be displayed in the fitting window custom_params = {"phi" : phi} # SESANS data file name sesans_file = "sphere.ses" # Initial parameter values (if other than defaults) # "model_parameter_name" : value initial_vals = { "sld" : 7.0, "radius" : 1000, "sld_solvent" : 1.0, } # Ranges for parameters if other than default # "model_parameter_name" : [min, max] param_range = { "phi" : [0.001, 0.5], "radius" : [1, 10000] } # Constraints # model.param_name = f(other params) # EXAMPLE: model.scale = model.radius*model.radius*(1 - phi) - where radius and scale are model functions and phi is # a custom parameter model.scale = phi*(1-phi) # Send to the fitting engine # DO NOT MODIFY THIS LINE problem = sesansfit.sesans_fit(sesans_file, model, initial_vals, custom_params, param_range) sasmodels/example/sesans_sphere_2micron.py000066400000000000000000000023311317715334700213620ustar00rootroot00000000000000""" This is a data file used to load in sesans data and fit it using the bumps engine """ from bumps.names import * import sesansfit # Enter the model name to use model_name = "sphere" # DO NOT MODIFY THIS LINE model = sesansfit.get_bumps_model(model_name) # Enter any custom parameters # name = Parameter(initial_value, name='name') phi = Parameter(0.0855, name='phi') # Add the parameters to this list that should be displayed in the fitting window custom_params = {"phi" : phi} # SESANS data file name sesans_file = "spheres2micron.ses" # Initial parameter values (if other than defaults) # "model_parameter_name" : value initial_vals = { "sld" : 1.41, "radius" : 10000, "sld_solvent" : 2.70, } # Ranges for parameters if other than default # "model_parameter_name" : [min, max] param_range = { "phi" : [0.001, 0.5], "radius" : [100, 100000] } # Constraints # model.param_name = f(other params) # EXAMPLE: model.scale = model.radius*model.radius*(1 - phi) - where radius and scale are model functions and phi is # a custom parameter model.scale = phi*(1-phi) # Send to the fitting engine # DO NOT MODIFY THIS LINE problem = sesansfit.sesans_fit(sesans_file, model, initial_vals, custom_params, param_range) sasmodels/example/sesansfit.py000066400000000000000000000060061317715334700170710ustar00rootroot00000000000000from bumps.names import * from sasmodels import core, bumps_model, sesans from sas.sascalc.dataloader.loader import Loader def get_bumps_model(model_name): kernel = core.load_model(model_name) model = bumps_model.Model(kernel) return model def sesans_fit(file, model, initial_vals={}, custom_params={}, param_range=[], acceptance_angle=None): """ @param file: SESANS file location @param model: Bumps model object or model name - can be model, model_1 * model_2, and/or model_1 + model_2 @param initial_vals: dictionary of {param_name : initial_value} @param custom_params: dictionary of {custom_parameter_name : Parameter() object} @param param_range: dictionary of {parameter_name : [minimum, maximum]} @param constraints: dictionary of {parameter_name : constraint} @return: FitProblem for Bumps usage """ initial_vals['background'] = 0.0 try: loader = Loader() data = loader.load(file) if data is None: raise IOError("Could not load file %r"%(file)) except: # If no loadable data file, generate random data SElength = np.linspace(0, 2400, 61) # [A] data = np.ones_like(SElength) err_data = np.ones_like(SElength)*0.03 class Sample: zacceptance = 0.1 # [A^-1] thickness = 0.2 # [cm] class SESANSData1D: #q_zmax = 0.23 # [A^-1] lam = 0.2 # [nm] x = SElength y = data dy = err_data sample = Sample() has_no_finite_acceptance = acceptance_angle is not None data = SESANSData1D() data.acceptance_angle = acceptance_angle data.has_no_finite_acceptance = acceptance_angle is not None radius = initial_vals.get("radius", 1000) data.Rmax = 30*radius # [A] if isinstance(model, basestring): model = get_bumps_model(model) # Load custom parameters, initial values and parameter ranges pars = model.parameters().copy() pars.update(custom_params) for k, v in custom_params.items(): if k not in pars: par_error("Can't set parameter %r in model"%k, pars) setattr(model, k, v) model._parameter_names.append(k) for k, v in initial_vals.items(): if k not in pars: par_error("Can't get parameter %r from model"%k, pars) param = pars[k] param.value = v for k, v in param_range.items(): if k not in pars: par_error("Can't set range on parameter %r in model"%k, pars) param = pars[k] param.range(*v) if False: # for future implementation M_sesans = bumps_model.Experiment(data=data, model=model) M_sans = bumps_model.Experiment(data=sans_data, model=model) problem = FitProblem([M_sesans, M_sans]) else: M_sesans = bumps_model.Experiment(data=data, model=model) problem = FitProblem(M_sesans) return problem def par_error(msg, pars): raise ValueError(msg+"\nAvailable parameters: %s"%", ".join(sorted(pars.keys()))) sasmodels/example/sesansfit_CodeCampIII.py000066400000000000000000000036541317715334700211650ustar00rootroot00000000000000from bumps.names import * from sasmodels import core, bumps_model if True: # fix when data loader exists # from sas.dataloader.readers\ from sas.dataloader.loader import Loader loader = Loader() filename = 'sphere.ses' data = loader.load(filename) if data is None: raise IOError("Could not load file %r"%(filename,)) data.x /= 10 # print data # data = load_sesans('mydatfile.pz') # sans_data = load_sans('mysansfile.xml') else: SElength = np.linspace(0, 2400, 61) # [A] data = np.ones_like(SElength) err_data = np.ones_like(SElength)*0.03 class Sample: zacceptance = 0.1 # [A^-1] thickness = 0.2 # [cm] class SESANSData1D: #q_zmax = 0.23 # [A^-1] lam = 0.2 # [nm] x = SElength y = data dy = err_data sample = Sample() data = SESANSData1D() radius = 1000 data.Rmax = 3*radius # [A] ## Sphere parameters kernel = core.load_model("sphere", dtype='single') phi = Parameter(0.1, name="phi") model = bumps_model.Model(kernel, scale=phi*(1-phi), sld=7.0, solvent_sld=1.0, radius=radius, ) phi.range(0.001,0.5) #model.radius.pmp(40) model.radius.range(1,10000) #model.sld.pm(5) #model.background #model.radius_pd=0 #model.radius_pd_n=0 ### Tri-Axial Ellipsoid # #kernel = core.load_model("triaxial_ellipsoid", dtype='single') #phi = Parameter(0.1, name='phi') #model = bumps_model.Model(kernel, # scale=phi*(1-phi), sld=7.0, solvent_sld=1.0, radius=radius, # ) #phi.range(0.001,0.90) ##model.radius.pmp(40) #model.radius.range(100,10000) ##model.sld.pmp(5) ##model.background ##model.radius_pd = 0 ##model.radius_pd_n = 0 if False: # have sans data M_sesans = bumps_model.Experiment(data=data, model=model) M_sans = bumps_model.Experiment(data=sans_data, model=model) problem = FitProblem([M_sesans, M_sans]) else: M_sesans = bumps_model.Experiment(data=data, model=model) problem = FitProblem(M_sesans)sasmodels/example/simul_fit.py000066400000000000000000000046001317715334700170630ustar00rootroot00000000000000from bumps.names import * from sasmodels.core import load_model from sasmodels.bumps_model import Model, Experiment from sasmodels.data import load_data, plot_data # latex data, same sample usans and sans # particles radius ~2300, uniform dispersity datasets = load_data('latex_smeared.xml', index='all') #[print(data) for data in datasets] # A single sphere model to share between the datasets. We will use # FreeVariables below to set the parameters that are independent between # the datasets. kernel = load_model('sphere') pars = dict(scale=0.01, background=0.0, sld=5.0, sld_solvent=0.0, radius=1500., #radius_pd=0.1, radius_pd_n=35, ) model = Model(kernel, **pars) # radius and polydispersity (if any) are shared model.radius.range(0, inf) #model.radius_pd.range(0, 1) # Contrast and dilution are the same for both measurements, but are not # separable with a single measurement (i.e., I(q) ~ F(q) contrast^2 Vf), # so fit one of scale, sld or solvent sld. With absolute scaling from # data reduction, can use the same parameter for both datasets. model.scale.range(0, inf) #model.sld.range(-inf, inf) #model.sld_solvent.range(-inf, inf) # Background is different for sans and usans so set it as a free variable # in the model. free = FreeVariables( names=[data.run[0] for data in datasets], background=model.background, ) free.background.range(-inf, inf) # Note: can access the parameters for the individual models using # free.background[0] and free.background[1], setting constraints or # ranges as appropriate. # For more complex systems where different datasets require independent models, # separate models can be defined, with parameters tied together using # constraint expressions. For example, the following could be used to fit # data set 1 to spheres and data set 2 to cylinders of the same volume: # model1 = Model(load_model('sphere')) # model2 = Model(load_model('cylinder')) # model1.sld = model2.sld # model1.sld_solvent = model2.sld_solvent # model1.scale = model2.scale # # set cylinders and spheres to the same volume # model1.radius = (3/4*model2.radius**2*model2.length)**(1/3) # model1.background.range(0, 2) # model2.background.range(0, 2) # Setup the experiments, sharing the same model across all datasets. M = [Experiment(data=data, model=model, name=data.run[0]) for data in datasets] problem = FitProblem(M, freevars=free)sasmodels/example/sphere.ses000066400000000000000000000142341317715334700165240ustar00rootroot00000000000000name se009051.dat sample "SiO2 pH=6 & NiO pH=10, nanosized, in D2O, Sine ++ only." collimation "D1=D2=20x8 mm,Ds = 16x10 mm (WxH), GF1 =scanning, GF2 = 2.5 A. " ID CPD Date di 27 jan 2015 18:17:50 Method sine one element scan Thickness [mm] 10 z-acceptance [nm^-1] 0.3 y-acceptance [nm^-1] 0.3 spin echo length [um] error spin-echo length wavelength [nm] error wavelength Sample 5 Sample 5 -error 29.882023 5 0.2095 0.01 0.997817556 0.00887342 0.029882023 29.882023 85.257531 5 0.2095 0.01 1.0026184 0.009572307 0.085257531 85.257531 140.798634 5 0.2095 0.01 0.996013172 0.012119508 0.140798634 140.798634 196.560502 5 0.2095 0.01 0.991752656 0.011651473 0.196560502 196.560502 252.528125 5 0.2095 0.01 0.995429571 0.012193294 0.252528125 252.528125 308.729274 5 0.2095 0.01 0.995119819 0.009621277 0.308729274 308.729274 365.037117 5 0.2095 0.01 0.997497767 0.012518842 0.365037117 365.037117 421.684677 5 0.2095 0.01 0.994733865 0.010585926 0.421684677 421.684677 478.564852 5 0.2095 0.01 0.992696275 0.010677724 0.478564852 478.564852 535.715521 5 0.2095 0.01 0.994534294 0.012909556 0.535715521 535.715521 593.24408 5 0.2095 0.01 0.986412268 0.014651894 0.59324408 593.24408 650.985498 5 0.2095 0.01 0.988788566 0.015736468 0.650985498 650.985498 709.203958 5 0.2095 0.01 0.989501168 0.013611615 0.709203958 709.203958 767.809943 5 0.2095 0.01 0.99203933 0.016501891 0.767809943 767.809943 826.762925 5 0.2095 0.01 0.994062723 0.010276207 0.826762925 826.762925 886.302296 5 0.2095 0.01 0.979647192 0.011089421 0.886302296 886.302296 946.236366 5 0.2095 0.01 0.97982075 0.013168527 0.946236366 946.236366 1006.784115 5 0.2095 0.01 0.977927712 0.014362819 1.006784115 1006.784115 1067.891213 5 0.2095 0.01 0.978351462 0.013239476 1.067891213 1067.891213 1129.598722 5 0.2095 0.01 0.981246471 0.013896898 1.129598722 1129.598722 1192.022694 5 0.2095 0.01 0.978275164 0.013747481 1.192022694 1192.022694 1255.271282 5 0.2095 0.01 0.976818842 0.013487944 1.255271282 1255.271282 1319.307134 5 0.2095 0.01 0.981546068 0.011972943 1.319307134 1319.307134 1384.197821 5 0.2095 0.01 0.96445854 0.013357572 1.384197821 1384.197821 1450.051342 5 0.2095 0.01 0.972756158 0.014756189 1.450051342 1450.051342 1516.978619 5 0.2095 0.01 0.971010184 0.014210504 1.516978619 1516.978619 1585.044577 5 0.2095 0.01 0.975009829 0.013648839 1.585044577 1585.044577 1654.356194 5 0.2095 0.01 0.969575209 0.014454336 1.654356194 1654.356194 1724.97535 5 0.2095 0.01 0.959907267 0.012806944 1.72497535 1724.97535 1796.962718 5 0.2095 0.01 0.96219203 0.011845496 1.796962718 1796.962718 1870.613025 5 0.2095 0.01 0.960157966 0.011721155 1.870613025 1870.613025 1945.921163 5 0.2095 0.01 0.95089937 0.009967287 1.945921163 1945.921163 2023.09841 5 0.2095 0.01 0.955584642 0.01104368 2.02309841 2023.09841 2102.189874 5 0.2095 0.01 0.950786938 0.011651582 2.102189874 2102.189874 2183.534527 5 0.2095 0.01 0.951403607 0.008784149 2.183534527 2183.534527 2267.173021 5 0.2095 0.01 0.94561823 0.009392383 2.267173021 2267.173021 2353.393035 5 0.2095 0.01 0.945882787 0.009468264 2.353393035 2353.393035 2442.350387 5 0.2095 0.01 0.939583158 0.009164239 2.442350387 2442.350387 2534.334343 5 0.2095 0.01 0.93731257 0.008621568 2.534334343 2534.334343 2629.473374 5 0.2095 0.01 0.936639557 0.010408821 2.629473374 2629.473374 2728.20036 5 0.2095 0.01 0.932091884 0.007112674 2.72820036 2728.20036 2830.74992 5 0.2095 0.01 0.933852763 0.009200431 2.83074992 2830.74992 2937.363026 5 0.2095 0.01 0.930283437 0.01022719 2.937363026 2937.363026 3048.510973 5 0.2095 0.01 0.930121334 0.007055747 3.048510973 3048.510973 3164.589926 5 0.2095 0.01 0.925944326 0.0078917 3.164589926 3164.589926 3285.843756 5 0.2095 0.01 0.92351759 0.005522582 3.285843756 3285.843756 3412.805801 5 0.2095 0.01 0.918228311 0.006917328 3.412805801 3412.805801 3546.016792 5 0.2095 0.01 0.908621563 0.006852313 3.546016792 3546.016792 3685.876213 5 0.2095 0.01 0.919087792 0.006995961 3.685876213 3685.876213 3833.174832 5 0.2095 0.01 0.910132214 0.006107336 3.833174832 3833.174832 3988.234456 5 0.2095 0.01 0.904491462 0.007078101 3.988234456 3988.234456 4151.940408 5 0.2095 0.01 0.90056919 0.005934428 4.151940408 4151.940408 4324.902332 5 0.2095 0.01 0.903155701 0.006249069 4.324902332 4324.902332 4507.963711 5 0.2095 0.01 0.894919827 0.006196232 4.507963711 4507.963711 4701.967049 5 0.2095 0.01 0.896358908 0.007324999 4.701967049 4701.967049 4907.785127 5 0.2095 0.01 0.88807923 0.004530465 4.907785127 4907.785127 5126.471149 5 0.2095 0.01 0.886649039 0.008924412 5.126471149 5126.471149 5359.059759 5 0.2095 0.01 0.882051947 0.006055081 5.359059759 5359.059759 5606.740304 5 0.2095 0.01 0.882573371 0.005727419 5.606740304 5606.740304 5870.903592 5 0.2095 0.01 0.876289825 0.006062306 5.870903592 5870.903592 6152.736235 5 0.2095 0.01 0.877318199 0.005307783 6.152736235 6152.736235 6453.893169 5 0.2095 0.01 0.873610284 0.006918104 6.453893169 6453.893169 6775.835415 5 0.2095 0.01 0.865954455 0.005625863 6.775835415 6775.835415 7120.530581 5 0.2095 0.01 0.868037308 0.008662141 7.120530581 7120.530581 7489.735939 5 0.2095 0.01 0.86676404 0.005761209 7.489735939 7489.735939 7885.556041 5 0.2095 0.01 0.85655072 0.005731411 7.885556041 7885.556041 8310.290162 5 0.2095 0.01 0.857936274 0.006954572 8.310290162 8310.290162 8766.315359 5 0.2095 0.01 0.85520525 0.006559622 8.766315359 8766.315359 9256.271706 5 0.2095 0.01 0.849739829 0.008907377 9.256271706 9256.271706 9783.031577 5 0.2095 0.01 0.841487161 0.006547659 9.783031577 9783.031577 10349.71409 5 0.2095 0.01 0.84801051 0.007574866 10.34971409 10349.71409 10959.67923 5 0.2095 0.01 0.843342861 0.006411993 10.95967923 10959.67923 11616.5969 5 0.2095 0.01 0.837488454 0.008141353 11.6165969 11616.5969 12324.44664 5 0.2095 0.01 0.839214922 0.009987535 12.32444664 12324.44664 13087.4723 5 0.2095 0.01 0.834336972 0.011467406 13.0874723 13087.4723 13910.29604 5 0.2095 0.01 0.828775634 0.012483365 13.91029604 13910.29604 14798.05061 5 0.2095 0.01 0.823088812 0.016035848 14.79805061 14798.05061 15756.09817 5 0.2095 0.01 0.824329178 0.014838138 15.75609817 15756.09817 16790.46783 5 0.2095 0.01 0.82023172 0.015286187 16.79046783 16790.46783 17907.62866 5 0.2095 0.01 0.827559752 0.012612741 17.90762866 17907.62866 sasmodels/example/spheres2micron.ses000066400000000000000000000137121317715334700202010ustar00rootroot00000000000000DataFileTitle Polystyrene of Markus Strobl, Full Sine, ++ only Sample Polystyrene 2 um in 53% H2O, 47% D2O Settings D1=D2=20x8 mm,Ds = 16x10 mm (WxH), GF1 =scanning, GF2 = 2.5 A. 2 um polystyrene in 53% H2O, 47% D2O; 8.55% contrast Operator CPD Date ma 7 jul 2014 18:54:43 ScanType sine one element scan Thickness [mm] 2 Q_zmax [\AA^-1] 0.05 Q_ymax [\AA^-1] 0.05 spin echo length [nm] error SEL wavelength [nm] error wavelength polarisation error pol 49.778 2.4889 0.211 0.01055 0.99782 0.0044367 63.041 3.152 0.211 0.01055 1.0026 0.0047862 76.487 3.8244 0.211 0.01055 0.99601 0.0060598 89.847 4.4924 0.211 0.01055 0.99175 0.0058257 103.41 5.1705 0.211 0.01055 0.99543 0.0060966 116.95 5.8475 0.211 0.01055 0.99512 0.0048106 130.61 6.5303 0.211 0.01055 0.9975 0.0062594 144.37 7.2184 0.211 0.01055 0.99473 0.005293 158.2 7.9102 0.211 0.01055 0.9927 0.0053389 172.12 8.6062 0.211 0.01055 0.99453 0.0064548 186.17 9.3087 0.211 0.01055 0.98641 0.0073259 200.28 10.014 0.211 0.01055 0.98879 0.0078682 214.46 10.723 0.211 0.01055 0.9895 0.0068058 228.73 11.436 0.211 0.01055 0.99204 0.0082509 243.12 12.156 0.211 0.01055 0.99406 0.0051381 257.55 12.878 0.211 0.01055 0.97965 0.0055447 272.22 13.611 0.211 0.01055 0.97982 0.0065843 286.9 14.345 0.211 0.01055 0.97793 0.0071814 301.73 15.087 0.211 0.01055 0.97835 0.0066197 316.75 15.838 0.211 0.01055 0.98125 0.0069484 331.82 16.591 0.211 0.01055 0.97828 0.0068737 347.16 17.358 0.211 0.01055 0.97682 0.006744 362.45 18.122 0.211 0.01055 0.98155 0.0059865 378.09 18.904 0.211 0.01055 0.96446 0.0066788 393.74 19.687 0.211 0.01055 0.97276 0.0073781 409.61 20.481 0.211 0.01055 0.97101 0.0071053 425.55 21.278 0.211 0.01055 0.97501 0.0068244 441.91 22.096 0.211 0.01055 0.96958 0.0072272 458.12 22.906 0.211 0.01055 0.95991 0.0064035 474.77 23.739 0.211 0.01055 0.96219 0.0059227 491.52 24.576 0.211 0.01055 0.96016 0.0058606 508.51 25.426 0.211 0.01055 0.9509 0.0049836 525.68 26.284 0.211 0.01055 0.95558 0.0055218 543.08 27.154 0.211 0.01055 0.95079 0.0058258 560.74 28.037 0.211 0.01055 0.9514 0.0043921 578.69 28.935 0.211 0.01055 0.94562 0.0046962 596.75 29.838 0.211 0.01055 0.94588 0.0047341 615.17 30.758 0.211 0.01055 0.93958 0.0045821 633.77 31.688 0.211 0.01055 0.93731 0.0043108 652.82 32.641 0.211 0.01055 0.93664 0.0052044 672.04 33.602 0.211 0.01055 0.93209 0.0035563 691.57 34.578 0.211 0.01055 0.93385 0.0046002 711.48 35.574 0.211 0.01055 0.93028 0.0051136 731.67 36.583 0.211 0.01055 0.93012 0.0035279 752.17 37.608 0.211 0.01055 0.92594 0.0039458 773.1 38.655 0.211 0.01055 0.92352 0.0027613 794.42 39.721 0.211 0.01055 0.91823 0.0034587 816.14 40.807 0.211 0.01055 0.90862 0.0034262 838.19 41.91 0.211 0.01055 0.91909 0.003498 860.69 43.034 0.211 0.01055 0.91013 0.0030537 883.74 44.187 0.211 0.01055 0.90449 0.0035391 907.04 45.352 0.211 0.01055 0.90057 0.0029672 930.95 46.547 0.211 0.01055 0.90316 0.0031245 955.38 47.769 0.211 0.01055 0.89492 0.0030981 980.25 49.013 0.211 0.01055 0.89636 0.0036625 1005.7 50.284 0.211 0.01055 0.88808 0.0022652 1031.7 51.586 0.211 0.01055 0.88665 0.0044622 1058.3 52.914 0.211 0.01055 0.88205 0.0030275 1085.5 54.276 0.211 0.01055 0.88257 0.0028637 1113.4 55.669 0.211 0.01055 0.87629 0.0030312 1141.9 57.093 0.211 0.01055 0.87732 0.0026539 1171 58.55 0.211 0.01055 0.87361 0.0034591 1201 60.052 0.211 0.01055 0.86595 0.0028129 1231.6 61.582 0.211 0.01055 0.86804 0.0043311 1263 63.151 0.211 0.01055 0.86676 0.0028806 1295.2 64.762 0.211 0.01055 0.85655 0.0028657 1328.4 66.419 0.211 0.01055 0.85794 0.0034773 1362.3 68.113 0.211 0.01055 0.85521 0.0032798 1397.1 69.854 0.211 0.01055 0.84974 0.0044537 1432.9 71.644 0.211 0.01055 0.84149 0.0032738 1469.7 73.487 0.211 0.01055 0.84801 0.0037874 1507.5 75.376 0.211 0.01055 0.84334 0.003206 1546.4 77.318 0.211 0.01055 0.83749 0.0040707 1586.4 79.322 0.211 0.01055 0.83921 0.0049938 1627.6 81.381 0.211 0.01055 0.83434 0.0057337 1669.9 83.497 0.211 0.01055 0.82878 0.0062417 1713.6 85.678 0.211 0.01055 0.82309 0.0080179 1758.5 87.927 0.211 0.01055 0.82433 0.0074191 1804.8 90.239 0.211 0.01055 0.82023 0.0076431 1852.5 92.627 0.211 0.01055 0.82756 0.0063064 1901.7 95.087 0.211 0.01055 0.82584 0.0052944 1952.4 97.622 0.211 0.01055 0.82799 0.0050662 2004.8 100.24 0.211 0.01055 0.82345 0.0043127 2058.8 102.94 0.211 0.01055 0.82296 0.0038 2114.5 105.72 0.211 0.01055 0.81987 0.0034072 2172 108.6 0.211 0.01055 0.82021 0.0036752 2231.4 111.57 0.211 0.01055 0.82765 0.0028851 2292.8 114.64 0.211 0.01055 0.82664 0.0038942 2356.2 117.81 0.211 0.01055 0.82702 0.0047371 2421.8 121.09 0.211 0.01055 0.81593 0.0043772 2489.6 124.48 0.211 0.01055 0.8251 0.0028026 2559.5 127.98 0.211 0.01055 0.8292 0.0024574 2631.9 131.59 0.211 0.01055 0.82626 0.0036198 2706.8 135.34 0.211 0.01055 0.8208 0.0032314 2784.3 139.22 0.211 0.01055 0.81959 0.0042731 2864.5 143.23 0.211 0.01055 0.82653 0.002699 2947.5 147.38 0.211 0.01055 0.82401 0.0036726 3033.5 151.67 0.211 0.01055 0.82361 0.0048224 3122.4 156.12 0.211 0.01055 0.82358 0.0041221 3214.5 160.73 0.211 0.01055 0.82187 0.0028807 3310.1 165.5 0.211 0.01055 0.82644 0.003516 3409 170.45 0.211 0.01055 0.82355 0.0021166 3511.4 175.57 0.211 0.01055 0.82513 0.0033911 3617.6 180.88 0.211 0.01055 0.82802 0.0015342 3727.6 186.38 0.211 0.01055 0.82663 0.0029222 3841.7 192.08 0.211 0.01055 0.82026 0.0020755 3960 198 0.211 0.01055 0.83079 0.0026394 4082.7 204.13 0.211 0.01055 0.82665 0.0027466 4209.9 210.5 0.211 0.01055 0.82774 0.0025199 4341.9 217.09 0.211 0.01055 0.83489 0.0030619 4478.7 223.94 0.211 0.01055 0.81987 0.0020988 4620.8 231.04 0.211 0.01055 0.8253 0.0023899 4768.2 238.41 0.211 0.01055 0.82653 0.0022851 4921.1 246.06 0.211 0.01055 0.82442 0.003383 5079.8 253.99 0.211 0.01055 0.82827 0.0015979 5244.7 262.23 0.211 0.01055 0.82494 0.0031129 5415.7 270.79 0.211 0.01055 0.82183 0.0030149 5593.3 279.67 0.211 0.01055 0.83217 0.0046976 5777.8 288.89 0.211 0.01055 0.82227 0.005574 5969.3 298.46 0.211 0.01055 0.82338 0.0025569 sasmodels/explore/000077500000000000000000000000001317715334700145415ustar00rootroot00000000000000sasmodels/explore/angular_pd.py000066400000000000000000000121411317715334700172260ustar00rootroot00000000000000""" Application to explore the difference between sasview 3.x orientation dispersity and possible replacement algorithms. """ import mpl_toolkits.mplot3d # Adds projection='3d' option to subplot import matplotlib.pyplot as plt from matplotlib.widgets import Slider, CheckButtons from matplotlib import cm import numpy as np from numpy import pi, cos, sin, sqrt, exp, degrees, radians def draw_sphere(ax, radius=10., steps=100): u = np.linspace(0, 2 * np.pi, steps) v = np.linspace(0, np.pi, steps) x = radius * np.outer(np.cos(u), np.sin(v)) y = radius * np.outer(np.sin(u), np.sin(v)) z = radius * np.outer(np.ones(np.size(u)), np.cos(v)) ax.plot_surface(x, y, z, rstride=4, cstride=4, color='w') def draw_mesh_current(ax, theta, dtheta, phi, dphi, radius=10., dist='gauss'): theta = radians(theta) phi = radians(phi) dtheta = radians(dtheta) dphi = radians(dphi) # 10 point 3-sigma gaussian weights t = np.linspace(-3., 3., 11) if dist == 'gauss': weights = exp(-0.5*t**2) elif dist == 'rect': weights = np.ones_like(t) else: raise ValueError("expected dist to be 'gauss' or 'rect'") theta = theta + dtheta*t phi = phi + dphi*t x = radius * np.outer(cos(phi), cos(theta)) y = radius * np.outer(sin(phi), cos(theta)) z = radius * np.outer(np.ones_like(phi), sin(theta)) w = np.outer(weights, weights*abs(cos(theta))) x,y,z,w = [v.flatten() for v in (x,y,z,w)] ax.scatter(x, y, z, c=w, marker='o', vmin=0., vmax=1.0) def draw_mesh_new(ax, theta, dtheta, phi, dphi, flow, radius=10., dist='gauss'): theta_center = radians(90-theta) phi_center = radians(phi) flow_center = radians(flow) dtheta = radians(dtheta) dphi = radians(dphi) # 10 point 3-sigma gaussian weights t = np.linspace(-3., 3., 11) if dist == 'gauss': weights = exp(-0.5*t**2) elif dist == 'rect': weights = np.ones_like(t) else: raise ValueError("expected dist to be 'gauss' or 'rect'") theta = dtheta*t phi = dphi*t x = radius * np.outer(cos(phi), cos(theta)) y = radius * np.outer(sin(phi), cos(theta)) z = radius * np.outer(np.ones_like(phi), sin(theta)) #w = np.outer(weights, weights*abs(cos(dtheta*t))) w = np.outer(weights, weights*abs(cos(theta))) x, y, z, w = [v.flatten() for v in (x,y,z,w)] x, y, z = rotate(x, y, z, phi_center, theta_center, flow_center) ax.scatter(x, y, z, c=w, marker='o', vmin=0., vmax=1.) def rotate(x, y, z, phi, theta, psi): R = rotation_matrix(psi, theta, phi) p = np.vstack([x,y,z]) q = np.dot(R,p) return q def rotation_matrix(xa,ya,za): Rz = [[cos(za), -sin(za), 0.], [sin(za), cos(za), 0.], [0., 0., 1.]] Ry = [[cos(ya), 0., -sin(ya)], [0., 1., 0.], [sin(ya), 0., cos(ya)]] Rx = [[1., 0., 0.], [0., cos(xa), sin(xa)], [0., -sin(xa), cos(xa)]] R = np.dot(np.dot(Rz, Ry), Rx) return R def main(): plt.hold(True) plt.set_cmap('gist_earth') plt.clf() #gs = gridspec.GridSpec(2,1,height_ratios=[4,1]) #ax = plt.subplot(gs[0], projection='3d') ax = plt.axes([0.0, 0.2, 1.0, 0.8], projection='3d') phi, dphi = -45., 3. theta, dtheta = 70., 10. flow = 0. #dist = 'rect' dist = 'gauss' axcolor = 'lightgoldenrodyellow' axphi = plt.axes([0.1, 0.1, 0.45, 0.04], axisbg=axcolor) axtheta = plt.axes([0.1, 0.15, 0.45, 0.04], axisbg=axcolor) sphi = Slider(axphi, 'Phi', -180, 180, valinit=phi) stheta = Slider(axtheta, 'Theta', -180, 180, valinit=theta) axdphi = plt.axes([0.75, 0.1, 0.15, 0.04], axisbg=axcolor) axdtheta = plt.axes([0.75, 0.15, 0.15, 0.04], axisbg=axcolor) sdphi = Slider(axdphi, 'dPhi', 0, 30, valinit=dphi) sdtheta = Slider(axdtheta, 'dTheta', 0, 30, valinit=dtheta) axflow = plt.axes([0.1, 0.05, 0.45, 0.04], axisbg=axcolor) sflow = Slider(axflow, 'Flow', -180, 180, valinit=flow) axusenew= plt.axes([0.75, 0.05, 0.15, 0.04], axisbg=axcolor) susenew = CheckButtons(axusenew, ['New'], [True]) def update(val, axis=None): phi, theta = sphi.val, stheta.val dphi, dtheta = sdphi.val, sdtheta.val flow = sflow.val use_new = susenew.lines[0][0].get_visible() ax.cla() draw_sphere(ax) if use_new: draw_mesh_new(ax, theta=theta, dtheta=dtheta, phi=phi, dphi=dphi, flow=flow, radius=11., dist=dist) else: draw_mesh_current(ax, theta=theta, dtheta=dtheta, phi=phi, dphi=dphi, radius=11., dist=dist) if not axis.startswith('d'): ax.view_init(elev=90-theta if use_new else theta, azim=phi) plt.gcf().canvas.draw() stheta.on_changed(lambda v: update(v,'theta')) sphi.on_changed(lambda v: update(v, 'phi')) sdtheta.on_changed(lambda v: update(v, 'dtheta')) sdphi.on_changed(lambda v: update(v, 'dphi')) sflow.on_changed(lambda v: update(v, 'dflow')) susenew.on_clicked(lambda v: update(v, 'use_new')) update(None, 'phi') plt.show() if __name__ == "__main__": main()sasmodels/explore/jitter.py000066400000000000000000000166731317715334700164310ustar00rootroot00000000000000""" Application to explore the difference between sasview 3.x orientation dispersity and possible replacement algorithms. """ import mpl_toolkits.mplot3d # Adds projection='3d' option to subplot import matplotlib.pyplot as plt from matplotlib.widgets import Slider, CheckButtons from matplotlib import cm import numpy as np from numpy import pi, cos, sin, sqrt, exp, degrees, radians def draw_beam(ax): #ax.plot([0,0],[0,0],[1,-1]) #ax.scatter([0]*100,[0]*100,np.linspace(1, -1, 100), alpha=0.8) steps = 25 u = np.linspace(0, 2 * np.pi, steps) v = np.linspace(-1, 1, steps) r = 0.02 x = r*np.outer(np.cos(u), np.ones_like(v)) y = r*np.outer(np.sin(u), np.ones_like(v)) z = np.outer(np.ones_like(u), v) ax.plot_surface(x, y, z, rstride=4, cstride=4, color='y', alpha=0.5) def draw_shimmy(ax, theta, phi, psi, dtheta, dphi, dpsi): size=[0.1, 0.4, 1.0] view=[theta, phi, psi] shimmy=[0,0,0] #draw_shape = draw_parallelepiped draw_shape = draw_ellipsoid #np.random.seed(10) #cloud = np.random.randn(10,3) cloud = [ [-1, -1, -1], [-1, -1, 0], [-1, -1, 1], [-1, 0, -1], [-1, 0, 0], [-1, 0, 1], [-1, 1, -1], [-1, 1, 0], [-1, 1, 1], [ 0, -1, -1], [ 0, -1, 0], [ 0, -1, 1], [ 0, 0, -1], [ 0, 0, 0], [ 0, 0, 1], [ 0, 1, -1], [ 0, 1, 0], [ 0, 1, 1], [ 1, -1, -1], [ 1, -1, 0], [ 1, -1, 1], [ 1, 0, -1], [ 1, 0, 0], [ 1, 0, 1], [ 1, 1, -1], [ 1, 1, 0], [ 1, 1, 1], ] if dtheta == 0: cloud = [v for v in cloud if v[0] == 0] if dphi == 0: cloud = [v for v in cloud if v[1] == 0] if dpsi == 0: cloud = [v for v in cloud if v[2] == 0] draw_shape(ax, size, view, shimmy, steps=100, alpha=0.8) for point in cloud: shimmy=[dtheta*point[0], dphi*point[1], dpsi*point[2]] draw_shape(ax, size, view, shimmy, alpha=0.8) for v in 'xyz': a, b, c = size lim = np.sqrt(a**2+b**2+c**2) getattr(ax, 'set_'+v+'lim')([-lim, lim]) getattr(ax, v+'axis').label.set_text(v) def draw_ellipsoid(ax, size, view, shimmy, steps=25, alpha=1): a,b,c = size theta, phi, psi = view dtheta, dphi, dpsi = shimmy u = np.linspace(0, 2 * np.pi, steps) v = np.linspace(0, np.pi, steps) x = a*np.outer(np.cos(u), np.sin(v)) y = b*np.outer(np.sin(u), np.sin(v)) z = c*np.outer(np.ones_like(u), np.cos(v)) shape = x.shape points = np.matrix([x.flatten(),y.flatten(),z.flatten()]) points = Rz(dpsi)*Ry(dtheta)*Rx(dphi)*points points = Rz(phi)*Ry(theta)*Rz(psi)*points x,y,z = [v.reshape(shape) for v in points] ax.plot_surface(x, y, z, rstride=4, cstride=4, color='w', alpha=alpha) def draw_parallelepiped(ax, size, view, shimmy, alpha=1): a,b,c = size theta, phi, psi = view dtheta, dphi, dpsi = shimmy x = a*np.array([ 1,-1, 1,-1, 1,-1, 1,-1]) y = b*np.array([ 1, 1,-1,-1, 1, 1,-1,-1]) z = c*np.array([ 1, 1, 1, 1,-1,-1,-1,-1]) tri = np.array([ # counter clockwise triangles # z: up/down, x: right/left, y: front/back [0,1,2], [3,2,1], # top face [6,5,4], [5,6,7], # bottom face [0,2,6], [6,4,0], # right face [1,5,7], [7,3,1], # left face [2,3,6], [7,6,3], # front face [4,1,0], [5,1,4], # back face ]) points = np.matrix([x,y,z]) points = Rz(dpsi)*Ry(dtheta)*Rx(dphi)*points points = Rz(phi)*Ry(theta)*Rz(psi)*points x,y,z = [np.array(v).flatten() for v in points] ax.plot_trisurf(x, y, triangles=tri, Z=z, color='w', alpha=alpha) def draw_sphere(ax, radius=10., steps=100): u = np.linspace(0, 2 * np.pi, steps) v = np.linspace(0, np.pi, steps) x = radius * np.outer(np.cos(u), np.sin(v)) y = radius * np.outer(np.sin(u), np.sin(v)) z = radius * np.outer(np.ones(np.size(u)), np.cos(v)) ax.plot_surface(x, y, z, rstride=4, cstride=4, color='w') def draw_mesh_new(ax, theta, dtheta, phi, dphi, flow, radius=10., dist='gauss'): theta_center = radians(theta) phi_center = radians(phi) flow_center = radians(flow) dtheta = radians(dtheta) dphi = radians(dphi) # 10 point 3-sigma gaussian weights t = np.linspace(-3., 3., 11) if dist == 'gauss': weights = exp(-0.5*t**2) elif dist == 'rect': weights = np.ones_like(t) else: raise ValueError("expected dist to be 'gauss' or 'rect'") theta = dtheta*t phi = dphi*t x = radius * np.outer(cos(phi), cos(theta)) y = radius * np.outer(sin(phi), cos(theta)) z = radius * np.outer(np.ones_like(phi), sin(theta)) #w = np.outer(weights, weights*abs(cos(dtheta*t))) w = np.outer(weights, weights*abs(cos(theta))) x, y, z, w = [v.flatten() for v in (x,y,z,w)] x, y, z = rotate(x, y, z, phi_center, theta_center, flow_center) ax.scatter(x, y, z, c=w, marker='o', vmin=0., vmax=1.) def rotate(x, y, z, phi, theta, psi): R = Rz(phi)*Ry(theta)*Rz(psi) p = np.vstack([x,y,z]) return R*p def Rx(angle): a = radians(angle) R = [[1., 0., 0.], [0., cos(a), sin(a)], [0., -sin(a), cos(a)]] return np.matrix(R) def Ry(angle): a = radians(angle) R = [[cos(a), 0., -sin(a)], [0., 1., 0.], [sin(a), 0., cos(a)]] return np.matrix(R) def Rz(angle): a = radians(angle) R = [[cos(a), -sin(a), 0.], [sin(a), cos(a), 0.], [0., 0., 1.]] return np.matrix(R) def main(): #plt.hold(True) plt.set_cmap('gist_earth') plt.clf() #gs = gridspec.GridSpec(2,1,height_ratios=[4,1]) #ax = plt.subplot(gs[0], projection='3d') ax = plt.axes([0.0, 0.2, 1.0, 0.8], projection='3d') theta, dtheta = 70., 10. phi, dphi = -45., 3. psi, dpsi = -45., 3. theta, phi, psi = 0, 0, 0 dtheta, dphi, dpsi = 0, 0, 0 #dist = 'rect' dist = 'gauss' axcolor = 'lightgoldenrodyellow' axtheta = plt.axes([0.1, 0.15, 0.45, 0.04], axisbg=axcolor) axphi = plt.axes([0.1, 0.1, 0.45, 0.04], axisbg=axcolor) axpsi = plt.axes([0.1, 0.05, 0.45, 0.04], axisbg=axcolor) stheta = Slider(axtheta, 'Theta', -90, 90, valinit=theta) sphi = Slider(axphi, 'Phi', -180, 180, valinit=phi) spsi = Slider(axpsi, 'Psi', -180, 180, valinit=psi) axdtheta = plt.axes([0.75, 0.15, 0.15, 0.04], axisbg=axcolor) axdphi = plt.axes([0.75, 0.1, 0.15, 0.04], axisbg=axcolor) axdpsi= plt.axes([0.75, 0.05, 0.15, 0.04], axisbg=axcolor) sdtheta = Slider(axdtheta, 'dTheta', 0, 30, valinit=dtheta) sdphi = Slider(axdphi, 'dPhi', 0, 30, valinit=dphi) sdpsi = Slider(axdpsi, 'dPsi', 0, 30, valinit=dphi) def update(val, axis=None): theta, phi, psi = stheta.val, sphi.val, spsi.val dtheta, dphi, dpsi = sdtheta.val, sdphi.val, sdpsi.val ax.cla() draw_beam(ax) draw_shimmy(ax, theta, phi, psi, dtheta, dphi, dpsi) #if not axis.startswith('d'): # ax.view_init(elev=theta, azim=phi) plt.gcf().canvas.draw() stheta.on_changed(lambda v: update(v,'theta')) sphi.on_changed(lambda v: update(v, 'phi')) spsi.on_changed(lambda v: update(v, 'psi')) sdtheta.on_changed(lambda v: update(v, 'dtheta')) sdphi.on_changed(lambda v: update(v, 'dphi')) sdpsi.on_changed(lambda v: update(v, 'dpsi')) update(None, 'phi') plt.show() if __name__ == "__main__": main()sasmodels/explore/precision.py000077500000000000000000000514511317715334700171170ustar00rootroot00000000000000#!/usr/bin/env python r""" Show numerical precision of $2 J_1(x)/x$. """ from __future__ import division, print_function import sys import os sys.path.insert(0, os.path.abspath(os.path.join(os.path.dirname(__file__), '..'))) import numpy as np from numpy import pi, inf import scipy.special try: from mpmath import mp except ImportError: # CRUFT: mpmath split out into its own package from sympy.mpmath import mp #import matplotlib; matplotlib.use('TkAgg') import pylab from sasmodels import core, data, direct_model, modelinfo class Comparator(object): def __init__(self, name, mp_function, np_function, ocl_function, xaxis, limits): self.name = name self.mp_function = mp_function self.np_function = np_function self.ocl_function = ocl_function self.xaxis = xaxis self.limits = limits def __repr__(self): return "Comparator(%s)"%self.name def call_mpmath(self, vec, bits=500): """ Direct calculation using mpmath extended precision library. """ with mp.workprec(bits): return [self.mp_function(mp.mpf(x)) for x in vec] def call_numpy(self, x, dtype): """ Direct calculation using numpy/scipy. """ x = np.asarray(x, dtype) return self.np_function(x) def call_ocl(self, x, dtype, platform='ocl'): """ Calculation using sasmodels ocl libraries. """ x = np.asarray(x, dtype) model = core.build_model(self.ocl_function, dtype=dtype) calculator = direct_model.DirectModel(data.empty_data1D(x), model) return calculator(background=0) def run(self, xrange="log", diff="relative"): r""" Compare accuracy of different methods for computing f. *xrange* is:: log: [10^-3,10^5] logq: [10^-4, 10^1] linear: [1,1000] zoom: [1000,1010] neg: [-100,100] *diff* is "relative", "absolute" or "none" *x_bits* is the precision with which the x values are specified. The default 23 should reproduce the equivalent of a single precisio """ linear = not xrange.startswith("log") if xrange == "zoom": lin_min, lin_max, lin_steps = 1000, 1010, 2000 elif xrange == "neg": lin_min, lin_max, lin_steps = -100.1, 100.1, 2000 elif xrange == "linear": lin_min, lin_max, lin_steps = 1, 1000, 2000 lin_min, lin_max, lin_steps = 0.001, 2, 2000 elif xrange == "log": log_min, log_max, log_steps = -3, 5, 400 elif xrange == "logq": log_min, log_max, log_steps = -4, 1, 400 else: raise ValueError("unknown range "+xrange) with mp.workprec(500): # Note: we make sure that we are comparing apples to apples... # The x points are set using single precision so that we are # examining the accuracy of the transformation from x to f(x) # rather than x to f(nearest(x)) where nearest(x) is the nearest # value to x in the given precision. if linear: lin_min = max(lin_min, self.limits[0]) lin_max = min(lin_max, self.limits[1]) qrf = np.linspace(lin_min, lin_max, lin_steps, dtype='single') #qrf = np.linspace(lin_min, lin_max, lin_steps, dtype='double') qr = [mp.mpf(float(v)) for v in qrf] #qr = mp.linspace(lin_min, lin_max, lin_steps) else: log_min = np.log10(max(10**log_min, self.limits[0])) log_max = np.log10(min(10**log_max, self.limits[1])) qrf = np.logspace(log_min, log_max, log_steps, dtype='single') #qrf = np.logspace(log_min, log_max, log_steps, dtype='double') qr = [mp.mpf(float(v)) for v in qrf] #qr = [10**v for v in mp.linspace(log_min, log_max, log_steps)] target = self.call_mpmath(qr, bits=500) pylab.subplot(121) self.compare(qr, 'single', target, linear, diff) pylab.legend(loc='best') pylab.subplot(122) self.compare(qr, 'double', target, linear, diff) pylab.legend(loc='best') pylab.suptitle(self.name + " compared to 500-bit mpmath") def compare(self, x, precision, target, linear=False, diff="relative"): r""" Compare the different computation methods using the given precision. """ if precision == 'single': #n=11; plotdiff(x, target, self.call_mpmath(x, n), 'mp %d bits'%n, diff=diff) #n=23; plotdiff(x, target, self.call_mpmath(x, n), 'mp %d bits'%n, diff=diff) pass elif precision == 'double': #n=53; plotdiff(x, target, self.call_mpmath(x, n), 'mp %d bits'%n, diff=diff) #n=83; plotdiff(x, target, self.call_mpmath(x, n), 'mp %d bits'%n, diff=diff) pass plotdiff(x, target, self.call_numpy(x, precision), 'numpy '+precision, diff=diff) plotdiff(x, target, self.call_ocl(x, precision, 0), 'OpenCL '+precision, diff=diff) pylab.xlabel(self.xaxis) if diff == "relative": pylab.ylabel("relative error") elif diff == "absolute": pylab.ylabel("absolute error") else: pylab.ylabel(self.name) pylab.semilogx(x, target, '-', label="true value") if linear: pylab.xscale('linear') def plotdiff(x, target, actual, label, diff): """ Plot the computed value. Use relative error if SHOW_DIFF, otherwise just plot the value directly. """ if diff == "relative": err = np.array([abs((t-a)/t) for t, a in zip(target, actual)], 'd') #err = np.clip(err, 0, 1) pylab.loglog(x, err, '-', label=label) elif diff == "absolute": err = np.array([abs((t-a)) for t, a in zip(target, actual)], 'd') pylab.loglog(x, err, '-', label=label) else: limits = np.min(target), np.max(target) pylab.semilogx(x, np.clip(actual, *limits), '-', label=label) def make_ocl(function, name, source=[]): class Kernel(object): pass Kernel.__file__ = name+".py" Kernel.name = name Kernel.parameters = [] Kernel.source = source Kernel.Iq = function model_info = modelinfo.make_model_info(Kernel) return model_info # =============== FUNCTION DEFINITIONS ================ FUNCTIONS = {} def add_function(name, mp_function, np_function, ocl_function, shortname=None, xaxis="x", limits=(-inf, inf)): if shortname is None: shortname = name.replace('(x)', '').replace(' ', '') FUNCTIONS[shortname] = Comparator(name, mp_function, np_function, ocl_function, xaxis, limits) add_function( name="J0(x)", mp_function=mp.j0, np_function=scipy.special.j0, ocl_function=make_ocl("return sas_J0(q);", "sas_J0", ["lib/polevl.c", "lib/sas_J0.c"]), ) add_function( name="J1(x)", mp_function=mp.j1, np_function=scipy.special.j1, ocl_function=make_ocl("return sas_J1(q);", "sas_J1", ["lib/polevl.c", "lib/sas_J1.c"]), ) add_function( name="JN(-3, x)", mp_function=lambda x: mp.besselj(-3, x), np_function=lambda x: scipy.special.jn(-3, x), ocl_function=make_ocl("return sas_JN(-3, q);", "sas_JN", ["lib/polevl.c", "lib/sas_J0.c", "lib/sas_J1.c", "lib/sas_JN.c"]), shortname="J-3", ) add_function( name="JN(3, x)", mp_function=lambda x: mp.besselj(3, x), np_function=lambda x: scipy.special.jn(3, x), ocl_function=make_ocl("return sas_JN(3, q);", "sas_JN", ["lib/polevl.c", "lib/sas_J0.c", "lib/sas_J1.c", "lib/sas_JN.c"]), shortname="J3", ) add_function( name="JN(2, x)", mp_function=lambda x: mp.besselj(2, x), np_function=lambda x: scipy.special.jn(2, x), ocl_function=make_ocl("return sas_JN(2, q);", "sas_JN", ["lib/polevl.c", "lib/sas_J0.c", "lib/sas_J1.c", "lib/sas_JN.c"]), shortname="J2", ) add_function( name="2 J1(x)/x", mp_function=lambda x: 2*mp.j1(x)/x, np_function=lambda x: 2*scipy.special.j1(x)/x, ocl_function=make_ocl("return sas_2J1x_x(q);", "sas_2J1x_x", ["lib/polevl.c", "lib/sas_J1.c"]), ) add_function( name="J1(x)", mp_function=mp.j1, np_function=scipy.special.j1, ocl_function=make_ocl("return sas_J1(q);", "sas_J1", ["lib/polevl.c", "lib/sas_J1.c"]), ) add_function( name="Si(x)", mp_function=mp.si, np_function=lambda x: scipy.special.sici(x)[0], ocl_function=make_ocl("return sas_Si(q);", "sas_Si", ["lib/sas_Si.c"]), ) #import fnlib #add_function( # name="fnlibJ1", # mp_function=mp.j1, # np_function=fnlib.J1, # ocl_function=make_ocl("return sas_J1(q);", "sas_J1", ["lib/polevl.c", "lib/sas_J1.c"]), #) add_function( name="sin(x)", mp_function=mp.sin, np_function=np.sin, #ocl_function=make_ocl("double sn, cn; SINCOS(q,sn,cn); return sn;", "sas_sin"), ocl_function=make_ocl("return sin(q);", "sas_sin"), ) add_function( name="sin(x)/x", mp_function=lambda x: mp.sin(x)/x if x != 0 else 1, ## scipy sinc function is inaccurate and has an implied pi*x term #np_function=lambda x: scipy.special.sinc(x/pi), ## numpy sin(x)/x needs to check for x=0 np_function=lambda x: np.sin(x)/x, ocl_function=make_ocl("return sas_sinx_x(q);", "sas_sinc"), ) add_function( name="cos(x)", mp_function=mp.cos, np_function=np.cos, #ocl_function=make_ocl("double sn, cn; SINCOS(q,sn,cn); return cn;", "sas_cos"), ocl_function=make_ocl("return cos(q);", "sas_cos"), ) add_function( name="gamma(x)", mp_function=mp.gamma, np_function=scipy.special.gamma, ocl_function=make_ocl("return sas_gamma(q);", "sas_gamma", ["lib/sas_gamma.c"]), limits=(-3.1, 10), ) add_function( name="erf(x)", mp_function=mp.erf, np_function=scipy.special.erf, ocl_function=make_ocl("return sas_erf(q);", "sas_erf", ["lib/polevl.c", "lib/sas_erf.c"]), limits=(-5., 5.), ) add_function( name="erfc(x)", mp_function=mp.erfc, np_function=scipy.special.erfc, ocl_function=make_ocl("return sas_erfc(q);", "sas_erfc", ["lib/polevl.c", "lib/sas_erf.c"]), limits=(-5., 5.), ) add_function( name="arctan(x)", mp_function=mp.atan, np_function=np.arctan, ocl_function=make_ocl("return atan(q);", "sas_arctan"), ) add_function( name="3 j1(x)/x", mp_function=lambda x: 3*(mp.sin(x)/x - mp.cos(x))/(x*x), # Note: no taylor expansion near 0 np_function=lambda x: 3*(np.sin(x)/x - np.cos(x))/(x*x), ocl_function=make_ocl("return sas_3j1x_x(q);", "sas_j1c", ["lib/sas_3j1x_x.c"]), ) add_function( name="(1-cos(x))/x^2", mp_function=lambda x: (1 - mp.cos(x))/(x*x), np_function=lambda x: (1 - np.cos(x))/(x*x), ocl_function=make_ocl("return (1-cos(q))/q/q;", "sas_1mcosx_x2"), ) add_function( name="(1-sin(x)/x)/x", mp_function=lambda x: 1/x - mp.sin(x)/(x*x), np_function=lambda x: 1/x - np.sin(x)/(x*x), ocl_function=make_ocl("return (1-sas_sinx_x(q))/q;", "sas_1msinx_x_x"), ) add_function( name="(1/2+(1-cos(x))/x^2-sin(x)/x)/x", mp_function=lambda x: (0.5 - mp.sin(x)/x + (1-mp.cos(x))/(x*x))/x, np_function=lambda x: (0.5 - np.sin(x)/x + (1-np.cos(x))/(x*x))/x, ocl_function=make_ocl("return (0.5-sin(q)/q + (1-cos(q))/q/q)/q;", "sas_T2"), ) add_function( name="fmod_2pi", mp_function=lambda x: mp.fmod(x, 2*mp.pi), np_function=lambda x: np.fmod(x, 2*np.pi), ocl_function=make_ocl("return fmod(q, 2*M_PI);", "sas_fmod"), ) add_function( name="debye", mp_function=lambda x: 2*(mp.exp(-x**2) + x**2 - 1)/x**4, np_function=lambda x: 2*(np.expm1(-x**2) + x**2)/x**4, ocl_function=make_ocl(""" const double qsq = q*q; if (qsq < 1.0) { // Pade approximation const double x = qsq; if (0) { // 0.36 single // PadeApproximant[2*Exp[-x^2] + x^2-1)/x^4, {x, 0, 4}] return (x*x/180. + 1.)/((1./30.*x + 1./3.)*x + 1); } else if (0) { // 1.0 for single // padeapproximant[2*exp[-x^2] + x^2-1)/x^4, {x, 0, 6}] const double A1=1./24., A2=1./84, A3=-1./3360; const double B1=3./8., B2=3./56., B3=1./336.; return (((A3*x + A2)*x + A1)*x + 1.)/(((B3*x + B2)*x + B1)*x + 1.); } else if (1) { // 1.0 for single, 0.25 for double // PadeApproximant[2*Exp[-x^2] + x^2-1)/x^4, {x, 0, 8}] const double A1=1./15., A2=1./60, A3=0., A4=1./75600.; const double B1=2./5., B2=1./15., B3=1./180., B4=1./5040.; return ((((A4*x + A3)*x + A2)*x + A1)*x + 1.) /((((B4*x + B3)*x + B2)*x + B1)*x + 1.); } else { // 1.0 for single, 0.5 for double // PadeApproximant[2*Exp[-x^2] + x^2-1)/x^4, {x, 0, 8}] const double A1=1./12., A2=2./99., A3=1./2640., A4=1./23760., A5=-1./1995840.; const double B1=5./12., B2=5./66., B3=1./132., B4=1./2376., B5=1./95040.; return (((((A5*x + A4)*x + A3)*x + A2)*x + A1)*x + 1.) /(((((B5*x + B4)*x + B3)*x + B2)*x + B1)*x + 1.); } } else if (qsq < 1.) { // Taylor series; 0.9 for single, 0.25 for double const double x = qsq; const double C0 = +1.; const double C1 = -1./3.; const double C2 = +1./12.; const double C3 = -1./60.; const double C4 = +1./360.; const double C5 = -1./2520.; const double C6 = +1./20160.; const double C7 = -1./181440.; //return ((((C5*x + C4)*x + C3)*x + C2)*x + C1)*x + C0; //return (((((C6*x + C5)*x + C4)*x + C3)*x + C2)*x + C1)*x + C0; return ((((((C7*x + C6)*x + C5)*x + C4)*x + C3)*x + C2)*x + C1)*x + C0; } else { return 2.*(expm1(-qsq) + qsq)/(qsq*qsq); } """, "sas_debye"), ) RADIUS=3000 LENGTH=30 THETA=45 def mp_cyl(x): f = mp.mpf theta = f(THETA)*mp.pi/f(180) qr = x * f(RADIUS)*mp.sin(theta) qh = x * f(LENGTH)/f(2)*mp.cos(theta) be = f(2)*mp.j1(qr)/qr si = mp.sin(qh)/qh background = f(0) #background = f(1)/f(1000) volume = mp.pi*f(RADIUS)**f(2)*f(LENGTH) contrast = f(5) units = f(1)/f(10000) #return be #return si return units*(volume*contrast*be*si)**f(2)/volume + background def np_cyl(x): f = np.float64 if x.dtype == np.float64 else np.float32 theta = f(THETA)*f(np.pi)/f(180) qr = x * f(RADIUS)*np.sin(theta) qh = x * f(LENGTH)/f(2)*np.cos(theta) be = f(2)*scipy.special.j1(qr)/qr si = np.sin(qh)/qh background = f(0) #background = f(1)/f(1000) volume = f(np.pi)*f(RADIUS)**2*f(LENGTH) contrast = f(5) units = f(1)/f(10000) #return be #return si return units*(volume*contrast*be*si)**f(2)/volume + background ocl_cyl = """\ double THETA = %(THETA).15e*M_PI_180; double qr = q*%(RADIUS).15e*sin(THETA); double qh = q*0.5*%(LENGTH).15e*cos(THETA); double be = sas_2J1x_x(qr); double si = sas_sinx_x(qh); double background = 0; //double background = 0.001; double volume = M_PI*square(%(RADIUS).15e)*%(LENGTH).15e; double contrast = 5.0; double units = 1e-4; //return be; //return si; return units*square(volume*contrast*be*si)/volume + background; """%{"LENGTH":LENGTH, "RADIUS": RADIUS, "THETA": THETA} add_function( name="cylinder(r=%g, l=%g, theta=%g)"%(RADIUS, LENGTH, THETA), mp_function=mp_cyl, np_function=np_cyl, ocl_function=make_ocl(ocl_cyl, "ocl_cyl", ["lib/polevl.c", "lib/sas_J1.c"]), shortname="cylinder", xaxis="$q/A^{-1}$", ) lanczos_gamma = """\ const double coeff[] = { 76.18009172947146, -86.50532032941677, 24.01409824083091, -1.231739572450155, 0.1208650973866179e-2,-0.5395239384953e-5 }; const double x = q; double tmp = x + 5.5; tmp -= (x + 0.5)*log(tmp); double ser = 1.000000000190015; for (int k=0; k < 6; k++) ser += coeff[k]/(x + k+1); return -tmp + log(2.5066282746310005*ser/x); """ add_function( name="log gamma(x)", mp_function=mp.loggamma, np_function=scipy.special.gammaln, ocl_function=make_ocl(lanczos_gamma, "lgamma"), ) # Alternate versions of 3 j1(x)/x, for posterity def taylor_3j1x_x(x): """ Calculation using taylor series. """ # Generate coefficients using the precision of the target value. n = 5 cinv = [3991680, -45360, 840, -30, 3] three = x.dtype.type(3) p = three/np.array(cinv, x.dtype) return np.polyval(p[-n:], x*x) add_function( name="3 j1(x)/x: taylor", mp_function=lambda x: 3*(mp.sin(x)/x - mp.cos(x))/(x*x), np_function=taylor_3j1x_x, ocl_function=make_ocl("return sas_3j1x_x(q);", "sas_j1c", ["lib/sas_3j1x_x.c"]), ) def trig_3j1x_x(x): r""" Direct calculation using linear combination of sin/cos. Use the following trig identity: .. math:: a \sin(x) + b \cos(x) = c \sin(x + \phi) where $c = \surd(a^2+b^2)$ and $\phi = \tan^{-1}(b/a) to calculate the numerator $\sin(x) - x\cos(x)$. """ one = x.dtype.type(1) three = x.dtype.type(3) c = np.sqrt(one + x*x) phi = np.arctan2(-x, one) return three*(c*np.sin(x+phi))/(x*x*x) add_function( name="3 j1(x)/x: trig", mp_function=lambda x: 3*(mp.sin(x)/x - mp.cos(x))/(x*x), np_function=trig_3j1x_x, ocl_function=make_ocl("return sas_3j1x_x(q);", "sas_j1c", ["lib/sas_3j1x_x.c"]), ) def np_2J1x_x(x): """ numpy implementation of 2J1(x)/x using single precision algorithm """ # pylint: disable=bad-continuation f = x.dtype.type ax = abs(x) if ax < f(8.0): y = x*x ans1 = f(2)*(f(72362614232.0) + y*(f(-7895059235.0) + y*(f(242396853.1) + y*(f(-2972611.439) + y*(f(15704.48260) + y*(f(-30.16036606))))))) ans2 = (f(144725228442.0) + y*(f(2300535178.0) + y*(f(18583304.74) + y*(f(99447.43394) + y*(f(376.9991397) + y))))) return ans1/ans2 else: y = f(64.0)/(ax*ax) xx = ax - f(2.356194491) ans1 = (f(1.0) + y*(f(0.183105e-2) + y*(f(-0.3516396496e-4) + y*(f(0.2457520174e-5) + y*f(-0.240337019e-6))))) ans2 = (f(0.04687499995) + y*(f(-0.2002690873e-3) + y*(f(0.8449199096e-5) + y*(f(-0.88228987e-6) + y*f(0.105787412e-6))))) sn, cn = np.sin(xx), np.cos(xx) ans = np.sqrt(f(0.636619772)/ax) * (cn*ans1 - (f(8.0)/ax)*sn*ans2) * f(2)/x return -ans if (x < f(0.0)) else ans add_function( name="2 J1(x)/x:alt", mp_function=lambda x: 2*mp.j1(x)/x, np_function=lambda x: np.asarray([np_2J1x_x(v) for v in x], x.dtype), ocl_function=make_ocl("return sas_2J1x_x(q);", "sas_2J1x_x", ["lib/polevl.c", "lib/sas_J1.c"]), ) ALL_FUNCTIONS = set(FUNCTIONS.keys()) ALL_FUNCTIONS.discard("loggamma") # OCL version not ready yet ALL_FUNCTIONS.discard("3j1/x:taylor") ALL_FUNCTIONS.discard("3j1/x:trig") ALL_FUNCTIONS.discard("2J1/x:alt") # =============== MAIN PROGRAM ================ def usage(): names = ", ".join(sorted(ALL_FUNCTIONS)) print("""\ usage: precision.py [-f/a/r] [-x] name... where -f indicates that the function value should be plotted, -a indicates that the absolute error should be plotted, -r indicates that the relative error should be plotted (default), -x indicates the steps in x, where is one of the following log indicates log stepping in [10^-3, 10^5] (default) logq indicates log stepping in [10^-4, 10^1] linear indicates linear stepping in [1, 1000] zoom indicates linear stepping in [1000, 1010] neg indicates linear stepping in [-100.1, 100.1] and name is "all [first]" or one of: """+names) sys.exit(1) def main(): import sys diff = "relative" xrange = "log" options = [v for v in sys.argv[1:] if v.startswith('-')] for opt in options: if opt == '-f': diff = "none" elif opt == '-r': diff = "relative" elif opt == '-a': diff = "absolute" elif opt.startswith('-x'): xrange = opt[2:] else: usage() names = [v for v in sys.argv[1:] if not v.startswith('-')] if not names: usage() if names[0] == "all": cutoff = names[1] if len(names) > 1 else "" names = list(sorted(ALL_FUNCTIONS)) names = [k for k in names if k >= cutoff] if any(k not in FUNCTIONS for k in names): usage() multiple = len(names) > 1 pylab.interactive(multiple) for k in names: pylab.clf() comparator = FUNCTIONS[k] comparator.run(xrange=xrange, diff=diff) if multiple: raw_input() if not multiple: pylab.show() if __name__ == "__main__": main() sasmodels/explore/rpa.py000066400000000000000000000133111317715334700156740ustar00rootroot00000000000000from collections import namedtuple import numpy as np from numpy import sqrt, exp, expm1 AVOGADRO = 6.022e23 Polymer = namedtuple("Polymer", "n phi v a b".split()) def E(q, poly): qrsq = (q*Rg(poly))**2 retval = exp(-qrsq) return retval def F(q, poly): qrsq = (q*Rg(poly))**2 retval = -expm1(-qrsq)/qrsq return retval def P_ii(q, poly): qrsq = (q*Rg(poly))**2 retval = 2 * (expm1(-qrsq) + qrsq)/qrsq**2 return retval def P_ij(q, poly_list): i, j = poly_list[0], poly_list[-1] retval = F(q, i) * np.prod([E(q,p) for p in poly_list[1:-1]]) * F(q, j) return retval def Rg(poly): return sqrt(poly.n/6.)*poly.a def S0_ii(q, poly): retval = poly.n*poly.phi*poly.v*P_ii(q, poly) return retval def S0_ij(q, poly_list): i,j = poly_list[0], poly_list[-1] retval = sqrt(i.n*i.phi*i.v*j.n*j.phi*j.v) * P_ij(q, poly_list) return retval def drho(poly, base): return (poly.b/poly.v - base.b/base.v)*1e-13*sqrt(AVOGADRO) def binary_blend(q, C, D, Kcd): """ de Gennes, 1979 """ S0cc = S0_ii(q, C) S0dd = S0_ii(q, D) vcc = 1/S0dd - 2*Kcd #/v0 Scc = S0cc/(1 + vcc*S0cc) rhocd = drho(C,D) Iq = rhocd**2 * Scc return Iq def ternary_blend(q, B, C, D, Kbc, Kbd, Kcd): S0bb = S0_ii(q, B) S0cc = S0_ii(q, C) S0dd = S0_ii(q, D) vbb = 1/S0dd - 2*Kbd vcc = 1/S0dd - 2*Kcd vbc = 1/S0dd + Kbd - Kbc - Kcd rhobd = drho(B,D) rhocd = drho(C,D) det = (1+vbb*S0bb)*(1+vcc*S0cc) - vbc**2*S0bb*S0cc Sbb = S0bb*(1+vcc*S0cc)/det Scc = S0cc*(1+vbb*S0bb)/det Sbc = -S0bb*vbc*S0cc/det Iq = rhobd**2*Sbb + rhocd**2*Scc + 2*rhobd*rhocd*Sbc return Iq def diblock_copolymer(q, C, D, Kcd): """ Leibler, 1980 """ S0cc = S0_ii(q, C) S0dd = S0_ii(q, D) S0cd = S0_ij(q, [C, D]) Scc = (S0cc*S0dd - S0cd**2)/((S0cc+S0dd + 2*S0cd)-2*Kcd*(S0cc+S0dd-2*S0cd)) rhocd = drho(C,D) Iq = rhocd**2 * Scc return Iq def matrix_form(q, case_num, polys, Kab=0., Kac=0., Kad=0., Kbc=0., Kbd=0., Kcd=0.): if case_num < 2: C, D = polys A = B = D elif case_num < 5: B, C, D = polys A = D else: A, B, C, D = polys rho = np.matrix([[drho(p, D)] for p in (A,B,C)]) S0aa = S0_ii(q, A) S0bb = S0_ii(q, B) S0cc = S0_ii(q, C) S0ab = S0_ij(q, [A, B]) S0ac = S0_ij(q, [A, B, C]) S0bc = S0_ij(q, [B, C]) if case_num == 4: # No a-c interaction in triblock copolymer S0ac *= 0.0 elif case_num == 9: # No a-c or a-d interaction in tetrablock copolymer S0ac *= 0.0 S0 = np.array([[S0aa, S0ab, S0ac], [S0ab, S0bb, S0bc], [S0ac, S0bc, S0cc]]) S0dd = S0_ii(q, D) vaa = 1./S0dd - 2*Kad vbb = 1./S0dd - 2*Kbd vcc = 1./S0dd - 2*Kcd vab = 1./S0dd + Kab - Kad - Kbd vac = 1./S0dd + Kac - Kad - Kcd vbc = 1./S0dd + Kbc - Kbd - Kcd v = np.array([[vaa, vab, vac], [vab, vbb, vbc], [vac, vbc, vcc]]) Iq = np.empty_like(q) for k, qk in enumerate(q): S0_k = S0[:,:,k].M v_k = v[:,:,k].M S_k = np.linalg.inv(1 + S0_k*v_k)*S0_k Iq[k] = rho.T * S_k * rho def build_pars(case_num, polys, **interactions): def set_poly(x, poly): pars["N"+x] = poly.n pars["Phi"+x] = poly.phi pars["v"+x] = poly.v pars["b"+x] = poly.a pars["L"+x] = poly.b pars = interactions.copy() pars["case_num"] = case_num polys = list(reversed(polys)) if len(polys) >= 4: set_poly("a",polys[3]) if len(polys) >= 3: set_poly("b",polys[2]) if len(polys) >= 2: set_poly("c",polys[1]) if len(polys) >= 1: set_poly("d",polys[0]) return pars def sasmodels_rpa(q, pars): from sasmodels.models import rpa from sasmodels.core import load_model from sasmodels.direct_model import DirectModel from sasmodels.data import empty_data1D data = empty_data1D(q, resolution=0.0) model = load_model(rpa, dtype="double", platform="dll") #model = load_model(rpa, dtype="single", platform="ocl") M = DirectModel(data, model) return M(**pars) def sasview_rpa(q, pars): from sasmodels.models import rpa from sasmodels.compare import eval_sasview from sasmodels.data import empty_data1D data = empty_data1D(q, resolution=0.0) M = eval_sasview(rpa, data) return M(**pars) def demo(): import sys case_num = 0 if len(sys.argv) < 2 else int(sys.argv[1]) B = Polymer(n=525,phi=0.57,v=97.5,b=-4.99,a=8) C = Polymer(n=525,phi=0.57,v=97.5,b=-4.99,a=8) D = Polymer(n=1105,phi=0.43,v=81.9,b=53.1,a=2) q = np.logspace(-4,-1,400) #q = np.array([0.1]) Kab=Kac=Kad=0.0 Kcd = 0.0106*0.0035 - 1.84e-5 Kbd = Kcd + 2e-4 Kbc = (Kcd + 1e-4)*0.5 K = dict(Kab=Kab,Kac=Kac,Kad=Kad,Kbc=Kbc,Kbd=Kbd,Kcd=Kcd) if case_num == 0: Iq = binary_blend(q, C, D, Kcd) elif case_num == 1: Iq = diblock_copolymer(q, C, D, Kcd) elif case_num == 2: Iq = ternary_blend(q, B, C, D, Kbc, Kbd, Kcd) else: raise ValueError("Case %d not implmented"%case_num) pars = build_pars(case_num, [B, C, D], **K) print "eval sasmodels" Iq_sasmodels = sasmodels_rpa(q, pars) print "eval sasview" Iq_sasview = sasview_rpa(q, pars) print 1./Iq[0], 1./Iq_sasmodels[0], 1./Iq_sasview[0] #return import pylab pylab.subplot(121) pylab.loglog(q, Iq, label='direct') pylab.loglog(q, Iq_sasmodels, label='sasmodels') pylab.loglog(q, Iq_sasview, label='sasview') pylab.legend() pylab.subplot(122) pylab.loglog(q, abs(Iq_sasview - Iq_sasmodels)/Iq_sasmodels, label='sasview-sasmodels') pylab.loglog(q, abs(Iq_sasmodels - Iq)/Iq, label='sasmodels-direct') pylab.legend() pylab.show() if __name__ == "__main__": demo() sasmodels/extra/000077500000000000000000000000001317715334700142065ustar00rootroot00000000000000sasmodels/extra/build_linux.sh000077500000000000000000000007421317715334700170660ustar00rootroot00000000000000#!/bin/bash test -z $WORKSPACE && WORKSPACE=. EASY_INSTALL=${EASY_INSTALL:-`which easy_install`} cd $WORKSPACE if [ ! -d "utils" ]; then mkdir utils fi export PYTHONPATH=$WORKSPACE/utils:$PYTHONPATH "$EASY_INSTALL" -d "$WORKSPACE/utils" unittest-xml-reporting pylint # Run tests STATUS=0 python -m sasmodels.model_test opencl_and_dll all || STATUS=$? python -m sasmodels.resolution || STATUS=$? # Run lint python extra/run-pylint.py > pylint_violations.txt exit $STATUS sasmodels/extra/pylint.rc000066400000000000000000000302441317715334700160560ustar00rootroot00000000000000[MASTER] # Specify a configuration file. #rcfile= # Python code to execute, usually for sys.path manipulation such as # pygtk.require(). #init-hook='import os, sys; sys.path.extend([os.getcwd(),os.path.join(os.getcwd(),"extra")])' init-hook='import sys; sys.path.append('extra') # Profiled execution. #profile=no # Add files or directories to the blacklist. They should be base names, not # paths. ignore=CVS # Pickle collected data for later comparisons. persistent=yes # List of plugins (as comma separated values of python modules names) to load, # usually to register additional checkers. load-plugins=pylint_numpy,pylint_pyopencl # Use multiple processes to speed up Pylint. #jobs=4 # Allow loading of arbitrary C extensions. Extensions are imported into the # active Python interpreter and may run arbitrary code. unsafe-load-any-extension=no # A comma-separated list of package or module names from where C extensions may # be loaded. Extensions are loading into the active Python interpreter and may # run arbitrary code extension-pkg-whitelist= [MESSAGES CONTROL] # Only show warnings with the listed confidence levels. Leave empty to show # all. Valid levels: HIGH, INFERENCE, INFERENCE_FAILURE, UNDEFINED confidence= # Enable the message, report, category or checker with the given id(s). You can # either give multiple identifier separated by comma (,) or put this option # multiple time. See also the "--disable" option for examples. #enable= # Disable the message, report, category or checker with the given id(s). You # can either give multiple identifiers separated by comma (,) or put this # option multiple times (only on the command line, not in the configuration # file where it should appear only once).You can also use "--disable=all" to # disable everything first and then reenable specific checks. For example, if # you want to run only the similarities checker, you can use "--disable=all # --enable=similarities". If you want to run only the classes checker, but have # no Warning level messages displayed, use"--disable=all --enable=classes # --disable=W" #disable=W0702,E1608,W1627,E1601,E1603,E1602,E1605,E1604,E1607,E1606,W1621,W1620,W1623,W1622,W1625,W1624,W1609,W1626,W1607,W1606,W1605,W1604,W1603,W1602,W1601,I0021,I0020,W1618,W1619,W1630,W1631,W1610,W1611,W1612,W1613,W1614,W1615,W1616,W1617,W1632,W1633,W0704,W1628,W1629,W1608 # Disable the message(s) with the given id(s). # http://pylint-messages.wikidot.com/all-codes disable= multiple-statements, bare-except, broad-except, star-args, unbalanced-tuple-unpacking, locally-enabled, locally-disabled, [REPORTS] # Set the output format. Available formats are text, parseable, colorized, msvs # (visual studio) and html. You can also give a reporter class, eg # mypackage.mymodule.MyReporterClass. output-format=text # Put messages in a separate file for each module / package specified on the # command line instead of printing them on stdout. Reports (if any) will be # written in a file name "pylint_global.[txt|html]". files-output=no # Tells whether to display a full report or only the messages reports=yes # Python expression which should return a note less than 10 (10 is the highest # note). You have access to the variables errors warning, statement which # respectively contain the number of errors / warnings messages and the total # number of statements analyzed. This is used by the global evaluation report # (RP0004). evaluation=10.0 - ((float(5 * error + warning + refactor + convention) / statement) * 10) # Add a comment according to your evaluation note. This is used by the global # evaluation report (RP0004). #comment=no # Template used to display messages. This is a python new-style format string # used to format the message information. See doc for all details #msg-template= [BASIC] # Required attributes for module, separated by a comma #required-attributes= # List of builtins function names that should not be used, separated by a comma bad-functions=map,filter,input # Good variable names which should always be accepted, separated by a comma good-names=_, input, id, h, i, j, k, n, p, v, w, x, y, z, q, qx, qy, qz, Q, Qx, Qy, Qz, dt, dx, dy, dz, dq, Iq, dIq, Iqxy, Iq_calc, ER, call_ER, VR, call_VR, Rmax, SElength, # Bad variable names which should always be refused, separated by a comma bad-names=foo,bar,baz,toto,tutu,tata # Colon-delimited sets of names that determine each other's naming style when # the name regexes allow several styles. name-group= # Include a hint for the correct naming format with invalid-name include-naming-hint=no # Regular expression matching correct function names function-rgx=[a-z_][a-z0-9_]{2,30}([123]D)?$ # Naming hint for function names function-name-hint=[a-z_][a-z0-9_]{2,30}$ # Regular expression matching correct variable names variable-rgx=[a-z_][a-z0-9_{2D}{1D}]{2,30}$ # Naming hint for variable names variable-name-hint=[a-z_][a-z0-9_]{2,30}$ # Regular expression matching correct constant names const-rgx=(([A-Za-z_][A-Za-z0-9_]*)|(__.*__))$ # Naming hint for constant names const-name-hint=(([A-Z_][A-Z0-9_]*)|(__.*__))$ # Regular expression matching correct attribute names attr-rgx=[a-z_][a-z0-9__{2D}{1D}]{2,30}$ # Naming hint for attribute names attr-name-hint=[a-z_][a-z0-9_]{2,30}$ # Regular expression matching correct argument names argument-rgx=[a-z_][a-z0-9_]{2,30}$ # Naming hint for argument names argument-name-hint=[a-z_][a-z0-9_]{2,30}$ # Regular expression matching correct class attribute names class-attribute-rgx=([A-Za-z_][A-Za-z0-9_]{2,30}|(__.*__))$ # Naming hint for class attribute names class-attribute-name-hint=([A-Za-z_][A-Za-z0-9_]{2,30}|(__.*__))$ # Regular expression matching correct inline iteration names inlinevar-rgx=[A-Za-z_][A-Za-z0-9_]*$ # Naming hint for inline iteration names inlinevar-name-hint=[A-Za-z_][A-Za-z0-9_]*$ # Regular expression matching correct class names class-rgx=[A-Z_][a-zA-Z0-9]+$ # Naming hint for class names class-name-hint=[A-Z_][a-zA-Z0-9]+$ # Regular expression matching correct module names module-rgx=(([a-z_][a-z0-9_]*)|([A-Z][a-zA-Z0-9]+))$ # Naming hint for module names module-name-hint=(([a-z_][a-z0-9_]*)|([A-Z][a-zA-Z0-9]+))$ # Regular expression matching correct method names method-rgx=[a-z_][a-z0-9_]{2,30}$ # Naming hint for method names method-name-hint=[a-z_][a-z0-9_]{2,30}$ # Regular expression which should only match function or class names that do # not require a docstring. #no-docstring-rgx=__.*__ no-docstring-rgx=_.* # Minimum line length for functions/classes that require docstrings, shorter # ones are exempt. docstring-min-length=-1 [FORMAT] # Maximum number of characters on a single line. max-line-length=100 # Regexp for a line that is allowed to be longer than the limit. #ignore-long-lines=^\s*(# )??$ # No comma in the last forty characters ignore-long-lines=([^-,+*/]{40},?|[^"]{40}")$ # Allow the body of an if to be on the same line as the test if there is no # else. single-line-if-stmt=no # List of optional constructs for which whitespace checking is disabled no-space-check=trailing-comma,dict-separator # Maximum number of lines in a module max-module-lines=1000 # String used as indentation unit. This is usually " " (4 spaces) or "\t" (1 # tab). indent-string=' ' # Number of spaces of indent required inside a hanging or continued line. indent-after-paren=4 # Expected format of line ending, e.g. empty (any line ending), LF or CRLF. expected-line-ending-format= [LOGGING] # Logging modules to check that the string format arguments are in logging # function parameter format logging-modules=logging [MISCELLANEOUS] # List of note tags to take in consideration, separated by a comma. notes=FIXME,XXX,TODO [SIMILARITIES] # Minimum lines number of a similarity. min-similarity-lines=4 # Ignore comments when computing similarities. ignore-comments=yes # Ignore docstrings when computing similarities. ignore-docstrings=yes # Ignore imports when computing similarities. ignore-imports=no [SPELLING] # Spelling dictionary name. Available dictionaries: none. To make it working # install python-enchant package. spelling-dict= # List of comma separated words that should not be checked. spelling-ignore-words= # A path to a file that contains private dictionary; one word per line. spelling-private-dict-file= # Tells whether to store unknown words to indicated private dictionary in # --spelling-private-dict-file option instead of raising a message. spelling-store-unknown-words=no [TYPECHECK] # Tells whether missing members accessed in mixin class should be ignored. A # mixin class is detected if its name ends with "mixin" (case insensitive). ignore-mixin-members=yes # List of module names for which member attributes should not be checked # (useful for modules/projects where namespaces are manipulated during runtime # and thus existing member attributes cannot be deduced by static analysis ignored-modules=numpy,np,numpy.random, bumps,sas, # List of classes names for which member attributes should not be checked # (useful for classes with attributes dynamically set). ignored-classes=SQLObject # When zope mode is activated, add a predefined set of Zope acquired attributes # to generated-members. #zope=no # List of members which are set dynamically and missed by pylint inference # system, and so shouldn't trigger E0201 when accessed. Python regular # expressions are accepted. generated-members=REQUEST,acl_users,aq_parent [VARIABLES] # Tells whether we should check for unused import in __init__ files. init-import=no # A regular expression matching the name of dummy variables (i.e. expectedly # not used). dummy-variables-rgx=_$|dummy # List of additional names supposed to be defined in builtins. Remember that # you should avoid to define new builtins when possible. additional-builtins= # List of strings which can identify a callback function by name. A callback # name must start or end with one of those strings. callbacks=cb_,_cb [CLASSES] # List of interface methods to ignore, separated by a comma. This is used for # instance to not check methods defines in Zope's Interface base class. #ignore-iface-methods=isImplementedBy,deferred,extends,names,namesAndDescriptions,queryDescriptionFor,getBases,getDescriptionFor,getDoc,getName,getTaggedValue,getTaggedValueTags,isEqualOrExtendedBy,setTaggedValue,isImplementedByInstancesOf,adaptWith,is_implemented_by # List of method names used to declare (i.e. assign) instance attributes. defining-attr-methods=__init__,__new__,setUp # List of valid names for the first argument in a class method. valid-classmethod-first-arg=cls # List of valid names for the first argument in a metaclass class method. valid-metaclass-classmethod-first-arg=mcs # List of member names, which should be excluded from the protected access # warning. exclude-protected=_asdict,_fields,_replace,_source,_make [DESIGN] # Maximum number of arguments for function / method max-args=15 # Argument names that match this expression will be ignored. Default to name # with leading underscore ignored-argument-names=_.* # Maximum number of locals for function / method body max-locals=25 # Maximum number of return / yield for function / method body max-returns=6 # Maximum number of branch for function / method body max-branches=12 # Maximum number of statements in function / method body max-statements=50 # Maximum number of parents for a class (see R0901). max-parents=7 # Maximum number of attributes for a class (see R0902). max-attributes=7 # Minimum number of public methods for a class (see R0903). min-public-methods=0 # Maximum number of public methods for a class (see R0904). max-public-methods=20 [IMPORTS] # Deprecated modules which should not be used, separated by a comma deprecated-modules=regsub,TERMIOS,Bastion,rexec # Create a graph of every (i.e. internal and external) dependencies in the # given file (report RP0402 must not be disabled) import-graph= # Create a graph of external dependencies in the given file (report RP0402 must # not be disabled) ext-import-graph= # Create a graph of internal dependencies in the given file (report RP0402 must # not be disabled) int-import-graph= [EXCEPTIONS] # Exceptions that will emit a warning when being caught. Defaults to # "Exception" overgeneral-exceptions=Exception sasmodels/extra/pylint_numpy.py000066400000000000000000000006631317715334700173340ustar00rootroot00000000000000from astroid import MANAGER from astroid import nodes def register(linter): MANAGER.register_transform(nodes.Module, transform) def transform(module): #print("processing",module.name) if module.name.startswith('numpy'): if module.name == 'numpy': import numpy elif module.name == 'numpy.random': import numpy.random from numpy.random import seed, get_state, set_state sasmodels/extra/pylint_pyopencl.py000066400000000000000000000004321317715334700200070ustar00rootroot00000000000000from astroid import MANAGER from astroid import nodes def register(linter): MANAGER.register_transform(nodes.Module, transform) def transform(module): #print("processing",module.name) if module.name == 'pyopencl': import pyopencl import pyopencl as cl sasmodels/extra/run-pylint.py000077500000000000000000000014241317715334700167050ustar00rootroot00000000000000#!/usr/bin/env python import os import sys from os.path import dirname, join as joinpath, abspath def main(): extra = abspath(dirname(__file__)) root = abspath(joinpath(extra, '..')) envpath = os.environ.get('PYTHONPATH',None) path = [envpath] if envpath else [] path.append(extra) #bumps = abspath(joinpath(root, "..", "bumps")) #periodictable = abspath(joinpath(root, "..", "periodictable")) #sasview = abspath(joinpath(root, "..", "sasview", "src")) #path.extend((bumps, periodictable, sasview)) os.environ['PYTHONPATH'] = ':'.join(path) # Run the lint command cmd = "pylint --rcfile extra/pylint.rc -f parseable sasmodels" os.chdir(root) status = os.system(cmd) sys.exit(status) if __name__ == "__main__": main() sasmodels/multi_compare.bat000066400000000000000000000006041317715334700164130ustar00rootroot00000000000000@echo off rem === Set the python path to include sasview for /D %%i in (..\sasview\build\lib*) do set SASVIEW=%%i set PYTHONPATH=..\bumps;../periodictable;%SASVIEW% rem echo PYTHONPATH=%PYTHONPATH% rem === Set the pyopencl control parameters rem set PYOPENCL_COMPILER_OUTPUT=1 rem set PYOPENCL_CTX=0 rem === Set OpenMP or not rem set SAS_OPENMP=1 python -m sasmodels.compare_many %* sasmodels/multi_compare.sh000077500000000000000000000013141317715334700162610ustar00rootroot00000000000000#!/bin/bash sasview=( ../sasview/build/lib.* ) sep=$(python -c "import os;print(os.pathsep)") PYTHONPATH=../bumps${sep}../periodictable${sep}$sasview export PYTHONPATH #echo PYTHONPATH=$PYTHONPATH #PYOPENCL_COMPILER_OUTPUT=1; export PYOPENCL_COMPILER_OUTPUT #PYOPENCL_CTX=${CTX:-1}; export PYOPENCL_CTX #SAS_OPENMP=1; export SAS_OPENMP python -m sasmodels.compare_many $* #for dim in 1d100 2d32; do # python -m sasmodels.compare_many all 100 $dim 0 > ${dim}_poly_0.csv # python -m sasmodels.compare_many all 100 $dim 1e-5 > ${dim}_poly_1e-5.csv # python -m sasmodels.compare_many all 100 $dim 1e-3 > ${dim}_poly_1e-3.csv # python -m sasmodels.compare_many all 100 $dim mono > ${dim}_mono.csv #done sasmodels/sascomp000077500000000000000000000012711317715334700144570ustar00rootroot00000000000000#!/usr/bin/env python import sys import os import glob import logging logging.basicConfig(level=logging.INFO) def main(): sasmodels = os.path.dirname(os.path.realpath(__file__)) root = os.path.dirname(sasmodels) sasview=glob.glob(os.path.join(root, 'sasview', 'build', 'lib*' )) sys.path.insert(0, os.path.join(root, 'bumps')) sys.path.insert(0, os.path.join(root, 'periodictable')) sys.path.insert(0, os.path.join(root, 'tinycc', 'build', 'lib')) if sasview: # glob returns a list sys.path.insert(0, sasview[0]) sys.path.insert(0, sasmodels) import sasmodels.compare sasmodels.compare.main(*sys.argv[1:]) if __name__ == "__main__": main() sasmodels/sasmodels/000077500000000000000000000000001317715334700150555ustar00rootroot00000000000000sasmodels/sasmodels/__init__.py000066400000000000000000000034021317715334700171650ustar00rootroot00000000000000""" sasmodels ========= **sasmodels** is a package containing models for small angle neutron and xray scattering. Models supported are the one dimensional circular average and two dimensional oriented patterns. As well as the form factor calculations for the individual shapes **sasmodels** also provides automatic shape polydispersity, angular dispersion and resolution convolution. SESANS patterns can be computed for any model. Models can be written in python or in C. C models can run on the GPU if OpenCL drivers are available. See :mod:`generate` for details on defining new models. """ __version__ = "0.97" def data_files(): """ Return the data files to be installed with the package. The format is a list of (directory, [files...]) pairs which can be used directly in setup(...,data_files=...) for setup.py. """ from os.path import join as joinpath import glob from .generate import EXTERNAL_DIR, DATA_PATH def _expand_patterns(path, patterns): target_path = joinpath(EXTERNAL_DIR, *path) source_path = joinpath(DATA_PATH, *path) files = [] for p in patterns: files.extend(glob.glob(joinpath(source_path, p))) return target_path, files # Place the source for the model tree in the distribution. Minimally we # need the c and cl files for running on OpenCL. Need the py files so # users can easily copy existing models. Need the img files so that we # can build model docs on the fly, including images. return_list = [ _expand_patterns([], ['*.c', '*.cl']), _expand_patterns(['models'], ['*.py', '*.c']), _expand_patterns(['models', 'lib'], ['*.c']), _expand_patterns(['models', 'img'], ['*.*']), ] return return_list sasmodels/sasmodels/alignment.py000066400000000000000000000027241317715334700174120ustar00rootroot00000000000000""" GPU data alignment. Some web sites say that maximizing performance for OpenCL code requires aligning data on certain memory boundaries. The following functions provide this service: :func:`align_data` aligns an existing array, returning a new array of the correct alignment. :func:`align_empty` to create an empty array of the correct alignment. Set alignment to :func:`gpu.environment()` attribute *boundary*. Note: This code is unused. So far, tests have not demonstrated any improvement from forcing correct alignment. The tests should be repeated with arrays forced away from the target boundaries to decide whether it is really required. """ import numpy as np # type: ignore def align_empty(shape, dtype, alignment=128): """ Return an empty array aligned on the alignment boundary. """ size = np.prod(shape) dtype = np.dtype(dtype) # allocate array with extra space for alignment extra = alignment//dtype.itemsize - 1 result = np.empty(size+extra, dtype) # build a view into allocated array which starts on a boundary offset = (result.ctypes.data%alignment)//dtype.itemsize view = np.reshape(result[offset:offset+size], shape) return view def align_data(x, dtype, alignment=128): """ Return a copy of an array on the alignment boundary. """ # if x is contiguous, aligned, and of the correct type then just return x view = align_empty(x.shape, dtype, alignment=alignment) view[:] = x return view sasmodels/sasmodels/bumps_model.py000066400000000000000000000177261317715334700177520ustar00rootroot00000000000000""" Wrap sasmodels for direct use by bumps. :class:`Model` is a wrapper for the sasmodels kernel which defines a bumps *Parameter* box for each kernel parameter. *Model* accepts keyword arguments to set the initial value for each parameter. :class:`Experiment` combines the *Model* function with a data file loaded by the sasview data loader. *Experiment* takes a *cutoff* parameter controlling how far the polydispersity integral extends. """ from __future__ import print_function __all__ = ["Model", "Experiment"] import numpy as np # type: ignore from .data import plot_theory from .direct_model import DataMixin try: from typing import Dict, Union, Tuple, Any from .data import Data1D, Data2D from .kernel import KernelModel from .modelinfo import ModelInfo Data = Union[Data1D, Data2D] except ImportError: pass try: # Optional import. This allows the doc builder and nosetests to run even # when bumps is not on the path. from bumps.names import Parameter # type: ignore except ImportError: pass def create_parameters(model_info, **kwargs): # type: (ModelInfo, **Union[float, str, Parameter]) -> Tuple[Dict[str, Parameter], Dict[str, str]] """ Generate Bumps parameters from the model info. *model_info* is returned from :func:`generate.model_info` on the model definition module. Any additional *key=value* pairs are initial values for the parameters to the models. Uninitialized parameters will use the model default value. The value can be a float, a bumps parameter, or in the case of the distribution type parameter, a string. Returns a dictionary of *{name: Parameter}* containing the bumps parameters for each model parameter, and a dictionary of *{name: str}* containing the polydispersity distribution types. """ pars = {} # type: Dict[str, Parameter] pd_types = {} # type: Dict[str, str] for p in model_info.parameters.call_parameters: value = kwargs.pop(p.name, p.default) pars[p.name] = Parameter.default(value, name=p.name, limits=p.limits) if p.polydisperse: for part, default, limits in [ ('_pd', 0., pars[p.name].limits), ('_pd_n', 35., (0, 1000)), ('_pd_nsigma', 3., (0, 10)), ]: name = p.name + part value = kwargs.pop(name, default) pars[name] = Parameter.default(value, name=name, limits=limits) name = p.name + '_pd_type' pd_types[name] = str(kwargs.pop(name, 'gaussian')) if kwargs: # args not corresponding to parameters raise TypeError("unexpected parameters: %s" % (", ".join(sorted(kwargs.keys())))) return pars, pd_types class Model(object): """ Bumps wrapper for a SAS model. *model* is a runnable module as returned from :func:`core.load_model`. *cutoff* is the polydispersity weight cutoff. Any additional *key=value* pairs are model dependent parameters. """ def __init__(self, model, **kwargs): # type: (KernelModel, **Dict[str, Union[float, Parameter]]) -> None self.sasmodel = model pars, pd_types = create_parameters(model.info, **kwargs) for k, v in pars.items(): setattr(self, k, v) for k, v in pd_types.items(): setattr(self, k, v) self._parameter_names = list(pars.keys()) self._pd_type_names = list(pd_types.keys()) def parameters(self): # type: () -> Dict[str, Parameter] """ Return a dictionary of parameters objects for the parameters, excluding polydispersity distribution type. """ return dict((k, getattr(self, k)) for k in self._parameter_names) def state(self): # type: () -> Dict[str, Union[Parameter, str]] """ Return a dictionary of current values for all the parameters, including polydispersity distribution type. """ pars = dict((k, getattr(self, k).value) for k in self._parameter_names) pars.update((k, getattr(self, k)) for k in self._pd_type_names) return pars class Experiment(DataMixin): r""" Bumps wrapper for a SAS experiment. *data* is a :class:`data.Data1D`, :class:`data.Data2D` or :class:`data.Sesans` object. Use :func:`data.empty_data1D` or :func:`data.empty_data2D` to define $q, \Delta q$ calculation points for displaying the SANS curve when there is no measured data. *model* is a :class:`Model` object. *cutoff* is the integration cutoff, which avoids computing the the SAS model where the polydispersity weight is low. The resulting model can be used directly in a Bumps FitProblem call. """ _cache = None # type: Dict[str, np.ndarray] def __init__(self, data, model, cutoff=1e-5, name=None): # type: (Data, Model, float) -> None # remember inputs so we can inspect from outside self.name = data.filename if name is None else name self.model = model self.cutoff = cutoff self._interpret_data(data, model.sasmodel) self._cache = {} def update(self): # type: () -> None """ Call when model parameters have changed and theory needs to be recalculated. """ self._cache.clear() def numpoints(self): # type: () -> float """ Return the number of data points """ return len(self.Iq) def parameters(self): # type: () -> Dict[str, Parameter] """ Return a dictionary of parameters """ return self.model.parameters() def theory(self): # type: () -> np.ndarray """ Return the theory corresponding to the model parameters. This method uses lazy evaluation, and requires model.update() to be called when the parameters have changed. """ if 'theory' not in self._cache: pars = self.model.state() self._cache['theory'] = self._calc_theory(pars, cutoff=self.cutoff) return self._cache['theory'] def residuals(self): # type: () -> np.ndarray """ Return theory minus data normalized by uncertainty. """ #if np.any(self.err ==0): print("zeros in err") return (self.theory() - self.Iq) / self.dIq def nllf(self): # type: () -> float """ Return the negative log likelihood of seeing data given the model parameters, up to a normalizing constant which depends on the data uncertainty. """ delta = self.residuals() #if np.any(np.isnan(R)): print("NaN in residuals") return 0.5 * np.sum(delta**2) #def __call__(self): # return 2 * self.nllf() / self.dof def plot(self, view='log'): # type: (str) -> None """ Plot the data and residuals. """ data, theory, resid = self._data, self.theory(), self.residuals() # TODO: hack to display oriented usans 2-D pattern Iq_calc = self.Iq_calc if isinstance(self.Iq_calc, tuple) else None plot_theory(data, theory, resid, view, Iq_calc=Iq_calc) def simulate_data(self, noise=None): # type: (float) -> None """ Generate simulated data. """ Iq = self.theory() self._set_data(Iq, noise) def save(self, basename): # type: (str) -> None """ Save the model parameters and data into a file. Not Implemented. """ if self.data_type == "sesans": np.savetxt(basename+".dat", np.array([self._data.x, self.theory()]).T) def __getstate__(self): # type: () -> Dict[str, Any] # Can't pickle gpu functions, so instead make them lazy state = self.__dict__.copy() state['_kernel'] = None return state def __setstate__(self, state): # type: (Dict[str, Any]) -> None # pylint: disable=attribute-defined-outside-init self.__dict__ = state sasmodels/sasmodels/compare.py000077500000000000000000001511251317715334700170650ustar00rootroot00000000000000#!/usr/bin/env python # -*- coding: utf-8 -*- """ Program to compare models using different compute engines. This program lets you compare results between OpenCL and DLL versions of the code and between precision (half, fast, single, double, quad), where fast precision is single precision using native functions for trig, etc., and may not be completely IEEE 754 compliant. This lets make sure that the model calculations are stable, or if you need to tag the model as double precision only. Run using ./compare.sh (Linux, Mac) or compare.bat (Windows) in the sasmodels root to see the command line options. Note that there is no way within sasmodels to select between an OpenCL CPU device and a GPU device, but you can do so by setting the PYOPENCL_CTX environment variable ahead of time. Start a python interpreter and enter:: import pyopencl as cl cl.create_some_context() This will prompt you to select from the available OpenCL devices and tell you which string to use for the PYOPENCL_CTX variable. On Windows you will need to remove the quotes. """ from __future__ import print_function import sys import os import math import datetime import traceback import re import numpy as np # type: ignore from . import core from . import kerneldll from . import exception from .data import plot_theory, empty_data1D, empty_data2D, load_data from .direct_model import DirectModel from .convert import revert_name, revert_pars, constrain_new_to_old from .generate import FLOAT_RE try: from typing import Optional, Dict, Any, Callable, Tuple except Exception: pass else: from .modelinfo import ModelInfo, Parameter, ParameterSet from .data import Data Calculator = Callable[[float], np.ndarray] USAGE = """ usage: sascomp model [options...] [key=val] Generate and compare SAS models. If a single model is specified it shows a plot of that model. Different models can be compared, or the same model with different parameters. The same model with the same parameters can be compared with different calculation engines to see the effects of precision on the resultant values. model or model1,model2 are the names of the models to compare (see below). Options (* for default): === data generation === -data="path" uses q, dq from the data file -noise=0 sets the measurement error dI/I -res=0 sets the resolution width dQ/Q if calculating with resolution -lowq*/-midq/-highq/-exq use q values up to 0.05, 0.2, 1.0, 10.0 -q=min:max alternative specification of qrange -nq=128 sets the number of Q points in the data set -1d*/-2d computes 1d or 2d data -zero indicates that q=0 should be included === model parameters === -preset*/-random[=seed] preset or random parameters -sets=n generates n random datasets with the seed given by -random=seed -pars/-nopars* prints the parameter set or not -default/-demo* use demo vs default parameters === calculation options === -mono*/-poly force monodisperse or allow polydisperse demo parameters -cutoff=1e-5* cutoff value for including a point in polydispersity -magnetic/-nonmagnetic* suppress magnetism -accuracy=Low accuracy of the resolution calculation Low, Mid, High, Xhigh -neval=1 sets the number of evals for more accurate timing === precision options === -calc=default uses the default calcution precision -single/-double/-half/-fast sets an OpenCL calculation engine -single!/-double!/-quad! sets an OpenMP calculation engine -sasview sets the sasview calculation engine === plotting === -plot*/-noplot plots or suppress the plot of the model -linear/-log*/-q4 intensity scaling on plots -hist/-nohist* plot histogram of relative error -abs/-rel* plot relative or absolute error -title="note" adds note to the plot title, after the model name === output options === -edit starts the parameter explorer -help/-html shows the model docs instead of running the model The interpretation of quad precision depends on architecture, and may vary from 64-bit to 128-bit, with 80-bit floats being common (1e-19 precision). On unix and mac you may need single quotes around the DLL computation engines, such as -calc='single!,double!' since !, is treated as a history expansion request in the shell. Key=value pairs allow you to set specific values for the model parameters. Key=value1,value2 to compare different values of the same parameter. The value can be an expression including other parameters. Items later on the command line override those that appear earlier. Examples: # compare single and double precision calculation for a barbell sascomp barbell -calc=single,double # generate 10 random lorentz models, with seed=27 sascomp lorentz -sets=10 -seed=27 # compare ellipsoid with R = R_polar = R_equatorial to sphere of radius R sascomp sphere,ellipsoid radius_polar=radius radius_equatorial=radius # model timing test requires multiple evals to perform the estimate sascomp pringle -calc=single,double -timing=100,100 -noplot """ # Update docs with command line usage string. This is separate from the usual # doc string so that we can display it at run time if there is an error. # lin __doc__ = (__doc__ # pylint: disable=redefined-builtin + """ Program description ------------------- """ + USAGE) kerneldll.ALLOW_SINGLE_PRECISION_DLLS = True # list of math functions for use in evaluating parameters MATH = dict((k,getattr(math, k)) for k in dir(math) if not k.startswith('_')) # CRUFT python 2.6 if not hasattr(datetime.timedelta, 'total_seconds'): def delay(dt): """Return number date-time delta as number seconds""" return dt.days * 86400 + dt.seconds + 1e-6 * dt.microseconds else: def delay(dt): """Return number date-time delta as number seconds""" return dt.total_seconds() class push_seed(object): """ Set the seed value for the random number generator. When used in a with statement, the random number generator state is restored after the with statement is complete. :Parameters: *seed* : int or array_like, optional Seed for RandomState :Example: Seed can be used directly to set the seed:: >>> from numpy.random import randint >>> push_seed(24) <...push_seed object at...> >>> print(randint(0,1000000,3)) [242082 899 211136] Seed can also be used in a with statement, which sets the random number generator state for the enclosed computations and restores it to the previous state on completion:: >>> with push_seed(24): ... print(randint(0,1000000,3)) [242082 899 211136] Using nested contexts, we can demonstrate that state is indeed restored after the block completes:: >>> with push_seed(24): ... print(randint(0,1000000)) ... with push_seed(24): ... print(randint(0,1000000,3)) ... print(randint(0,1000000)) 242082 [242082 899 211136] 899 The restore step is protected against exceptions in the block:: >>> with push_seed(24): ... print(randint(0,1000000)) ... try: ... with push_seed(24): ... print(randint(0,1000000,3)) ... raise Exception() ... except Exception: ... print("Exception raised") ... print(randint(0,1000000)) 242082 [242082 899 211136] Exception raised 899 """ def __init__(self, seed=None): # type: (Optional[int]) -> None self._state = np.random.get_state() np.random.seed(seed) def __enter__(self): # type: () -> None pass def __exit__(self, exc_type, exc_value, traceback): # type: (Any, BaseException, Any) -> None # TODO: better typing for __exit__ method np.random.set_state(self._state) def tic(): # type: () -> Callable[[], float] """ Timer function. Use "toc=tic()" to start the clock and "toc()" to measure a time interval. """ then = datetime.datetime.now() return lambda: delay(datetime.datetime.now() - then) def set_beam_stop(data, radius, outer=None): # type: (Data, float, float) -> None """ Add a beam stop of the given *radius*. If *outer*, make an annulus. Note: this function does not require sasview """ if hasattr(data, 'qx_data'): q = np.sqrt(data.qx_data**2 + data.qy_data**2) data.mask = (q < radius) if outer is not None: data.mask |= (q >= outer) else: data.mask = (data.x < radius) if outer is not None: data.mask |= (data.x >= outer) def parameter_range(p, v): # type: (str, float) -> Tuple[float, float] """ Choose a parameter range based on parameter name and initial value. """ # process the polydispersity options if p.endswith('_pd_n'): return 0., 100. elif p.endswith('_pd_nsigma'): return 0., 5. elif p.endswith('_pd_type'): raise ValueError("Cannot return a range for a string value") elif any(s in p for s in ('theta', 'phi', 'psi')): # orientation in [-180,180], orientation pd in [0,45] if p.endswith('_pd'): return 0., 45. else: return -180., 180. elif p.endswith('_pd'): return 0., 1. elif 'sld' in p: return -0.5, 10. elif p == 'background': return 0., 10. elif p == 'scale': return 0., 1.e3 elif v < 0.: return 2.*v, -2.*v else: return 0., (2.*v if v > 0. else 1.) def _randomize_one(model_info, name, value): # type: (ModelInfo, str, float) -> float # type: (ModelInfo, str, str) -> str """ Randomize a single parameter. """ # Set the amount of polydispersity/angular dispersion, but by default pd_n # is zero so there is no polydispersity. This allows us to turn on/off # pd by setting pd_n, and still have randomly generated values if name.endswith('_pd'): par = model_info.parameters[name[:-3]] if par.type == 'orientation': # Let oriention variation peak around 13 degrees; 95% < 42 degrees return 180*np.random.beta(2.5, 20) else: # Let polydispersity peak around 15%; 95% < 0.4; max=100% return np.random.beta(1.5, 7) # pd is selected globally rather than per parameter, so set to 0 for no pd # In particular, when multiple pd dimensions, want to decrease the number # of points per dimension for faster computation if name.endswith('_pd_n'): return 0 # Don't mess with distribution type for now if name.endswith('_pd_type'): return 'gaussian' # type-dependent value of number of sigmas; for gaussian use 3. if name.endswith('_pd_nsigma'): return 3. # background in the range [0.01, 1] if name == 'background': return 10**np.random.uniform(-2, 0) # scale defaults to 0.1% to 30% volume fraction if name == 'scale': return 10**np.random.uniform(-3, -0.5) # If it is a list of choices, pick one at random with equal probability # In practice, the model specific random generator will override. par = model_info.parameters[name] if len(par.limits) > 2: # choice list return np.random.randint(len(par.limits)) # If it is a fixed range, pick from it with equal probability. # For logarithmic ranges, the model will have to override. if np.isfinite(par.limits).all(): return np.random.uniform(*par.limits) # If the paramter is marked as an sld use the range of neutron slds # TODO: ought to randomly contrast match a pair of SLDs if par.type == 'sld': return np.random.uniform(-0.5, 12) # Limit magnetic SLDs to a smaller range, from zero to iron=5/A^2 if par.name.startswith('M0:'): return np.random.uniform(0, 5) # Guess at the random length/radius/thickness. In practice, all models # are going to set their own reasonable ranges. if par.type == 'volume': if ('length' in par.name or 'radius' in par.name or 'thick' in par.name): return 10**np.random.uniform(2, 4) # In the absence of any other info, select a value in [0, 2v], or # [-2|v|, 2|v|] if v is negative, or [0, 1] if v is zero. Mostly the # model random parameter generators will override this default. low, high = parameter_range(par.name, value) limits = (max(par.limits[0], low), min(par.limits[1], high)) return np.random.uniform(*limits) def _random_pd(model_info, pars): pd = [p for p in model_info.parameters.kernel_parameters if p.polydisperse] pd_volume = [] pd_oriented = [] for p in pd: if p.type == 'orientation': pd_oriented.append(p.name) elif p.length_control is not None: n = int(pars.get(p.length_control, 1) + 0.5) pd_volume.extend(p.name+str(k+1) for k in range(n)) elif p.length > 1: pd_volume.extend(p.name+str(k+1) for k in range(p.length)) else: pd_volume.append(p.name) u = np.random.rand() n = len(pd_volume) if u < 0.01 or n < 1: pass # 1% chance of no polydispersity elif u < 0.86 or n < 2: pars[np.random.choice(pd_volume)+"_pd_n"] = 35 elif u < 0.99 or n < 3: choices = np.random.choice(len(pd_volume), size=2) pars[pd_volume[choices[0]]+"_pd_n"] = 25 pars[pd_volume[choices[1]]+"_pd_n"] = 10 else: choices = np.random.choice(len(pd_volume), size=3) pars[pd_volume[choices[0]]+"_pd_n"] = 25 pars[pd_volume[choices[1]]+"_pd_n"] = 10 pars[pd_volume[choices[2]]+"_pd_n"] = 5 if pd_oriented: pars['theta_pd_n'] = 20 if np.random.rand() < 0.1: pars['phi_pd_n'] = 5 if np.random.rand() < 0.1: if any(p.name == 'psi' for p in model_info.parameters.kernel_parameters): #print("generating psi_pd_n") pars['psi_pd_n'] = 5 ## Show selected polydispersity #for name, value in pars.items(): # if name.endswith('_pd_n') and value > 0: # print(name, value, pars.get(name[:-5], 0), pars.get(name[:-2], 0)) def randomize_pars(model_info, pars): # type: (ModelInfo, ParameterSet) -> ParameterSet """ Generate random values for all of the parameters. Valid ranges for the random number generator are guessed from the name of the parameter; this will not account for constraints such as cap radius greater than cylinder radius in the capped_cylinder model, so :func:`constrain_pars` needs to be called afterward.. """ # Note: the sort guarantees order of calls to random number generator random_pars = dict((p, _randomize_one(model_info, p, v)) for p, v in sorted(pars.items())) if model_info.random is not None: random_pars.update(model_info.random()) _random_pd(model_info, random_pars) return random_pars def constrain_pars(model_info, pars): # type: (ModelInfo, ParameterSet) -> None """ Restrict parameters to valid values. This includes model specific code for models such as capped_cylinder which need to support within model constraints (cap radius more than cylinder radius in this case). Warning: this updates the *pars* dictionary in place. """ # TODO: move the model specific code to the individual models name = model_info.id # if it is a product model, then just look at the form factor since # none of the structure factors need any constraints. if '*' in name: name = name.split('*')[0] # Suppress magnetism for python models (not yet implemented) if callable(model_info.Iq): pars.update(suppress_magnetism(pars)) if name == 'barbell': if pars['radius_bell'] < pars['radius']: pars['radius'], pars['radius_bell'] = pars['radius_bell'], pars['radius'] elif name == 'capped_cylinder': if pars['radius_cap'] < pars['radius']: pars['radius'], pars['radius_cap'] = pars['radius_cap'], pars['radius'] elif name == 'guinier': # Limit guinier to an Rg such that Iq > 1e-30 (single precision cutoff) # I(q) = A e^-(Rg^2 q^2/3) > e^-(30 ln 10) # => ln A - (Rg^2 q^2/3) > -30 ln 10 # => Rg^2 q^2/3 < 30 ln 10 + ln A # => Rg < sqrt(90 ln 10 + 3 ln A)/q #q_max = 0.2 # mid q maximum q_max = 1.0 # high q maximum rg_max = np.sqrt(90*np.log(10) + 3*np.log(pars['scale']))/q_max pars['rg'] = min(pars['rg'], rg_max) elif name == 'pearl_necklace': if pars['radius'] < pars['thick_string']: pars['radius'], pars['thick_string'] = pars['thick_string'], pars['radius'] pass elif name == 'rpa': # Make sure phi sums to 1.0 if pars['case_num'] < 2: pars['Phi1'] = 0. pars['Phi2'] = 0. elif pars['case_num'] < 5: pars['Phi1'] = 0. total = sum(pars['Phi'+c] for c in '1234') for c in '1234': pars['Phi'+c] /= total def parlist(model_info, pars, is2d): # type: (ModelInfo, ParameterSet, bool) -> str """ Format the parameter list for printing. """ lines = [] parameters = model_info.parameters magnetic = False magnetic_pars = [] for p in parameters.user_parameters(pars, is2d): if any(p.id.startswith(x) for x in ('M0:', 'mtheta:', 'mphi:')): continue if p.id.startswith('up:'): magnetic_pars.append("%s=%s"%(p.id, pars.get(p.id, p.default))) continue fields = dict( value=pars.get(p.id, p.default), pd=pars.get(p.id+"_pd", 0.), n=int(pars.get(p.id+"_pd_n", 0)), nsigma=pars.get(p.id+"_pd_nsgima", 3.), pdtype=pars.get(p.id+"_pd_type", 'gaussian'), relative_pd=p.relative_pd, M0=pars.get('M0:'+p.id, 0.), mphi=pars.get('mphi:'+p.id, 0.), mtheta=pars.get('mtheta:'+p.id, 0.), ) lines.append(_format_par(p.name, **fields)) magnetic = magnetic or fields['M0'] != 0. if magnetic and magnetic_pars: lines.append(" ".join(magnetic_pars)) return "\n".join(lines) #return "\n".join("%s: %s"%(p, v) for p, v in sorted(pars.items())) def _format_par(name, value=0., pd=0., n=0, nsigma=3., pdtype='gaussian', relative_pd=False, M0=0., mphi=0., mtheta=0.): # type: (str, float, float, int, float, str) -> str line = "%s: %g"%(name, value) if pd != 0. and n != 0: if relative_pd: pd *= value line += " +/- %g (%d points in [-%g,%g] sigma %s)"\ % (pd, n, nsigma, nsigma, pdtype) if M0 != 0.: line += " M0:%.3f mtheta:%.1f mphi:%.1f" % (M0, mtheta, mphi) return line def suppress_pd(pars, suppress=True): # type: (ParameterSet) -> ParameterSet """ If suppress is True complete eliminate polydispersity of the model to test models more quickly. If suppress is False, make sure at least one parameter is polydisperse, setting the first polydispersity parameter to 15% if no polydispersity is given (with no explicit demo parameters given in the model, there will be no default polydispersity). """ pars = pars.copy() #print("pars=", pars) if suppress: for p in pars: if p.endswith("_pd_n"): pars[p] = 0 else: any_pd = False first_pd = None for p in pars: if p.endswith("_pd_n"): pd = pars.get(p[:-2], 0.) any_pd |= (pars[p] != 0 and pd != 0.) if first_pd is None: first_pd = p if not any_pd and first_pd is not None: if pars[first_pd] == 0: pars[first_pd] = 35 if first_pd[:-2] not in pars or pars[first_pd[:-2]] == 0: pars[first_pd[:-2]] = 0.15 return pars def suppress_magnetism(pars, suppress=True): # type: (ParameterSet) -> ParameterSet """ If suppress is True complete eliminate magnetism of the model to test models more quickly. If suppress is False, make sure at least one sld parameter is magnetic, setting the first parameter to have a strong magnetic sld (8/A^2) at 60 degrees (with no explicit demo parameters given in the model, there will be no default magnetism). """ pars = pars.copy() if suppress: for p in pars: if p.startswith("M0:"): pars[p] = 0 else: any_mag = False first_mag = None for p in pars: if p.startswith("M0:"): any_mag |= (pars[p] != 0) if first_mag is None: first_mag = p if not any_mag and first_mag is not None: pars[first_mag] = 8. return pars def eval_sasview(model_info, data): # type: (Modelinfo, Data) -> Calculator """ Return a model calculator using the pre-4.0 SasView models. """ # importing sas here so that the error message will be that sas failed to # import rather than the more obscure smear_selection not imported error import sas import sas.models from sas.models.qsmearing import smear_selection from sas.models.MultiplicationModel import MultiplicationModel from sas.models.dispersion_models import models as dispersers def get_model_class(name): # type: (str) -> "sas.models.BaseComponent" #print("new",sorted(_pars.items())) __import__('sas.models.' + name) ModelClass = getattr(getattr(sas.models, name, None), name, None) if ModelClass is None: raise ValueError("could not find model %r in sas.models"%name) return ModelClass # WARNING: ugly hack when handling model! # Sasview models with multiplicity need to be created with the target # multiplicity, so we cannot create the target model ahead of time for # for multiplicity models. Instead we store the model in a list and # update the first element of that list with the new multiplicity model # every time we evaluate. # grab the sasview model, or create it if it is a product model if model_info.composition: composition_type, parts = model_info.composition if composition_type == 'product': P, S = [get_model_class(revert_name(p))() for p in parts] model = [MultiplicationModel(P, S)] else: raise ValueError("sasview mixture models not supported by compare") else: old_name = revert_name(model_info) if old_name is None: raise ValueError("model %r does not exist in old sasview" % model_info.id) ModelClass = get_model_class(old_name) model = [ModelClass()] model[0].disperser_handles = {} # build a smearer with which to call the model, if necessary smearer = smear_selection(data, model=model) if hasattr(data, 'qx_data'): q = np.sqrt(data.qx_data**2 + data.qy_data**2) index = ((~data.mask) & (~np.isnan(data.data)) & (q >= data.qmin) & (q <= data.qmax)) if smearer is not None: smearer.model = model # because smear_selection has a bug smearer.accuracy = data.accuracy smearer.set_index(index) def _call_smearer(): smearer.model = model[0] return smearer.get_value() theory = _call_smearer else: theory = lambda: model[0].evalDistribution([data.qx_data[index], data.qy_data[index]]) elif smearer is not None: theory = lambda: smearer(model[0].evalDistribution(data.x)) else: theory = lambda: model[0].evalDistribution(data.x) def calculator(**pars): # type: (float, ...) -> np.ndarray """ Sasview calculator for model. """ oldpars = revert_pars(model_info, pars) # For multiplicity models, create a model with the correct multiplicity control = oldpars.pop("CONTROL", None) if control is not None: # sphericalSLD has one fewer multiplicity. This update should # happen in revert_pars, but it hasn't been called yet. model[0] = ModelClass(control) # paying for parameter conversion each time to keep life simple, if not fast for k, v in oldpars.items(): if k.endswith('.type'): par = k[:-5] if v == 'gaussian': continue cls = dispersers[v if v != 'rectangle' else 'rectangula'] handle = cls() model[0].disperser_handles[par] = handle try: model[0].set_dispersion(par, handle) except Exception: exception.annotate_exception("while setting %s to %r" %(par, v)) raise #print("sasview pars",oldpars) for k, v in oldpars.items(): name_attr = k.split('.') # polydispersity components if len(name_attr) == 2: par, disp_par = name_attr model[0].dispersion[par][disp_par] = v else: model[0].setParam(k, v) return theory() calculator.engine = "sasview" return calculator DTYPE_MAP = { 'half': '16', 'fast': 'fast', 'single': '32', 'double': '64', 'quad': '128', 'f16': '16', 'f32': '32', 'f64': '64', 'float16': '16', 'float32': '32', 'float64': '64', 'float128': '128', 'longdouble': '128', } def eval_opencl(model_info, data, dtype='single', cutoff=0.): # type: (ModelInfo, Data, str, float) -> Calculator """ Return a model calculator using the OpenCL calculation engine. """ if not core.HAVE_OPENCL: raise RuntimeError("OpenCL not available") model = core.build_model(model_info, dtype=dtype, platform="ocl") calculator = DirectModel(data, model, cutoff=cutoff) calculator.engine = "OCL%s"%DTYPE_MAP[str(model.dtype)] return calculator def eval_ctypes(model_info, data, dtype='double', cutoff=0.): # type: (ModelInfo, Data, str, float) -> Calculator """ Return a model calculator using the DLL calculation engine. """ model = core.build_model(model_info, dtype=dtype, platform="dll") calculator = DirectModel(data, model, cutoff=cutoff) calculator.engine = "OMP%s"%DTYPE_MAP[str(model.dtype)] return calculator def time_calculation(calculator, pars, evals=1): # type: (Calculator, ParameterSet, int) -> Tuple[np.ndarray, float] """ Compute the average calculation time over N evaluations. An additional call is generated without polydispersity in order to initialize the calculation engine, and make the average more stable. """ # initialize the code so time is more accurate if evals > 1: calculator(**suppress_pd(pars)) toc = tic() # make sure there is at least one eval value = calculator(**pars) for _ in range(evals-1): value = calculator(**pars) average_time = toc()*1000. / evals #print("I(q)",value) return value, average_time def make_data(opts): # type: (Dict[str, Any]) -> Tuple[Data, np.ndarray] """ Generate an empty dataset, used with the model to set Q points and resolution. *opts* contains the options, with 'qmax', 'nq', 'res', 'accuracy', 'is2d' and 'view' parsed from the command line. """ qmin, qmax, nq, res = opts['qmin'], opts['qmax'], opts['nq'], opts['res'] if opts['is2d']: q = np.linspace(-qmax, qmax, nq) # type: np.ndarray data = empty_data2D(q, resolution=res) data.accuracy = opts['accuracy'] set_beam_stop(data, 0.0004) index = ~data.mask else: if opts['view'] == 'log' and not opts['zero']: q = np.logspace(math.log10(qmin), math.log10(qmax), nq) else: q = np.linspace(qmin, qmax, nq) if opts['zero']: q = np.hstack((0, q)) data = empty_data1D(q, resolution=res) index = slice(None, None) return data, index def make_engine(model_info, data, dtype, cutoff): # type: (ModelInfo, Data, str, float) -> Calculator """ Generate the appropriate calculation engine for the given datatype. Datatypes with '!' appended are evaluated using external C DLLs rather than OpenCL. """ if dtype == 'sasview': return eval_sasview(model_info, data) elif dtype is None or not dtype.endswith('!'): return eval_opencl(model_info, data, dtype=dtype, cutoff=cutoff) else: return eval_ctypes(model_info, data, dtype=dtype[:-1], cutoff=cutoff) def _show_invalid(data, theory): # type: (Data, np.ma.ndarray) -> None """ Display a list of the non-finite values in theory. """ if not theory.mask.any(): return if hasattr(data, 'x'): bad = zip(data.x[theory.mask], theory[theory.mask]) print(" *** ", ", ".join("I(%g)=%g"%(x, y) for x, y in bad)) def compare(opts, limits=None): # type: (Dict[str, Any], Optional[Tuple[float, float]]) -> Tuple[float, float] """ Preform a comparison using options from the command line. *limits* are the limits on the values to use, either to set the y-axis for 1D or to set the colormap scale for 2D. If None, then they are inferred from the data and returned. When exploring using Bumps, the limits are set when the model is initially called, and maintained as the values are adjusted, making it easier to see the effects of the parameters. """ limits = np.Inf, -np.Inf for k in range(opts['sets']): opts['pars'] = parse_pars(opts) if opts['pars'] is None: return result = run_models(opts, verbose=True) if opts['plot']: limits = plot_models(opts, result, limits=limits, setnum=k) if opts['plot']: import matplotlib.pyplot as plt plt.show() def run_models(opts, verbose=False): # type: (Dict[str, Any]) -> Dict[str, Any] base, comp = opts['engines'] base_n, comp_n = opts['count'] base_pars, comp_pars = opts['pars'] data = opts['data'] comparison = comp is not None base_time = comp_time = None base_value = comp_value = resid = relerr = None # Base calculation try: base_raw, base_time = time_calculation(base, base_pars, base_n) base_value = np.ma.masked_invalid(base_raw) if verbose: print("%s t=%.2f ms, intensity=%.0f" % (base.engine, base_time, base_value.sum())) _show_invalid(data, base_value) except ImportError: traceback.print_exc() # Comparison calculation if comparison: try: comp_raw, comp_time = time_calculation(comp, comp_pars, comp_n) comp_value = np.ma.masked_invalid(comp_raw) if verbose: print("%s t=%.2f ms, intensity=%.0f" % (comp.engine, comp_time, comp_value.sum())) _show_invalid(data, comp_value) except ImportError: traceback.print_exc() # Compare, but only if computing both forms if comparison: resid = (base_value - comp_value) relerr = resid/np.where(comp_value != 0., abs(comp_value), 1.0) if verbose: _print_stats("|%s-%s|" % (base.engine, comp.engine) + (" "*(3+len(comp.engine))), resid) _print_stats("|(%s-%s)/%s|" % (base.engine, comp.engine, comp.engine), relerr) return dict(base_value=base_value, comp_value=comp_value, base_time=base_time, comp_time=comp_time, resid=resid, relerr=relerr) def _print_stats(label, err): # type: (str, np.ma.ndarray) -> None # work with trimmed data, not the full set sorted_err = np.sort(abs(err.compressed())) if len(sorted_err) == 0.: print(label + " no valid values") return p50 = int((len(sorted_err)-1)*0.50) p98 = int((len(sorted_err)-1)*0.98) data = [ "max:%.3e"%sorted_err[-1], "median:%.3e"%sorted_err[p50], "98%%:%.3e"%sorted_err[p98], "rms:%.3e"%np.sqrt(np.mean(sorted_err**2)), "zero-offset:%+.3e"%np.mean(sorted_err), ] print(label+" "+" ".join(data)) def plot_models(opts, result, limits=(np.Inf, -np.Inf), setnum=0): # type: (Dict[str, Any], Dict[str, Any], Optional[Tuple[float, float]]) -> Tuple[float, float] base_value, comp_value = result['base_value'], result['comp_value'] base_time, comp_time = result['base_time'], result['comp_time'] resid, relerr = result['resid'], result['relerr'] have_base, have_comp = (base_value is not None), (comp_value is not None) base, comp = opts['engines'] data = opts['data'] use_data = (opts['datafile'] is not None) and (have_base ^ have_comp) # Plot if requested view = opts['view'] import matplotlib.pyplot as plt vmin, vmax = limits if have_base: vmin = min(vmin, base_value.min()) vmax = max(vmax, base_value.max()) if have_comp: vmin = min(vmin, comp_value.min()) vmax = max(vmax, comp_value.max()) limits = vmin, vmax if have_base: if have_comp: plt.subplot(131) plot_theory(data, base_value, view=view, use_data=use_data, limits=limits) plt.title("%s t=%.2f ms"%(base.engine, base_time)) #cbar_title = "log I" if have_comp: if have_base: plt.subplot(132) if not opts['is2d'] and have_base: plot_theory(data, base_value, view=view, use_data=use_data, limits=limits) plot_theory(data, comp_value, view=view, use_data=use_data, limits=limits) plt.title("%s t=%.2f ms"%(comp.engine, comp_time)) #cbar_title = "log I" if have_base and have_comp: plt.subplot(133) if not opts['rel_err']: err, errstr, errview = resid, "abs err", "linear" else: err, errstr, errview = abs(relerr), "rel err", "log" if (err == 0.).all(): errview = 'linear' if 0: # 95% cutoff sorted = np.sort(err.flatten()) cutoff = sorted[int(sorted.size*0.95)] err[err > cutoff] = cutoff #err,errstr = base/comp,"ratio" plot_theory(data, None, resid=err, view=view, use_data=use_data) plt.yscale(errview) plt.title("max %s = %.3g"%(errstr, abs(err).max())) #cbar_title = errstr if errview=="linear" else "log "+errstr #if is2D: # h = plt.colorbar() # h.ax.set_title(cbar_title) fig = plt.gcf() extra_title = ' '+opts['title'] if opts['title'] else '' fig.suptitle(":".join(opts['name']) + extra_title) if have_base and have_comp and opts['show_hist']: plt.figure() v = relerr v[v == 0] = 0.5*np.min(np.abs(v[v != 0])) plt.hist(np.log10(np.abs(v)), normed=1, bins=50) plt.xlabel('log10(err), err = |(%s - %s) / %s|' % (base.engine, comp.engine, comp.engine)) plt.ylabel('P(err)') plt.title('Distribution of relative error between calculation engines') return limits # =========================================================================== # # Set of command line options. # Normal options such as -plot/-noplot are specified as 'name'. # For options such as -nq=500 which require a value use 'name='. # OPTIONS = [ # Plotting 'plot', 'noplot', 'linear', 'log', 'q4', 'rel', 'abs', 'hist', 'nohist', 'title=', # Data generation 'data=', 'noise=', 'res=', 'nq=', 'q=', 'lowq', 'midq', 'highq', 'exq', 'zero', '2d', '1d', # Parameter set 'preset', 'random', 'random=', 'sets=', 'demo', 'default', # TODO: remove demo/default 'nopars', 'pars', # Calculation options 'poly', 'mono', 'cutoff=', 'magnetic', 'nonmagnetic', 'accuracy=', 'neval=', # for timing... # Precision options 'calc=', 'half', 'fast', 'single', 'double', 'single!', 'double!', 'quad!', 'sasview', # TODO: remove sasview 3.x support # Output options 'help', 'html', 'edit', ] NAME_OPTIONS = set(k for k in OPTIONS if not k.endswith('=')) VALUE_OPTIONS = [k[:-1] for k in OPTIONS if k.endswith('=')] def columnize(items, indent="", width=79): # type: (List[str], str, int) -> str """ Format a list of strings into columns. Returns a string with carriage returns ready for printing. """ column_width = max(len(w) for w in items) + 1 num_columns = (width - len(indent)) // column_width num_rows = len(items) // num_columns items = items + [""] * (num_rows * num_columns - len(items)) columns = [items[k*num_rows:(k+1)*num_rows] for k in range(num_columns)] lines = [" ".join("%-*s"%(column_width, entry) for entry in row) for row in zip(*columns)] output = indent + ("\n"+indent).join(lines) return output def get_pars(model_info, use_demo=False): # type: (ModelInfo, bool) -> ParameterSet """ Extract demo parameters from the model definition. """ # Get the default values for the parameters pars = {} for p in model_info.parameters.call_parameters: parts = [('', p.default)] if p.polydisperse: parts.append(('_pd', 0.0)) parts.append(('_pd_n', 0)) parts.append(('_pd_nsigma', 3.0)) parts.append(('_pd_type', "gaussian")) for ext, val in parts: if p.length > 1: dict(("%s%d%s" % (p.id, k, ext), val) for k in range(1, p.length+1)) else: pars[p.id + ext] = val # Plug in values given in demo if use_demo and model_info.demo: pars.update(model_info.demo) return pars INTEGER_RE = re.compile("^[+-]?[1-9][0-9]*$") def isnumber(str): match = FLOAT_RE.match(str) isfloat = (match and not str[match.end():]) return isfloat or INTEGER_RE.match(str) # For distinguishing pairs of models for comparison # key-value pair separator = # shell characters | & ; <> $ % ' " \ # ` # model and parameter names _ # parameter expressions - + * / . ( ) # path characters including tilde expansion and windows drive ~ / : # not sure about brackets [] {} # maybe one of the following @ ? ^ ! , PAR_SPLIT = ',' def parse_opts(argv): # type: (List[str]) -> Dict[str, Any] """ Parse command line options. """ MODELS = core.list_models() flags = [arg for arg in argv if arg.startswith('-')] values = [arg for arg in argv if not arg.startswith('-') and '=' in arg] positional_args = [arg for arg in argv if not arg.startswith('-') and '=' not in arg] models = "\n ".join("%-15s"%v for v in MODELS) if len(positional_args) == 0: print(USAGE) print("\nAvailable models:") print(columnize(MODELS, indent=" ")) return None invalid = [o[1:] for o in flags if o[1:] not in NAME_OPTIONS and not any(o.startswith('-%s='%t) for t in VALUE_OPTIONS)] if invalid: print("Invalid options: %s"%(", ".join(invalid))) return None name = positional_args[-1] # pylint: disable=bad-whitespace # Interpret the flags opts = { 'plot' : True, 'view' : 'log', 'is2d' : False, 'qmin' : None, 'qmax' : 0.05, 'nq' : 128, 'res' : 0.0, 'noise' : 0.0, 'accuracy' : 'Low', 'cutoff' : '0.0', 'seed' : -1, # default to preset 'mono' : True, # Default to magnetic a magnetic moment is set on the command line 'magnetic' : False, 'show_pars' : False, 'show_hist' : False, 'rel_err' : True, 'explore' : False, 'use_demo' : True, 'zero' : False, 'html' : False, 'title' : None, 'datafile' : None, 'sets' : 0, 'engine' : 'default', 'evals' : '1', } for arg in flags: if arg == '-noplot': opts['plot'] = False elif arg == '-plot': opts['plot'] = True elif arg == '-linear': opts['view'] = 'linear' elif arg == '-log': opts['view'] = 'log' elif arg == '-q4': opts['view'] = 'q4' elif arg == '-1d': opts['is2d'] = False elif arg == '-2d': opts['is2d'] = True elif arg == '-exq': opts['qmax'] = 10.0 elif arg == '-highq': opts['qmax'] = 1.0 elif arg == '-midq': opts['qmax'] = 0.2 elif arg == '-lowq': opts['qmax'] = 0.05 elif arg == '-zero': opts['zero'] = True elif arg.startswith('-nq='): opts['nq'] = int(arg[4:]) elif arg.startswith('-q='): opts['qmin'], opts['qmax'] = [float(v) for v in arg[3:].split(':')] elif arg.startswith('-res='): opts['res'] = float(arg[5:]) elif arg.startswith('-noise='): opts['noise'] = float(arg[7:]) elif arg.startswith('-sets='): opts['sets'] = int(arg[6:]) elif arg.startswith('-accuracy='): opts['accuracy'] = arg[10:] elif arg.startswith('-cutoff='): opts['cutoff'] = arg[8:] elif arg.startswith('-random='): opts['seed'] = int(arg[8:]) elif arg.startswith('-title='): opts['title'] = arg[7:] elif arg.startswith('-data='): opts['datafile'] = arg[6:] elif arg.startswith('-calc='): opts['engine'] = arg[6:] elif arg.startswith('-neval='): opts['evals'] = arg[7:] elif arg == '-random': opts['seed'] = np.random.randint(1000000) elif arg == '-preset': opts['seed'] = -1 elif arg == '-mono': opts['mono'] = True elif arg == '-poly': opts['mono'] = False elif arg == '-magnetic': opts['magnetic'] = True elif arg == '-nonmagnetic': opts['magnetic'] = False elif arg == '-pars': opts['show_pars'] = True elif arg == '-nopars': opts['show_pars'] = False elif arg == '-hist': opts['show_hist'] = True elif arg == '-nohist': opts['show_hist'] = False elif arg == '-rel': opts['rel_err'] = True elif arg == '-abs': opts['rel_err'] = False elif arg == '-half': opts['engine'] = 'half' elif arg == '-fast': opts['engine'] = 'fast' elif arg == '-single': opts['engine'] = 'single' elif arg == '-double': opts['engine'] = 'double' elif arg == '-single!': opts['engine'] = 'single!' elif arg == '-double!': opts['engine'] = 'double!' elif arg == '-quad!': opts['engine'] = 'quad!' elif arg == '-sasview': opts['engine'] = 'sasview' elif arg == '-edit': opts['explore'] = True elif arg == '-demo': opts['use_demo'] = True elif arg == '-default': opts['use_demo'] = False elif arg == '-html': opts['html'] = True elif arg == '-help': opts['html'] = True # pylint: enable=bad-whitespace # Magnetism forces 2D for now if opts['magnetic']: opts['is2d'] = True # Force random if sets is used if opts['sets'] >= 1 and opts['seed'] < 0: opts['seed'] = np.random.randint(1000000) if opts['sets'] == 0: opts['sets'] = 1 # Create the computational engines if opts['qmin'] is None: opts['qmin'] = 0.001*opts['qmax'] if opts['datafile'] is not None: data = load_data(os.path.expanduser(opts['datafile'])) else: data, _ = make_data(opts) comparison = any(PAR_SPLIT in v for v in values) if PAR_SPLIT in name: names = name.split(PAR_SPLIT, 2) comparison = True else: names = [name]*2 try: model_info = [core.load_model_info(k) for k in names] except ImportError as exc: print(str(exc)) print("Could not find model; use one of:\n " + models) return None if PAR_SPLIT in opts['engine']: engine_types = opts['engine'].split(PAR_SPLIT, 2) comparison = True else: engine_types = [opts['engine']]*2 if PAR_SPLIT in opts['evals']: evals = [int(k) for k in opts['evals'].split(PAR_SPLIT, 2)] comparison = True else: evals = [int(opts['evals'])]*2 if PAR_SPLIT in opts['cutoff']: cutoff = [float(k) for k in opts['cutoff'].split(PAR_SPLIT, 2)] comparison = True else: cutoff = [float(opts['cutoff'])]*2 base = make_engine(model_info[0], data, engine_types[0], cutoff[0]) if comparison: comp = make_engine(model_info[1], data, engine_types[1], cutoff[1]) else: comp = None # pylint: disable=bad-whitespace # Remember it all opts.update({ 'data' : data, 'name' : names, 'def' : model_info, 'count' : evals, 'engines' : [base, comp], 'values' : values, }) # pylint: enable=bad-whitespace return opts def parse_pars(opts): model_info, model_info2 = opts['def'] # Get demo parameters from model definition, or use default parameters # if model does not define demo parameters pars = get_pars(model_info, opts['use_demo']) pars2 = get_pars(model_info2, opts['use_demo']) pars2.update((k, v) for k, v in pars.items() if k in pars2) # randomize parameters #pars.update(set_pars) # set value before random to control range if opts['seed'] > -1: pars = randomize_pars(model_info, pars) if model_info != model_info2: pars2 = randomize_pars(model_info2, pars2) # Share values for parameters with the same name for k, v in pars.items(): if k in pars2: pars2[k] = v else: pars2 = pars.copy() constrain_pars(model_info, pars) constrain_pars(model_info2, pars2) pars = suppress_pd(pars, opts['mono']) pars2 = suppress_pd(pars2, opts['mono']) pars = suppress_magnetism(pars, not opts['magnetic']) pars2 = suppress_magnetism(pars2, not opts['magnetic']) # Fill in parameters given on the command line presets = {} presets2 = {} for arg in opts['values']: k, v = arg.split('=', 1) if k not in pars and k not in pars2: # extract base name without polydispersity info s = set(p.split('_pd')[0] for p in pars) print("%r invalid; parameters are: %s"%(k, ", ".join(sorted(s)))) return None v1, v2 = v.split(PAR_SPLIT, 2) if PAR_SPLIT in v else (v,v) if v1 and k in pars: presets[k] = float(v1) if isnumber(v1) else v1 if v2 and k in pars2: presets2[k] = float(v2) if isnumber(v2) else v2 # If pd given on the command line, default pd_n to 35 for k, v in list(presets.items()): if k.endswith('_pd'): presets.setdefault(k+'_n', 35.) for k, v in list(presets2.items()): if k.endswith('_pd'): presets2.setdefault(k+'_n', 35.) # Evaluate preset parameter expressions context = MATH.copy() context['np'] = np context.update(pars) context.update((k, v) for k, v in presets.items() if isinstance(v, float)) for k, v in presets.items(): if not isinstance(v, float) and not k.endswith('_type'): presets[k] = eval(v, context) context.update(presets) context.update((k, v) for k, v in presets2.items() if isinstance(v, float)) for k, v in presets2.items(): if not isinstance(v, float) and not k.endswith('_type'): presets2[k] = eval(v, context) # update parameters with presets pars.update(presets) # set value after random to control value pars2.update(presets2) # set value after random to control value #import pprint; pprint.pprint(model_info) if opts['show_pars']: if model_info.name != model_info2.name or pars != pars2: print("==== %s ====="%model_info.name) print(str(parlist(model_info, pars, opts['is2d']))) print("==== %s ====="%model_info2.name) print(str(parlist(model_info2, pars2, opts['is2d']))) else: print(str(parlist(model_info, pars, opts['is2d']))) return pars, pars2 def show_docs(opts): # type: (Dict[str, Any]) -> None """ show html docs for the model """ import os from .generate import make_html from . import rst2html info = opts['def'][0] html = make_html(info) path = os.path.dirname(info.filename) url = "file://"+path.replace("\\","/")[2:]+"/" rst2html.view_html_qtapp(html, url) def explore(opts): # type: (Dict[str, Any]) -> None """ explore the model using the bumps gui. """ import wx # type: ignore from bumps.names import FitProblem # type: ignore from bumps.gui.app_frame import AppFrame # type: ignore from bumps.gui import signal is_mac = "cocoa" in wx.version() # Create an app if not running embedded app = wx.App() if wx.GetApp() is None else None model = Explore(opts) problem = FitProblem(model) frame = AppFrame(parent=None, title="explore", size=(1000, 700)) if not is_mac: frame.Show() frame.panel.set_model(model=problem) frame.panel.Layout() frame.panel.aui.Split(0, wx.TOP) def reset_parameters(event): model.revert_values() signal.update_parameters(problem) frame.Bind(wx.EVT_TOOL, reset_parameters, frame.ToolBar.GetToolByPos(1)) if is_mac: frame.Show() # If running withing an app, start the main loop if app: app.MainLoop() class Explore(object): """ Bumps wrapper for a SAS model comparison. The resulting object can be used as a Bumps fit problem so that parameters can be adjusted in the GUI, with plots updated on the fly. """ def __init__(self, opts): # type: (Dict[str, Any]) -> None from bumps.cli import config_matplotlib # type: ignore from . import bumps_model config_matplotlib() self.opts = opts opts['pars'] = list(opts['pars']) p1, p2 = opts['pars'] m1, m2 = opts['def'] self.fix_p2 = m1 != m2 or p1 != p2 model_info = m1 pars, pd_types = bumps_model.create_parameters(model_info, **p1) # Initialize parameter ranges, fixing the 2D parameters for 1D data. if not opts['is2d']: for p in model_info.parameters.user_parameters({}, is2d=False): for ext in ['', '_pd', '_pd_n', '_pd_nsigma']: k = p.name+ext v = pars.get(k, None) if v is not None: v.range(*parameter_range(k, v.value)) else: for k, v in pars.items(): v.range(*parameter_range(k, v.value)) self.pars = pars self.starting_values = dict((k, v.value) for k, v in pars.items()) self.pd_types = pd_types self.limits = np.Inf, -np.Inf def revert_values(self): for k, v in self.starting_values.items(): self.pars[k].value = v def model_update(self): pass def numpoints(self): # type: () -> int """ Return the number of points. """ return len(self.pars) + 1 # so dof is 1 def parameters(self): # type: () -> Any # Dict/List hierarchy of parameters """ Return a dictionary of parameters. """ return self.pars def nllf(self): # type: () -> float """ Return cost. """ # pylint: disable=no-self-use return 0. # No nllf def plot(self, view='log'): # type: (str) -> None """ Plot the data and residuals. """ pars = dict((k, v.value) for k, v in self.pars.items()) pars.update(self.pd_types) self.opts['pars'][0] = pars if not self.fix_p2: self.opts['pars'][1] = pars result = run_models(self.opts) limits = plot_models(self.opts, result, limits=self.limits) if self.limits is None: vmin, vmax = limits self.limits = vmax*1e-7, 1.3*vmax import pylab; pylab.clf() plot_models(self.opts, result, limits=self.limits) def main(*argv): # type: (*str) -> None """ Main program. """ opts = parse_opts(argv) if opts is not None: if opts['seed'] > -1: print("Randomize using -random=%i"%opts['seed']) np.random.seed(opts['seed']) if opts['html']: show_docs(opts) elif opts['explore']: opts['pars'] = parse_pars(opts) if opts['pars'] is None: return explore(opts) else: compare(opts) if __name__ == "__main__": main(*sys.argv[1:]) sasmodels/sasmodels/compare_many.py000077500000000000000000000227111317715334700201070ustar00rootroot00000000000000#!/usr/bin/env python """ Program to compare results from many random parameter sets for a given model. The result is a comma separated value (CSV) table that can be redirected from standard output into a file and loaded into a spreadsheet. The models are compared for each parameter set and if the difference is greater than expected for that precision, the parameter set is labeled as bad and written to the output, along with the random seed used to generate that parameter value. This seed can be used with :mod:`compare` to reload and display the details of the model. """ from __future__ import print_function import sys import traceback import numpy as np # type: ignore from . import core from .compare import (randomize_pars, suppress_pd, make_data, make_engine, get_pars, columnize, constrain_pars, constrain_new_to_old) MODELS = core.list_models() def calc_stats(target, value, index): """ Calculate statistics between the target value and the computed value. *target* and *value* are the vectors being compared, with the difference normalized by *target* to get relative error. Only the elements listed in *index* are used, though index may be and empty slice defined by *slice(None, None)*. Returns: *maxrel* the maximum relative difference *rel95* the relative difference with the 5% biggest differences ignored *maxabs* the maximum absolute difference for the 5% biggest differences *maxval* the maximum value for the 5% biggest differences """ resid = abs(value-target)[index] relerr = resid/target[index] sorted_rel_index = np.argsort(relerr) #p90 = int(len(relerr)*0.90) p95 = int(len(relerr)*0.95) maxrel = np.max(relerr) rel95 = relerr[sorted_rel_index[p95]] maxabs = np.max(resid[sorted_rel_index[p95:]]) maxval = np.max(value[sorted_rel_index[p95:]]) return maxrel, rel95, maxabs, maxval def print_column_headers(pars, parts): """ Generate column headers for the differences and for the parameters, and print them to standard output. """ stats = list('Max rel err|95% rel err|Max abs err above 90% rel|Max value above 90% rel'.split('|')) groups = [''] for p in parts: groups.append(p) groups.extend(['']*(len(stats)-1)) groups.append("Parameters") columns = ['Seed'] + stats*len(parts) + list(sorted(pars.keys())) print(','.join('"%s"'%c for c in groups)) print(','.join('"%s"'%c for c in columns)) # Target 'good' value for various precision levels. PRECISION = { 'fast': 1e-3, 'half': 1e-3, 'single': 5e-5, 'double': 5e-14, 'single!': 5e-5, 'double!': 5e-14, 'quad!': 5e-18, 'sasview': 5e-14, } def compare_instance(name, data, index, N=1, mono=True, cutoff=1e-5, base='sasview', comp='double'): r""" Compare the model under different calculation engines. *name* is the name of the model. *data* is the data object giving $q, \Delta q$ calculation points. *index* is the active set of points. *N* is the number of comparisons to make. *cutoff* is the polydispersity weight cutoff to make the calculation a little bit faster. *base* and *comp* are the names of the calculation engines to compare. """ is_2d = hasattr(data, 'qx_data') model_info = core.load_model_info(name) pars = get_pars(model_info, use_demo=True) header = ('\n"Model","%s","Count","%d","Dimension","%s"' % (name, N, "2D" if is_2d else "1D")) if not mono: header += ',"Cutoff",%g'%(cutoff,) print(header) if is_2d: if not model_info.parameters.has_2d: print(',"1-D only"') return # Some not very clean macros for evaluating the models and checking the # results. They freely use variables from the current scope, even some # which have not been defined yet, complete with abuse of mutable lists # to allow them to update values in the current scope since nonlocal # declarations are not available in python 2.7. def try_model(fn, pars): """ Return the model evaluated at *pars*. If there is an exception, print it and return NaN of the right shape. """ try: result = fn(**pars) except Exception: traceback.print_exc() print("when comparing %s for %d"%(name, seed)) if hasattr(data, 'qx_data'): result = np.NaN*data.data else: result = np.NaN*data.x return result def check_model(pars): """ Run the two calculators against *pars*, returning statistics on the differences. See :func:`calc_stats` for the list of stats. """ base_value = try_model(calc_base, pars) comp_value = try_model(calc_comp, pars) stats = calc_stats(base_value, comp_value, index) max_diff[0] = max(max_diff[0], stats[0]) good[0] = good[0] and (stats[0] < expected) return list(stats) try: calc_base = make_engine(model_info, data, base, cutoff) calc_comp = make_engine(model_info, data, comp, cutoff) except Exception as exc: #raise print('"Error: %s"'%str(exc).replace('"', "'")) print('"good","%d of %d","max diff",%g' % (0, N, np.NaN)) return expected = max(PRECISION[base], PRECISION[comp]) num_good = 0 first = True max_diff = [0] for k in range(N): print("Model %s %d"%(name, k+1), file=sys.stderr) seed = np.random.randint(1e6) pars_i = randomize_pars(model_info, pars, seed) constrain_pars(model_info, pars_i) if 'sasview' in (base, comp): constrain_new_to_old(model_info, pars_i) if mono: pars_i = suppress_pd(pars_i) good = [True] columns = check_model(pars_i) columns += [v for _, v in sorted(pars_i.items())] if first: labels = [" vs. ".join((calc_base.engine, calc_comp.engine))] print_column_headers(pars_i, labels) first = False if good[0]: num_good += 1 else: print(("%d,"%seed)+','.join("%s"%v for v in columns)) print('"good","%d of %d","max diff",%g'%(num_good, N, max_diff[0])) def print_usage(): """ Print the command usage string. """ print("usage: compare_many.py MODEL COUNT (1dNQ|2dNQ) (CUTOFF|mono) (single|double|quad)", file=sys.stderr) def print_models(): """ Print the list of available models in columns. """ print(columnize(MODELS, indent=" ")) def print_help(): """ Print usage string, the option description and the list of available models. """ print_usage() print("""\ MODEL is the model name of the model or one of the model types listed in sasmodels.core.list_models (all, py, c, double, single, opencl, 1d, 2d, nonmagnetic, magnetic). Model types can be combined, such as 2d+single. COUNT is the number of randomly generated parameter sets to try. A value of "10000" is a reasonable check for monodisperse models, or "100" for polydisperse models. For a quick check, use "100" and "5" respectively. NQ is the number of Q values to calculate. If it starts with "1d", then it is a 1-dimensional problem, with log spaced Q points from 1e-3 to 1.0. If it starts with "2d" then it is a 2-dimensional problem, with linearly spaced points Q points from -1.0 to 1.0 in each dimension. The usual values are "1d100" for 1-D and "2d32" for 2-D. CUTOFF is the cutoff value to use for the polydisperse distribution. Weights below the cutoff will be ignored. Use "mono" for monodisperse models. The choice of polydisperse parameters, and the number of points in the distribution is set in compare.py defaults for each model. Polydispersity is given in the "demo" attribute of each model. PRECISION is the floating point precision to use for comparisons. If two precisions are given, then compare one to the other. Precision is one of fast, single, double for GPU or single!, double!, quad! for DLL. If no precision is given, then use single and double! respectively. Available models: """) print_models() def main(argv): """ Main program. """ if len(argv) not in (3, 4, 5, 6): print_help() return target = argv[0] try: model_list = [target] if target in MODELS else core.list_models(target) except ValueError: print('Bad model %s. Use model type or one of:' % target, file=sys.stderr) print_models() print('model types: all, py, c, double, single, opencl, 1d, 2d, nonmagnetic, magnetic') return try: count = int(argv[1]) is2D = argv[2].startswith('2d') assert argv[2][1] == 'd' Nq = int(argv[2][2:]) mono = len(argv) <= 3 or argv[3] == 'mono' cutoff = float(argv[3]) if not mono else 0 base = argv[4] if len(argv) > 4 else "single" comp = argv[5] if len(argv) > 5 else "double!" except Exception: traceback.print_exc() print_usage() return data, index = make_data({'qmax':1.0, 'is2d':is2D, 'nq':Nq, 'res':0., 'accuracy': 'Low', 'view':'log', 'zero': False}) for model in model_list: compare_instance(model, data, index, N=count, mono=mono, cutoff=cutoff, base=base, comp=comp) if __name__ == "__main__": #from .compare import push_seed #with push_seed(1): main(sys.argv[1:]) main(sys.argv[1:]) sasmodels/sasmodels/conversion_table.py000066400000000000000000000607371317715334700210000ustar00rootroot00000000000000""" Parameter conversion table *CONVERSION_TABLE* gives the old model name and a dictionary of old parameter names for each parameter in sasmodels. This is used by :mod:`convert` to determine the equivalent parameter set when comparing a sasmodels model to the models defined in previous versions of SasView and sasmodels. This is now versioned based on the version number of SasView. When any sasmodels parameter or model name is changed, this must be modified to account for that. Usage:: : { : [ , { : , ... : } ] } Any future parameter and model name changes can and should be given in this table for future compatibility. """ CONVERSION_TABLE = { (3,1,2) : { "adsorbed_layer": [ "Core2ndMomentModel", { "scale": "scale", "second_moment": "second_moment", "density_shell": "density_poly", "sld_solvent": "sld_solv", "radius": "radius_core", "volfraction": "volf_cores", "background": "background", "adsorbed_amount": "ads_amount", "sld_shell": "sld_poly" } ], "barbell": [ "BarBellModel", { "sld": "sld_barbell", "length": "len_bar", "radius_bell": "rad_bell", "radius": "rad_bar", "sld_solvent": "sld_solv" } ], "bcc_paracrystal": [ "BCCrystalModel", { "sld": "sldSph", "sld_solvent": "sldSolv" } ], "be_polyelectrolyte": [ "BEPolyelectrolyte", { "ionization_degree": "alpha", "polymer_concentration": "c", "salt_concentration": "cs", "virial_param": "h", "background": "background", "contrast_factor": "k", "bjerrum_length": "lb", "monomer_length": "b" } ], "binary_hard_sphere": [ "BinaryHSModel", { "sld_sm": "ss_sld", "sld_lg": "ls_sld", "volfraction_sm": "vol_frac_ss", "radius_lg": "l_radius", "radius_sm": "s_radius", "volfraction_lg": "vol_frac_ls", "sld_solvent": "solvent_sld" } ], "broad_peak": [ "BroadPeakModel", { "peak_pos": "q_peak", "scale": None, "lorentz_length": "length_l", "porod_scale": "scale_p", "lorentz_exp": "exponent_l", "lorentz_scale": "scale_l", "porod_exp": "exponent_p" } ], "capped_cylinder": [ "CappedCylinderModel", { "sld": "sld_capcyl", "length": "len_cyl", "radius_cap": "rad_cap", "radius": "rad_cyl", "sld_solvent": "sld_solv" } ], "core_multi_shell": [ "CoreMultiShellModel", { "thickness": "thick_shell", "sld": "sld_shell", "radius": "rad_core0", "sld_core": "sld_core0", "sld_solvent": "sld_solv", "n": "n_shells", "M0:sld_core": "M0_sld_core0", "mtheta:sld_core": "M_theta_core0", "mphi:sld_core": "M_phi_core0", "M0:sld1": "M0_sld_shell1", "mtheta:sld1": "M_theta_shell1", "mphi:sld1": "M_phi_shell1", "M0:sld2": "M0_sld_shell2", "mtheta:sld2": "M_theta_shell2", "mphi:sld2": "M_phi_shell2", "M0:sld3": "M0_sld_shell3", "mtheta:sld3": "M_theta_shell3", "mphi:sld3": "M_phi_shell3", "M0:sld4": "M0_sld_shell4", "mtheta:sld4": "M_theta_shell4", "mphi:sld4": "M_phi_shell4", "M0:sld_solvent": "M0_sld_solv", "mtheta:sld_solvent": "M_theta_solv", "mphi:sld_solvent": "M_phi_solv", "up:frac_i": "Up_frac_i", "up:frac_f": "Up_frac_f", "up:angle": "Up_theta", } ], "core_shell_bicelle": [ "CoreShellBicelleModel", { "phi": "axis_phi", "sld_core": "core_sld", "sld_rim": "rim_sld", "thick_face": "face_thick", "sld_solvent": "solvent_sld", "thick_rim": "rim_thick", "sld_face": "face_sld", "theta": "axis_theta" } ], "core_shell_cylinder": [ "CoreShellCylinderModel", { "theta": "axis_theta", "phi": "axis_phi", "sld_shell": "shell_sld", "sld_solvent": "solvent_sld", "sld_core": "core_sld" } ], "core_shell_ellipsoid:1": [ "CoreShellEllipsoidModel", { "sld_core": "sld_core", "sld_shell": "sld_shell", "sld_solvent": "sld_solvent", "radius_equat_core": "equat_core", "x_core": "polar_core", "thick_shell": "equat_shell", "x_polar_shell": "polar_shell", "theta": "axis_theta", "phi": "axis_phi", } ], "core_shell_ellipsoid": [ "CoreShellEllipsoidXTModel", { "sld_core": "sld_core", "sld_shell": "sld_shell", "sld_solvent": "sld_solvent", "radius_equat_core": "equat_core", "thick_shell": "T_shell", "x_core": "X_core", "x_polar_shell": "XpolarShell", "theta": "axis_theta", "phi": "axis_phi", } ], "core_shell_parallelepiped": [ "CSParallelepipedModel", { "sld_core": "sld_pcore", "sld_a": "sld_rimA", "sld_b": "sld_rimB", "sld_c": "sld_rimC", "sld_solvent": "sld_solv", "length_a": "shortA", "length_b": "midB", "length_c": "longC", "thick_rim_a": "rimA", "thick_rim_c": "rimC", "thick_rim_b": "rimB", "theta": "parallel_theta", "phi": "parallel_phi", "psi": "parallel_psi", } ], "core_shell_sphere": [ "CoreShellModel", { "sld_core": "core_sld", "sld_shell": "shell_sld", "sld_solvent": "solvent_sld", "M0:sld_core": "M0_sld_core", "mtheta:sld_core": "M_theta_core", "mphi:sld_core": "M_phi_core", "M0:sld_shell": "M0_sld_shell", "mtheta:sld_shell": "M_theta_shell", "mphi:sld_shell": "M_phi_shell", "M0:sld_solvent": "M0_sld_solv", "mtheta:sld_solvent": "M_theta_solv", "mphi:sld_solvent": "M_phi_solv", "up:frac_i": "Up_frac_i", "up:frac_f": "Up_frac_f", "up:angle": "Up_theta" } ], "correlation_length": [ "CorrLength", { "porod_scale": "scale_p", "lorentz_scale": "scale_l", "porod_exp": "exponent_p", "lorentz_exp": "exponent_l", "cor_length": "length_l" }, "CorrLengthModel" ], "cylinder": [ "CylinderModel", { "sld": "sldCyl", "theta": "cyl_theta", "phi": "cyl_phi", "sld_solvent": "sldSolv", "M0:sld": "M0_sld_cyl", "mtheta:sld": "M_theta_cyl", "mphi:sld": "M_phi_cyl", "M0:sld_solvent": "M0_sld_solv", "mtheta:sld_solvent": "M_theta_solv", "mphi:sld_solvent": "M_phi_solv", "up:frac_i": "Up_frac_i", "up:frac_f": "Up_frac_f", "up:angle": "Up_theta" } ], "dab": [ "DABModel", { "cor_length": "length" } ], "ellipsoid": [ "EllipsoidModel", { "phi": "axis_phi", "radius_equatorial": "radius_b", "sld": "sldEll", "theta": "axis_theta", "radius_polar": "radius_a", "sld_solvent": "sldSolv" } ], "elliptical_cylinder": [ "EllipticalCylinderModel", { "axis_ratio": "r_ratio", "radius_minor": "r_minor", "sld": "sldCyl", "sld_solvent": "sldSolv", "theta": "cyl_theta", "phi": "cyl_phi", "psi": "cyl_psi", } ], "fcc_paracrystal": [ "FCCrystalModel", { "sld": "sldSph", "sld_solvent": "sldSolv" } ], "flexible_cylinder": [ "FlexibleCylinderModel", { "sld": "sldCyl", "sld_solvent": "sldSolv" } ], "flexible_cylinder_elliptical": [ "FlexCylEllipXModel", { "sld": "sldCyl", "sld_solvent": "sldSolv" } ], "fractal": [ "FractalModel", { "sld_block": "sldBlock", "radius": "radius", "cor_length": "cor_length", "sld_solvent": "sldSolv", "fractal_dim": "fractal_dim" } ], "fractal_core_shell": [ "FractalCoreShell", { "sld_core": "core_sld", "sld_shell": "shell_sld", "sld_solvent": "solvent_sld", "radius": "radius", "thickness": "thickness", "fractal_dim": "frac_dim", "cor_length": "cor_length", "volfraction": "volfraction", }, "FractalCoreShellModel" ], "fuzzy_sphere": [ "FuzzySphereModel", { "sld": "sldSph", "fuzziness": "fuzziness", "radius": "radius", "sld_solvent": "sldSolv" } ], "gauss_lorentz_gel": [ "GaussLorentzGel", { "gauss_scale": "scale_g", "cor_length_dynamic": "dyn_colength", "cor_length_static": "stat_colength", "background": "background", "lorentz_scale": "scale_l" }, "GaussLorentzGelModel" ], "gaussian_peak": [ "Peak Gauss Model", { "peak_pos": "q0", "sigma": "B", }, "PeakGaussModel", ], "gel_fit": [ "GelFitModel", { "rg": "radius", "lorentz_scale": "lScale", "guinier_scale": "gScale", "fractal_dim": "FractalExp", "cor_length": "zeta", } ], "guinier": [ "Guinier", { "rg": "rg" }, "GuinierModel", ], "guinier_porod": [ "GuinierPorod", { "s": "dim", "rg": "rg", "porod_exp": "m", "scale": "scale", "background": "background" }, "GuinierPorodModel", ], "hardsphere": [ "HardsphereStructure", { "scale": "scale_factor", "radius_effective": "effect_radius", } ], "hayter_msa": [ "HayterMSAStructure", { "scale": "scale_factor", "radius_effective": "effect_radius", "volfraction": "volfraction", "charge": "charge", "temperature": "temperature", "concentration_salt": "saltconc", "dielectconst": "dielectconst", } ], "hollow_cylinder": [ "HollowCylinderModel", { "sld": "sldCyl", "sld_solvent": "sldSolv", "radius": "core_radius", "thickness": "radius", "length": "length", "theta": "axis_theta", "phi": "axis_phi", } ], "hollow_rectangular_prism": [ "RectangularHollowPrismModel", { "sld": "sldPipe", "sld_solvent": "sldSolv", "length_a": "short_side", "b2a_ratio": "b2a_ratio", "c2a_ratio": "c2a_ratio", "thickness": "thickness", } ], "hollow_rectangular_prism_thin_walls": [ "RectangularHollowPrismInfThinWallsModel", { "sld": "sldPipe", "sld_solvent": "sldSolv", "length_a": "short_side", "b2a_ratio": "b2a_ratio", "c2a_ratio": "c2a_ratio", } ], "lamellar": [ "LamellarModel", { "sld": "sld_bi", "sld_solvent": "sld_sol", "thickness": "bi_thick" } ], "lamellar_hg": [ "LamellarFFHGModel", { "sld": "sld_tail", "sld_solvent": "sld_solvent", "sld_head": "sld_head", "length_tail": "t_length", "length_head": "h_thickness" } ], "lamellar_hg_stack_caille": [ "LamellarPSHGModel", { "sld": "sld_tail", "sld_head": "sld_head", "sld_solvent": "sld_solvent", "length_tail": "deltaT", "length_head": "deltaH", "d_spacing": "spacing", "Caille_parameter": "caille", "Nlayers": "n_plates", } ], "lamellar_stack_caille": [ "LamellarPSModel", { "sld": "sld_bi", "sld_solvent": "sld_sol", "thickness": "delta", "d_spacing": "spacing", "Caille_parameter": "caille", "Nlayers": "n_plates", } ], "lamellar_stack_paracrystal": [ "LamellarPCrystalModel", { "sld": "sld_layer", "sld_solvent": "sld_solvent", "thickness": "thickness", "d_spacing": "spacing", "sigma_d": "pd_spacing", "Nlayers": "Nlayers", } ], "line": [ "LineModel", { "slope": "B", "scale": None, "background": None, "intercept": "A" } ], "linear_pearls": [ "LinearPearlsModel", { "sld": "sld_pearl", "sld_solvent": "sld_solv", "edge_sep": "edge_separation" } ], "lorentz": [ "Lorentz", { "cor_length": "length" }, "LorentzModel", ], "mass_fractal": [ "MassFractalModel", { "cutoff_length": "co_length", "radius": "radius", "fractal_dim_mass": "mass_dim" } ], "mass_surface_fractal": [ "MassSurfaceFractal", { "rg_cluster": "cluster_rg", "fractal_dim_mass": "mass_dim", "radius": "radius", "fractal_dim_surf": "surface_dim", "rg_primary": "primary_rg" } ], "mono_gauss_coil": [ "Debye", { "rg": "rg", "i_zero": "scale", "background": "background", }, "DebyeModel", ], "multilayer_vesicle": [ "MultiShellModel", { "radius": "core_radius", "sld_solvent": "core_sld", "n_shells": "n_pairs", "thick_shell": "s_thickness", "sld": "shell_sld", "thick_solvent": "w_thickness", } ], "onion": [ "OnionExpShellModel", { "n_shells": "n_shells", "A": "A_shell", "sld_core": "sld_core0", "radius_core": "rad_core0", "sld_solvent": "sld_solv", "thickness": "thick_shell", "sld_in": "sld_in_shell", "sld_out": "sld_out_shell" } ], "parallelepiped": [ "ParallelepipedModel", { "phi": "parallel_phi", "psi": "parallel_psi", "sld_solvent": "sldSolv", "length_a": "short_a", "length_b": "short_b", "sld": "sldPipe", "theta": "parallel_theta", "length_c": "long_c", "M0:sld": "M0_sld_pipe", "mtheta:sld": "M_theta_pipe", "mphi:sld": "M_phi_pipe", "M0:sld_solvent": "M0_sld_solv", "mtheta:sld_solvent": "M_theta_solv", "mphi:sld_solvent": "M_phi_solv", "up:frac_i": "Up_frac_i", "up:frac_f": "Up_frac_f", "up:angle": "Up_theta", } ], "peak_lorentz": [ "Peak Lorentz Model", { "peak_pos": "q0", "peak_hwhm": "B" }, "PeakLorentzModel", ], "pearl_necklace": [ "PearlNecklaceModel", { "scale": "scale", "thick_string": "thick_string", "sld_string": "sld_string", "sld_solvent": "sld_solv", "edge_sep": "edge_separation", "num_pearls": "num_pearls", "radius": "radius", "background": "background", "sld": "sld_pearl" } ], "poly_gauss_coil": [ "Poly_GaussCoil", { "rg": "rg", "polydispersity": "poly_m", "i_zero": "scale", "background": "background", } ], "polymer_excl_volume": [ "PolymerExclVolume", { "rg": "rg", "scale": "scale", "background": "background", "porod_exp": "m" } ], "polymer_micelle": [ "MicelleSphCoreModel", { "sld_corona": "rho_corona", "sld_solvent": "rho_solv", "sld_core": "rho_core", "ndensity": "ndensity", "v_core": "v_core", "v_corona": "v_corona", "radius_core": "radius_core", "rg": "radius_gyr", "d_penetration": "d_penetration", "n_aggreg": "n_aggreg", } ], "porod": [ "PorodModel", { "scale": "scale", "background": "background" } ], "power_law": [ "PowerLawAbsModel", { "scale": "scale", "background": "background", "power": "m" } ], "pringle": [ "PringlesModel", { "scale": "scale", "sld_solvent": "sld_solvent", "thickness": "thickness", "beta": "beta", "radius": "radius", "background": "background", "alpha": "alpha", "sld": "sld_pringle" } ], "raspberry": [ "RaspBerryModel", { "volfraction_lg": "volf_Lsph", "volfraction_sm": "volf_Ssph", "radius_sm": "radius_Ssph", "radius_lg": "radius_Lsph", "sld_lg": "sld_Lsph", "sld_sm": "sld_Ssph", "sld_solvent": "sld_solv", "surface_fraction": "surfrac_Ssph", "penetration": "delta_Ssph" } ], "rectangular_prism": [ "RectangularPrismModel", { "sld": "sldPipe", "length_a": "short_side", "b2a_ratio": "b2a_ratio", "c2a_ratio": "c2a_ratio", "sld_solvent": "sldSolv" } ], "rpa": [ "RPA10Model", { "K12": "Kab", "K13": "Kac", "K14": "Kad", "K23": "Kbc", "K24": "Kbd", "K34": "Kcd", "N1": "Na", "N2": "Nb", "N3": "Nc", "N4": "Nd", "L1": "La", "L2": "Lb", "L3": "Lc", "L4": "Ld", "v1": "va", "v2": "vb", "v3": "vc", "v4": "vd", "b1": "ba", "b2": "bb", "b3": "bc", "b4": "bd", "Phi1": "Phia", "Phi2": "Phib", "Phi3": "Phic", "Phi4": "Phid", "case_num": "lcase_n" } ], "sc_paracrystal": [ "SCCrystalModel", { "sld": "sldSph", "sld_solvent": "sldSolv" } ], "sphere": [ "SphereModel", { "sld": "sldSph", "radius": "radius", "sld_solvent": "sldSolv", "M0:sld": "M0_sld_sph", "mtheta:sld": "M_theta_sph", "mphi:sld": "M_phi_sph", "M0:sld_solvent": "M0_sld_solv", "mtheta:sld_solvent": "M_theta_solv", "mphi:sld_solvent": "M_phi_solv", "up:frac_i": "Up_frac_i", "up:frac_f": "Up_frac_f", "up:angle": "Up_theta" } ], "spherical_sld": [ "SphericalSLDModel", # Be lazy and use a generator expression to define # sld1: sld_flat0, ... # thickness1: thick_flat0, ... # interface1: thick_inter0, ... # shape1: func_inter0, ... # nu1: nu_inter0, ... # but override thickness1 => rad_cor0 and sld1 => sld_core0. # Note: explicit key,value pairs given by **{...} override the # keys from the gnerator expression ((k,v) for k,v in seq) when # used as dict((generator), **{...}) dict(((field_new+str(index+1), field_old+str(index)) for field_new, field_old in [("sld", "sld_flat"), ("thickness", "thick_flat"), ("interface", "thick_inter"), ("shape", "func_inter"), ("nu", "nu_inter"),] for index in range(11)), **{ "n_shells": "n_shells", "n_steps": "npts_inter", "sld_solvent": "sld_solv", "thickness1": "rad_core0", "sld1": "sld_core0", }) ], "squarewell": [ "SquareWellStructure", { "scale": "scale_factor", "radius_effective": "effect_radius", "wellwidth": "wellwidth", "welldepth": "welldepth", } ], "stacked_disks": [ "StackedDisksModel", { "phi": "axis_phi", "sld_layer": "layer_sld", "sld_core": "core_sld", "theta": "axis_theta", "sld_solvent": "solvent_sld", "n_stacking": "n_stacking", "thick_layer": "layer_thick", "thick_core": "core_thick", } ], "star_polymer": [ "StarPolymer", { "arms": "arms", "rg_squared": "R2" } ], "stickyhardsphere": [ "StickyHSStructure", { "scale": "scale_factor", "radius_effective": "effect_radius", } ], "surface_fractal": [ "SurfaceFractalModel", { "cutoff_length": "co_length", "radius": "radius", "fractal_dim_surf": "surface_dim" } ], "teubner_strey": [ "TeubnerStreyModel", { # Note: parameters are completely rewritten in convert.py "volfraction_a": "volfraction_a", "sld_a": "sld_a", "sld_b": "sld_b", "d": "d", "xi": "xi", } ], "triaxial_ellipsoid": [ "TriaxialEllipsoidModel", { "phi": "axis_phi", "radius_equat_minor": "semi_axisA", "radius_polar": "semi_axisC", "radius_equat_major": "semi_axisB", "sld_solvent": "sldSolv", "psi": "axis_psi", "sld": "sldEll", "theta": "axis_theta" } ], "two_lorentzian": [ "TwoLorentzian", { "lorentz_scale_1": "scale_1", "lorentz_scale_2": "scale_2", "lorentz_exp_1": "exponent_1", "lorentz_exp_2": "exponent_2", "lorentz_length_2": "length_2", "lorentz_length_1": "length_1", "background": "background" }, "TwoLorentzianModel", ], "two_power_law": [ "TwoPowerLaw", { "coefficent_1": "coef_A", "power_2": "power2", "power_1": "power1", "background": "background", "crossover": "qc" }, "TwoPowerLawModel", ], "unified_power_Rg": [ "UnifiedPowerRg", dict(((field_new+str(index), field_old+str(index)) for field_new, field_old in [("rg", "Rg"), ("power", "power"), ("G", "G"), ("B", "B"),] for index in range(11)), **{ "background": "background", "scale": "scale", }), "UnifiedPowerRgModel", ], "vesicle": [ "VesicleModel", { "sld": "shell_sld", "sld_solvent": "solv_sld" } ] } } sasmodels/sasmodels/convert.py000066400000000000000000000577241317715334700171260ustar00rootroot00000000000000""" Convert models to and from sasview. """ from __future__ import print_function, division import re import math import warnings from .conversion_table import CONVERSION_TABLE from .core import load_model_info # List of models which SasView versions don't contain the explicit 'scale' argument. # When converting such a model, please update this list. MODELS_WITHOUT_SCALE = [ 'teubner_strey', 'broad_peak', 'two_lorentzian', "two_power_law", 'gauss_lorentz_gel', 'be_polyelectrolyte', 'correlation_length', 'fractal_core_shell', 'binary_hard_sphere', 'raspberry' ] # List of models which SasView versions don't contain the explicit 'background' argument. # When converting such a model, please update this list. MODELS_WITHOUT_BACKGROUND = [ 'guinier', ] MODELS_WITHOUT_VOLFRACTION = [ 'fractal', 'vesicle', 'multilayer_vesicle', ] MAGNETIC_SASVIEW_MODELS = [ 'core_shell', 'core_multi_shell', 'cylinder', 'parallelepiped', 'sphere', ] # Convert new style names for polydispersity info to old style names PD_DOT = [ ("_pd", ".width"), ("_pd_n", ".npts"), ("_pd_nsigma", ".nsigmas"), ("_pd_type", ".type"), (".lower", ".lower"), (".upper", ".upper"), (".fittable", ".fittable"), (".std", ".std"), (".units", ".units"), ("", "") ] def _rescale(par, scale): return [pk*scale for pk in par] if isinstance(par, list) else par*scale def _is_sld(model_info, id): """ Return True if parameter is a magnetic magnitude or SLD parameter. """ if id.startswith('M0:'): return True if '_pd' in id or '.' in id: return False for p in model_info.parameters.call_parameters: if p.id == id: return p.type == 'sld' # check through kernel parameters in case it is a named as a vector for p in model_info.parameters.kernel_parameters: if p.id == id: return p.type == 'sld' return False def _rescale_sld(model_info, pars, scale): """ rescale all sld parameters in the new model definition by *scale* so the numbers are nicer. Relies on the fact that all sld parameters in the new model definition end with sld. For backward conversion use *scale=1e-6*. For forward conversion use *scale=1e6*. """ return dict((id, (_rescale(v, scale) if _is_sld(model_info, id) else v)) for id, v in pars.items()) def _get_translation_table(model_info, version=(3,1,2)): conv_param = CONVERSION_TABLE.get(version, {}).get(model_info.id, [None, {}]) translation = conv_param[1].copy() for p in model_info.parameters.kernel_parameters: if p.length > 1: newid = p.id oldid = translation.get(p.id, p.id) translation.pop(newid, None) for k in range(1, p.length+1): if newid+str(k) not in translation: translation[newid+str(k)] = oldid+str(k) # Remove control parameter from the result if model_info.control: translation[model_info.control] = "CONTROL" return translation # ========= FORWARD CONVERSION sasview 3.x => sasmodels =========== def _dot_pd_to_underscore_pd(par): if par.endswith(".width"): return par[:-6]+"_pd" elif par.endswith(".type"): return par[:-5]+"_pd_type" elif par.endswith(".nsigmas"): return par[:-8]+"_pd_nsigma" elif par.endswith(".npts"): return par[:-5]+"_pd_n" else: return par def _pd_to_underscores(pars): return dict((_dot_pd_to_underscore_pd(k), v) for k, v in pars.items()) def _convert_pars(pars, mapping): """ Rename the parameters and any associated polydispersity attributes. """ newpars = pars.copy() for new, old in mapping.items(): if old == new: continue if old is None: continue for underscore, dot in PD_DOT: source = old+dot if source in newpars: if new is not None: target = new+dot else: target = None if source != target: if target: newpars[target] = pars[old+dot] del newpars[source] return newpars def _conversion_target(model_name, version=(3,1,2)): """ Find the sasmodel name which translates into the sasview name. Note: *CoreShellEllipsoidModel* translates into *core_shell_ellipsoid:1*. This is necessary since there is only one variant in sasmodels for the two variants in sasview. """ for sasmodels_name, sasview_dict in \ CONVERSION_TABLE.get(version, {}).items(): if sasview_dict[0] == model_name: return sasmodels_name return None def _hand_convert(name, oldpars, version=(3,1,2)): if version == (3,1,2): oldpars = _hand_convert_3_1_2_to_4_1(name, oldpars) return oldpars def _hand_convert_3_1_2_to_4_1(name, oldpars): if name == 'core_shell_parallelepiped': # Make sure pd on rim parameters defaults to zero # ... probably not necessary. oldpars['rimA.width'] = 0.0 oldpars['rimB.width'] = 0.0 oldpars['rimC.width'] = 0.0 elif name == 'core_shell_ellipsoid:1': # Reverse translation (from new to old), from core_shell_ellipsoid.c # equat_shell = equat_core + thick_shell # polar_core = equat_core * x_core # polar_shell = equat_core * x_core + thick_shell*x_polar_shell # Forward translation (from old to new), inverting reverse translation: # thick_shell = equat_shell - equat_core # x_core = polar_core / equat_core # x_polar_shell = (polar_shell - polar_core)/(equat_shell - equat_core) # Auto translation (old <=> new) happens after hand_convert # equat_shell <=> thick_shell # polar_core <=> x_core # polar_shell <=> x_polar_shell # So... equat_core, equat_shell = oldpars['equat_core'], oldpars['equat_shell'] polar_core, polar_shell = oldpars['polar_core'], oldpars['polar_shell'] oldpars['equat_shell'] = equat_shell - equat_core oldpars['polar_core'] = polar_core / equat_core oldpars['polar_shell'] = (polar_shell-polar_core)/(equat_shell-equat_core) elif name == 'hollow_cylinder': # now uses radius and thickness thickness = oldpars['radius'] - oldpars['core_radius'] oldpars['radius'] = thickness if 'radius.width' in oldpars: pd = oldpars['radius.width']*oldpars['radius']/thickness oldpars['radius.width'] = pd elif name == 'multilayer_vesicle': if 'scale' in oldpars: oldpars['volfraction'] = oldpars['scale'] oldpars['scale'] = 1.0 if 'scale.lower' in oldpars: oldpars['volfraction.lower'] = oldpars['scale.lower'] if 'scale.upper' in oldpars: oldpars['volfraction.upper'] = oldpars['scale.upper'] if 'scale.fittable' in oldpars: oldpars['volfraction.fittable'] = oldpars['scale.fittable'] if 'scale.std' in oldpars: oldpars['volfraction.std'] = oldpars['scale.std'] if 'scale.units' in oldpars: oldpars['volfraction.units'] = oldpars['scale.units'] elif name == 'pearl_necklace': pass #_remove_pd(oldpars, 'num_pearls', name) #_remove_pd(oldpars, 'thick_string', name) elif name == 'polymer_micelle': if 'ndensity' in oldpars: oldpars['ndensity'] /= 1e15 if 'ndensity.lower' in oldpars: oldpars['ndensity.lower'] /= 1e15 if 'ndensity.upper' in oldpars: oldpars['ndensity.upper'] /= 1e15 elif name == 'rpa': # convert scattering lengths from femtometers to centimeters for p in "L1", "L2", "L3", "L4": if p in oldpars: oldpars[p] /= 1e-13 if p + ".lower" in oldpars: oldpars[p + ".lower"] /= 1e-13 if p + ".upper" in oldpars: oldpars[p + ".upper"] /= 1e-13 elif name == 'spherical_sld': j = 0 while "func_inter" + str(j) in oldpars: name = "func_inter" + str(j) new_name = "shape" + str(j + 1) if oldpars[name] == 'Erf(|nu|*z)': oldpars[new_name] = int(0) elif oldpars[name] == 'RPower(z^|nu|)': oldpars[new_name] = int(1) elif oldpars[name] == 'LPower(z^|nu|)': oldpars[new_name] = int(2) elif oldpars[name] == 'RExp(-|nu|*z)': oldpars[new_name] = int(3) elif oldpars[name] == 'LExp(-|nu|*z)': oldpars[new_name] = int(4) else: oldpars[new_name] = int(0) oldpars.pop(name) oldpars['n_shells'] = str(j + 1) j += 1 elif name == 'teubner_strey': # basically undoing the entire Teubner-Strey calculations here. # drho = (sld_a - sld_b) # k = 2.0*math.pi*xi/d # a2 = (1.0 + k**2)**2 # c1 = 2.0 * xi**2 * (1.0 - k**2) # c2 = xi**4 # prefactor = 8.0*math.pi*phi*(1.0-phi)*drho**2*c2/xi # scale = 1e-4*prefactor # oldpars['scale'] = a2/scale # oldpars['c1'] = c1/scale # oldpars['c2'] = c2/scale # need xi, d, sld_a, sld_b, phi=volfraction_a # assume contrast is 1.0e-6, scale=1, background=0 sld_a, sld_b = 1.0, 0. drho = sld_a - sld_b # find xi p_scale = oldpars['scale'] p_c1 = oldpars['c1'] p_c2= oldpars['c2'] i_1 = 0.5*p_c1/p_c2 i_2 = math.sqrt(math.fabs(p_scale/p_c2)) i_3 = 2/(i_1 + i_2) xi = math.sqrt(math.fabs(i_3)) # find d from xi k = math.sqrt(math.fabs(1 - 0.5*p_c1/p_c2*xi**2)) d = 2*math.pi*xi/k # solve quadratic phi (1-phi) = xi/(1e-4 8 pi drho^2 c2) # favour volume fraction in [0, 0.5] c = xi / (1e-4 * 8.0 * math.pi * drho**2 * p_c2) phi = 0.5 - math.sqrt(0.25 - c) # scale sld_a by 1e-6 because the translator will scale it back oldpars.update(volfraction_a=phi, xi=xi, d=d, sld_a=sld_a*1e-6, sld_b=sld_b, scale=1.0) oldpars.pop('c1') oldpars.pop('c2') return oldpars def convert_model(name, pars, use_underscore=False, model_version=(3,1,2)): """ Convert model from old style parameter names to new style. """ newpars = pars keys = sorted(CONVERSION_TABLE.keys()) for i, version in enumerate(keys): # Don't allow indices outside list next_i = i + 1 if next_i == len(keys): next_i = i # If the save state is from a later version, skip the check if model_version <= keys[next_i]: newname = _conversion_target(name, version) else: newname = None # If no conversion is found, move on if newname is None: newname = name continue if ':' in newname: # core_shell_ellipsoid:1 model_info = load_model_info(newname[:-2]) # Know the table exists and isn't multiplicity so grab it directly # Can't use _get_translation_table since that will return the 'bare' # version. translation = CONVERSION_TABLE.get(version, {})[newname][1] else: model_info = load_model_info(newname) translation = _get_translation_table(model_info, version) newpars = _hand_convert(newname, newpars, version) newpars = _convert_pars(newpars, translation) # TODO: Still not convinced this is the best check if not model_info.structure_factor and version == (3,1,2): newpars = _rescale_sld(model_info, newpars, 1e6) newpars.setdefault('scale', 1.0) newpars.setdefault('background', 0.0) if use_underscore: newpars = _pd_to_underscores(newpars) name = newname return newname, newpars # ========= BACKWARD CONVERSION sasmodels => sasview 3.x =========== def _revert_pars(pars, mapping): """ Rename the parameters and any associated polydispersity attributes. """ newpars = pars.copy() for new, old in mapping.items(): for underscore, dot in PD_DOT: if old and old+underscore == new+dot: continue if new+underscore in newpars: if old is not None: newpars[old+dot] = pars[new+underscore] del newpars[new+underscore] for k in list(newpars.keys()): for underscore, dot in PD_DOT[1:]: # skip "" => "" if k.endswith(underscore): newpars[k[:-len(underscore)]+dot] = newpars[k] del newpars[k] return newpars def revert_name(model_info): oldname, _ = CONVERSION_TABLE.get(model_info.id, [None, {}]) return oldname def _remove_pd(pars, key, name): """ Remove polydispersity from the parameter list. Note: operates in place """ # Bumps style parameter names width = pars.pop(key+".width", 0.0) n_points = pars.pop(key+".npts", 0) if width != 0.0 and n_points != 0: warnings.warn("parameter %s not polydisperse in sasview %s"%(key, name)) pars.pop(key+".nsigmas", None) pars.pop(key+".type", None) return pars def _trim_vectors(model_info, pars, oldpars): _, translation = CONVERSION_TABLE.get(model_info.id, [None, {}]) for p in model_info.parameters.kernel_parameters: if p.length_control is not None: n = int(pars[p.length_control]) oldname = translation.get(p.id, p.id) for k in range(n+1, p.length+1): for _, old in PD_DOT: oldpars.pop(oldname+str(k)+old, None) return oldpars def revert_pars(model_info, pars): """ Convert model from new style parameter names to old style. """ if model_info.composition is not None: composition_type, parts = model_info.composition if composition_type == 'product': translation = _get_translation_table(parts[0]) # structure factor models include scale:scale_factor mapping translation.update(_get_translation_table(parts[1])) else: raise NotImplementedError("cannot convert to sasview sum") else: translation = _get_translation_table(model_info) oldpars = _revert_pars(_rescale_sld(model_info, pars, 1e-6), translation) oldpars = _trim_vectors(model_info, pars, oldpars) # Make sure the control parameter is an integer if "CONTROL" in oldpars: oldpars["CONTROL"] = int(oldpars["CONTROL"]) # Note: update compare.constrain_pars to match name = model_info.id if name in MODELS_WITHOUT_SCALE or model_info.structure_factor: if oldpars.pop('scale', 1.0) != 1.0: warnings.warn("parameter scale not used in sasview %s"%name) if name in MODELS_WITHOUT_BACKGROUND or model_info.structure_factor: if oldpars.pop('background', 0.0) != 0.0: warnings.warn("parameter background not used in sasview %s"%name) # Remove magnetic parameters from non-magnetic sasview models if name not in MAGNETIC_SASVIEW_MODELS: oldpars = dict((k, v) for k, v in oldpars.items() if ':' not in k) # If it is a product model P*S, then check the individual forms for special # cases. Note: despite the structure factor alone not having scale or # background, the product model does, so this is below the test for # models without scale or background. namelist = name.split('*') if '*' in name else [name] for name in namelist: if name in MODELS_WITHOUT_VOLFRACTION: del oldpars['volfraction'] elif name == 'core_multi_shell': # kill extra shells for k in range(5, 11): oldpars.pop('sld_shell'+str(k), 0) oldpars.pop('thick_shell'+str(k), 0) oldpars.pop('mtheta:sld'+str(k), 0) oldpars.pop('mphi:sld'+str(k), 0) oldpars.pop('M0:sld'+str(k), 0) _remove_pd(oldpars, 'sld_shell'+str(k), 'sld') _remove_pd(oldpars, 'thick_shell'+str(k), 'thickness') elif name == 'core_shell_parallelepiped': _remove_pd(oldpars, 'rimA', name) _remove_pd(oldpars, 'rimB', name) _remove_pd(oldpars, 'rimC', name) elif name == 'hollow_cylinder': # now uses radius and thickness thickness = oldpars['core_radius'] oldpars['radius'] += thickness oldpars['radius.width'] *= thickness/oldpars['radius'] #elif name in ['mono_gauss_coil', 'poly_gauss_coil']: # del oldpars['i_zero'] elif name == 'onion': oldpars.pop('n_shells', None) elif name == 'pearl_necklace': _remove_pd(oldpars, 'num_pearls', name) _remove_pd(oldpars, 'thick_string', name) elif name == 'polymer_micelle': if 'ndensity' in oldpars: oldpars['ndensity'] *= 1e15 elif name == 'rpa': # convert scattering lengths from femtometers to centimeters for p in "L1", "L2", "L3", "L4": if p in oldpars: oldpars[p] *= 1e-13 if pars['case_num'] < 2: for k in ("a", "b"): for p in ("L", "N", "Phi", "b", "v"): oldpars.pop(p+k, None) for k in "Kab,Kac,Kad,Kbc,Kbd".split(','): oldpars.pop(k, None) elif pars['case_num'] < 5: for k in ("a",): for p in ("L", "N", "Phi", "b", "v"): oldpars.pop(p+k, None) for k in "Kab,Kac,Kad".split(','): oldpars.pop(k, None) elif name == 'spherical_sld': oldpars["CONTROL"] -= 1 # remove polydispersity from shells for k in range(1, 11): _remove_pd(oldpars, 'thick_flat'+str(k), 'thickness') _remove_pd(oldpars, 'thick_inter'+str(k), 'interface') # remove extra shells for k in range(int(pars['n_shells']), 11): oldpars.pop('sld_flat'+str(k), 0) oldpars.pop('thick_flat'+str(k), 0) oldpars.pop('thick_inter'+str(k), 0) oldpars.pop('func_inter'+str(k), 0) oldpars.pop('nu_inter'+str(k), 0) elif name == 'stacked_disks': _remove_pd(oldpars, 'n_stacking', name) elif name == 'teubner_strey': # basically redoing the entire Teubner-Strey calculations here. volfraction = oldpars.pop('volfraction_a') xi = oldpars.pop('xi') d = oldpars.pop('d') sld_a = oldpars.pop('sld_a') sld_b = oldpars.pop('sld_b') drho = 1e6*(sld_a - sld_b) # conversion autoscaled these k = 2.0*math.pi*xi/d a2 = (1.0 + k**2)**2 c1 = 2.0 * xi**2 * (1.0 - k**2) c2 = xi**4 prefactor = 8.0*math.pi*volfraction*(1.0-volfraction)*drho**2*c2/xi scale = 1e-4*prefactor oldpars['scale'] = a2/scale oldpars['c1'] = c1/scale oldpars['c2'] = c2/scale #print("convert from",list(sorted(pars))) #print("convert to",list(sorted(oldpars.items()))) return oldpars def constrain_new_to_old(model_info, pars): """ Restrict parameter values to those that will match sasview. """ name = model_info.id # Note: update convert.revert_model to match if name in MODELS_WITHOUT_SCALE or model_info.structure_factor: pars['scale'] = 1 if name in MODELS_WITHOUT_BACKGROUND or model_info.structure_factor: pars['background'] = 0 # sasview multiplies background by structure factor if '*' in name: pars['background'] = 0 # Shut off magnetism when comparing non-magnetic sasview models if name not in MAGNETIC_SASVIEW_MODELS: suppress_magnetism = False for key in pars.keys(): if key.startswith("M0:"): suppress_magnetism = suppress_magnetism or (pars[key] != 0) pars[key] = 0 if suppress_magnetism: warnings.warn("suppressing magnetism for comparison with sasview") # Shut off theta polydispersity since algorithm has changed if 'theta_pd_n' in pars: if pars['theta_pd_n'] != 0: warnings.warn("suppressing theta polydispersity for comparison with sasview") pars['theta_pd_n'] = 0 # If it is a product model P*S, then check the individual forms for special # cases. Note: despite the structure factor alone not having scale or # background, the product model does, so this is below the test for # models without scale or background. namelist = name.split('*') if '*' in name else [name] for name in namelist: if name in MODELS_WITHOUT_VOLFRACTION: pars['volfraction'] = 1 if name == 'core_multi_shell': pars['n'] = min(math.ceil(pars['n']), 4) elif name == 'gel_fit': pars['scale'] = 1 elif name == 'line': pars['scale'] = 1 pars['background'] = 0 elif name == 'mono_gauss_coil': pars['scale'] = 1 elif name == 'onion': pars['n_shells'] = math.ceil(pars['n_shells']) elif name == 'pearl_necklace': pars['string_thickness_pd_n'] = 0 pars['number_of_pearls_pd_n'] = 0 elif name == 'poly_gauss_coil': pars['scale'] = 1 elif name == 'rpa': pars['case_num'] = int(pars['case_num']) elif name == 'spherical_sld': pars['n_shells'] = math.ceil(pars['n_shells']) pars['n_steps'] = math.ceil(pars['n_steps']) for k in range(1, 11): pars['shape%d'%k] = math.trunc(pars['shape%d'%k]+0.5) for k in range(2, 11): pars['thickness%d_pd_n'%k] = 0 pars['interface%d_pd_n'%k] = 0 elif name == 'teubner_strey': pars['scale'] = 1 if pars['volfraction_a'] > 0.5: pars['volfraction_a'] = 1.0 - pars['volfraction_a'] elif name == 'unified_power_Rg': pars['level'] = int(pars['level']) def _check_one(name, seed=None): """ Generate a random set of parameters for *name*, and check that they can be converted back to SasView 3.x and forward again to sasmodels. Raises an error if the parameters are changed. """ from . import compare model_info = load_model_info(name) old_name = revert_name(model_info) if old_name is None: return pars = compare.get_pars(model_info, use_demo=False) pars = compare.randomize_pars(model_info, pars, seed=seed) if name == "teubner_strey": # T-S model is underconstrained, so fix the assumptions. pars['sld_a'], pars['sld_b'] = 1.0, 0.0 compare.constrain_pars(model_info, pars) constrain_new_to_old(model_info, pars) old_pars = revert_pars(model_info, pars) new_name, new_pars = convert_model(old_name, old_pars, use_underscore=True) if 1: print("==== %s in ====="%name) print(str(compare.parlist(model_info, pars, True))) print("==== %s ====="%old_name) for k, v in sorted(old_pars.items()): print(k, v) print("==== %s out ====="%new_name) print(str(compare.parlist(model_info, new_pars, True))) assert name==new_name, "%r != %r"%(name, new_name) for k, v in new_pars.items(): assert k in pars, "%s: %r appeared from conversion"%(name, k) if isinstance(v, float): assert abs(v-pars[k])<=abs(1e-12*v), "%s: %r %s != %s"%(name, k, v, pars[k]) else: assert v == pars[k], "%s: %r %s != %s"%(name, k, v, pars[k]) for k, v in pars.items(): assert k in pars, "%s: %r not converted"%(name, k) def test_backward_forward(): from .core import list_models for name in list_models('all'): L = lambda: _check_one(name, seed=1) L.description = name yield L sasmodels/sasmodels/core.py000066400000000000000000000304601317715334700163620ustar00rootroot00000000000000""" Core model handling routines. """ from __future__ import print_function __all__ = [ "list_models", "load_model", "load_model_info", "build_model", "precompile_dlls", ] import os import re from os.path import basename, dirname, join as joinpath from glob import glob import numpy as np # type: ignore from . import generate from . import modelinfo from . import product from . import mixture from . import kernelpy from . import kerneldll from . import custom if os.environ.get("SAS_OPENCL", "").lower() == "none": HAVE_OPENCL = False else: try: from . import kernelcl HAVE_OPENCL = True except Exception: HAVE_OPENCL = False CUSTOM_MODEL_PATH = os.environ.get('SAS_MODELPATH', "") if CUSTOM_MODEL_PATH == "": path = joinpath(os.path.expanduser("~"), ".sasmodels", "custom_models") if not os.path.isdir(path): os.makedirs(path) CUSTOM_MODEL_PATH = path try: from typing import List, Union, Optional, Any from .kernel import KernelModel from .modelinfo import ModelInfo except ImportError: pass # TODO: refactor composite model support # The current load_model_info/build_model does not reuse existing model # definitions when loading a composite model, instead reloading and # rebuilding the kernel for each component model in the expression. This # is fine in a scripting environment where the model is built when the script # starts and is thrown away when the script ends, but may not be the best # solution in a long-lived application. This affects the following functions: # # load_model # load_model_info # build_model KINDS = ("all", "py", "c", "double", "single", "opencl", "1d", "2d", "nonmagnetic", "magnetic") def list_models(kind=None): # type: (str) -> List[str] """ Return the list of available models on the model path. *kind* can be one of the following: * all: all models * py: python models only * c: compiled models only * single: models which support single precision * double: models which require double precision * opencl: controls if OpenCL is supperessed * 1d: models which are 1D only, or 2D using abs(q) * 2d: models which can be 2D * magnetic: models with an sld * nommagnetic: models without an sld For multiple conditions, combine with plus. For example, *c+single+2d* would return all oriented models implemented in C which can be computed accurately with single precision arithmetic. """ if kind and any(k not in KINDS for k in kind.split('+')): raise ValueError("kind not in " + ", ".join(KINDS)) files = sorted(glob(joinpath(generate.MODEL_PATH, "[a-zA-Z]*.py"))) available_models = [basename(f)[:-3] for f in files] if kind and '+' in kind: all_kinds = kind.split('+') condition = lambda name: all(_matches(name, k) for k in all_kinds) else: condition = lambda name: _matches(name, kind) selected = [name for name in available_models if condition(name)] return selected def _matches(name, kind): if kind is None or kind == "all": return True info = load_model_info(name) pars = info.parameters.kernel_parameters if kind == "py" and callable(info.Iq): return True elif kind == "c" and not callable(info.Iq): return True elif kind == "double" and not info.single: return True elif kind == "single" and info.single: return True elif kind == "opencl" and info.opencl: return True elif kind == "2d" and any(p.type == 'orientation' for p in pars): return True elif kind == "1d" and all(p.type != 'orientation' for p in pars): return True elif kind == "magnetic" and any(p.type == 'sld' for p in pars): return True elif kind == "nonmagnetic" and any(p.type != 'sld' for p in pars): return True return False def load_model(model_name, dtype=None, platform='ocl'): # type: (str, str, str) -> KernelModel """ Load model info and build model. *model_name* is the name of the model, or perhaps a model expression such as sphere*hardsphere or sphere+cylinder. *dtype* and *platform* are given by :func:`build_model`. """ return build_model(load_model_info(model_name), dtype=dtype, platform=platform) def load_model_info(model_string): # type: (str) -> modelinfo.ModelInfo """ Load a model definition given the model name. *model_string* is the name of the model, or perhaps a model expression such as sphere*cylinder or sphere+cylinder. Use '@' for a structure factor product, e.g. sphere@hardsphere. Custom models can be specified by prefixing the model name with 'custom.', e.g. 'custom.MyModel+sphere'. This returns a handle to the module defining the model. This can be used with functions in generate to build the docs or extract model info. """ if '@' in model_string: parts = model_string.split('@') if len(parts) != 2: raise ValueError("Use P@S to apply a structure factor S to model P") P_info, Q_info = [load_model_info(part) for part in parts] return product.make_product_info(P_info, Q_info) product_parts = [] addition_parts = [] addition_parts_names = model_string.split('+') if len(addition_parts_names) >= 2: addition_parts = [load_model_info(part) for part in addition_parts_names] elif len(addition_parts_names) == 1: product_parts_names = model_string.split('*') if len(product_parts_names) >= 2: product_parts = [load_model_info(part) for part in product_parts_names] elif len(product_parts_names) == 1: if "custom." in product_parts_names[0]: # Extract ModelName from "custom.ModelName" pattern = "custom.([A-Za-z0-9_-]+)" result = re.match(pattern, product_parts_names[0]) if result is None: raise ValueError("Model name in invalid format: " + product_parts_names[0]) model_name = result.group(1) # Use ModelName to find the path to the custom model file model_path = joinpath(CUSTOM_MODEL_PATH, model_name + ".py") if not os.path.isfile(model_path): raise ValueError("The model file {} doesn't exist".format(model_path)) kernel_module = custom.load_custom_kernel_module(model_path) return modelinfo.make_model_info(kernel_module) # Model is a core model kernel_module = generate.load_kernel_module(product_parts_names[0]) return modelinfo.make_model_info(kernel_module) model = None if len(product_parts) > 1: model = mixture.make_mixture_info(product_parts, operation='*') if len(addition_parts) > 1: if model is not None: addition_parts.append(model) model = mixture.make_mixture_info(addition_parts, operation='+') return model def build_model(model_info, dtype=None, platform="ocl"): # type: (modelinfo.ModelInfo, str, str) -> KernelModel """ Prepare the model for the default execution platform. This will return an OpenCL model, a DLL model or a python model depending on the model and the computing platform. *model_info* is the model definition structure returned from :func:`load_model_info`. *dtype* indicates whether the model should use single or double precision for the calculation. Choices are 'single', 'double', 'quad', 'half', or 'fast'. If *dtype* ends with '!', then force the use of the DLL rather than OpenCL for the calculation. *platform* should be "dll" to force the dll to be used for C models, otherwise it uses the default "ocl". """ composition = model_info.composition if composition is not None: composition_type, parts = composition models = [build_model(p, dtype=dtype, platform=platform) for p in parts] if composition_type == 'mixture': return mixture.MixtureModel(model_info, models) elif composition_type == 'product': P, S = models return product.ProductModel(model_info, P, S) else: raise ValueError('unknown mixture type %s'%composition_type) # If it is a python model, return it immediately if callable(model_info.Iq): return kernelpy.PyModel(model_info) numpy_dtype, fast, platform = parse_dtype(model_info, dtype, platform) source = generate.make_source(model_info) if platform == "dll": #print("building dll", numpy_dtype) return kerneldll.load_dll(source['dll'], model_info, numpy_dtype) else: #print("building ocl", numpy_dtype) return kernelcl.GpuModel(source, model_info, numpy_dtype, fast=fast) def precompile_dlls(path, dtype="double"): # type: (str, str) -> List[str] """ Precompile the dlls for all builtin models, returning a list of dll paths. *path* is the directory in which to save the dlls. It will be created if it does not already exist. This can be used when build the windows distribution of sasmodels which may be missing the OpenCL driver and the dll compiler. """ numpy_dtype = np.dtype(dtype) if not os.path.exists(path): os.makedirs(path) compiled_dlls = [] for model_name in list_models(): model_info = load_model_info(model_name) if not callable(model_info.Iq): source = generate.make_source(model_info)['dll'] old_path = kerneldll.DLL_PATH try: kerneldll.DLL_PATH = path dll = kerneldll.make_dll(source, model_info, dtype=numpy_dtype) finally: kerneldll.DLL_PATH = old_path compiled_dlls.append(dll) return compiled_dlls def parse_dtype(model_info, dtype=None, platform=None): # type: (ModelInfo, str, str) -> (np.dtype, bool, str) """ Interpret dtype string, returning np.dtype and fast flag. Possible types include 'half', 'single', 'double' and 'quad'. If the type is 'fast', then this is equivalent to dtype 'single' but using fast native functions rather than those with the precision level guaranteed by the OpenCL standard. Platform preference can be specfied ("ocl" vs "dll"), with the default being OpenCL if it is availabe. If the dtype name ends with '!' then platform is forced to be DLL rather than OpenCL. This routine ignores the preferences within the model definition. This is by design. It allows us to test models in single precision even when we have flagged them as requiring double precision so we can easily check the performance on different platforms without having to change the model definition. """ # Assign default platform, overriding ocl with dll if OpenCL is unavailable # If opencl=False OpenCL is switched off if platform is None: platform = "ocl" if platform == "ocl" and not HAVE_OPENCL or not model_info.opencl: platform = "dll" # Check if type indicates dll regardless of which platform is given if dtype is not None and dtype.endswith('!'): platform = "dll" dtype = dtype[:-1] # Convert special type names "half", "fast", and "quad" fast = (dtype == "fast") if fast: dtype = "single" elif dtype == "quad": dtype = "longdouble" elif dtype == "half": dtype = "float16" # Convert dtype string to numpy dtype. if dtype is None or dtype == "default": numpy_dtype = (generate.F32 if platform == "ocl" and model_info.single else generate.F64) else: numpy_dtype = np.dtype(dtype) # Make sure that the type is supported by opencl, otherwise use dll if platform == "ocl": env = kernelcl.environment() if not env.has_type(numpy_dtype): platform = "dll" if dtype is None: numpy_dtype = generate.F64 return numpy_dtype, fast, platform def list_models_main(): # type: () -> None """ Run list_models as a main program. See :func:`list_models` for the kinds of models that can be requested on the command line. """ import sys kind = sys.argv[1] if len(sys.argv) > 1 else "all" print("\n".join(list_models(kind))) if __name__ == "__main__": list_models_main() sasmodels/sasmodels/custom/000077500000000000000000000000001317715334700163675ustar00rootroot00000000000000sasmodels/sasmodels/custom/__init__.py000066400000000000000000000033541317715334700205050ustar00rootroot00000000000000""" Custom Models ------------- This is a place holder for the custom models namespace. When models are loaded from a file by :func:`generate.load_kernel_module` they are loaded as if they exist in *sasmodels.custom*. This package needs to exist for this to occur without error. """ from __future__ import division, print_function import sys import os from os.path import basename, splitext try: # Python 3.5 and up from importlib.util import spec_from_file_location, module_from_spec # type: ignore def load_module_from_path(fullname, path): """load module from *path* as *fullname*""" spec = spec_from_file_location(fullname, os.path.expanduser(path)) module = module_from_spec(spec) spec.loader.exec_module(module) return module except ImportError: # CRUFT: python 2 import imp def load_module_from_path(fullname, path): """load module from *path* as *fullname*""" # Clear out old definitions, if any if fullname in sys.modules: del sys.modules[fullname] if path.endswith(".py") and os.path.exists(path) and os.path.exists(path+"c"): # remove automatic pyc file before loading a py file os.unlink(path+"c") module = imp.load_source(fullname, os.path.expanduser(path)) return module def load_custom_kernel_module(path): """load SAS kernel from *path* as *sasmodels.custom.modelname*""" # Pull off the last .ext if it exists; there may be others name = basename(splitext(path)[0]) # Placing the model in the 'sasmodels.custom' name space. kernel_module = load_module_from_path('sasmodels.custom.'+name, os.path.expanduser(path)) return kernel_module sasmodels/sasmodels/data.py000066400000000000000000000530441317715334700163460ustar00rootroot00000000000000""" SAS data representations. Plotting functions for data sets: :func:`plot_data` plots the data file. :func:`plot_theory` plots a calculated result from the model. Wrappers for the sasview data loader and data manipulations: :func:`load_data` loads a sasview data file. :func:`set_beam_stop` masks the beam stop from the data. :func:`set_half` selects the right or left half of the data, which can be useful for shear measurements which have not been properly corrected for path length and reflections. :func:`set_top` cuts the top part off the data. Empty data sets for evaluating models without data: :func:`empty_data1D` creates an empty dataset, which is useful for plotting a theory function before the data is measured. :func:`empty_data2D` creates an empty 2D dataset. Note that the empty datasets use a minimal representation of the SasView objects so that models can be run without SasView on the path. You could also use these for your own data loader. """ import traceback import numpy as np # type: ignore try: from typing import Union, Dict, List, Optional except ImportError: pass else: Data = Union["Data1D", "Data2D", "SesansData"] def load_data(filename, index=0): # type: (str) -> Data """ Load data using a sasview loader. """ from sas.sascalc.dataloader.loader import Loader # type: ignore loader = Loader() # Allow for one part in multipart file if '[' in filename: filename, indexstr = filename[:-1].split('[') index = int(indexstr) datasets = loader.load(filename) if not datasets: # None or [] raise IOError("Data %r could not be loaded" % filename) if not isinstance(datasets, list): datasets = [datasets] for data in datasets: if hasattr(data, 'x'): data.qmin, data.qmax = data.x.min(), data.x.max() data.mask = (np.isnan(data.y) if data.y is not None else np.zeros_like(data.x, dtype='bool')) elif hasattr(data, 'qx_data'): data.mask = ~data.mask return datasets[index] if index != 'all' else datasets def set_beam_stop(data, radius, outer=None): # type: (Data, float, Optional[float]) -> None """ Add a beam stop of the given *radius*. If *outer*, make an annulus. """ from sas.sascalc.dataloader.manipulations import Ringcut if hasattr(data, 'qx_data'): data.mask = Ringcut(0, radius)(data) if outer is not None: data.mask += Ringcut(outer, np.inf)(data) else: data.mask = (data.x < radius) if outer is not None: data.mask |= (data.x >= outer) def set_half(data, half): # type: (Data, str) -> None """ Select half of the data, either "right" or "left". """ from sas.sascalc.dataloader.manipulations import Boxcut if half == 'right': data.mask += \ Boxcut(x_min=-np.inf, x_max=0.0, y_min=-np.inf, y_max=np.inf)(data) if half == 'left': data.mask += \ Boxcut(x_min=0.0, x_max=np.inf, y_min=-np.inf, y_max=np.inf)(data) def set_top(data, cutoff): # type: (Data, float) -> None """ Chop the top off the data, above *cutoff*. """ from sas.sascalc.dataloader.manipulations import Boxcut data.mask += \ Boxcut(x_min=-np.inf, x_max=np.inf, y_min=-np.inf, y_max=cutoff)(data) class Data1D(object): """ 1D data object. Note that this definition matches the attributes from sasview, with some generic 1D data vectors and some SAS specific definitions. Some refactoring to allow consistent naming conventions between 1D, 2D and SESANS data would be helpful. **Attributes** *x*, *dx*: $q$ vector and gaussian resolution *y*, *dy*: $I(q)$ vector and measurement uncertainty *mask*: values to include in plotting/analysis *dxl*: slit widths for slit smeared data, with *dx* ignored *qmin*, *qmax*: range of $q$ values in *x* *filename*: label for the data line *_xaxis*, *_xunit*: label and units for the *x* axis *_yaxis*, *_yunit*: label and units for the *y* axis """ def __init__(self, x=None, y=None, dx=None, dy=None): # type: (Optional[np.ndarray], Optional[np.ndarray], Optional[np.ndarray], Optional[np.ndarray]) -> None self.x, self.y, self.dx, self.dy = x, y, dx, dy self.dxl = None self.filename = None self.qmin = x.min() if x is not None else np.NaN self.qmax = x.max() if x is not None else np.NaN # TODO: why is 1D mask False and 2D mask True? self.mask = (np.isnan(y) if y is not None else np.zeros_like(x, 'b') if x is not None else None) self._xaxis, self._xunit = "x", "" self._yaxis, self._yunit = "y", "" def xaxis(self, label, unit): # type: (str, str) -> None """ set the x axis label and unit """ self._xaxis = label self._xunit = unit def yaxis(self, label, unit): # type: (str, str) -> None """ set the y axis label and unit """ self._yaxis = label self._yunit = unit class SesansData(Data1D): """ SESANS data object. This is just :class:`Data1D` with a wavelength parameter. *x* is spin echo length and *y* is polarization (P/P0). """ def __init__(self, **kw): Data1D.__init__(self, **kw) self.lam = None # type: Optional[np.ndarray] class Data2D(object): """ 2D data object. Note that this definition matches the attributes from sasview. Some refactoring to allow consistent naming conventions between 1D, 2D and SESANS data would be helpful. **Attributes** *qx_data*, *dqx_data*: $q_x$ matrix and gaussian resolution *qy_data*, *dqy_data*: $q_y$ matrix and gaussian resolution *data*, *err_data*: $I(q)$ matrix and measurement uncertainty *mask*: values to exclude from plotting/analysis *qmin*, *qmax*: range of $q$ values in *x* *filename*: label for the data line *_xaxis*, *_xunit*: label and units for the *x* axis *_yaxis*, *_yunit*: label and units for the *y* axis *_zaxis*, *_zunit*: label and units for the *y* axis *Q_unit*, *I_unit*: units for Q and intensity *x_bins*, *y_bins*: grid steps in *x* and *y* directions """ def __init__(self, x=None, y=None, z=None, dx=None, dy=None, dz=None): # type: (Optional[np.ndarray], Optional[np.ndarray], Optional[np.ndarray], Optional[np.ndarray], Optional[np.ndarray], Optional[np.ndarray]) -> None self.qx_data, self.dqx_data = x, dx self.qy_data, self.dqy_data = y, dy self.data, self.err_data = z, dz self.mask = (np.isnan(z) if z is not None else np.zeros_like(x, dtype='bool') if x is not None else None) self.q_data = np.sqrt(x**2 + y**2) self.qmin = 1e-16 self.qmax = np.inf self.detector = [] self.source = Source() self.Q_unit = "1/A" self.I_unit = "1/cm" self.xaxis("Q_x", "1/A") self.yaxis("Q_y", "1/A") self.zaxis("Intensity", "1/cm") self._xaxis, self._xunit = "x", "" self._yaxis, self._yunit = "y", "" self._zaxis, self._zunit = "z", "" self.x_bins, self.y_bins = None, None self.filename = None def xaxis(self, label, unit): # type: (str, str) -> None """ set the x axis label and unit """ self._xaxis = label self._xunit = unit def yaxis(self, label, unit): # type: (str, str) -> None """ set the y axis label and unit """ self._yaxis = label self._yunit = unit def zaxis(self, label, unit): # type: (str, str) -> None """ set the y axis label and unit """ self._zaxis = label self._zunit = unit class Vector(object): """ 3-space vector of *x*, *y*, *z* """ def __init__(self, x=None, y=None, z=None): # type: (float, float, Optional[float]) -> None self.x, self.y, self.z = x, y, z class Detector(object): """ Detector attributes. """ def __init__(self, pixel_size=(None, None), distance=None): # type: (Tuple[float, float], float) -> None self.pixel_size = Vector(*pixel_size) self.distance = distance class Source(object): """ Beam attributes. """ def __init__(self): # type: () -> None self.wavelength = np.NaN self.wavelength_unit = "A" def empty_data1D(q, resolution=0.0): # type: (np.ndarray, float) -> Data1D """ Create empty 1D data using the given *q* as the x value. *resolution* dq/q defaults to 5%. """ #Iq = 100 * np.ones_like(q) #dIq = np.sqrt(Iq) Iq, dIq = None, None q = np.asarray(q) data = Data1D(q, Iq, dx=resolution * q, dy=dIq) data.filename = "fake data" return data def empty_data2D(qx, qy=None, resolution=0.0): # type: (np.ndarray, Optional[np.ndarray], float) -> Data2D """ Create empty 2D data using the given mesh. If *qy* is missing, create a square mesh with *qy=qx*. *resolution* dq/q defaults to 5%. """ if qy is None: qy = qx qx, qy = np.asarray(qx), np.asarray(qy) # 5% dQ/Q resolution Qx, Qy = np.meshgrid(qx, qy) Qx, Qy = Qx.flatten(), Qy.flatten() Iq = 100 * np.ones_like(Qx) # type: np.ndarray dIq = np.sqrt(Iq) if resolution != 0: # https://www.ncnr.nist.gov/staff/hammouda/distance_learning/chapter_15.pdf # Should have an additional constant which depends on distances and # radii of the aperture, pixel dimensions and wavelength spread # Instead, assume radial dQ/Q is constant, and perpendicular matches # radial (which instead it should be inverse). Q = np.sqrt(Qx**2 + Qy**2) dqx = resolution * Q dqy = resolution * Q else: dqx = dqy = None data = Data2D(x=Qx, y=Qy, z=Iq, dx=dqx, dy=dqy, dz=dIq) data.x_bins = qx data.y_bins = qy data.filename = "fake data" # pixel_size in mm, distance in m detector = Detector(pixel_size=(5, 5), distance=4) data.detector.append(detector) data.source.wavelength = 5 # angstroms data.source.wavelength_unit = "A" return data def plot_data(data, view='log', limits=None): # type: (Data, str, Optional[Tuple[float, float]]) -> None """ Plot data loaded by the sasview loader. *data* is a sasview data object, either 1D, 2D or SESANS. *view* is log or linear. *limits* sets the intensity limits on the plot; if None then the limits are inferred from the data. """ # Note: kind of weird using the plot result functions to plot just the # data, but they already handle the masking and graph markup already, so # do not repeat. if hasattr(data, 'isSesans') and data.isSesans: _plot_result_sesans(data, None, None, use_data=True, limits=limits) elif hasattr(data, 'qx_data'): _plot_result2D(data, None, None, view, use_data=True, limits=limits) else: _plot_result1D(data, None, None, view, use_data=True, limits=limits) def plot_theory(data, theory, resid=None, view='log', use_data=True, limits=None, Iq_calc=None): # type: (Data, Optional[np.ndarray], Optional[np.ndarray], str, bool, Optional[Tuple[float,float]], Optional[np.ndarray]) -> None """ Plot theory calculation. *data* is needed to define the graph properties such as labels and units, and to define the data mask. *theory* is a matrix of the same shape as the data. *view* is log or linear *use_data* is True if the data should be plotted as well as the theory. *limits* sets the intensity limits on the plot; if None then the limits are inferred from the data. *Iq_calc* is the raw theory values without resolution smearing """ if hasattr(data, 'isSesans') and data.isSesans: _plot_result_sesans(data, theory, resid, use_data=True, limits=limits) elif hasattr(data, 'qx_data'): _plot_result2D(data, theory, resid, view, use_data, limits=limits) else: _plot_result1D(data, theory, resid, view, use_data, limits=limits, Iq_calc=Iq_calc) def protect(func): # type: (Callable) -> Callable """ Decorator to wrap calls in an exception trapper which prints the exception and continues. Keyboard interrupts are ignored. """ def wrapper(*args, **kw): """ Trap and print errors from function. """ try: return func(*args, **kw) except Exception: traceback.print_exc() return wrapper @protect def _plot_result1D(data, theory, resid, view, use_data, limits=None, Iq_calc=None): # type: (Data1D, Optional[np.ndarray], Optional[np.ndarray], str, bool, Optional[Tuple[float, float]], Optional[np.ndarray]) -> None """ Plot the data and residuals for 1D data. """ import matplotlib.pyplot as plt # type: ignore from numpy.ma import masked_array, masked # type: ignore use_data = use_data and data.y is not None use_theory = theory is not None use_resid = resid is not None use_calc = use_theory and Iq_calc is not None num_plots = (use_data or use_theory) + use_calc + use_resid non_positive_x = (data.x <= 0.0).any() scale = data.x**4 if view == 'q4' else 1.0 xscale = yscale = 'linear' if view == 'linear' else 'log' if use_data or use_theory: if num_plots > 1: plt.subplot(1, num_plots, 1) #print(vmin, vmax) all_positive = True some_present = False if use_data: mdata = masked_array(data.y, data.mask.copy()) mdata[~np.isfinite(mdata)] = masked if view is 'log': mdata[mdata <= 0] = masked plt.errorbar(data.x, scale*mdata, yerr=data.dy, fmt='.') all_positive = all_positive and (mdata > 0).all() some_present = some_present or (mdata.count() > 0) if use_theory: # Note: masks merge, so any masked theory points will stay masked, # and the data mask will be added to it. mtheory = masked_array(theory, data.mask.copy()) mtheory[~np.isfinite(mtheory)] = masked if view is 'log': mtheory[mtheory <= 0] = masked plt.plot(data.x, scale*mtheory, '-') all_positive = all_positive and (mtheory > 0).all() some_present = some_present or (mtheory.count() > 0) if limits is not None: plt.ylim(*limits) xscale = ('linear' if not some_present or non_positive_x else view if view is not None else 'log') yscale = ('linear' if view == 'q4' or not some_present or not all_positive else view if view is not None else 'log') plt.xscale(xscale) plt.xlabel("$q$/A$^{-1}$") plt.yscale(yscale) plt.ylabel('$I(q)$') title = ("data and model" if use_theory and use_data else "data" if use_data else "model") plt.title(title) if use_calc: # Only have use_calc if have use_theory plt.subplot(1, num_plots, 2) qx, qy, Iqxy = Iq_calc plt.pcolormesh(qx, qy[qy > 0], np.log10(Iqxy[qy > 0, :])) plt.xlabel("$q_x$/A$^{-1}$") plt.xlabel("$q_y$/A$^{-1}$") plt.xscale('log') plt.yscale('log') #plt.axis('equal') if use_resid: mresid = masked_array(resid, data.mask.copy()) mresid[~np.isfinite(mresid)] = masked some_present = (mresid.count() > 0) if num_plots > 1: plt.subplot(1, num_plots, use_calc + 2) plt.plot(data.x, mresid, '.') plt.xlabel("$q$/A$^{-1}$") plt.ylabel('residuals') plt.title('(model - Iq)/dIq') plt.xscale(xscale) plt.yscale('linear') @protect def _plot_result_sesans(data, theory, resid, use_data, limits=None): # type: (SesansData, Optional[np.ndarray], Optional[np.ndarray], bool, Optional[Tuple[float, float]]) -> None """ Plot SESANS results. """ import matplotlib.pyplot as plt # type: ignore use_data = use_data and data.y is not None use_theory = theory is not None use_resid = resid is not None num_plots = (use_data or use_theory) + use_resid if use_data or use_theory: is_tof = (data.lam != data.lam[0]).any() if num_plots > 1: plt.subplot(1, num_plots, 1) if use_data: if is_tof: plt.errorbar(data.x, np.log(data.y)/(data.lam*data.lam), yerr=data.dy/data.y/(data.lam*data.lam)) else: plt.errorbar(data.x, data.y, yerr=data.dy) if theory is not None: if is_tof: plt.plot(data.x, np.log(theory)/(data.lam*data.lam), '-') else: plt.plot(data.x, theory, '-') if limits is not None: plt.ylim(*limits) plt.xlabel('spin echo length ({})'.format(data._xunit)) if is_tof: plt.ylabel(r'(Log (P/P$_0$))/$\lambda^2$') else: plt.ylabel('polarization (P/P0)') if resid is not None: if num_plots > 1: plt.subplot(1, num_plots, (use_data or use_theory) + 1) plt.plot(data.x, resid, 'x') plt.xlabel('spin echo length ({})'.format(data._xunit)) plt.ylabel('residuals (P/P0)') @protect def _plot_result2D(data, theory, resid, view, use_data, limits=None): # type: (Data2D, Optional[np.ndarray], Optional[np.ndarray], str, bool, Optional[Tuple[float,float]]) -> None """ Plot the data and residuals for 2D data. """ import matplotlib.pyplot as plt # type: ignore use_data = use_data and data.data is not None use_theory = theory is not None use_resid = resid is not None num_plots = use_data + use_theory + use_resid # Put theory and data on a common colormap scale vmin, vmax = np.inf, -np.inf target = None # type: Optional[np.ndarray] if use_data: target = data.data[~data.mask] datamin = target[target > 0].min() if view == 'log' else target.min() datamax = target.max() vmin = min(vmin, datamin) vmax = max(vmax, datamax) if use_theory: theorymin = theory[theory > 0].min() if view == 'log' else theory.min() theorymax = theory.max() vmin = min(vmin, theorymin) vmax = max(vmax, theorymax) # Override data limits from the caller if limits is not None: vmin, vmax = limits # Plot data if use_data: if num_plots > 1: plt.subplot(1, num_plots, 1) _plot_2d_signal(data, target, view=view, vmin=vmin, vmax=vmax) plt.title('data') h = plt.colorbar() h.set_label('$I(q)$') # plot theory if use_theory: if num_plots > 1: plt.subplot(1, num_plots, use_data+1) _plot_2d_signal(data, theory, view=view, vmin=vmin, vmax=vmax) plt.title('theory') h = plt.colorbar() h.set_label(r'$\log_{10}I(q)$' if view == 'log' else r'$q^4 I(q)$' if view == 'q4' else '$I(q)$') # plot resid if use_resid: if num_plots > 1: plt.subplot(1, num_plots, use_data+use_theory+1) _plot_2d_signal(data, resid, view='linear') plt.title('residuals') h = plt.colorbar() h.set_label(r'$\Delta I(q)$') @protect def _plot_2d_signal(data, signal, vmin=None, vmax=None, view='log'): # type: (Data2D, np.ndarray, Optional[float], Optional[float], str) -> Tuple[float, float] """ Plot the target value for the data. This could be the data itself, the theory calculation, or the residuals. *scale* can be 'log' for log scale data, or 'linear'. """ import matplotlib.pyplot as plt # type: ignore from numpy.ma import masked_array # type: ignore image = np.zeros_like(data.qx_data) image[~data.mask] = signal valid = np.isfinite(image) if view == 'log': valid[valid] = (image[valid] > 0) if vmin is None: vmin = image[valid & ~data.mask].min() if vmax is None: vmax = image[valid & ~data.mask].max() image[valid] = np.log10(image[valid]) elif view == 'q4': image[valid] *= (data.qx_data[valid]**2+data.qy_data[valid]**2)**2 if vmin is None: vmin = image[valid & ~data.mask].min() if vmax is None: vmax = image[valid & ~data.mask].max() else: if vmin is None: vmin = image[valid & ~data.mask].min() if vmax is None: vmax = image[valid & ~data.mask].max() image[~valid | data.mask] = 0 #plottable = Iq plottable = masked_array(image, ~valid | data.mask) # Divide range by 10 to convert from angstroms to nanometers xmin, xmax = min(data.qx_data), max(data.qx_data) ymin, ymax = min(data.qy_data), max(data.qy_data) if view == 'log': vmin, vmax = np.log10(vmin), np.log10(vmax) plt.imshow(plottable.reshape(len(data.x_bins), len(data.y_bins)), interpolation='nearest', aspect=1, origin='lower', extent=[xmin, xmax, ymin, ymax], vmin=vmin, vmax=vmax) plt.xlabel("$q_x$/A$^{-1}$") plt.ylabel("$q_y$/A$^{-1}$") return vmin, vmax def demo(): # type: () -> None """ Load and plot a SAS dataset. """ data = load_data('DEC07086.DAT') set_beam_stop(data, 0.004) plot_data(data) import matplotlib.pyplot as plt # type: ignore plt.show() if __name__ == "__main__": demo() sasmodels/sasmodels/details.py000066400000000000000000000256561317715334700170720ustar00rootroot00000000000000""" Kernel Call Details =================== When calling sas computational kernels with polydispersity there are a number of details that need to be sent to the caller. This includes the list of polydisperse parameters, the number of points in the polydispersity weight distribution, and which parameter is the "theta" parameter for polar coordinate integration. The :class:`CallDetails` object maintains this data. Use :func:`build_details` to build a *details* object which can be passed to one of the computational kernels. """ from __future__ import print_function import numpy as np # type: ignore from numpy import pi, cos, sin try: np.meshgrid([]) meshgrid = np.meshgrid except Exception: # CRUFT: np.meshgrid requires multiple vectors def meshgrid(*args): if len(args) > 1: return np.meshgrid(*args) else: return [np.asarray(v) for v in args] try: from typing import List except ImportError: pass else: from .modelinfo import ModelInfo class CallDetails(object): """ Manage the polydispersity information for the kernel call. Conceptually, a polydispersity calculation is an integral over a mesh in n-D space where n is the number of polydisperse parameters. In order to keep the program responsive, and not crash the GPU, only a portion of the mesh is computed at a time. Meshes with a large number of points will therefore require many calls to the polydispersity loop. Restarting a nested loop in the middle requires that the indices of the individual mesh dimensions can be computed for the current loop location. This is handled by the *pd_stride* vector, with n//stride giving the loop index and n%stride giving the position in the sub loops. One of the parameters may be the latitude. When integrating in polar coordinates, the total circumference decreases as latitude varies from pi r^2 at the equator to 0 at the pole, and the weight associated with a range of phi values needs to be scaled by this circumference. This scale factor needs to be updated each time the theta value changes. *theta_par* indicates which of the values in the parameter vector is the latitude parameter, or -1 if there is no latitude parameter in the model. In practice, the normalization term cancels if the latitude is not a polydisperse parameter. """ parts = None # type: List["CallDetails"] def __init__(self, model_info): # type: (ModelInfo) -> None parameters = model_info.parameters max_pd = parameters.max_pd # Structure of the call details buffer: # pd_par[max_pd] pd params in order of length # pd_length[max_pd] length of each pd param # pd_offset[max_pd] offset of pd values in parameter array # pd_stride[max_pd] index of pd value in loop = n//stride[k] # num_eval total length of pd loop # num_weights total length of the weight vector # num_active number of pd params # theta_par parameter number for theta parameter self.buffer = np.empty(4*max_pd + 4, 'i4') # generate views on different parts of the array self._pd_par = self.buffer[0 * max_pd:1 * max_pd] self._pd_length = self.buffer[1 * max_pd:2 * max_pd] self._pd_offset = self.buffer[2 * max_pd:3 * max_pd] self._pd_stride = self.buffer[3 * max_pd:4 * max_pd] # theta_par is fixed self.theta_par = parameters.theta_offset # offset and length are for all parameters, not just pd parameters # They are not sent to the kernel function, though they could be. # They are used by the composite models (sum and product) to # figure out offsets into the combined value list. self.offset = None # type: np.ndarray self.length = None # type: np.ndarray # keep hold of ifno show() so we can break a values vector # into the individual components self.info = model_info @property def pd_par(self): """List of polydisperse parameters""" return self._pd_par @property def pd_length(self): """Number of weights for each polydisperse parameter""" return self._pd_length @property def pd_offset(self): """Offsets for the individual weight vectors in the set of weights""" return self._pd_offset @property def pd_stride(self): """Stride in the pd mesh for each pd dimension""" return self._pd_stride @property def num_eval(self): """Total size of the pd mesh""" return self.buffer[-4] @num_eval.setter def num_eval(self, v): """Total size of the pd mesh""" self.buffer[-4] = v @property def num_weights(self): """Total length of all the weight vectors""" return self.buffer[-3] @num_weights.setter def num_weights(self, v): """Total length of all the weight vectors""" self.buffer[-3] = v @property def num_active(self): """Number of active polydispersity loops""" return self.buffer[-2] @num_active.setter def num_active(self, v): """Number of active polydispersity loops""" self.buffer[-2] = v @property def theta_par(self): """Location of the theta parameter in the parameter vector""" return self.buffer[-1] @theta_par.setter def theta_par(self, v): """Location of the theta parameter in the parameter vector""" self.buffer[-1] = v def show(self, values=None): """Print the polydispersity call details to the console""" print("===== %s details ===="%self.info.name) print("num_active:%d num_eval:%d num_weights:%d theta=%d" % (self.num_active, self.num_eval, self.num_weights, self.theta_par)) if self.pd_par.size: print("pd_par", self.pd_par) print("pd_length", self.pd_length) print("pd_offset", self.pd_offset) print("pd_stride", self.pd_stride) if values is not None: nvalues = self.info.parameters.nvalues print("scale, background", values[:2]) print("val", values[2:nvalues]) print("pd", values[nvalues:nvalues+self.num_weights]) print("wt", values[nvalues+self.num_weights:nvalues+2*self.num_weights]) print("offsets", self.offset) def make_details(model_info, length, offset, num_weights): # type: (ModelInfo, np.ndarray, np.ndarray, int) -> CallDetails """ Return a :class:`CallDetails` object for a polydisperse calculation of the model defined by *model_info*. Polydispersity is defined by the *length* of the polydispersity distribution for each parameter and the *offset* of the distribution in the polydispersity array. Monodisperse parameters should use a polydispersity length of one with weight 1.0. *num_weights* is the total length of the polydispersity array. """ #pars = model_info.parameters.call_parameters[2:model_info.parameters.npars+2] #print(", ".join(str(i)+"-"+p.id for i,p in enumerate(pars))) #print("len:",length) #print("off:",offset) # Check that we arn't using too many polydispersity loops num_active = np.sum(length > 1) max_pd = model_info.parameters.max_pd if num_active > max_pd: raise ValueError("Too many polydisperse parameters") # Decreasing list of polydpersity lengths # Note: the reversing view, x[::-1], does not require a copy idx = np.argsort(length)[::-1][:max_pd] pd_stride = np.cumprod(np.hstack((1, length[idx]))) call_details = CallDetails(model_info) call_details.pd_par[:max_pd] = idx call_details.pd_length[:max_pd] = length[idx] call_details.pd_offset[:max_pd] = offset[idx] call_details.pd_stride[:max_pd] = pd_stride[:-1] call_details.num_eval = pd_stride[-1] call_details.num_weights = num_weights call_details.num_active = num_active call_details.length = length call_details.offset = offset #call_details.show() return call_details ZEROS = tuple([0.]*31) def make_kernel_args(kernel, pairs): # type: (Kernel, Tuple[List[np.ndarray], List[np.ndarray]]) -> Tuple[CallDetails, np.ndarray, bool] """ Converts (value, weight) pairs into parameters for the kernel call. Returns a CallDetails object indicating the polydispersity, a data object containing the different values, and the magnetic flag indicating whether any magnetic magnitudes are non-zero. Magnetic vectors (M0, phi, theta) are converted to rectangular coordinates (mx, my, mz). """ npars = kernel.info.parameters.npars nvalues = kernel.info.parameters.nvalues scalars = [(v[0] if len(v) else np.NaN) for v, w in pairs] values, weights = zip(*pairs[2:npars+2]) if npars else ((),()) length = np.array([len(w) for w in weights]) offset = np.cumsum(np.hstack((0, length))) call_details = make_details(kernel.info, length, offset[:-1], offset[-1]) # Pad value array to a 32 value boundaryd data_len = nvalues + 2*sum(len(v) for v in values) extra = (32 - data_len%32)%32 data = np.hstack((scalars,) + values + weights + ZEROS[:extra]) data = data.astype(kernel.dtype) is_magnetic = convert_magnetism(kernel.info.parameters, data) #call_details.show() return call_details, data, is_magnetic def convert_magnetism(parameters, values): """ Convert magnetism values from polar to rectangular coordinates. Returns True if any magnetism is present. """ mag = values[parameters.nvalues-3*parameters.nmagnetic:parameters.nvalues] mag = mag.reshape(-1, 3) scale = mag[:,0] if np.any(scale): theta, phi = mag[:, 1]*pi/180., mag[:, 2]*pi/180. cos_theta = cos(theta) mag[:, 0] = scale*cos_theta*cos(phi) # mx mag[:, 1] = scale*sin(theta) # my mag[:, 2] = -scale*cos_theta*sin(phi) # mz return True else: return False def dispersion_mesh(model_info, pars): # type: (ModelInfo) -> Tuple[List[np.ndarray], List[np.ndarray]] """ Create a mesh grid of dispersion parameters and weights. Returns [p1,p2,...],w where pj is a vector of values for parameter j and w is a vector containing the products for weights for each parameter set in the vector. """ value, weight = zip(*pars) #weight = [w if len(w)>0 else [1.] for w in weight] weight = np.vstack([v.flatten() for v in meshgrid(*weight)]) weight = np.prod(weight, axis=0) value = [v.flatten() for v in meshgrid(*value)] lengths = [par.length for par in model_info.parameters.kernel_parameters if par.type == 'volume'] if any(n > 1 for n in lengths): pars = [] offset = 0 for n in lengths: pars.append(np.vstack(value[offset:offset+n]) if n > 1 else value[offset]) offset += n value = pars return value, weight sasmodels/sasmodels/direct_model.py000066400000000000000000000405521317715334700200670ustar00rootroot00000000000000""" Class interface to the model calculator. Calling a model is somewhat non-trivial since the functions called depend on the data type. For 1D data the *Iq* kernel needs to be called, for 2D data the *Iqxy* kernel needs to be called, and for SESANS data the *Iq* kernel needs to be called followed by a Hankel transform. Before the kernel is called an appropriate *q* calculation vector needs to be constructed. This is not the simple *q* vector where you have measured the data since the resolution calculation will require values beyond the range of the measured data. After the calculation the resolution calculator must be called to return the predicted value for each measured data point. :class:`DirectModel` is a callable object that takes *parameter=value* keyword arguments and returns the appropriate theory values for the data. :class:`DataMixin` does the real work of interpreting the data and calling the model calculator. This is used by :class:`DirectModel`, which uses direct parameter values and by :class:`bumps_model.Experiment` which wraps the parameter values in boxes so that the user can set fitting ranges, etc. on the individual parameters and send the model to the Bumps optimizers. """ from __future__ import print_function import numpy as np # type: ignore # TODO: fix sesans module from . import sesans # type: ignore from . import weights from . import resolution from . import resolution2d from .details import make_kernel_args, dispersion_mesh try: from typing import Optional, Dict, Tuple except ImportError: pass else: from .data import Data from .kernel import Kernel, KernelModel from .modelinfo import Parameter, ParameterSet def call_kernel(calculator, pars, cutoff=0., mono=False): # type: (Kernel, ParameterSet, float, bool) -> np.ndarray """ Call *kernel* returned from *model.make_kernel* with parameters *pars*. *cutoff* is the limiting value for the product of dispersion weights used to perform the multidimensional dispersion calculation more quickly at a slight cost to accuracy. The default value of *cutoff=0* integrates over the entire dispersion cube. Using *cutoff=1e-5* can be 50% faster, but with an error of about 1%, which is usually less than the measurement uncertainty. *mono* is True if polydispersity should be set to none on all parameters. """ parameters = calculator.info.parameters if mono: active = lambda name: False elif calculator.dim == '1d': active = lambda name: name in parameters.pd_1d elif calculator.dim == '2d': active = lambda name: name in parameters.pd_2d else: active = lambda name: True #print("pars",[p.id for p in parameters.call_parameters]) vw_pairs = [(get_weights(p, pars) if active(p.name) else ([pars.get(p.name, p.default)], [1.0])) for p in parameters.call_parameters] call_details, values, is_magnetic = make_kernel_args(calculator, vw_pairs) #print("values:", values) return calculator(call_details, values, cutoff, is_magnetic) def call_ER(model_info, pars): # type: (ModelInfo, ParameterSet) -> float """ Call the model ER function using *values*. *model_info* is either *model.info* if you have a loaded model, or *kernel.info* if you have a model kernel prepared for evaluation. """ if model_info.ER is None: return 1.0 elif not model_info.parameters.form_volume_parameters: # handle the case where ER is provided but model is not polydisperse return model_info.ER() else: value, weight = _vol_pars(model_info, pars) individual_radii = model_info.ER(*value) return np.sum(weight*individual_radii) / np.sum(weight) def call_VR(model_info, pars): # type: (ModelInfo, ParameterSet) -> float """ Call the model VR function using *pars*. *model_info* is either *model.info* if you have a loaded model, or *kernel.info* if you have a model kernel prepared for evaluation. """ if model_info.VR is None: return 1.0 elif not model_info.parameters.form_volume_parameters: # handle the case where ER is provided but model is not polydisperse return model_info.VR() else: value, weight = _vol_pars(model_info, pars) whole, part = model_info.VR(*value) return np.sum(weight*part)/np.sum(weight*whole) def call_profile(model_info, **pars): # type: (ModelInfo, ...) -> Tuple[np.ndarray, np.ndarray, Tuple[str, str]] """ Returns the profile *x, y, (xlabel, ylabel)* representing the model. """ args = {} for p in model_info.parameters.kernel_parameters: if p.length > 1: value = np.array([pars.get(p.id+str(j), p.default) for j in range(1, p.length+1)]) else: value = pars.get(p.id, p.default) args[p.id] = value x, y = model_info.profile(**args) return x, y, model_info.profile_axes def get_weights(parameter, values): # type: (Parameter, Dict[str, float]) -> Tuple[np.ndarray, np.ndarray] """ Generate the distribution for parameter *name* given the parameter values in *pars*. Uses "name", "name_pd", "name_pd_type", "name_pd_n", "name_pd_sigma" from the *pars* dictionary for parameter value and parameter dispersion. """ value = float(values.get(parameter.name, parameter.default)) relative = parameter.relative_pd limits = parameter.limits disperser = values.get(parameter.name+'_pd_type', 'gaussian') npts = values.get(parameter.name+'_pd_n', 0) width = values.get(parameter.name+'_pd', 0.0) nsigma = values.get(parameter.name+'_pd_nsigma', 3.0) if npts == 0 or width == 0: return [value], [1.0] value, weight = weights.get_weights( disperser, npts, width, nsigma, value, limits, relative) return value, weight / np.sum(weight) def _vol_pars(model_info, pars): # type: (ModelInfo, ParameterSet) -> Tuple[np.ndarray, np.ndarray] vol_pars = [get_weights(p, pars) for p in model_info.parameters.call_parameters if p.type == 'volume'] #import pylab; pylab.plot(vol_pars[0][0],vol_pars[0][1]); pylab.show() value, weight = dispersion_mesh(model_info, vol_pars) return value, weight class DataMixin(object): """ DataMixin captures the common aspects of evaluating a SAS model for a particular data set, including calculating Iq and evaluating the resolution function. It is used in particular by :class:`DirectModel`, which evaluates a SAS model parameters as key word arguments to the calculator method, and by :class:`bumps_model.Experiment`, which wraps the model and data for use with the Bumps fitting engine. It is not currently used by :class:`sasview_model.SasviewModel` since this will require a number of changes to SasView before we can do it. :meth:`_interpret_data` initializes the data structures necessary to manage the calculations. This sets attributes in the child class such as *data_type* and *resolution*. :meth:`_calc_theory` evaluates the model at the given control values. :meth:`_set_data` sets the intensity data in the data object, possibly with random noise added. This is useful for simulating a dataset with the results from :meth:`_calc_theory`. """ def _interpret_data(self, data, model): # type: (Data, KernelModel) -> None # pylint: disable=attribute-defined-outside-init self._data = data self._model = model # interpret data if hasattr(data, 'isSesans') and data.isSesans: self.data_type = 'sesans' elif hasattr(data, 'qx_data'): self.data_type = 'Iqxy' elif getattr(data, 'oriented', False): self.data_type = 'Iq-oriented' else: self.data_type = 'Iq' if self.data_type == 'sesans': q = sesans.make_q(data.sample.zacceptance, data.Rmax) index = slice(None, None) res = None if data.y is not None: Iq, dIq = data.y, data.dy else: Iq, dIq = None, None #self._theory = np.zeros_like(q) q_vectors = [q] q_mono = sesans.make_all_q(data) elif self.data_type == 'Iqxy': #if not model.info.parameters.has_2d: # raise ValueError("not 2D without orientation or magnetic parameters") q = np.sqrt(data.qx_data**2 + data.qy_data**2) qmin = getattr(data, 'qmin', 1e-16) qmax = getattr(data, 'qmax', np.inf) accuracy = getattr(data, 'accuracy', 'Low') index = ~data.mask & (q >= qmin) & (q <= qmax) if data.data is not None: index &= ~np.isnan(data.data) Iq = data.data[index] dIq = data.err_data[index] else: Iq, dIq = None, None res = resolution2d.Pinhole2D(data=data, index=index, nsigma=3.0, accuracy=accuracy) #self._theory = np.zeros_like(self.Iq) q_vectors = res.q_calc q_mono = [] elif self.data_type == 'Iq': index = (data.x >= data.qmin) & (data.x <= data.qmax) if data.y is not None: index &= ~np.isnan(data.y) Iq = data.y[index] dIq = data.dy[index] else: Iq, dIq = None, None if getattr(data, 'dx', None) is not None: q, dq = data.x[index], data.dx[index] if (dq > 0).any(): res = resolution.Pinhole1D(q, dq) else: res = resolution.Perfect1D(q) elif (getattr(data, 'dxl', None) is not None and getattr(data, 'dxw', None) is not None): res = resolution.Slit1D(data.x[index], qx_width=data.dxl[index], qy_width=data.dxw[index]) else: res = resolution.Perfect1D(data.x[index]) #self._theory = np.zeros_like(self.Iq) q_vectors = [res.q_calc] q_mono = [] elif self.data_type == 'Iq-oriented': index = (data.x >= data.qmin) & (data.x <= data.qmax) if data.y is not None: index &= ~np.isnan(data.y) Iq = data.y[index] dIq = data.dy[index] else: Iq, dIq = None, None if (getattr(data, 'dxl', None) is None or getattr(data, 'dxw', None) is None): raise ValueError("oriented sample with 1D data needs slit resolution") res = resolution2d.Slit2D(data.x[index], qx_width=data.dxw[index], qy_width=data.dxl[index]) q_vectors = res.q_calc q_mono = [] else: raise ValueError("Unknown data type") # never gets here # Remember function inputs so we can delay loading the function and # so we can save/restore state self._kernel_inputs = q_vectors self._kernel_mono_inputs = q_mono self._kernel = None self.Iq, self.dIq, self.index = Iq, dIq, index self.resolution = res def _set_data(self, Iq, noise=None): # type: (np.ndarray, Optional[float]) -> None # pylint: disable=attribute-defined-outside-init if noise is not None: self.dIq = Iq*noise*0.01 dy = self.dIq y = Iq + np.random.randn(*dy.shape) * dy self.Iq = y if self.data_type in ('Iq', 'Iq-oriented'): if self._data.y is None: self._data.y = np.empty(len(self._data.x), 'd') if self._data.dy is None: self._data.dy = np.empty(len(self._data.x), 'd') self._data.dy[self.index] = dy self._data.y[self.index] = y elif self.data_type == 'Iqxy': if self._data.data is None: self._data.data = np.empty_like(self._data.qx_data, 'd') if self._data.err_data is None: self._data.err_data = np.empty_like(self._data.qx_data, 'd') self._data.data[self.index] = y self._data.err_data[self.index] = dy elif self.data_type == 'sesans': if self._data.y is None: self._data.y = np.empty(len(self._data.x), 'd') self._data.y[self.index] = y else: raise ValueError("Unknown model") def _calc_theory(self, pars, cutoff=0.0): # type: (ParameterSet, float) -> np.ndarray if self._kernel is None: self._kernel = self._model.make_kernel(self._kernel_inputs) self._kernel_mono = ( self._model.make_kernel(self._kernel_mono_inputs) if self._kernel_mono_inputs else None) Iq_calc = call_kernel(self._kernel, pars, cutoff=cutoff) # Storing the calculated Iq values so that they can be plotted. # Only applies to oriented USANS data for now. # TODO: extend plotting of calculate Iq to other measurement types # TODO: refactor so we don't store the result in the model self.Iq_calc = Iq_calc if self.data_type == 'sesans': Iq_mono = (call_kernel(self._kernel_mono, pars, mono=True) if self._kernel_mono_inputs else None) result = sesans.transform(self._data, self._kernel_inputs[0], Iq_calc, self._kernel_mono_inputs, Iq_mono) else: result = self.resolution.apply(Iq_calc) if hasattr(self.resolution, 'nx'): self.Iq_calc = ( self.resolution.qx_calc, self.resolution.qy_calc, np.reshape(Iq_calc, (self.resolution.ny, self.resolution.nx)) ) return result class DirectModel(DataMixin): """ Create a calculator object for a model. *data* is 1D SAS, 2D SAS or SESANS data *model* is a model calculator return from :func:`generate.load_model` *cutoff* is the polydispersity weight cutoff. """ def __init__(self, data, model, cutoff=1e-5): # type: (Data, KernelModel, float) -> None self.model = model self.cutoff = cutoff # Note: _interpret_data defines the model attributes self._interpret_data(data, model) def __call__(self, **pars): # type: (**float) -> np.ndarray return self._calc_theory(pars, cutoff=self.cutoff) def simulate_data(self, noise=None, **pars): # type: (Optional[float], **float) -> None """ Generate simulated data for the model. """ Iq = self.__call__(**pars) self._set_data(Iq, noise=noise) def profile(self, **pars): # type: (**float) -> None """ Generate a plottable profile. """ return call_profile(self.model.info, **pars) def main(): # type: () -> None """ Program to evaluate a particular model at a set of q values. """ import sys from .data import empty_data1D, empty_data2D from .core import load_model_info, build_model if len(sys.argv) < 3: print("usage: python -m sasmodels.direct_model modelname (q|qx,qy) par=val ...") sys.exit(1) model_name = sys.argv[1] call = sys.argv[2].upper() if call != "ER_VR": try: values = [float(v) for v in call.split(',')] except Exception: values = [] if len(values) == 1: q, = values data = empty_data1D([q]) elif len(values) == 2: qx, qy = values data = empty_data2D([qx], [qy]) else: print("use q or qx,qy or ER or VR") sys.exit(1) else: data = empty_data1D([0.001]) # Data not used in ER/VR model_info = load_model_info(model_name) model = build_model(model_info) calculator = DirectModel(data, model) pars = dict((k, (float(v) if not k.endswith("_pd_type") else v)) for pair in sys.argv[3:] for k, v in [pair.split('=')]) if call == "ER_VR": ER = call_ER(model_info, pars) VR = call_VR(model_info, pars) print(ER, VR) else: Iq = calculator(**pars) print(Iq[0]) if __name__ == "__main__": main() sasmodels/sasmodels/exception.py000066400000000000000000000026611317715334700174320ustar00rootroot00000000000000""" Utility to add annotations to python exceptions. """ import sys # Platform cruft: WindowsError is only defined on Windows. try: WindowsError except NameError: class WindowsError(Exception): """ Fake WindowsException when not on Windows. """ pass def annotate_exception(msg, exc=None): """ Add an annotation to the current exception, which can then be forwarded to the caller using a bare "raise" statement to raise the annotated exception. If the exception *exc* is provided, then that exception is the one that is annotated, otherwise *sys.exc_info* is used. Example:: >>> D = {} >>> try: ... print(D['hello']) ... except: ... annotate_exception("while accessing 'D'") ... raise Traceback (most recent call last): ... KeyError: "hello while accessing 'D'" """ if not exc: exc = sys.exc_info()[1] # Can't extend WindowsError exceptions; instead raise a new exception. # TODO: try to incorporate current stack trace in the raised exception if isinstance(exc, WindowsError): raise OSError(str(exc) + " " + msg) args = exc.args if not args: exc.args = (msg,) else: try: arg0 = " ".join((args[0], msg)) exc.args = tuple([arg0] + list(args[1:])) except: exc.args = (" ".join((str(exc), msg)),) sasmodels/sasmodels/generate.py000066400000000000000000001027051317715334700172260ustar00rootroot00000000000000""" SAS model constructor. Small angle scattering models are defined by a set of kernel functions: *Iq(q, p1, p2, ...)* returns the scattering at q for a form with particular dimensions averaged over all orientations. *Iqxy(qx, qy, p1, p2, ...)* returns the scattering at qx, qy for a form with particular dimensions for a single orientation. *Imagnetic(qx, qy, result[], p1, p2, ...)* returns the scattering for the polarized neutron spin states (up-up, up-down, down-up, down-down) for a form with particular dimensions for a single orientation. *form_volume(p1, p2, ...)* returns the volume of the form with particular dimension, or 1.0 if no volume normalization is required. *ER(p1, p2, ...)* returns the effective radius of the form with particular dimensions. *VR(p1, p2, ...)* returns the volume ratio for core-shell style forms. #define INVALID(v) (expr) returns False if v.parameter is invalid for some parameter or other (e.g., v.bell_radius < v.radius). If necessary, the expression can call a function. These functions are defined in a kernel module .py script and an associated set of .c files. The model constructor will use them to create models with polydispersity across volume and orientation parameters, and provide scale and background parameters for each model. *Iq*, *Iqxy*, *Imagnetic* and *form_volume* should be stylized C-99 functions written for OpenCL. All functions need prototype declarations even if the are defined before they are used. OpenCL does not support *#include* preprocessor directives, so instead the list of includes needs to be given as part of the metadata in the kernel module definition. The included files should be listed using a path relative to the kernel module, or if using "lib/file.c" if it is one of the standard includes provided with the sasmodels source. The includes need to be listed in order so that functions are defined before they are used. Floating point values should be declared as *double*. For single precision calculations, *double* will be replaced by *float*. The single precision conversion will also tag floating point constants with "f" to make them single precision constants. When using integral values in floating point expressions, they should be expressed as floating point values by including a decimal point. This includes 0., 1. and 2. OpenCL has a *sincos* function which can improve performance when both the *sin* and *cos* values are needed for a particular argument. Since this function does not exist in C99, all use of *sincos* should be replaced by the macro *SINCOS(value, sn, cn)* where *sn* and *cn* are previously declared *double* variables. When compiled for systems without OpenCL, *SINCOS* will be replaced by *sin* and *cos* calls. If *value* is an expression, it will appear twice in this case; whether or not it will be evaluated twice depends on the quality of the compiler. If the input parameters are invalid, the scattering calculator should return a negative number. Particularly with polydispersity, there are some sets of shape parameters which lead to nonsensical forms, such as a capped cylinder where the cap radius is smaller than the cylinder radius. The polydispersity calculation will ignore these points, effectively chopping the parameter weight distributions at the boundary of the infeasible region. The resulting scattering will be set to background. This will work correctly even when polydispersity is off. *ER* and *VR* are python functions which operate on parameter vectors. The constructor code will generate the necessary vectors for computing them with the desired polydispersity. The kernel module must set variables defining the kernel meta data: *id* is an implicit variable formed from the filename. It will be a valid python identifier, and will be used as the reference into the html documentation, with '_' replaced by '-'. *name* is the model name as displayed to the user. If it is missing, it will be constructed from the id. *title* is a short description of the model, suitable for a tool tip, or a one line model summary in a table of models. *description* is an extended description of the model to be displayed while the model parameters are being edited. *parameters* is the list of parameters. Parameters in the kernel functions must appear in the same order as they appear in the parameters list. Two additional parameters, *scale* and *background* are added to the beginning of the parameter list. They will show up in the documentation as model parameters, but they are never sent to the kernel functions. Note that *effect_radius* and *volfraction* must occur first in structure factor calculations. *category* is the default category for the model. The category is two level structure, with the form "group:section", indicating where in the manual the model will be located. Models are alphabetical within their section. *source* is the list of C-99 source files that must be joined to create the OpenCL kernel functions. The files defining the functions need to be listed before the files which use the functions. *ER* is a python function defining the effective radius. If it is not present, the effective radius is 0. *VR* is a python function defining the volume ratio. If it is not present, the volume ratio is 1. *form_volume*, *Iq*, *Iqxy*, *Imagnetic* are strings containing the C source code for the body of the volume, Iq, and Iqxy functions respectively. These can also be defined in the last source file. *Iq* and *Iqxy* also be instead be python functions defining the kernel. If they are marked as *Iq.vectorized = True* then the kernel is passed the entire *q* vector at once, otherwise it is passed values one *q* at a time. The performance improvement of this step is significant. *demo* is a dictionary of parameter=value defining a set of parameters to use by default when *compare* is called. Any parameter not set in *demo* gets the initial value from the parameter list. *demo* is mostly needed to set the default polydispersity values for tests. A :class:`modelinfo.ModelInfo` structure is constructed from the kernel meta data and returned to the caller. The doc string at the start of the kernel module will be used to construct the model documentation web pages. Embedded figures should appear in the subdirectory "img" beside the model definition, and tagged with the kernel module name to avoid collision with other models. Some file systems are case-sensitive, so only use lower case characters for file names and extensions. Code follows the C99 standard with the following extensions and conditions:: M_PI_180 = pi/180 M_4PI_3 = 4pi/3 square(x) = x*x cube(x) = x*x*x sas_sinx_x(x) = sin(x)/x, with sin(0)/0 -> 1 all double precision constants must include the decimal point all double declarations may be converted to half, float, or long double FLOAT_SIZE is the number of bytes in the converted variables :func:`load_kernel_module` loads the model definition file and :func:`modelinfo.make_model_info` parses it. :func:`make_source` converts C-based model definitions to C source code, including the polydispersity integral. :func:`model_sources` returns the list of source files the model depends on, and :func:`timestamp` returns the latest time stamp amongst the source files (so you can check if the model needs to be rebuilt). The function :func:`make_doc` extracts the doc string and adds the parameter table to the top. *make_figure* in *sasmodels/doc/genmodel* creates the default figure for the model. [These two sets of code should mignrate into docs.py so docs can be updated in one place]. """ from __future__ import print_function # TODO: determine which functions are useful outside of generate #__all__ = ["model_info", "make_doc", "make_source", "convert_type"] import sys from os.path import abspath, dirname, join as joinpath, exists, isdir, getmtime import re import string from zlib import crc32 import numpy as np # type: ignore from .modelinfo import Parameter from .custom import load_custom_kernel_module try: from typing import Tuple, Sequence, Iterator, Dict from .modelinfo import ModelInfo except ImportError: pass def get_data_path(external_dir, target_file): path = abspath(dirname(__file__)) if exists(joinpath(path, target_file)): return path # check next to exe/zip file exepath = dirname(sys.executable) path = joinpath(exepath, external_dir) if exists(joinpath(path, target_file)): return path # check in py2app Contents/Resources path = joinpath(exepath, '..', 'Resources', external_dir) if exists(joinpath(path, target_file)): return abspath(path) raise RuntimeError('Could not find '+joinpath(external_dir, target_file)) EXTERNAL_DIR = 'sasmodels-data' DATA_PATH = get_data_path(EXTERNAL_DIR, 'kernel_template.c') MODEL_PATH = joinpath(DATA_PATH, 'models') F16 = np.dtype('float16') F32 = np.dtype('float32') F64 = np.dtype('float64') try: # CRUFT: older numpy does not support float128 F128 = np.dtype('float128') except TypeError: F128 = None # Conversion from units defined in the parameter table for each model # to units displayed in the sphinx documentation. # This section associates the unit with the macro to use to produce the LaTex # code. The macro itself needs to be defined in sasmodels/doc/rst_prolog. # # NOTE: there is an RST_PROLOG at the end of this file which is NOT # used for the bundled documentation. Still as long as we are defining the macros # in two places any new addition should define the macro in both places. RST_UNITS = { "Ang": "|Ang|", "1/Ang": "|Ang^-1|", "1/Ang^2": "|Ang^-2|", "Ang^3": "|Ang^3|", "Ang^2": "|Ang^2|", "1e15/cm^3": "|1e15cm^3|", "Ang^3/mol": "|Ang^3|/mol", "1e-6/Ang^2": "|1e-6Ang^-2|", "degrees": "degree", "1/cm": "|cm^-1|", "Ang/cm": "|Ang*cm^-1|", "g/cm^3": "|g/cm^3|", "mg/m^2": "|mg/m^2|", "": "None", } # Headers for the parameters tables in th sphinx documentation PARTABLE_HEADERS = [ "Parameter", "Description", "Units", "Default value", ] # Minimum width for a default value (this is shorter than the column header # width, so will be ignored). PARTABLE_VALUE_WIDTH = 10 # Documentation header for the module, giving the model name, its short # description and its parameter table. The remainder of the doc comes # from the module docstring. DOC_HEADER = """.. _%(id)s: %(name)s ======================================================= %(title)s %(parameters)s %(returns)s %(docs)s """ def format_units(units): # type: (str) -> str """ Convert units into ReStructured Text format. """ return "string" if isinstance(units, list) else RST_UNITS.get(units, units) def make_partable(pars): # type: (List[Parameter]) -> str """ Generate the parameter table to include in the sphinx documentation. """ column_widths = [ max(len(p.name) for p in pars), max(len(p.description) for p in pars), max(len(format_units(p.units)) for p in pars), PARTABLE_VALUE_WIDTH, ] column_widths = [max(w, len(h)) for w, h in zip(column_widths, PARTABLE_HEADERS)] sep = " ".join("="*w for w in column_widths) lines = [ sep, " ".join("%-*s" % (w, h) for w, h in zip(column_widths, PARTABLE_HEADERS)), sep, ] for p in pars: lines.append(" ".join([ "%-*s" % (column_widths[0], p.name), "%-*s" % (column_widths[1], p.description), "%-*s" % (column_widths[2], format_units(p.units)), "%*g" % (column_widths[3], p.default), ])) lines.append(sep) return "\n".join(lines) def _search(search_path, filename): # type: (List[str], str) -> str """ Find *filename* in *search_path*. Raises ValueError if file does not exist. """ for path in search_path: target = joinpath(path, filename) if exists(target): return target raise ValueError("%r not found in %s" % (filename, search_path)) def model_sources(model_info): # type: (ModelInfo) -> List[str] """ Return a list of the sources file paths for the module. """ search_path = [dirname(model_info.filename), MODEL_PATH] return [_search(search_path, f) for f in model_info.source] def dll_timestamp(model_info): # type: (ModelInfo) -> int """ Return a timestamp for the model corresponding to the most recently changed file or dependency. """ # TODO: fails DRY; templates appear two places. model_templates = [joinpath(DATA_PATH, filename) for filename in ('kernel_header.c', 'kernel_iq.c')] source_files = (model_sources(model_info) + model_templates + [model_info.filename]) # Note: file may not exist when it is a standard model from library.zip times = [getmtime(f) for f in source_files if exists(f)] newest = max(times) if times else 0 return newest def ocl_timestamp(model_info): # type: (ModelInfo) -> int """ Return a timestamp for the model corresponding to the most recently changed file or dependency. Note that this does not look at the time stamps for the OpenCL header information since that need not trigger a recompile of the DLL. """ # TODO: fails DRY; templates appear two places. model_templates = [joinpath(DATA_PATH, filename) for filename in ('kernel_header.c', 'kernel_iq.cl')] source_files = (model_sources(model_info) + model_templates + [model_info.filename]) # Note: file may not exist when it is a standard model from library.zip times = [getmtime(f) for f in source_files if exists(f)] newest = max(times) if times else 0 return newest def tag_source(source): # type: (str) -> str """ Return a unique tag for the source code. """ # Note: need 0xffffffff&val to force an unsigned 32-bit number try: source = source.encode('utf8') except AttributeError: # bytes has no encode attribute in python 3 pass return "%08X"%(0xffffffff&crc32(source)) def convert_type(source, dtype): # type: (str, np.dtype) -> str """ Convert code from double precision to the desired type. Floating point constants are tagged with 'f' for single precision or 'L' for long double precision. """ source = _fix_tgmath_int(source) if dtype == F16: fbytes = 2 source = _convert_type(source, "half", "f") elif dtype == F32: fbytes = 4 source = _convert_type(source, "float", "f") elif dtype == F64: fbytes = 8 # no need to convert if it is already double elif dtype == F128: fbytes = 16 source = _convert_type(source, "long double", "L") else: raise ValueError("Unexpected dtype in source conversion: %s" % dtype) return ("#define FLOAT_SIZE %d\n" % fbytes)+source def _convert_type(source, type_name, constant_flag): # type: (str, str, str) -> str """ Replace 'double' with *type_name* in *source*, tagging floating point constants with *constant_flag*. """ # Convert double keyword to float/long double/half. # Accept an 'n' # parameter for vector # values, where n is 2, 4, 8 or 16. # Assume complex numbers are represented as cdouble which is typedef'd # to double2. source = re.sub(r'(^|[^a-zA-Z0-9_]c?)double(([248]|16)?($|[^a-zA-Z0-9_]))', r'\1%s\2'%type_name, source) source = _tag_float(source, constant_flag) return source TGMATH_INT_RE = re.compile(r""" (?: # Non-capturing match; not lookbehind since pattern length is variable \b # word boundary # various math functions (a?(sin|cos|tan)h? | atan2 | erfc? | tgamma | exp(2|10|m1)? | log(2|10|1p)? | pow[nr]? | sqrt | rsqrt | rootn | fabs | fmax | fmin ) \s*[(]\s* # open parenthesis ) [+-]?(0|[1-9]\d*) # integer (?= # lookahead match: don't want to move from end of int \s*[,)] # comma or close parenthesis for end of argument ) # end lookahead """, re.VERBOSE) def _fix_tgmath_int(source): # type: (str) -> str """ Replace f(integer) with f(integer.) for sin, cos, pow, etc. OS X OpenCL complains that it can't resolve the type generic calls to the standard math functions when they are called with integer constants, but this does not happen with the Windows Intel driver for example. To avoid confusion on the matrix marketplace, automatically promote integers to floats if we recognize them in the source. The specific functions we look for are: trigonometric: sin, asin, sinh, asinh, etc., and atan2 exponential: exp, exp2, exp10, expm1, log, log2, log10, logp1 power: pow, pown, powr, sqrt, rsqrt, rootn special: erf, erfc, tgamma float: fabs, fmin, fmax Note that we don't convert the second argument of dual argument functions: atan2, fmax, fmin, pow, powr. This could potentially be a problem for pow(x, 2), but that case seems to work without change. """ out = TGMATH_INT_RE.sub(r'\g<0>.', source) return out # Floating point regular expression # # Define parts: # # E = [eE][+-]?\d+ : Exponent # P = [.] : Decimal separator # N = [1-9]\d* : Natural number, no leading zeros # Z = 0 : Zero # F = \d+ : Fractional number, maybe leading zeros # F? = \d* : Optional fractional number # # We want to reject bare natural numbers and bare decimal points, so we # need to tediously outline the cases where we have either a fraction or # an exponent: # # ( ZP | ZPF | ZE | ZPE | ZPFE | NP | NPF | NE | NPE | NPFE | PF | PFE ) # # # We can then join cases by making parts optional. The following are # some ways to do this: # # ( (Z|N)(P|PF|E|PE|PFE) | PFE? ) # Split on lead # => ( (Z|N)(PF?|(PF?)?E) | PFE? ) # ( ((Z|N)PF?|PF)E? | (Z|N)E) # Split on point # ( (ZP|ZPF|NP|NPF|PF) | (Z|ZP|ZPF|N|NP|NPF|PF)E ) # Split on E # => ( ((Z|N)PF?|PF) | ((Z|N)(PF?)? | PF) E ) FLOAT_RE = re.compile(r""" (?%s'%constant_flag, source) #print("in",repr(source),"out",repr(out), constant_flag) return out def test_tag_float(): """check that floating point constants are properly identified and tagged with 'f'""" cases = """ ZP : 0. ZPF : 0.0,0.01,0.1 Z E: 0e+001 ZP E: 0.E0 ZPFE: 0.13e-031 NP : 1., 12. NPF : 1.0001, 1.1, 1.0 N E: 1e0, 37E-080 NP E: 1.e0, 37.E-080 NPFE: 845.017e+22 PF : .1, .0, .0100 PFE: .6e+9, .82E-004 # isolated cases 0. 1e0 0.13e-013 # untouched struct3.e3, 03.05.67, 37 # expressions 3.75+-1.6e-7-27+13.2 a3.e2 - 0. 4*atan(1) 4.*atan(1.) """ output = """ ZP : 0.f ZPF : 0.0f,0.01f,0.1f Z E: 0e+001f ZP E: 0.E0f ZPFE: 0.13e-031f NP : 1.f, 12.f NPF : 1.0001f, 1.1f, 1.0f N E: 1e0f, 37E-080f NP E: 1.e0f, 37.E-080f NPFE: 845.017e+22f PF : .1f, .0f, .0100f PFE: .6e+9f, .82E-004f # isolated cases 0.f 1e0f 0.13e-013f # untouched struct3.e3, 03.05.67, 37 # expressions 3.75f+-1.6e-7f-27+13.2f a3.e2 - 0.f 4*atan(1) 4.f*atan(1.f) """ for case_in, case_out in zip(cases.split('\n'), output.split('\n')): out = _tag_float(case_in, 'f') assert case_out == out, "%r => %r"%(case_in, out) def kernel_name(model_info, variant): # type: (ModelInfo, str) -> str """ Name of the exported kernel symbol. *variant* is "Iq", "Iqxy" or "Imagnetic". """ return model_info.name + "_" + variant def indent(s, depth): # type: (str, int) -> str """ Indent a string of text with *depth* additional spaces on each line. """ spaces = " "*depth sep = "\n" + spaces return spaces + sep.join(s.split("\n")) _template_cache = {} # type: Dict[str, Tuple[int, str, str]] def load_template(filename): # type: (str) -> str path = joinpath(DATA_PATH, filename) mtime = getmtime(path) if filename not in _template_cache or mtime > _template_cache[filename][0]: with open(path) as fid: _template_cache[filename] = (mtime, fid.read(), path) return _template_cache[filename][1], path _FN_TEMPLATE = """\ double %(name)s(%(pars)s); double %(name)s(%(pars)s) { #line %(line)d "%(filename)s" %(body)s } """ def _gen_fn(name, pars, body, filename, line): # type: (str, List[Parameter], str, str, int) -> str """ Generate a function given pars and body. Returns the following string:: double fn(double a, double b, ...); double fn(double a, double b, ...) { .... } """ par_decl = ', '.join(p.as_function_argument() for p in pars) if pars else 'void' return _FN_TEMPLATE % { 'name': name, 'pars': par_decl, 'body': body, 'filename': filename.replace('\\', '\\\\'), 'line': line, } def _call_pars(prefix, pars): # type: (str, List[Parameter]) -> List[str] """ Return a list of *prefix+parameter* from parameter items. *prefix* should be "v." if v is a struct. """ return [p.as_call_reference(prefix) for p in pars] # type in IQXY pattern could be single, float, double, long double, ... _IQXY_PATTERN = re.compile("^((inline|static) )? *([a-z ]+ )? *Iqxy *([(]|$)", flags=re.MULTILINE) def _have_Iqxy(sources): # type: (List[str]) -> bool """ Return true if any file defines Iqxy. Note this is not a C parser, and so can be easily confused by non-standard syntax. Also, it will incorrectly identify the following as having Iqxy:: /* double Iqxy(qx, qy, ...) { ... fill this in later ... } */ If you want to comment out an Iqxy function, use // on the front of the line instead. """ for path, code in sources: if _IQXY_PATTERN.search(code): return True else: return False def _add_source(source, code, path): """ Add a file to the list of source code chunks, tagged with path and line. """ path = path.replace('\\', '\\\\') source.append('#line 1 "%s"' % path) source.append(code) def make_source(model_info): # type: (ModelInfo) -> Dict[str, str] """ Generate the OpenCL/ctypes kernel from the module info. Uses source files found in the given search path. Returns None if this is a pure python model, with no C source components. """ if callable(model_info.Iq): raise ValueError("can't compile python model") #return None # TODO: need something other than volume to indicate dispersion parameters # No volume normalization despite having a volume parameter. # Thickness is labelled a volume in order to trigger polydispersity. # May want a separate dispersion flag, or perhaps a separate category for # disperse, but not volume. Volume parameters also use relative values # for the distribution rather than the absolute values used by angular # dispersion. Need to be careful that necessary parameters are available # for computing volume even if we allow non-disperse volume parameters. partable = model_info.parameters # Load templates and user code kernel_header = load_template('kernel_header.c') dll_code = load_template('kernel_iq.c') ocl_code = load_template('kernel_iq.cl') #ocl_code = load_template('kernel_iq_local.cl') user_code = [(f, open(f).read()) for f in model_sources(model_info)] # Build initial sources source = [] _add_source(source, *kernel_header) for path, code in user_code: _add_source(source, code, path) # Make parameters for q, qx, qy so that we can use them in declarations q, qx, qy = [Parameter(name=v) for v in ('q', 'qx', 'qy')] # Generate form_volume function, etc. from body only if isinstance(model_info.form_volume, str): pars = partable.form_volume_parameters source.append(_gen_fn('form_volume', pars, model_info.form_volume, model_info.filename, model_info._form_volume_line)) if isinstance(model_info.Iq, str): pars = [q] + partable.iq_parameters source.append(_gen_fn('Iq', pars, model_info.Iq, model_info.filename, model_info._Iq_line)) if isinstance(model_info.Iqxy, str): pars = [qx, qy] + partable.iqxy_parameters source.append(_gen_fn('Iqxy', pars, model_info.Iqxy, model_info.filename, model_info._Iqxy_line)) # Define the parameter table # TODO: plug in current line number source.append('#line 542 "sasmodels/generate.py"') source.append("#define PARAMETER_TABLE \\") source.append("\\\n".join(p.as_definition() for p in partable.kernel_parameters)) # Define the function calls if partable.form_volume_parameters: refs = _call_pars("_v.", partable.form_volume_parameters) call_volume = "#define CALL_VOLUME(_v) form_volume(%s)"%(",".join(refs)) else: # Model doesn't have volume. We could make the kernel run a little # faster by not using/transferring the volume normalizations, but # the ifdef's reduce readability more than is worthwhile. call_volume = "#define CALL_VOLUME(v) 1.0" source.append(call_volume) refs = ["_q[_i]"] + _call_pars("_v.", partable.iq_parameters) call_iq = "#define CALL_IQ(_q,_i,_v) Iq(%s)" % (",".join(refs)) if _have_Iqxy(user_code) or isinstance(model_info.Iqxy, str): # Call 2D model refs = ["_q[2*_i]", "_q[2*_i+1]"] + _call_pars("_v.", partable.iqxy_parameters) call_iqxy = "#define CALL_IQ(_q,_i,_v) Iqxy(%s)" % (",".join(refs)) else: # Call 1D model with sqrt(qx^2 + qy^2) #warnings.warn("Creating Iqxy = Iq(sqrt(qx^2 + qy^2))") # still defined:: refs = ["q[i]"] + _call_pars("v", iq_parameters) pars_sqrt = ["sqrt(_q[2*_i]*_q[2*_i]+_q[2*_i+1]*_q[2*_i+1])"] + refs[1:] call_iqxy = "#define CALL_IQ(_q,_i,_v) Iq(%s)" % (",".join(pars_sqrt)) magpars = [k-2 for k, p in enumerate(partable.call_parameters) if p.type == 'sld'] # Fill in definitions for numbers of parameters source.append("#define MAX_PD %s"%partable.max_pd) source.append("#define NUM_PARS %d"%partable.npars) source.append("#define NUM_VALUES %d" % partable.nvalues) source.append("#define NUM_MAGNETIC %d" % partable.nmagnetic) source.append("#define MAGNETIC_PARS %s"%",".join(str(k) for k in magpars)) for k, v in enumerate(magpars[:3]): source.append("#define MAGNETIC_PAR%d %d"%(k+1, v)) # TODO: allow mixed python/opencl kernels? ocl = kernels(ocl_code, call_iq, call_iqxy, model_info.name) dll = kernels(dll_code, call_iq, call_iqxy, model_info.name) result = { 'dll': '\n'.join(source+dll[0]+dll[1]+dll[2]), 'opencl': '\n'.join(source+ocl[0]+ocl[1]+ocl[2]), } return result def kernels(kernel, call_iq, call_iqxy, name): # type: ([str,str], str, str, str) -> List[str] code = kernel[0] path = kernel[1].replace('\\', '\\\\') iq = [ # define the Iq kernel "#define KERNEL_NAME %s_Iq" % name, call_iq, '#line 1 "%s Iq"' % path, code, "#undef CALL_IQ", "#undef KERNEL_NAME", ] iqxy = [ # define the Iqxy kernel from the same source with different #defines "#define KERNEL_NAME %s_Iqxy" % name, call_iqxy, '#line 1 "%s Iqxy"' % path, code, "#undef CALL_IQ", "#undef KERNEL_NAME", ] imagnetic = [ # define the Imagnetic kernel "#define KERNEL_NAME %s_Imagnetic" % name, "#define MAGNETIC 1", call_iqxy, '#line 1 "%s Imagnetic"' % path, code, "#undef MAGNETIC", "#undef CALL_IQ", "#undef KERNEL_NAME", ] return iq, iqxy, imagnetic def load_kernel_module(model_name): # type: (str) -> module """ Return the kernel module named in *model_name*. If the name ends in *.py* then load it as a custom model using :func:`sasmodels.custom.load_custom_kernel_module`, otherwise load it from :mod:`sasmodels.models`. """ if model_name.endswith('.py'): kernel_module = load_custom_kernel_module(model_name) else: from sasmodels import models __import__('sasmodels.models.'+model_name) kernel_module = getattr(models, model_name, None) return kernel_module section_marker = re.compile(r'\A(?P[%s])(?P=first)*\Z' % re.escape(string.punctuation)) def _convert_section_titles_to_boldface(lines): # type: (Sequence[str]) -> Iterator[str] """ Do the actual work of identifying and converting section headings. """ prior = None for line in lines: if prior is None: prior = line elif section_marker.match(line): if len(line) >= len(prior): yield "".join(("**", prior, "**")) prior = None else: yield prior prior = line else: yield prior prior = line if prior is not None: yield prior def convert_section_titles_to_boldface(s): # type: (str) -> str """ Use explicit bold-face rather than section headings so that the table of contents is not polluted with section names from the model documentation. Sections are identified as the title line followed by a line of punctuation at least as long as the title line. """ return "\n".join(_convert_section_titles_to_boldface(s.split('\n'))) def make_doc(model_info): # type: (ModelInfo) -> str """ Return the documentation for the model. """ Iq_units = "The returned value is scaled to units of |cm^-1| |sr^-1|, absolute scale." Sq_units = "The returned value is a dimensionless structure factor, $S(q)$." docs = model_info.docs if model_info.docs is not None else "" docs = convert_section_titles_to_boldface(docs) pars = make_partable(model_info.parameters.COMMON + model_info.parameters.kernel_parameters) subst = dict(id=model_info.id.replace('_', '-'), name=model_info.name, title=model_info.title, parameters=pars, returns=Sq_units if model_info.structure_factor else Iq_units, docs=docs) return DOC_HEADER % subst # TODO: need a single source for rst_prolog; it is also in doc/rst_prolog RST_PROLOG = r"""\ .. |Ang| unicode:: U+212B .. |Ang^-1| replace:: |Ang|\ :sup:`-1` .. |Ang^2| replace:: |Ang|\ :sup:`2` .. |Ang^-2| replace:: |Ang|\ :sup:`-2` .. |1e-6Ang^-2| replace:: 10\ :sup:`-6`\ |Ang|\ :sup:`-2` .. |Ang^3| replace:: |Ang|\ :sup:`3` .. |Ang^-3| replace:: |Ang|\ :sup:`-3` .. |Ang^-4| replace:: |Ang|\ :sup:`-4` .. |cm^-1| replace:: cm\ :sup:`-1` .. |cm^2| replace:: cm\ :sup:`2` .. |cm^-2| replace:: cm\ :sup:`-2` .. |cm^3| replace:: cm\ :sup:`3` .. |1e15cm^3| replace:: 10\ :sup:`15`\ cm\ :sup:`3` .. |cm^-3| replace:: cm\ :sup:`-3` .. |sr^-1| replace:: sr\ :sup:`-1` .. |cdot| unicode:: U+00B7 .. |deg| unicode:: U+00B0 .. |g/cm^3| replace:: g\ |cdot|\ cm\ :sup:`-3` .. |mg/m^2| replace:: mg\ |cdot|\ m\ :sup:`-2` .. |fm^2| replace:: fm\ :sup:`2` .. |Ang*cm^-1| replace:: |Ang|\ |cdot|\ cm\ :sup:`-1` """ # TODO: make a better fake reference role RST_ROLES = """\ .. role:: ref .. role:: numref """ def make_html(model_info): """ Convert model docs directly to html. """ from . import rst2html rst = make_doc(model_info) return rst2html.rst2html("".join((RST_ROLES, RST_PROLOG, rst))) def view_html(model_name): from . import modelinfo kernel_module = load_kernel_module(model_name) info = modelinfo.make_model_info(kernel_module) view_html_from_info(info) def view_html_from_info(info): from . import rst2html url = "file://"+dirname(info.filename)+"/" rst2html.view_html(make_html(info), url=url) def demo_time(): # type: () -> None """ Show how long it takes to process a model. """ import datetime from .modelinfo import make_model_info from .models import cylinder tic = datetime.datetime.now() make_source(make_model_info(cylinder)) toc = (datetime.datetime.now() - tic).total_seconds() print("time: %g"%toc) def main(): # type: () -> None """ Program which prints the source produced by the model. """ import sys from .modelinfo import make_model_info if len(sys.argv) <= 1: print("usage: python -m sasmodels.generate modelname") else: name = sys.argv[1] kernel_module = load_kernel_module(name) model_info = make_model_info(kernel_module) source = make_source(model_info) print(source['dll']) if __name__ == "__main__": main() sasmodels/sasmodels/kernel.py000066400000000000000000000026641317715334700167170ustar00rootroot00000000000000""" Execution kernel interface ========================== :class:`KernelModel` defines the interface to all kernel models. In particular, each model should provide a :meth:`KernelModel.make_kernel` call which returns an executable kernel, :class:`Kernel`, that operates on the given set of *q_vector* inputs. On completion of the computation, the kernel should be released, which also releases the inputs. """ from __future__ import division, print_function import numpy as np try: from typing import List except ImportError: pass else: from .details import CallDetails from .modelinfo import ModelInfo import numpy as np # type: ignore class KernelModel(object): info = None # type: ModelInfo dtype = None # type: np.dtype def make_kernel(self, q_vectors): # type: (List[np.ndarray]) -> "Kernel" raise NotImplementedError("need to implement make_kernel") def release(self): # type: () -> None pass class Kernel(object): #: kernel dimension, either "1d" or "2d" dim = None # type: str info = None # type: ModelInfo results = None # type: List[np.ndarray] dtype = None # type: np.dtype def __call__(self, call_details, values, cutoff, magnetic): # type: (CallDetails, np.ndarray, np.ndarray, float, bool) -> np.ndarray raise NotImplementedError("need to implement __call__") def release(self): # type: () -> None pass sasmodels/sasmodels/kernel_header.c000066400000000000000000000177771317715334700200340ustar00rootroot00000000000000#ifdef __OPENCL_VERSION__ # define USE_OPENCL #elif defined(_OPENMP) # define USE_OPENMP #endif // If opencl is not available, then we are compiling a C function // Note: if using a C++ compiler, then define kernel as extern "C" #ifdef USE_OPENCL typedef int int32_t; # if defined(USE_SINCOS) # define SINCOS(angle,svar,cvar) svar=sincos(angle,&cvar) # else # define SINCOS(angle,svar,cvar) do {const double _t_=angle; svar=sin(_t_);cvar=cos(_t_);} while (0) # endif // Intel CPU on Mac gives strange values for erf(); on the verified // platforms (intel, nvidia, amd), the cephes erf() is significantly // faster than that available in the native OpenCL. #define NEED_ERF // OpenCL only has type generic math #define expf exp #ifndef NEED_ERF # define erff erf # define erfcf erfc #endif #else // !USE_OPENCL // Use SAS_DOUBLE to force the use of double even for float kernels # define SAS_DOUBLE dou ## ble # ifdef __cplusplus #include #include using namespace std; #if defined(_MSC_VER) #include #include #define kernel extern "C" __declspec( dllexport ) inline double trunc(double x) { return x>=0?floor(x):-floor(-x); } inline double fmin(double x, double y) { return x>y ? y : x; } inline double fmax(double x, double y) { return x::quiet_NaN()) // non-signalling NaN #define INFINITY (std::numeric_limits::infinity()) #define NEED_ERF #define NEED_EXPM1 #define NEED_TGAMMA #else #define kernel extern "C" #include #endif inline void SINCOS(double angle, double &svar, double &cvar) { svar=sin(angle); cvar=cos(angle); } # else // !__cplusplus #include // C99 guarantees that int32_t types is here #include #if defined(__TINYC__) typedef int int32_t; #include // TODO: check isnan is correct inline double _isnan(double x) { return x != x; } // hope this doesn't optimize away! #undef isnan #define isnan(x) _isnan(x) // Defeat the double->float conversion since we don't have tgmath inline SAS_DOUBLE trunc(SAS_DOUBLE x) { return x>=0?floor(x):-floor(-x); } inline SAS_DOUBLE fmin(SAS_DOUBLE x, SAS_DOUBLE y) { return x>y ? y : x; } inline SAS_DOUBLE fmax(SAS_DOUBLE x, SAS_DOUBLE y) { return x // C99 type-generic math, so sin(float) => sinf #endif // MSVC doesn't support C99, so no need for dllexport on C99 branch #define kernel #define SINCOS(angle,svar,cvar) do {const double _t_=angle; svar=sin(_t_);cvar=cos(_t_);} while (0) # endif // !__cplusplus # define global # define local # define constant const // OpenCL powr(a,b) = C99 pow(a,b), b >= 0 // OpenCL pown(a,b) = C99 pow(a,b), b integer # define powr(a,b) pow(a,b) # define pown(a,b) pow(a,b) #endif // !USE_OPENCL #if defined(NEED_EXPM1) static SAS_DOUBLE expm1(SAS_DOUBLE x_in) { double x = (double)x_in; // go back to float for single precision kernels // Adapted from the cephes math library. // Copyright 1984 - 1992 by Stephen L. Moshier if (x != x || x == 0.0) { return x; // NaN and +/- 0 } else if (x < -0.5 || x > 0.5) { return exp(x) - 1.0; } else { const double xsq = x*x; const double p = ((( +1.2617719307481059087798E-4)*xsq +3.0299440770744196129956E-2)*xsq +9.9999999999999999991025E-1); const double q = (((( +3.0019850513866445504159E-6)*xsq +2.5244834034968410419224E-3)*xsq +2.2726554820815502876593E-1)*xsq +2.0000000000000000000897E0); double r = x * p; r = r / (q - r); return r+r; } } #endif // Standard mathematical constants: // M_E, M_LOG2E, M_LOG10E, M_LN2, M_LN10, M_PI, M_PI_2=pi/2, M_PI_4=pi/4, // M_1_PI=1/pi, M_2_PI=2/pi, M_2_SQRTPI=2/sqrt(pi), SQRT2, SQRT1_2=sqrt(1/2) // OpenCL defines M_constant_F for float constants, and nothing if double // is not enabled on the card, which is why these constants may be missing #ifndef M_PI # define M_PI 3.141592653589793 #endif #ifndef M_PI_2 # define M_PI_2 1.570796326794897 #endif #ifndef M_PI_4 # define M_PI_4 0.7853981633974483 #endif #ifndef M_E # define M_E 2.718281828459045091 #endif #ifndef M_SQRT1_2 # define M_SQRT1_2 0.70710678118654746 #endif // Non-standard function library // pi/180, used for converting between degrees and radians // 4/3 pi for computing sphere volumes // square and cube for computing squares and cubes #ifndef M_PI_180 # define M_PI_180 0.017453292519943295 #endif #ifndef M_4PI_3 # define M_4PI_3 4.18879020478639 #endif inline double square(double x) { return x*x; } inline double cube(double x) { return x*x*x; } inline double sas_sinx_x(double x) { return x==0 ? 1.0 : sin(x)/x; } // To rotate from the canonical position to theta, phi, psi, first rotate by // psi about the major axis, oriented along z, which is a rotation in the // detector plane xy. Next rotate by theta about the y axis, aligning the major // axis in the xz plane. Finally, rotate by phi in the detector plane xy. // To compute the scattering, undo these rotations in reverse order: // rotate in xy by -phi, rotate in xz by -theta, rotate in xy by -psi // The returned q is the length of the q vector and (xhat, yhat, zhat) is a unit // vector in the q direction. // To change between counterclockwise and clockwise rotation, change the // sign of phi and psi. #if 1 //think cos(theta) should be sin(theta) in new coords, RKH 11Jan2017 #define ORIENT_SYMMETRIC(qx, qy, theta, phi, q, sn, cn) do { \ SINCOS(phi*M_PI_180, sn, cn); \ q = sqrt(qx*qx + qy*qy); \ cn = (q==0. ? 1.0 : (cn*qx + sn*qy)/q * sin(theta*M_PI_180)); \ sn = sqrt(1 - cn*cn); \ } while (0) #else // SasView 3.x definition of orientation #define ORIENT_SYMMETRIC(qx, qy, theta, phi, q, sn, cn) do { \ SINCOS(theta*M_PI_180, sn, cn); \ q = sqrt(qx*qx + qy*qy);\ cn = (q==0. ? 1.0 : (cn*cos(phi*M_PI_180)*qx + sn*qy)/q); \ sn = sqrt(1 - cn*cn); \ } while (0) #endif #if 1 #define ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat) do { \ q = sqrt(qx*qx + qy*qy); \ const double qxhat = qx/q; \ const double qyhat = qy/q; \ double sin_theta, cos_theta; \ double sin_phi, cos_phi; \ double sin_psi, cos_psi; \ SINCOS(theta*M_PI_180, sin_theta, cos_theta); \ SINCOS(phi*M_PI_180, sin_phi, cos_phi); \ SINCOS(psi*M_PI_180, sin_psi, cos_psi); \ xhat = qxhat*(-sin_phi*sin_psi + cos_theta*cos_phi*cos_psi) \ + qyhat*( cos_phi*sin_psi + cos_theta*sin_phi*cos_psi); \ yhat = qxhat*(-sin_phi*cos_psi - cos_theta*cos_phi*sin_psi) \ + qyhat*( cos_phi*cos_psi - cos_theta*sin_phi*sin_psi); \ zhat = qxhat*(-sin_theta*cos_phi) \ + qyhat*(-sin_theta*sin_phi); \ } while (0) #else // SasView 3.x definition of orientation #define ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, cos_alpha, cos_mu, cos_nu) do { \ q = sqrt(qx*qx + qy*qy); \ const double qxhat = qx/q; \ const double qyhat = qy/q; \ double sin_theta, cos_theta; \ double sin_phi, cos_phi; \ double sin_psi, cos_psi; \ SINCOS(theta*M_PI_180, sin_theta, cos_theta); \ SINCOS(phi*M_PI_180, sin_phi, cos_phi); \ SINCOS(psi*M_PI_180, sin_psi, cos_psi); \ cos_alpha = cos_theta*cos_phi*qxhat + sin_theta*qyhat; \ cos_mu = (-sin_theta*cos_psi*cos_phi - sin_psi*sin_phi)*qxhat + cos_theta*cos_psi*qyhat; \ cos_nu = (-cos_phi*sin_psi*sin_theta + sin_phi*cos_psi)*qxhat + sin_psi*cos_theta*qyhat; \ } while (0) #endif sasmodels/sasmodels/kernel_iq.c000066400000000000000000000273701317715334700172030ustar00rootroot00000000000000 /* ########################################################## # # # !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! # # !! !! # # !! KEEP THIS CODE CONSISTENT WITH KERNELPY.PY !! # # !! !! # # !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! # # # ########################################################## */ #ifndef _PAR_BLOCK_ // protected block so we can include this code twice. #define _PAR_BLOCK_ typedef struct { #if MAX_PD > 0 int32_t pd_par[MAX_PD]; // id of the nth polydispersity variable int32_t pd_length[MAX_PD]; // length of the nth polydispersity weight vector int32_t pd_offset[MAX_PD]; // offset of pd weights in the value & weight vector int32_t pd_stride[MAX_PD]; // stride to move to the next index at this level #endif // MAX_PD > 0 int32_t num_eval; // total number of voxels in hypercube int32_t num_weights; // total length of the weights vector int32_t num_active; // number of non-trivial pd loops int32_t theta_par; // id of spherical correction variable } ProblemDetails; // Intel HD 4000 needs private arrays to be a multiple of 4 long typedef struct { PARAMETER_TABLE } ParameterTable; typedef union { ParameterTable table; double vector[4*((NUM_PARS+3)/4)]; } ParameterBlock; #endif // _PAR_BLOCK_ #if defined(MAGNETIC) && NUM_MAGNETIC>0 // Return value restricted between low and high static double clip(double value, double low, double high) { return (value < low ? low : (value > high ? high : value)); } // Compute spin cross sections given in_spin and out_spin // To convert spin cross sections to sld b: // uu * (sld - m_sigma_x); // dd * (sld + m_sigma_x); // ud * (m_sigma_y + 1j*m_sigma_z); // du * (m_sigma_y - 1j*m_sigma_z); static void set_spins(double in_spin, double out_spin, double spins[4]) { in_spin = clip(in_spin, 0.0, 1.0); out_spin = clip(out_spin, 0.0, 1.0); spins[0] = sqrt(sqrt((1.0-in_spin) * (1.0-out_spin))); // dd spins[1] = sqrt(sqrt((1.0-in_spin) * out_spin)); // du spins[2] = sqrt(sqrt(in_spin * (1.0-out_spin))); // ud spins[3] = sqrt(sqrt(in_spin * out_spin)); // uu } static double mag_sld(double qx, double qy, double p, double mx, double my, double sld) { const double perp = qy*mx - qx*my; return sld + perp*p; } #endif // MAGNETIC kernel void KERNEL_NAME( int32_t nq, // number of q values const int32_t pd_start, // where we are in the polydispersity loop const int32_t pd_stop, // where we are stopping in the polydispersity loop global const ProblemDetails *details, global const double *values, global const double *q, // nq q values, with padding to boundary global double *result, // nq+1 return values, again with padding const double cutoff // cutoff in the polydispersity weight product ) { // Storage for the current parameter values. These will be updated as we // walk the polydispersity cube. ParameterBlock local_values; #if defined(MAGNETIC) && NUM_MAGNETIC>0 // Location of the sld parameters in the parameter vector. // These parameters are updated with the effective sld due to magnetism. #if NUM_MAGNETIC > 3 const int32_t slds[] = { MAGNETIC_PARS }; #endif // TODO: could precompute these outside of the kernel. // Interpret polarization cross section. // up_frac_i = values[NUM_PARS+2]; // up_frac_f = values[NUM_PARS+3]; // up_angle = values[NUM_PARS+4]; double spins[4]; double cos_mspin, sin_mspin; set_spins(values[NUM_PARS+2], values[NUM_PARS+3], spins); SINCOS(-values[NUM_PARS+4]*M_PI_180, sin_mspin, cos_mspin); #endif // MAGNETIC // Fill in the initial variables // values[0] is scale // values[1] is background #ifdef USE_OPENMP #pragma omp parallel for #endif for (int i=0; i < NUM_PARS; i++) { local_values.vector[i] = values[2+i]; //printf("p%d = %g\n",i, local_values.vector[i]); } //printf("NUM_VALUES:%d NUM_PARS:%d MAX_PD:%d\n", NUM_VALUES, NUM_PARS, MAX_PD); //printf("start:%d stop:%d\n", pd_start, pd_stop); double pd_norm = (pd_start == 0 ? 0.0 : result[nq]); if (pd_start == 0) { #ifdef USE_OPENMP #pragma omp parallel for #endif for (int q_index=0; q_index < nq; q_index++) result[q_index] = 0.0; } //printf("start %d %g %g\n", pd_start, pd_norm, result[0]); #if MAX_PD>0 global const double *pd_value = values + NUM_VALUES; global const double *pd_weight = pd_value + details->num_weights; #endif // Jump into the middle of the polydispersity loop #if MAX_PD>4 int n4=details->pd_length[4]; int i4=(pd_start/details->pd_stride[4])%n4; const int p4=details->pd_par[4]; global const double *v4 = pd_value + details->pd_offset[4]; global const double *w4 = pd_weight + details->pd_offset[4]; #endif #if MAX_PD>3 int n3=details->pd_length[3]; int i3=(pd_start/details->pd_stride[3])%n3; const int p3=details->pd_par[3]; global const double *v3 = pd_value + details->pd_offset[3]; global const double *w3 = pd_weight + details->pd_offset[3]; //printf("offset %d: %d %d\n", 3, details->pd_offset[3], NUM_VALUES); #endif #if MAX_PD>2 int n2=details->pd_length[2]; int i2=(pd_start/details->pd_stride[2])%n2; const int p2=details->pd_par[2]; global const double *v2 = pd_value + details->pd_offset[2]; global const double *w2 = pd_weight + details->pd_offset[2]; #endif #if MAX_PD>1 int n1=details->pd_length[1]; int i1=(pd_start/details->pd_stride[1])%n1; const int p1=details->pd_par[1]; global const double *v1 = pd_value + details->pd_offset[1]; global const double *w1 = pd_weight + details->pd_offset[1]; #endif #if MAX_PD>0 int n0=details->pd_length[0]; int i0=(pd_start/details->pd_stride[0])%n0; const int p0=details->pd_par[0]; global const double *v0 = pd_value + details->pd_offset[0]; global const double *w0 = pd_weight + details->pd_offset[0]; //printf("w0:%p, values:%p, diff:%ld, %d\n",w0,values,(w0-values), NUM_VALUES); #endif #if MAX_PD>0 const int theta_par = details->theta_par; const int fast_theta = (theta_par == p0); const int slow_theta = (theta_par >= 0 && !fast_theta); double spherical_correction = 1.0; #else // Note: if not polydisperse the weights cancel and we don't need the // spherical correction. const double spherical_correction = 1.0; #endif int step = pd_start; #if MAX_PD>4 const double weight5 = 1.0; while (i4 < n4) { local_values.vector[p4] = v4[i4]; double weight4 = w4[i4] * weight5; //printf("step:%d level %d: p:%d i:%d n:%d value:%g weight:%g\n", step, 4, p4, i4, n4, local_values.vector[p4], weight4); #elif MAX_PD>3 const double weight4 = 1.0; #endif #if MAX_PD>3 while (i3 < n3) { local_values.vector[p3] = v3[i3]; double weight3 = w3[i3] * weight4; //printf("step:%d level %d: p:%d i:%d n:%d value:%g weight:%g\n", step, 3, p3, i3, n3, local_values.vector[p3], weight3); #elif MAX_PD>2 const double weight3 = 1.0; #endif #if MAX_PD>2 while (i2 < n2) { local_values.vector[p2] = v2[i2]; double weight2 = w2[i2] * weight3; //printf("step:%d level %d: p:%d i:%d n:%d value:%g weight:%g\n", step, 2, p2, i2, n2, local_values.vector[p2], weight2); #elif MAX_PD>1 const double weight2 = 1.0; #endif #if MAX_PD>1 while (i1 < n1) { local_values.vector[p1] = v1[i1]; double weight1 = w1[i1] * weight2; //printf("step:%d level %d: p:%d i:%d n:%d value:%g weight:%g\n", step, 1, p1, i1, n1, local_values.vector[p1], weight1); #elif MAX_PD>0 const double weight1 = 1.0; #endif #if MAX_PD>0 if (slow_theta) { // Theta is not in inner loop spherical_correction = fmax(fabs(cos(M_PI_180*local_values.vector[theta_par])), 1.e-6); } while(i0 < n0) { local_values.vector[p0] = v0[i0]; double weight0 = w0[i0] * weight1; //printf("step:%d level %d: p:%d i:%d n:%d value:%g weight:%g\n", step, 0, p0, i0, n0, local_values.vector[p0], weight0); if (fast_theta) { // Theta is in inner loop spherical_correction = fmax(fabs(cos(M_PI_180*local_values.vector[p0])), 1.e-6); } #else const double weight0 = 1.0; #endif //printf("step:%d of %d, pars:",step,pd_stop); for (int i=0; i < NUM_PARS; i++) printf("p%d=%g ",i, local_values.vector[i]); printf("\n"); //printf("sphcor: %g\n", spherical_correction); #ifdef INVALID if (!INVALID(local_values.table)) #endif { // Accumulate I(q) // Note: weight==0 must always be excluded if (weight0 > cutoff) { // spherical correction is set at a minimum of 1e-6, otherwise there // would be problems looking at models with theta=90. const double weight = weight0 * spherical_correction; pd_norm += weight * CALL_VOLUME(local_values.table); #ifdef USE_OPENMP #pragma omp parallel for #endif for (int q_index=0; q_index 0 const double qx = q[2*q_index]; const double qy = q[2*q_index+1]; const double qsq = qx*qx + qy*qy; // Constant across orientation, polydispersity for given qx, qy double scattering = 0.0; // TODO: what is the magnetic scattering at q=0 if (qsq > 1.e-16) { double p[4]; // dd, du, ud, uu p[0] = (qy*cos_mspin + qx*sin_mspin)/qsq; p[3] = -p[0]; p[1] = p[2] = (qy*sin_mspin - qx*cos_mspin)/qsq; for (int index=0; index<4; index++) { const double xs = spins[index]; if (xs > 1.e-8) { const int spin_flip = (index==1) || (index==2); const double pk = p[index]; for (int axis=0; axis<=spin_flip; axis++) { #define M1 NUM_PARS+5 #define M2 NUM_PARS+8 #define M3 NUM_PARS+13 #define SLD(_M_offset, _sld_offset) \ local_values.vector[_sld_offset] = xs * (axis \ ? (index==1 ? -values[_M_offset+2] : values[_M_offset+2]) \ : mag_sld(qx, qy, pk, values[_M_offset], values[_M_offset+1], \ (spin_flip ? 0.0 : values[_sld_offset+2]))) #if NUM_MAGNETIC==1 SLD(M1, MAGNETIC_PAR1); #elif NUM_MAGNETIC==2 SLD(M1, MAGNETIC_PAR1); SLD(M2, MAGNETIC_PAR2); #elif NUM_MAGNETIC==3 SLD(M1, MAGNETIC_PAR1); SLD(M2, MAGNETIC_PAR2); SLD(M3, MAGNETIC_PAR3); #else for (int sk=0; sk0 if (step >= pd_stop) break; ++i0; } i0 = 0; #endif #if MAX_PD>1 if (step >= pd_stop) break; ++i1; } i1 = 0; #endif #if MAX_PD>2 if (step >= pd_stop) break; ++i2; } i2 = 0; #endif #if MAX_PD>3 if (step >= pd_stop) break; ++i3; } i3 = 0; #endif #if MAX_PD>4 if (step >= pd_stop) break; ++i4; } i4 = 0; #endif //printf("res: %g/%g\n", result[0], pd_norm); // Remember the updated norm. result[nq] = pd_norm; } sasmodels/sasmodels/kernel_iq.cl000066400000000000000000000271621317715334700173560ustar00rootroot00000000000000 /* ########################################################## # # # !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! # # !! !! # # !! KEEP THIS CODE CONSISTENT WITH KERNELPY.PY !! # # !! !! # # !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! # # # ########################################################## */ #ifndef _PAR_BLOCK_ // protected block so we can include this code twice. #define _PAR_BLOCK_ typedef struct { #if MAX_PD > 0 int32_t pd_par[MAX_PD]; // id of the nth polydispersity variable int32_t pd_length[MAX_PD]; // length of the nth polydispersity weight vector int32_t pd_offset[MAX_PD]; // offset of pd weights in the value & weight vector int32_t pd_stride[MAX_PD]; // stride to move to the next index at this level #endif // MAX_PD > 0 int32_t num_eval; // total number of voxels in hypercube int32_t num_weights; // total length of the weights vector int32_t num_active; // number of non-trivial pd loops int32_t theta_par; // id of spherical correction variable } ProblemDetails; // Intel HD 4000 needs private arrays to be a multiple of 4 long typedef struct { PARAMETER_TABLE } ParameterTable; typedef union { ParameterTable table; double vector[4*((NUM_PARS+3)/4)]; } ParameterBlock; #endif // _PAR_BLOCK_ #if defined(MAGNETIC) && NUM_MAGNETIC>0 // Return value restricted between low and high static double clip(double value, double low, double high) { return (value < low ? low : (value > high ? high : value)); } // Compute spin cross sections given in_spin and out_spin // To convert spin cross sections to sld b: // uu * (sld - m_sigma_x); // dd * (sld + m_sigma_x); // ud * (m_sigma_y + 1j*m_sigma_z); // du * (m_sigma_y - 1j*m_sigma_z); static void set_spins(double in_spin, double out_spin, double spins[4]) { in_spin = clip(in_spin, 0.0, 1.0); out_spin = clip(out_spin, 0.0, 1.0); spins[0] = sqrt(sqrt((1.0-in_spin) * (1.0-out_spin))); // dd spins[1] = sqrt(sqrt((1.0-in_spin) * out_spin)); // du spins[2] = sqrt(sqrt(in_spin * (1.0-out_spin))); // ud spins[3] = sqrt(sqrt(in_spin * out_spin)); // uu } static double mag_sld(double qx, double qy, double p, double mx, double my, double sld) { const double perp = qy*mx - qx*my; return sld + perp*p; } #endif // MAGNETIC kernel void KERNEL_NAME( int32_t nq, // number of q values const int32_t pd_start, // where we are in the polydispersity loop const int32_t pd_stop, // where we are stopping in the polydispersity loop global const ProblemDetails *details, global const double *values, global const double *q, // nq q values, with padding to boundary global double *result, // nq+1 return values, again with padding const double cutoff // cutoff in the polydispersity weight product ) { // who we are and what element we are working with const int q_index = get_global_id(0); if (q_index >= nq) return; // Storage for the current parameter values. These will be updated as we // walk the polydispersity cube. ParameterBlock local_values; #if defined(MAGNETIC) && NUM_MAGNETIC>0 // Location of the sld parameters in the parameter vector. // These parameters are updated with the effective sld due to magnetism. #if NUM_MAGNETIC > 3 const int32_t slds[] = { MAGNETIC_PARS }; #endif // TODO: could precompute these outside of the kernel. // Interpret polarization cross section. // up_frac_i = values[NUM_PARS+2]; // up_frac_f = values[NUM_PARS+3]; // up_angle = values[NUM_PARS+4]; double spins[4]; double cos_mspin, sin_mspin; set_spins(values[NUM_PARS+2], values[NUM_PARS+3], spins); SINCOS(-values[NUM_PARS+4]*M_PI_180, sin_mspin, cos_mspin); #endif // MAGNETIC // Fill in the initial variables // values[0] is scale // values[1] is background for (int i=0; i < NUM_PARS; i++) { local_values.vector[i] = values[2+i]; //if (q_index==0) printf("p%d = %g\n",i, local_values.vector[i]); } //if (q_index==0) printf("NUM_VALUES:%d NUM_PARS:%d MAX_PD:%d\n", NUM_VALUES, NUM_PARS, MAX_PD); //if (q_index==0) printf("start:%d stop:%d\n", pd_start, pd_stop); double pd_norm = (pd_start == 0 ? 0.0 : result[nq]); double this_result = (pd_start == 0 ? 0.0 : result[q_index]); //if (q_index==0) printf("start %d %g %g\n", pd_start, pd_norm, this_result); #if MAX_PD>0 global const double *pd_value = values + NUM_VALUES; global const double *pd_weight = pd_value + details->num_weights; #endif // Jump into the middle of the polydispersity loop #if MAX_PD>4 int n4=details->pd_length[4]; int i4=(pd_start/details->pd_stride[4])%n4; const int p4=details->pd_par[4]; global const double *v4 = pd_value + details->pd_offset[4]; global const double *w4 = pd_weight + details->pd_offset[4]; #endif #if MAX_PD>3 int n3=details->pd_length[3]; int i3=(pd_start/details->pd_stride[3])%n3; const int p3=details->pd_par[3]; global const double *v3 = pd_value + details->pd_offset[3]; global const double *w3 = pd_weight + details->pd_offset[3]; //if (q_index==0) printf("offset %d: %d %d\n", 3, details->pd_offset[3], NUM_VALUES); #endif #if MAX_PD>2 int n2=details->pd_length[2]; int i2=(pd_start/details->pd_stride[2])%n2; const int p2=details->pd_par[2]; global const double *v2 = pd_value + details->pd_offset[2]; global const double *w2 = pd_weight + details->pd_offset[2]; #endif #if MAX_PD>1 int n1=details->pd_length[1]; int i1=(pd_start/details->pd_stride[1])%n1; const int p1=details->pd_par[1]; global const double *v1 = pd_value + details->pd_offset[1]; global const double *w1 = pd_weight + details->pd_offset[1]; #endif #if MAX_PD>0 int n0=details->pd_length[0]; int i0=(pd_start/details->pd_stride[0])%n0; const int p0=details->pd_par[0]; global const double *v0 = pd_value + details->pd_offset[0]; global const double *w0 = pd_weight + details->pd_offset[0]; #endif #if MAX_PD>0 const int theta_par = details->theta_par; const bool fast_theta = (theta_par == p0); const bool slow_theta = (theta_par >= 0 && !fast_theta); double spherical_correction = 1.0; #else // Note: if not polydisperse the weights cancel and we don't need the // spherical correction. const double spherical_correction = 1.0; #endif int step = pd_start; #if MAX_PD>4 const double weight5 = 1.0; while (i4 < n4) { local_values.vector[p4] = v4[i4]; double weight4 = w4[i4] * weight5; //if (q_index == 0) printf("step:%d level %d: p:%d i:%d n:%d value:%g weight:%g\n", step, 4, p4, i4, n4, local_values.vector[p4], weight4); #elif MAX_PD>3 const double weight4 = 1.0; #endif #if MAX_PD>3 while (i3 < n3) { local_values.vector[p3] = v3[i3]; double weight3 = w3[i3] * weight4; //if (q_index == 0) printf("step:%d level %d: p:%d i:%d n:%d value:%g weight:%g\n", step, 3, p3, i3, n3, local_values.vector[p3], weight3); #elif MAX_PD>2 const double weight3 = 1.0; #endif #if MAX_PD>2 while (i2 < n2) { local_values.vector[p2] = v2[i2]; double weight2 = w2[i2] * weight3; //if (q_index == 0) printf("step:%d level %d: p:%d i:%d n:%d value:%g weight:%g\n", step, 2, p2, i2, n2, local_values.vector[p2], weight2); #elif MAX_PD>1 const double weight2 = 1.0; #endif #if MAX_PD>1 while (i1 < n1) { local_values.vector[p1] = v1[i1]; double weight1 = w1[i1] * weight2; //if (q_index == 0) printf("step:%d level %d: p:%d i:%d n:%d value:%g weight:%g\n", step, 1, p1, i1, n1, local_values.vector[p1], weight1); #elif MAX_PD>0 const double weight1 = 1.0; #endif #if MAX_PD>0 if (slow_theta) { // Theta is not in inner loop spherical_correction = fmax(fabs(cos(M_PI_180*local_values.vector[theta_par])), 1.e-6); } while(i0 < n0) { local_values.vector[p0] = v0[i0]; double weight0 = w0[i0] * weight1; //if (q_index == 0) printf("step:%d level %d: p:%d i:%d n:%d value:%g weight:%g\n", step, 0, p0, i0, n0, local_values.vector[p0], weight0); if (fast_theta) { // Theta is in inner loop spherical_correction = fmax(fabs(cos(M_PI_180*local_values.vector[p0])), 1.e-6); } #else const double weight0 = 1.0; #endif //if (q_index == 0) {printf("step:%d of %d, pars:",step,pd_stop); for (int i=0; i < NUM_PARS; i++) printf("p%d=%g ",i, local_values.vector[i]); printf("\n"); } //if (q_index == 0) printf("sphcor: %g\n", spherical_correction); #ifdef INVALID if (!INVALID(local_values.table)) #endif { // Accumulate I(q) // Note: weight==0 must always be excluded if (weight0 > cutoff) { // spherical correction is set at a minimum of 1e-6, otherwise there // would be problems looking at models with theta=90. const double weight = weight0 * spherical_correction; pd_norm += weight * CALL_VOLUME(local_values.table); #if defined(MAGNETIC) && NUM_MAGNETIC > 0 const double qx = q[2*q_index]; const double qy = q[2*q_index+1]; const double qsq = qx*qx + qy*qy; // Constant across orientation, polydispersity for given qx, qy double scattering = 0.0; // TODO: what is the magnetic scattering at q=0 if (qsq > 1.e-16) { double p[4]; // dd, du, ud, uu p[0] = (qy*cos_mspin + qx*sin_mspin)/qsq; p[3] = -p[0]; p[1] = p[2] = (qy*sin_mspin - qx*cos_mspin)/qsq; for (int index=0; index<4; index++) { const double xs = spins[index]; if (xs > 1.e-8) { const int spin_flip = (index==1) || (index==2); const double pk = p[index]; for (int axis=0; axis<=spin_flip; axis++) { #define M1 NUM_PARS+5 #define M2 NUM_PARS+8 #define M3 NUM_PARS+13 #define SLD(_M_offset, _sld_offset) \ local_values.vector[_sld_offset] = xs * (axis \ ? (index==1 ? -values[_M_offset+2] : values[_M_offset+2]) \ : mag_sld(qx, qy, pk, values[_M_offset], values[_M_offset+1], \ (spin_flip ? 0.0 : values[_sld_offset+2]))) #if NUM_MAGNETIC==1 SLD(M1, MAGNETIC_PAR1); #elif NUM_MAGNETIC==2 SLD(M1, MAGNETIC_PAR1); SLD(M2, MAGNETIC_PAR2); #elif NUM_MAGNETIC==3 SLD(M1, MAGNETIC_PAR1); SLD(M2, MAGNETIC_PAR2); SLD(M3, MAGNETIC_PAR3); #else for (int sk=0; sk0 if (step >= pd_stop) break; ++i0; } i0 = 0; #endif #if MAX_PD>1 if (step >= pd_stop) break; ++i1; } i1 = 0; #endif #if MAX_PD>2 if (step >= pd_stop) break; ++i2; } i2 = 0; #endif #if MAX_PD>3 if (step >= pd_stop) break; ++i3; } i3 = 0; #endif #if MAX_PD>4 if (step >= pd_stop) break; ++i4; } i4 = 0; #endif //if (q_index==0) printf("res: %g/%g\n", this_result, pd_norm); // Remember the current result and the updated norm. result[q_index] = this_result; if (q_index == 0) result[nq] = pd_norm; } sasmodels/sasmodels/kernel_template.c000066400000000000000000000226321317715334700204010ustar00rootroot00000000000000#line 1 "kernel_template.c" // GENERATED CODE --- DO NOT EDIT --- // Code is produced by sasmodels.gen from sasmodels/models/MODEL.c #ifdef __OPENCL_VERSION__ # define USE_OPENCL #endif #define USE_KAHAN_SUMMATION 0 // If opencl is not available, then we are compiling a C function // Note: if using a C++ compiler, then define kernel as extern "C" #ifndef USE_OPENCL // Use SAS_DOUBLE to force the use of double even for float kernels # define SAS_DOUBLE dou ## ble # ifdef __cplusplus #include #include using namespace std; #if defined(_MSC_VER) #include #include #define kernel extern "C" __declspec( dllexport ) inline double trunc(double x) { return x>=0?floor(x):-floor(-x); } inline double fmin(double x, double y) { return x>y ? y : x; } inline double fmax(double x, double y) { return x::quiet_NaN()) // non-signalling NaN #define INFINITY (std::numeric_limits::infinity()) #define NEED_EXPM1 #define NEED_TGAMMA #define NEED_ERF #else #define kernel extern "C" #endif inline void SINCOS(double angle, double &svar, double &cvar) { svar=sin(angle); cvar=cos(angle); } # else #include #if defined(__TINYC__) #include // TODO: test isnan inline double _isnan(double x) { return x != x; } // hope this doesn't optimize away! #undef isnan #define isnan(x) _isnan(x) // Defeat the double->float conversion since we don't have tgmath inline SAS_DOUBLE trunc(SAS_DOUBLE x) { return x>=0?floor(x):-floor(-x); } inline SAS_DOUBLE fmin(SAS_DOUBLE x, SAS_DOUBLE y) { return x>y ? y : x; } inline SAS_DOUBLE fmax(SAS_DOUBLE x, SAS_DOUBLE y) { return x // C99 type-generic math, so sin(float) => sinf #endif // MSVC doesn't support C99, so no need for dllexport on C99 branch #define kernel #define SINCOS(angle,svar,cvar) do {const double _t_=angle; svar=sin(_t_);cvar=cos(_t_);} while (0) # endif # define global # define local # define constant const // OpenCL powr(a,b) = C99 pow(a,b), b >= 0 // OpenCL pown(a,b) = C99 pow(a,b), b integer # define powr(a,b) pow(a,b) # define pown(a,b) pow(a,b) #else # if defined(USE_SINCOS) # define SINCOS(angle,svar,cvar) svar=sincos(angle,&cvar) # else # define SINCOS(angle,svar,cvar) do {const double _t_=angle; svar=sin(_t_);cvar=cos(_t_);} while (0) # endif #endif #if defined(NEED_EXPM1) static SAS_DOUBLE expm1(SAS_DOUBLE x_in) { double x = (double)x_in; // go back to float for single precision kernels // Adapted from the cephes math library. // Copyright 1984 - 1992 by Stephen L. Moshier if (x != x || x == 0.0) { return x; // NaN and +/- 0 } else if (x < -0.5 || x > 0.5) { return exp(x) - 1.0; } else { const double xsq = x*x; const double p = ((( +1.2617719307481059087798E-4)*xsq +3.0299440770744196129956E-2)*xsq +9.9999999999999999991025E-1); const double q = (((( +3.0019850513866445504159E-6)*xsq +2.5244834034968410419224E-3)*xsq +2.2726554820815502876593E-1)*xsq +2.0000000000000000000897E0); double r = x * p; r = r / (q - r); return r+r; } } #endif // Standard mathematical constants: // M_E, M_LOG2E, M_LOG10E, M_LN2, M_LN10, M_PI, M_PI_2=pi/2, M_PI_4=pi/4, // M_1_PI=1/pi, M_2_PI=2/pi, M_2_SQRTPI=2/sqrt(pi), SQRT2, SQRT1_2=sqrt(1/2) // OpenCL defines M_constant_F for float constants, and nothing if double // is not enabled on the card, which is why these constants may be missing #ifndef M_PI # define M_PI 3.141592653589793 #endif #ifndef M_PI_2 # define M_PI_2 1.570796326794897 #endif #ifndef M_PI_4 # define M_PI_4 0.7853981633974483 #endif #ifndef M_E # define M_E 2.718281828459045091 #endif // Non-standard function library // pi/180, used for converting between degrees and radians // 4/3 pi for computing sphere volumes // square and cube for computing squares and cubes #ifndef M_PI_180 # define M_PI_180 0.017453292519943295 #endif #ifndef M_4PI_3 # define M_4PI_3 4.18879020478639 #endif //inline double square(double x) { return pow(x,2.0); } //inline double square(double x) { return pown(x,2); } inline double square(double x) { return x*x; } inline double cube(double x) { return x*x*x; } inline double sas_sinx_x(double x) { return x==0 ? 1.0 : sin(x)/x; } %(DEFINES)s %(SOURCES)s /* ########################################################## # # # !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! # # !! !! # # !! KEEP THIS CODE CONSISTENT WITH KERNELPY.PY !! # # !! !! # # !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! # # # ########################################################## */ #ifdef IQ_KERNEL_NAME kernel void IQ_KERNEL_NAME( global const double *q, global double *result, const int Nq, #ifdef IQ_OPEN_LOOPS #ifdef USE_OPENCL global double *loops_g, #endif local double *loops, const double cutoff, IQ_DISPERSION_LENGTH_DECLARATIONS, #endif IQ_FIXED_PARAMETER_DECLARATIONS ) { #ifdef USE_OPENCL #ifdef IQ_OPEN_LOOPS // copy loops info to local memory event_t e = async_work_group_copy(loops, loops_g, (IQ_DISPERSION_LENGTH_SUM)*2, 0); wait_group_events(1, &e); #endif int i = get_global_id(0); if (i < Nq) #else #pragma omp parallel for for (int i=0; i < Nq; i++) #endif { const double qi = q[i]; #ifdef IQ_OPEN_LOOPS double ret=0.0, norm=0.0; IQ_OPEN_LOOPS //for (int radius_i=0; radius_i < Nradius; radius_i++) { // const double radius = loops[2*(radius_i)]; // const double radius_w = loops[2*(radius_i)+1]; const double weight = IQ_WEIGHT_PRODUCT; if (weight > cutoff) { const double scattering = Iq(qi, IQ_PARAMETERS); // allow kernels to exclude invalid regions by returning NaN if (!isnan(scattering)) { ret += weight*scattering; #ifdef VOLUME_PARAMETERS norm += weight * form_volume(VOLUME_PARAMETERS); #else norm += weight; #endif } //else { printf("exclude qx,qy,I:%%g,%%g,%%g\n",qi,scattering); } } IQ_CLOSE_LOOPS // norm can only be zero if volume is zero, so no scattering result[i] = (norm > 0. ? scale*ret/norm + background : background); #else result[i] = scale*Iq(qi, IQ_PARAMETERS) + background; #endif } } #endif #ifdef IQXY_KERNEL_NAME kernel void IQXY_KERNEL_NAME( global const double *qx, global const double *qy, global double *result, const int Nq, #ifdef IQXY_OPEN_LOOPS #ifdef USE_OPENCL global double *loops_g, #endif local double *loops, const double cutoff, IQXY_DISPERSION_LENGTH_DECLARATIONS, #endif IQXY_FIXED_PARAMETER_DECLARATIONS ) { #ifdef USE_OPENCL #ifdef IQXY_OPEN_LOOPS // copy loops info to local memory event_t e = async_work_group_copy(loops, loops_g, (IQXY_DISPERSION_LENGTH_SUM)*2, 0); wait_group_events(1, &e); #endif int i = get_global_id(0); if (i < Nq) #else #pragma omp parallel for for (int i=0; i < Nq; i++) #endif { const double qxi = qx[i]; const double qyi = qy[i]; #if USE_KAHAN_SUMMATION double accumulated_error = 0.0; #endif #ifdef IQXY_OPEN_LOOPS double ret=0.0, norm=0.0; IQXY_OPEN_LOOPS //for (int radius_i=0; radius_i < Nradius; radius_i++) { // const double radius = loops[2*(radius_i)]; // const double radius_w = loops[2*(radius_i)+1]; double weight = IQXY_WEIGHT_PRODUCT; if (weight > cutoff) { const double scattering = Iqxy(qxi, qyi, IQXY_PARAMETERS); if (!isnan(scattering)) { // if scattering is bad, exclude it from sum #if defined(IQXY_HAS_THETA) // Force a nominal value for the spherical correction even when // theta is +0/180 so that there are no divide by zero problems. // For sin(theta) fixed at 0 and 180, we effectively multiply top and bottom // by 1e-6, so the effect cancels. const double spherical_correction = fmax(fabs(cos(M_PI_180*theta)), 1.e-6); weight *= spherical_correction; #endif const double next = weight * scattering; #if USE_KAHAN_SUMMATION const double y = next - accumulated_error; const double t = ret + y; accumulated_error = (t - ret) - y; ret = t; #else ret += next; #endif #ifdef VOLUME_PARAMETERS norm += weight*form_volume(VOLUME_PARAMETERS); #else norm += weight; #endif } //else { printf("exclude qx,qy,I:%%g,%%g,%%g\n",qi,scattering); } } IQXY_CLOSE_LOOPS // norm can only be zero if volume is zero, so no scattering result[i] = (norm>0. ? scale*ret/norm + background : background); #else result[i] = scale*Iqxy(qxi, qyi, IQXY_PARAMETERS) + background; #endif } } #endif sasmodels/sasmodels/kernelcl.py000066400000000000000000000565101317715334700172350ustar00rootroot00000000000000""" GPU driver for C kernels There should be a single GPU environment running on the system. This environment is constructed on the first call to :func:`env`, and the same environment is returned on each call. After retrieving the environment, the next step is to create the kernel. This is done with a call to :meth:`GpuEnvironment.make_kernel`, which returns the type of data used by the kernel. Next a :class:`GpuData` object should be created with the correct kind of data. This data object can be used by multiple kernels, for example, if the target model is a weighted sum of multiple kernels. The data should include any extra evaluation points required to compute the proper data smearing. This need not match the square grid for 2D data if there is an index saying which q points are active. Together the GpuData, the program, and a device form a :class:`GpuKernel`. This kernel is used during fitting, receiving new sets of parameters and evaluating them. The output value is stored in an output buffer on the devices, where it can be combined with other structure factors and form factors and have instrumental resolution effects applied. In order to use OpenCL for your models, you will need OpenCL drivers for your machine. These should be available from your graphics card vendor. Intel provides OpenCL drivers for CPUs as well as their integrated HD graphics chipsets. AMD also provides drivers for Intel CPUs, but as of this writing the performance is lacking compared to the Intel drivers. NVidia combines drivers for CUDA and OpenCL in one package. The result is a bit messy if you have multiple drivers installed. You can see which drivers are available by starting python and running: import pyopencl as cl cl.create_some_context(interactive=True) Once you have done that, it will show the available drivers which you can select. It will then tell you that you can use these drivers automatically by setting the SAS_OPENCL environment variable, which is PYOPENCL_CTX equivalent but not conflicting with other pyopnecl programs. Some graphics cards have multiple devices on the same card. You cannot yet use both of them concurrently to evaluate models, but you can run the program twice using a different device for each session. OpenCL kernels are compiled when needed by the device driver. Some drivers produce compiler output even when there is no error. You can see the output by setting PYOPENCL_COMPILER_OUTPUT=1. It should be harmless, albeit annoying. """ from __future__ import print_function import os import warnings import logging import time import numpy as np # type: ignore try: #raise NotImplementedError("OpenCL not yet implemented for new kernel template") import pyopencl as cl # type: ignore # Ask OpenCL for the default context so that we know that one exists cl.create_some_context(interactive=False) except Exception as exc: warnings.warn("OpenCL startup failed with ***" + str(exc) + "***; using C compiler instead") raise RuntimeError("OpenCL not available") from pyopencl import mem_flags as mf from pyopencl.characterize import get_fast_inaccurate_build_options from . import generate from .kernel import KernelModel, Kernel try: from typing import Tuple, Callable, Any from .modelinfo import ModelInfo from .details import CallDetails except ImportError: pass # CRUFT: pyopencl < 2017.1 (as of June 2016 needs quotes around include path) def quote_path(v): """ Quote the path if it is not already quoted. If v starts with '-', then assume that it is a -I option or similar and do not quote it. This is fragile: -Ipath with space needs to be quoted. """ return '"'+v+'"' if v and ' ' in v and not v[0] in "\"'-" else v def fix_pyopencl_include(): """ Monkey patch pyopencl to allow spaces in include file path. """ import pyopencl as cl if hasattr(cl, '_DEFAULT_INCLUDE_OPTIONS'): cl._DEFAULT_INCLUDE_OPTIONS = [quote_path(v) for v in cl._DEFAULT_INCLUDE_OPTIONS] fix_pyopencl_include() # The max loops number is limited by the amount of local memory available # on the device. You don't want to make this value too big because it will # waste resources, nor too small because it may interfere with users trying # to do their polydispersity calculations. A value of 1024 should be much # larger than necessary given that cost grows as npts^k where k is the number # of polydisperse parameters. MAX_LOOPS = 2048 # Pragmas for enable OpenCL features. Be sure to protect them so that they # still compile even if OpenCL is not present. _F16_PRAGMA = """\ #if defined(__OPENCL_VERSION__) // && !defined(cl_khr_fp16) # pragma OPENCL EXTENSION cl_khr_fp16: enable #endif """ _F64_PRAGMA = """\ #if defined(__OPENCL_VERSION__) // && !defined(cl_khr_fp64) # pragma OPENCL EXTENSION cl_khr_fp64: enable #endif """ ENV = None def environment(): # type: () -> "GpuEnvironment" """ Returns a singleton :class:`GpuEnvironment`. This provides an OpenCL context and one queue per device. """ global ENV if ENV is None: ENV = GpuEnvironment() return ENV def has_type(device, dtype): # type: (cl.Device, np.dtype) -> bool """ Return true if device supports the requested precision. """ if dtype == generate.F32: return True elif dtype == generate.F64: return "cl_khr_fp64" in device.extensions elif dtype == generate.F16: return "cl_khr_fp16" in device.extensions else: return False def get_warp(kernel, queue): # type: (cl.Kernel, cl.CommandQueue) -> int """ Return the size of an execution batch for *kernel* running on *queue*. """ return kernel.get_work_group_info( cl.kernel_work_group_info.PREFERRED_WORK_GROUP_SIZE_MULTIPLE, queue.device) def _stretch_input(vector, dtype, extra=1e-3, boundary=32): # type: (np.ndarray, np.dtype, float, int) -> np.ndarray """ Stretch an input vector to the correct boundary. Performance on the kernels can drop by a factor of two or more if the number of values to compute does not fall on a nice power of two boundary. The trailing additional vector elements are given a value of *extra*, and so f(*extra*) will be computed for each of them. The returned array will thus be a subset of the computed array. *boundary* should be a power of 2 which is at least 32 for good performance on current platforms (as of Jan 2015). It should probably be the max of get_warp(kernel,queue) and device.min_data_type_align_size//4. """ remainder = vector.size % boundary if remainder != 0: size = vector.size + (boundary - remainder) vector = np.hstack((vector, [extra] * (size - vector.size))) return np.ascontiguousarray(vector, dtype=dtype) def compile_model(context, source, dtype, fast=False): # type: (cl.Context, str, np.dtype, bool) -> cl.Program """ Build a model to run on the gpu. Returns the compiled program and its type. The returned type will be float32 even if the desired type is float64 if any of the devices in the context do not support the cl_khr_fp64 extension. """ dtype = np.dtype(dtype) if not all(has_type(d, dtype) for d in context.devices): raise RuntimeError("%s not supported for devices"%dtype) source_list = [generate.convert_type(source, dtype)] if dtype == generate.F16: source_list.insert(0, _F16_PRAGMA) elif dtype == generate.F64: source_list.insert(0, _F64_PRAGMA) # Note: USE_SINCOS makes the intel cpu slower under opencl if context.devices[0].type == cl.device_type.GPU: source_list.insert(0, "#define USE_SINCOS\n") options = (get_fast_inaccurate_build_options(context.devices[0]) if fast else []) source = "\n".join(source_list) program = cl.Program(context, source).build(options=options) #print("done with "+program) return program # for now, this returns one device in the context # TODO: create a context that contains all devices on all platforms class GpuEnvironment(object): """ GPU context, with possibly many devices, and one queue per device. """ def __init__(self): # type: () -> None # find gpu context #self.context = cl.create_some_context() self.context = None if 'SAS_OPENCL' in os.environ: #Setting PYOPENCL_CTX as a SAS_OPENCL to create cl context os.environ["PYOPENCL_CTX"] = os.environ["SAS_OPENCL"] if 'PYOPENCL_CTX' in os.environ: self._create_some_context() if not self.context: self.context = _get_default_context() # Byte boundary for data alignment #self.data_boundary = max(d.min_data_type_align_size # for d in self.context.devices) self.queues = [cl.CommandQueue(context, context.devices[0]) for context in self.context] self.compiled = {} def has_type(self, dtype): # type: (np.dtype) -> bool """ Return True if all devices support a given type. """ return any(has_type(d, dtype) for context in self.context for d in context.devices) def get_queue(self, dtype): # type: (np.dtype) -> cl.CommandQueue """ Return a command queue for the kernels of type dtype. """ for context, queue in zip(self.context, self.queues): if all(has_type(d, dtype) for d in context.devices): return queue def get_context(self, dtype): # type: (np.dtype) -> cl.Context """ Return a OpenCL context for the kernels of type dtype. """ for context in self.context: if all(has_type(d, dtype) for d in context.devices): return context def _create_some_context(self): # type: () -> cl.Context """ Protected call to cl.create_some_context without interactivity. Use this if SAS_OPENCL is set in the environment. Sets the *context* attribute. """ try: self.context = [cl.create_some_context(interactive=False)] except Exception as exc: warnings.warn(str(exc)) warnings.warn("pyopencl.create_some_context() failed") warnings.warn("the environment variable 'SAS_OPENCL' might not be set correctly") def compile_program(self, name, source, dtype, fast, timestamp): # type: (str, str, np.dtype, bool, float) -> cl.Program """ Compile the program for the device in the given context. """ # Note: PyOpenCL caches based on md5 hash of source, options and device # so we don't really need to cache things for ourselves. I'll do so # anyway just to save some data munging time. tag = generate.tag_source(source) key = "%s-%s-%s%s"%(name, dtype, tag, ("-fast" if fast else "")) # Check timestamp on program program, program_timestamp = self.compiled.get(key, (None, np.inf)) if program_timestamp < timestamp: del self.compiled[key] if key not in self.compiled: context = self.get_context(dtype) logging.info("building %s for OpenCL %s", key, context.devices[0].name.strip()) program = compile_model(self.get_context(dtype), str(source), dtype, fast) self.compiled[key] = (program, timestamp) return program def _get_default_context(): # type: () -> List[cl.Context] """ Get an OpenCL context, preferring GPU over CPU, and preferring Intel drivers over AMD drivers. """ # Note: on mobile devices there is automatic clock scaling if either the # CPU or the GPU is underutilized; probably doesn't affect us, but we if # it did, it would mean that putting a busy loop on the CPU while the GPU # is running may increase throughput. # # Macbook pro, base install: # {'Apple': [Intel CPU, NVIDIA GPU]} # Macbook pro, base install: # {'Apple': [Intel CPU, Intel GPU]} # 2 x nvidia 295 with Intel and NVIDIA opencl drivers installed # {'Intel': [CPU], 'NVIDIA': [GPU, GPU, GPU, GPU]} gpu, cpu = None, None for platform in cl.get_platforms(): # AMD provides a much weaker CPU driver than Intel/Apple, so avoid it. # If someone has bothered to install the AMD/NVIDIA drivers, prefer # them over the integrated graphics driver that may have been supplied # with the CPU chipset. preferred_cpu = (platform.vendor.startswith('Intel') or platform.vendor.startswith('Apple')) preferred_gpu = (platform.vendor.startswith('Advanced') or platform.vendor.startswith('NVIDIA')) for device in platform.get_devices(): if device.type == cl.device_type.GPU: # If the existing type is not GPU then it will be CUSTOM # or ACCELERATOR so don't override it. if gpu is None or (preferred_gpu and gpu.type == cl.device_type.GPU): gpu = device elif device.type == cl.device_type.CPU: if cpu is None or preferred_cpu: cpu = device else: # System has cl.device_type.ACCELERATOR or cl.device_type.CUSTOM # Intel Phi for example registers as an accelerator # Since the user installed a custom device on their system # and went through the pain of sorting out OpenCL drivers for # it, lets assume they really do want to use it as their # primary compute device. gpu = device # order the devices by gpu then by cpu; when searching for an available # device by data type they will be checked in this order, which means # that if the gpu supports double then the cpu will never be used (though # we may make it possible to explicitly request the cpu at some point). devices = [] if gpu is not None: devices.append(gpu) if cpu is not None: devices.append(cpu) return [cl.Context([d]) for d in devices] class GpuModel(KernelModel): """ GPU wrapper for a single model. *source* and *model_info* are the model source and interface as returned from :func:`generate.make_source` and :func:`generate.make_model_info`. *dtype* is the desired model precision. Any numpy dtype for single or double precision floats will do, such as 'f', 'float32' or 'single' for single and 'd', 'float64' or 'double' for double. Double precision is an optional extension which may not be available on all devices. Half precision ('float16','half') may be available on some devices. Fast precision ('fast') is a loose version of single precision, indicating that the compiler is allowed to take shortcuts. """ def __init__(self, source, model_info, dtype=generate.F32, fast=False): # type: (Dict[str,str], ModelInfo, np.dtype, bool) -> None self.info = model_info self.source = source self.dtype = dtype self.fast = fast self.program = None # delay program creation self._kernels = None def __getstate__(self): # type: () -> Tuple[ModelInfo, str, np.dtype, bool] return self.info, self.source, self.dtype, self.fast def __setstate__(self, state): # type: (Tuple[ModelInfo, str, np.dtype, bool]) -> None self.info, self.source, self.dtype, self.fast = state self.program = None def make_kernel(self, q_vectors): # type: (List[np.ndarray]) -> "GpuKernel" if self.program is None: compile_program = environment().compile_program timestamp = generate.ocl_timestamp(self.info) self.program = compile_program( self.info.name, self.source['opencl'], self.dtype, self.fast, timestamp) variants = ['Iq', 'Iqxy', 'Imagnetic'] names = [generate.kernel_name(self.info, k) for k in variants] kernels = [getattr(self.program, k) for k in names] self._kernels = dict((k, v) for k, v in zip(variants, kernels)) is_2d = len(q_vectors) == 2 if is_2d: kernel = [self._kernels['Iqxy'], self._kernels['Imagnetic']] else: kernel = [self._kernels['Iq']]*2 return GpuKernel(kernel, self.dtype, self.info, q_vectors) def release(self): # type: () -> None """ Free the resources associated with the model. """ if self.program is not None: self.program = None def __del__(self): # type: () -> None self.release() # TODO: check that we don't need a destructor for buffers which go out of scope class GpuInput(object): """ Make q data available to the gpu. *q_vectors* is a list of q vectors, which will be *[q]* for 1-D data, and *[qx, qy]* for 2-D data. Internally, the vectors will be reallocated to get the best performance on OpenCL, which may involve shifting and stretching the array to better match the memory architecture. Additional points will be evaluated with *q=1e-3*. *dtype* is the data type for the q vectors. The data type should be set to match that of the kernel, which is an attribute of :class:`GpuProgram`. Note that not all kernels support double precision, so even if the program was created for double precision, the *GpuProgram.dtype* may be single precision. Call :meth:`release` when complete. Even if not called directly, the buffer will be released when the data object is freed. """ def __init__(self, q_vectors, dtype=generate.F32): # type: (List[np.ndarray], np.dtype) -> None # TODO: do we ever need double precision q? env = environment() self.nq = q_vectors[0].size self.dtype = np.dtype(dtype) self.is_2d = (len(q_vectors) == 2) # TODO: stretch input based on get_warp() # not doing it now since warp depends on kernel, which is not known # at this point, so instead using 32, which is good on the set of # architectures tested so far. if self.is_2d: # Note: 16 rather than 15 because result is 1 longer than input. width = ((self.nq+16)//16)*16 self.q = np.empty((width, 2), dtype=dtype) self.q[:self.nq, 0] = q_vectors[0] self.q[:self.nq, 1] = q_vectors[1] else: # Note: 32 rather than 31 because result is 1 longer than input. width = ((self.nq+32)//32)*32 self.q = np.empty(width, dtype=dtype) self.q[:self.nq] = q_vectors[0] self.global_size = [self.q.shape[0]] context = env.get_context(self.dtype) #print("creating inputs of size", self.global_size) self.q_b = cl.Buffer(context, mf.READ_ONLY | mf.COPY_HOST_PTR, hostbuf=self.q) def release(self): # type: () -> None """ Free the memory. """ if self.q_b is not None: self.q_b.release() self.q_b = None def __del__(self): # type: () -> None self.release() class GpuKernel(Kernel): """ Callable SAS kernel. *kernel* is the GpuKernel object to call *model_info* is the module information *q_vectors* is the q vectors at which the kernel should be evaluated *dtype* is the kernel precision The resulting call method takes the *pars*, a list of values for the fixed parameters to the kernel, and *pd_pars*, a list of (value,weight) vectors for the polydisperse parameters. *cutoff* determines the integration limits: any points with combined weight less than *cutoff* will not be calculated. Call :meth:`release` when done with the kernel instance. """ def __init__(self, kernel, dtype, model_info, q_vectors): # type: (cl.Kernel, np.dtype, ModelInfo, List[np.ndarray]) -> None q_input = GpuInput(q_vectors, dtype) self.kernel = kernel self.info = model_info self.dtype = dtype self.dim = '2d' if q_input.is_2d else '1d' # plus three for the normalization values self.result = np.empty(q_input.nq+1, dtype) # Inputs and outputs for each kernel call # Note: res may be shorter than res_b if global_size != nq env = environment() self.queue = env.get_queue(dtype) self.result_b = cl.Buffer(self.queue.context, mf.READ_WRITE, q_input.global_size[0] * dtype.itemsize) self.q_input = q_input # allocated by GpuInput above self._need_release = [self.result_b, self.q_input] self.real = (np.float32 if dtype == generate.F32 else np.float64 if dtype == generate.F64 else np.float16 if dtype == generate.F16 else np.float32) # will never get here, so use np.float32 def __call__(self, call_details, values, cutoff, magnetic): # type: (CallDetails, np.ndarray, np.ndarray, float, bool) -> np.ndarray context = self.queue.context # Arrange data transfer to card details_b = cl.Buffer(context, mf.READ_ONLY | mf.COPY_HOST_PTR, hostbuf=call_details.buffer) values_b = cl.Buffer(context, mf.READ_ONLY | mf.COPY_HOST_PTR, hostbuf=values) kernel = self.kernel[1 if magnetic else 0] args = [ np.uint32(self.q_input.nq), None, None, details_b, values_b, self.q_input.q_b, self.result_b, self.real(cutoff), ] #print("Calling OpenCL") #call_details.show(values) # Call kernel and retrieve results wait_for = None last_nap = time.clock() step = 1000000//self.q_input.nq + 1 for start in range(0, call_details.num_eval, step): stop = min(start + step, call_details.num_eval) #print("queuing",start,stop) args[1:3] = [np.int32(start), np.int32(stop)] wait_for = [kernel(self.queue, self.q_input.global_size, None, *args, wait_for=wait_for)] if stop < call_details.num_eval: # Allow other processes to run wait_for[0].wait() current_time = time.clock() if current_time - last_nap > 0.5: time.sleep(0.05) last_nap = current_time cl.enqueue_copy(self.queue, self.result, self.result_b) #print("result", self.result) # Free buffers for v in (details_b, values_b): if v is not None: v.release() pd_norm = self.result[self.q_input.nq] scale = values[0]/(pd_norm if pd_norm != 0.0 else 1.0) background = values[1] #print("scale",scale,values[0],self.result[self.q_input.nq],background) return scale*self.result[:self.q_input.nq] + background # return self.result[:self.q_input.nq] def release(self): # type: () -> None """ Release resources associated with the kernel. """ for v in self._need_release: v.release() self._need_release = [] def __del__(self): # type: () -> None self.release() sasmodels/sasmodels/kerneldll.py000066400000000000000000000363341317715334700174140ustar00rootroot00000000000000r""" DLL driver for C kernels If the environment variable *SAS_OPENMP* is set, then sasmodels will attempt to compile with OpenMP flags so that the model can use all available kernels. This may or may not be available on your compiler toolchain. Depending on operating system and environment. Windows does not have provide a compiler with the operating system. Instead, we assume that TinyCC is installed and available. This can be done with a simple pip command if it is not already available:: pip install tinycc If Microsoft Visual C++ is available (because VCINSTALLDIR is defined in the environment), then that will be used instead. Microsoft Visual C++ for Python is available from Microsoft: ``_ If neither compiler is available, sasmodels will check for *MinGW*, the GNU compiler toolchain. This available in packages such as Anaconda and PythonXY, or available stand alone. This toolchain has had difficulties on some systems, and may or may not work for you. You can control which compiler to use by setting SAS_COMPILER in the environment: - tinycc (Windows): use the TinyCC compiler shipped with SasView - msvc (Windows): use the Microsoft Visual C++ compiler - mingw (Windows): use the MinGW GNU cc compiler - unix (Linux): use the system cc compiler. - unix (Mac): use the clang compiler. You will need XCode installed, and the XCode command line tools. Mac comes with OpenCL drivers, so generally this will not be needed. Both *msvc* and *mingw* require that the compiler is available on your path. For *msvc*, this can done by running vcvarsall.bat in a windows terminal. Install locations are system dependent, such as: C:\Program Files (x86)\Common Files\Microsoft\Visual C++ for Python\9.0\vcvarsall.bat or maybe C:\Users\yourname\AppData\Local\Programs\Common\Microsoft\Visual C++ for Python\9.0\vcvarsall.bat OpenMP for *msvc* requires the Microsoft vcomp90.dll library, which doesn't seem to be included with the compiler, nor does there appear to be a public download location. There may be one on your machine already in a location such as: C:\Windows\winsxs\x86_microsoft.vc90.openmp*\vcomp90.dll If you copy this to somewhere on your path, such as the python directory or the install directory for this application, then OpenMP should be supported. For full control of the compiler, define a function *compile_command(source,output)* which takes the name of the source file and the name of the output file and returns a compile command that can be evaluated in the shell. For even more control, replace the entire *compile(source,output)* function. The global attribute *ALLOW_SINGLE_PRECISION_DLLS* should be set to *False* if you wish to prevent single precision floating point evaluation for the compiled models, otherwise set it defaults to *True*. """ from __future__ import print_function import sys import os from os.path import join as joinpath, splitext import subprocess import tempfile import ctypes as ct # type: ignore import _ctypes as _ct import logging import numpy as np # type: ignore try: import tinycc except ImportError: tinycc = None from . import generate from .kernel import KernelModel, Kernel from .kernelpy import PyInput from .exception import annotate_exception from .generate import F16, F32, F64 try: from typing import Tuple, Callable, Any from .modelinfo import ModelInfo from .details import CallDetails except ImportError: pass if "SAS_COMPILER" in os.environ: COMPILER = os.environ["SAS_COMPILER"] elif os.name == 'nt': if tinycc is not None: COMPILER = "tinycc" elif "VCINSTALLDIR" in os.environ: # If vcvarsall.bat has been called, then VCINSTALLDIR is in the environment # and we can use the MSVC compiler. Otherwise, if tinycc is available # the use it. Otherwise, hope that mingw is available. COMPILER = "msvc" else: COMPILER = "mingw" else: COMPILER = "unix" ARCH = "" if ct.sizeof(ct.c_void_p) > 4 else "x86" # 4 byte pointers on x86 if COMPILER == "unix": # Generic unix compile # On mac users will need the X code command line tools installed #COMPILE = "gcc-mp-4.7 -shared -fPIC -std=c99 -fopenmp -O2 -Wall %s -o %s -lm -lgomp" CC = "cc -shared -fPIC -std=c99 -O2 -Wall".split() # add openmp support if not running on a mac if sys.platform != "darwin": CC.append("-fopenmp") def compile_command(source, output): """unix compiler command""" return CC + [source, "-o", output, "-lm"] elif COMPILER == "msvc": # Call vcvarsall.bat before compiling to set path, headers, libs, etc. # MSVC compiler is available, so use it. OpenMP requires a copy of # vcomp90.dll on the path. One may be found here: # C:/Windows/winsxs/x86_microsoft.vc90.openmp*/vcomp90.dll # Copy this to the python directory and uncomment the OpenMP COMPILE # TODO: remove intermediate OBJ file created in the directory # TODO: maybe don't use randomized name for the c file # TODO: maybe ask distutils to find MSVC CC = "cl /nologo /Ox /MD /W3 /GS- /DNDEBUG".split() if "SAS_OPENMP" in os.environ: CC.append("/openmp") LN = "/link /DLL /INCREMENTAL:NO /MANIFEST".split() def compile_command(source, output): """MSVC compiler command""" return CC + ["/Tp%s"%source] + LN + ["/OUT:%s"%output] elif COMPILER == "tinycc": # TinyCC compiler. CC = [tinycc.TCC] + "-shared -rdynamic -Wall".split() def compile_command(source, output): """tinycc compiler command""" return CC + [source, "-o", output] elif COMPILER == "mingw": # MinGW compiler. CC = "gcc -shared -std=c99 -O2 -Wall".split() if "SAS_OPENMP" in os.environ: CC.append("-fopenmp") def compile_command(source, output): """mingw compiler command""" return CC + [source, "-o", output, "-lm"] # Windows-specific solution if os.name == 'nt': # Assume the default location of module DLLs is in .sasmodels/compiled_models. DLL_PATH = os.path.join(os.path.expanduser("~"), ".sasmodels", "compiled_models") if not os.path.exists(DLL_PATH): os.makedirs(DLL_PATH) else: # Set up the default path for compiled modules. DLL_PATH = tempfile.gettempdir() ALLOW_SINGLE_PRECISION_DLLS = True def compile(source, output): # type: (str, str) -> None """ Compile *source* producing *output*. Raises RuntimeError if the compile failed or the output wasn't produced. """ command = compile_command(source=source, output=output) command_str = " ".join('"%s"'%p if ' ' in p else p for p in command) logging.info(command_str) try: # need shell=True on windows to keep console box from popping up shell = (os.name == 'nt') subprocess.check_output(command, shell=shell, stderr=subprocess.STDOUT) except subprocess.CalledProcessError as exc: raise RuntimeError("compile failed.\n%s\n%s"%(command_str, exc.output)) if not os.path.exists(output): raise RuntimeError("compile failed. File is in %r"%source) def dll_name(model_info, dtype): # type: (ModelInfo, np.dtype) -> str """ Name of the dll containing the model. This is the base file name without any path or extension, with a form such as 'sas_sphere32'. """ bits = 8*dtype.itemsize basename = "sas%d_%s"%(bits, model_info.id) basename += ARCH + ".so" # Hack to find precompiled dlls path = joinpath(generate.DATA_PATH, '..', 'compiled_models', basename) if os.path.exists(path): return path return joinpath(DLL_PATH, basename) def dll_path(model_info, dtype): # type: (ModelInfo, np.dtype) -> str """ Complete path to the dll for the model. Note that the dll may not exist yet if it hasn't been compiled. """ return os.path.join(DLL_PATH, dll_name(model_info, dtype)) def make_dll(source, model_info, dtype=F64): # type: (str, ModelInfo, np.dtype) -> str """ Returns the path to the compiled model defined by *kernel_module*. If the model has not been compiled, or if the source file(s) are newer than the dll, then *make_dll* will compile the model before returning. This routine does not load the resulting dll. *dtype* is a numpy floating point precision specifier indicating whether the model should be single, double or long double precision. The default is double precision, *np.dtype('d')*. Set *sasmodels.ALLOW_SINGLE_PRECISION_DLLS* to False if single precision models are not allowed as DLLs. Set *sasmodels.kerneldll.DLL_PATH* to the compiled dll output path. The default is the system temporary directory. """ if dtype == F16: raise ValueError("16 bit floats not supported") if dtype == F32 and not ALLOW_SINGLE_PRECISION_DLLS: dtype = F64 # Force 64-bit dll # Note: dtype may be F128 for long double precision dll = dll_path(model_info, dtype) if not os.path.exists(dll): need_recompile = True else: dll_time = os.path.getmtime(dll) newest_source = generate.dll_timestamp(model_info) need_recompile = dll_time < newest_source if need_recompile: basename = splitext(os.path.basename(dll))[0] + "_" system_fd, filename = tempfile.mkstemp(suffix=".c", prefix=basename) source = generate.convert_type(source, dtype) with os.fdopen(system_fd, "w") as file_handle: file_handle.write(source) compile(source=filename, output=dll) # comment the following to keep the generated c file # Note: if there is a syntax error then compile raises an error # and the source file will not be deleted. os.unlink(filename) #print("saving compiled file in %r"%filename) return dll def load_dll(source, model_info, dtype=F64): # type: (str, ModelInfo, np.dtype) -> "DllModel" """ Create and load a dll corresponding to the source, info pair returned from :func:`sasmodels.generate.make` compiled for the target precision. See :func:`make_dll` for details on controlling the dll path and the allowed floating point precision. """ filename = make_dll(source, model_info, dtype=dtype) return DllModel(filename, model_info, dtype=dtype) class DllModel(KernelModel): """ ctypes wrapper for a single model. *source* and *model_info* are the model source and interface as returned from :func:`gen.make`. *dtype* is the desired model precision. Any numpy dtype for single or double precision floats will do, such as 'f', 'float32' or 'single' for single and 'd', 'float64' or 'double' for double. Double precision is an optional extension which may not be available on all devices. Call :meth:`release` when done with the kernel. """ def __init__(self, dllpath, model_info, dtype=generate.F32): # type: (str, ModelInfo, np.dtype) -> None self.info = model_info self.dllpath = dllpath self._dll = None # type: ct.CDLL self._kernels = None # type: List[Callable, Callable] self.dtype = np.dtype(dtype) def _load_dll(self): # type: () -> None try: self._dll = ct.CDLL(self.dllpath) except: annotate_exception("while loading "+self.dllpath) raise float_type = (ct.c_float if self.dtype == generate.F32 else ct.c_double if self.dtype == generate.F64 else ct.c_longdouble) # int, int, int, int*, double*, double*, double*, double*, double argtypes = [ct.c_int32]*3 + [ct.c_void_p]*4 + [float_type] names = [generate.kernel_name(self.info, variant) for variant in ("Iq", "Iqxy", "Imagnetic")] self._kernels = [self._dll[name] for name in names] for k in self._kernels: k.argtypes = argtypes def __getstate__(self): # type: () -> Tuple[ModelInfo, str] return self.info, self.dllpath def __setstate__(self, state): # type: (Tuple[ModelInfo, str]) -> None self.info, self.dllpath = state self._dll = None def make_kernel(self, q_vectors): # type: (List[np.ndarray]) -> DllKernel q_input = PyInput(q_vectors, self.dtype) # Note: pickle not supported for DllKernel if self._dll is None: self._load_dll() is_2d = len(q_vectors) == 2 kernel = self._kernels[1:3] if is_2d else [self._kernels[0]]*2 return DllKernel(kernel, self.info, q_input) def release(self): # type: () -> None """ Release any resources associated with the model. """ dll_handle = self._dll._handle if os.name == 'nt': ct.windll.kernel32.FreeLibrary(dll_handle) else: _ct.dlclose(dll_handle) del self._dll self._dll = None class DllKernel(Kernel): """ Callable SAS kernel. *kernel* is the c function to call. *model_info* is the module information *q_input* is the DllInput q vectors at which the kernel should be evaluated. The resulting call method takes the *pars*, a list of values for the fixed parameters to the kernel, and *pd_pars*, a list of (value, weight) vectors for the polydisperse parameters. *cutoff* determines the integration limits: any points with combined weight less than *cutoff* will not be calculated. Call :meth:`release` when done with the kernel instance. """ def __init__(self, kernel, model_info, q_input): # type: (Callable[[], np.ndarray], ModelInfo, PyInput) -> None self.kernel = kernel self.info = model_info self.q_input = q_input self.dtype = q_input.dtype self.dim = '2d' if q_input.is_2d else '1d' self.result = np.empty(q_input.nq+1, q_input.dtype) self.real = (np.float32 if self.q_input.dtype == generate.F32 else np.float64 if self.q_input.dtype == generate.F64 else np.float128) def __call__(self, call_details, values, cutoff, magnetic): # type: (CallDetails, np.ndarray, np.ndarray, float, bool) -> np.ndarray kernel = self.kernel[1 if magnetic else 0] args = [ self.q_input.nq, # nq None, # pd_start None, # pd_stop pd_stride[MAX_PD] call_details.buffer.ctypes.data, # problem values.ctypes.data, #pars self.q_input.q.ctypes.data, #q self.result.ctypes.data, # results self.real(cutoff), # cutoff ] #print("Calling DLL") #call_details.show(values) step = 100 for start in range(0, call_details.num_eval, step): stop = min(start + step, call_details.num_eval) args[1:3] = [start, stop] kernel(*args) # type: ignore #print("returned",self.q_input.q, self.result) pd_norm = self.result[self.q_input.nq] scale = values[0]/(pd_norm if pd_norm != 0.0 else 1.0) background = values[1] #print("scale",scale,background) return scale*self.result[:self.q_input.nq] + background def release(self): # type: () -> None """ Release any resources associated with the kernel. """ self.q_input.release() sasmodels/sasmodels/kernelpy.py000066400000000000000000000267331317715334700172730ustar00rootroot00000000000000""" Python driver for python kernels Calls the kernel with a vector of $q$ values for a single parameter set. Polydispersity is supported by looping over different parameter sets and summing the results. The interface to :class:`PyModel` matches those for :class:`kernelcl.GpuModel` and :class:`kerneldll.DllModel`. """ from __future__ import division, print_function import logging import numpy as np # type: ignore from numpy import pi, sin, cos #type: ignore from . import details from .generate import F64 from .kernel import KernelModel, Kernel try: from typing import Union, Callable except ImportError: pass else: DType = Union[None, str, np.dtype] class PyModel(KernelModel): """ Wrapper for pure python models. """ def __init__(self, model_info): # Make sure Iq and Iqxy are available and vectorized _create_default_functions(model_info) self.info = model_info self.dtype = np.dtype('d') logging.info("load python model " + self.info.name) def make_kernel(self, q_vectors): q_input = PyInput(q_vectors, dtype=F64) kernel = self.info.Iqxy if q_input.is_2d else self.info.Iq return PyKernel(kernel, self.info, q_input) def release(self): """ Free resources associated with the model. """ pass class PyInput(object): """ Make q data available to the gpu. *q_vectors* is a list of q vectors, which will be *[q]* for 1-D data, and *[qx, qy]* for 2-D data. Internally, the vectors will be reallocated to get the best performance on OpenCL, which may involve shifting and stretching the array to better match the memory architecture. Additional points will be evaluated with *q=1e-3*. *dtype* is the data type for the q vectors. The data type should be set to match that of the kernel, which is an attribute of :class:`GpuProgram`. Note that not all kernels support double precision, so even if the program was created for double precision, the *GpuProgram.dtype* may be single precision. Call :meth:`release` when complete. Even if not called directly, the buffer will be released when the data object is freed. """ def __init__(self, q_vectors, dtype): self.nq = q_vectors[0].size self.dtype = dtype self.is_2d = (len(q_vectors) == 2) if self.is_2d: self.q = np.empty((self.nq, 2), dtype=dtype) self.q[:, 0] = q_vectors[0] self.q[:, 1] = q_vectors[1] else: self.q = np.empty(self.nq, dtype=dtype) self.q[:self.nq] = q_vectors[0] def release(self): """ Free resources associated with the model inputs. """ self.q = None class PyKernel(Kernel): """ Callable SAS kernel. *kernel* is the DllKernel object to call. *model_info* is the module information *q_input* is the DllInput q vectors at which the kernel should be evaluated. The resulting call method takes the *pars*, a list of values for the fixed parameters to the kernel, and *pd_pars*, a list of (value,weight) vectors for the polydisperse parameters. *cutoff* determines the integration limits: any points with combined weight less than *cutoff* will not be calculated. Call :meth:`release` when done with the kernel instance. """ def __init__(self, kernel, model_info, q_input): # type: (callable, ModelInfo, List[np.ndarray]) -> None self.dtype = np.dtype('d') self.info = model_info self.q_input = q_input self.res = np.empty(q_input.nq, q_input.dtype) self.kernel = kernel self.dim = '2d' if q_input.is_2d else '1d' partable = model_info.parameters kernel_parameters = (partable.iqxy_parameters if q_input.is_2d else partable.iq_parameters) volume_parameters = partable.form_volume_parameters # Create an array to hold the parameter values. There will be a # single array whose values are updated as the calculator goes # through the loop. Arguments to the kernel and volume functions # will use views into this vector, relying on the fact that a # an array of no dimensions acts like a scalar. parameter_vector = np.empty(len(partable.call_parameters)-2, 'd') # Create views into the array to hold the arguments offset = 0 kernel_args, volume_args = [], [] for p in partable.kernel_parameters: if p.length == 1: # Scalar values are length 1 vectors with no dimensions. v = parameter_vector[offset:offset+1].reshape(()) else: # Vector values are simple views. v = parameter_vector[offset:offset+p.length] offset += p.length if p in kernel_parameters: kernel_args.append(v) if p in volume_parameters: volume_args.append(v) # Hold on to the parameter vector so we can use it to call kernel later. # This may also be required to preserve the views into the vector. self._parameter_vector = parameter_vector # Generate a closure which calls the kernel with the views into the # parameter array. if q_input.is_2d: form = model_info.Iqxy qx, qy = q_input.q[:, 0], q_input.q[:, 1] self._form = lambda: form(qx, qy, *kernel_args) else: form = model_info.Iq q = q_input.q self._form = lambda: form(q, *kernel_args) # Generate a closure which calls the form_volume if it exists. form_volume = model_info.form_volume self._volume = ((lambda: form_volume(*volume_args)) if form_volume else (lambda: 1.0)) def __call__(self, call_details, values, cutoff, magnetic): # type: (CallDetails, np.ndarray, np.ndarray, float, bool) -> np.ndarray if magnetic: raise NotImplementedError("Magnetism not implemented for pure python models") #print("Calling python kernel") #call_details.show(values) res = _loops(self._parameter_vector, self._form, self._volume, self.q_input.nq, call_details, values, cutoff) return res def release(self): # type: () -> None """ Free resources associated with the kernel. """ self.q_input.release() self.q_input = None def _loops(parameters, form, form_volume, nq, call_details, values, cutoff): # type: (np.ndarray, Callable[[], np.ndarray], Callable[[], float], int, details.CallDetails, np.ndarray, np.ndarray, float) -> None ################################################################ # # # !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! # # !! !! # # !! KEEP THIS CODE CONSISTENT WITH KERNEL_TEMPLATE.C !! # # !! !! # # !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! # # # ################################################################ n_pars = len(parameters) parameters[:] = values[2:n_pars+2] if call_details.num_active == 0: pd_norm = float(form_volume()) scale = values[0]/(pd_norm if pd_norm != 0.0 else 1.0) background = values[1] return scale*form() + background pd_value = values[2+n_pars:2+n_pars + call_details.num_weights] pd_weight = values[2+n_pars + call_details.num_weights:] pd_norm = 0.0 spherical_correction = 1.0 partial_weight = np.NaN weight = np.NaN p0_par = call_details.pd_par[0] p0_is_theta = (p0_par == call_details.theta_par) p0_length = call_details.pd_length[0] p0_index = p0_length p0_offset = call_details.pd_offset[0] pd_par = call_details.pd_par[:call_details.num_active] pd_offset = call_details.pd_offset[:call_details.num_active] pd_stride = call_details.pd_stride[:call_details.num_active] pd_length = call_details.pd_length[:call_details.num_active] total = np.zeros(nq, 'd') for loop_index in range(call_details.num_eval): # update polydispersity parameter values if p0_index == p0_length: pd_index = (loop_index//pd_stride)%pd_length parameters[pd_par] = pd_value[pd_offset+pd_index] partial_weight = np.prod(pd_weight[pd_offset+pd_index][1:]) if call_details.theta_par >= 0: cor = sin(pi / 180 * parameters[call_details.theta_par]) spherical_correction = max(abs(cor), 1e-6) p0_index = loop_index%p0_length weight = partial_weight * pd_weight[p0_offset + p0_index] parameters[p0_par] = pd_value[p0_offset + p0_index] if p0_is_theta: cor = cos(pi/180 * parameters[p0_par]) spherical_correction = max(abs(cor), 1e-6) p0_index += 1 if weight > cutoff: # Call the scattering function # Assume that NaNs are only generated if the parameters are bad; # exclude all q for that NaN. Even better would be to have an # INVALID expression like the C models, but that is too expensive. Iq = np.asarray(form(), 'd') if np.isnan(Iq).any(): continue # update value and norm weight *= spherical_correction total += weight * Iq pd_norm += weight * form_volume() scale = values[0]/(pd_norm if pd_norm != 0.0 else 1.0) background = values[1] return scale*total + background def _create_default_functions(model_info): """ Autogenerate missing functions, such as Iqxy from Iq. This only works for Iqxy when Iq is written in python. :func:`make_source` performs a similar role for Iq written in C. This also vectorizes any functions that are not already marked as vectorized. """ _create_vector_Iq(model_info) _create_vector_Iqxy(model_info) # call create_vector_Iq() first def _create_vector_Iq(model_info): """ Define Iq as a vector function if it exists. """ Iq = model_info.Iq if callable(Iq) and not getattr(Iq, 'vectorized', False): #print("vectorizing Iq") def vector_Iq(q, *args): """ Vectorized 1D kernel. """ return np.array([Iq(qi, *args) for qi in q]) vector_Iq.vectorized = True model_info.Iq = vector_Iq def _create_vector_Iqxy(model_info): """ Define Iqxy as a vector function if it exists, or default it from Iq(). """ Iq, Iqxy = model_info.Iq, model_info.Iqxy if callable(Iqxy): if not getattr(Iqxy, 'vectorized', False): #print("vectorizing Iqxy") def vector_Iqxy(qx, qy, *args): """ Vectorized 2D kernel. """ return np.array([Iqxy(qxi, qyi, *args) for qxi, qyi in zip(qx, qy)]) vector_Iqxy.vectorized = True model_info.Iqxy = vector_Iqxy elif callable(Iq): #print("defaulting Iqxy") # Iq is vectorized because create_vector_Iq was already called. def default_Iqxy(qx, qy, *args): """ Default 2D kernel. """ return Iq(np.sqrt(qx**2 + qy**2), *args) default_Iqxy.vectorized = True model_info.Iqxy = default_Iqxy sasmodels/sasmodels/list_pars.py000066400000000000000000000037101317715334700174300ustar00rootroot00000000000000""" List all parameters used along with the models which use them. Usage: python -m sasmodels.list_pars [-v] If '-v' is given, then list the models containing the parameter in addition to just the parameter name. """ from __future__ import print_function import sys import argparse from .core import load_model_info, list_models from .compare import columnize def find_pars(type=None): """ Find all parameters in all models. Returns the reference table *{parameter: [model, model, ...]}* """ partable = {} for name in list_models(): model_info = load_model_info(name) for p in model_info.parameters.kernel_parameters: if type is None or p.type == type: partable.setdefault(p.name, []) partable[p.name].append(name) return partable def list_pars(names_only=True, type=None): """ Print all parameters in all models. If *names_only* then only print the parameter name, not the models it occurs in. """ partable = find_pars(type) if names_only: print(columnize(list(sorted(partable.keys())))) else: for k, v in sorted(partable.items()): print("%s: %s"%(k, ", ".join(v))) def main(): """ Program to list the parameters used across all models. """ parser = argparse.ArgumentParser( description="Find all parameters in all models", ) parser.add_argument( '-v', '--verbose', action='store_true', help="list models which use this argument") parser.add_argument( 'type', default="any", nargs='?', metavar="volume|orientation|sld|none|any", choices=['volume', 'orientation', 'sld', None, 'any'], type=lambda v: None if v == 'any' else '' if v == 'none' else v, help="only list arguments of the given type") args = parser.parse_args() list_pars(names_only=not args.verbose, type=args.type) if __name__ == "__main__": main() sasmodels/sasmodels/mixture.py000066400000000000000000000300501317715334700171220ustar00rootroot00000000000000""" Mixture model ------------- The product model multiplies the structure factor by the form factor, modulated by the effective radius of the form. The resulting model has a attributes of both the model description (with parameters, etc.) and the module evaluator (with call, release, etc.). To use it, first load form factor P and structure factor S, then create *ProductModel(P, S)*. """ from __future__ import print_function from copy import copy import numpy as np # type: ignore from .modelinfo import Parameter, ParameterTable, ModelInfo from .kernel import KernelModel, Kernel from .details import make_details try: from typing import List except ImportError: pass def make_mixture_info(parts, operation='+'): # type: (List[ModelInfo]) -> ModelInfo """ Create info block for mixture model. """ # Build new parameter list combined_pars = [] model_num = 0 all_parts = copy(parts) is_flat = False while not is_flat: is_flat = True for part in all_parts: if part.composition and part.composition[0] == 'mixture' and \ len(part.composition[1]) > 1: all_parts += part.composition[1] all_parts.remove(part) is_flat = False # When creating a mixture model that is a sum of product models (ie (1*2)+(3*4)) # the parameters for models 1 & 2 will be prefixed with A & B respectively, # but so will the parameters for models 3 & 4. We need to rename models 3 & 4 # so that they are prefixed with C & D to avoid overlap of parameter names. used_prefixes = [] for part in parts: i = 0 if part.composition and part.composition[0] == 'mixture': npars_list = [info.parameters.npars for info in part.composition[1]] for npars in npars_list: # List of params of one of the constituent models of part submodel_pars = part.parameters.kernel_parameters[i:i+npars] # Prefix of the constituent model prefix = submodel_pars[0].name[0] if prefix not in used_prefixes: # Haven't seen this prefix so far used_prefixes.append(prefix) i += npars continue while prefix in used_prefixes: # This prefix has been already used, so change it to the # next letter that hasn't been used prefix = chr(ord(prefix) + 1) used_prefixes.append(prefix) prefix += "_" # Update the parameters of this constituent model to use the # new prefix for par in submodel_pars: par.id = prefix + par.id[2:] par.name = prefix + par.name[2:] if par.length_control is not None: par.length_control = prefix + par.length_control[2:] i += npars for part in parts: # Parameter prefix per model, A_, B_, ... # Note that prefix must also be applied to id and length_control # to support vector parameters prefix = '' if not part.composition: # Model isn't a composition model, so it's parameters don't have a # a prefix. Add the next available prefix prefix = chr(ord('A')+len(used_prefixes)) used_prefixes.append(prefix) prefix += '_' if operation == '+': # If model is a sum model, each constituent model gets its own scale parameter scale_prefix = prefix if prefix == '' and part.operation == '*': # `part` is a composition product model. Find the prefixes of # it's parameters to form a new prefix for the scale, eg: # a model with A*B*C will have ABC_scale sub_prefixes = [] for param in part.parameters.kernel_parameters: # Prefix of constituent model sub_prefix = param.id.split('_')[0] if sub_prefix not in sub_prefixes: sub_prefixes.append(sub_prefix) # Concatenate sub_prefixes to form prefix for the scale scale_prefix = ''.join(sub_prefixes) + '_' scale = Parameter(scale_prefix + 'scale', default=1.0, description="model intensity for " + part.name) combined_pars.append(scale) for p in part.parameters.kernel_parameters: p = copy(p) p.name = prefix + p.name p.id = prefix + p.id if p.length_control is not None: p.length_control = prefix + p.length_control combined_pars.append(p) parameters = ParameterTable(combined_pars) parameters.max_pd = sum(part.parameters.max_pd for part in parts) def random(): combined_pars = {} for k, part in enumerate(parts): prefix = chr(ord('A')+k) + '_' pars = part.random() combined_pars.update((prefix+k, v) for k, v in pars.items()) return combined_pars model_info = ModelInfo() model_info.id = operation.join(part.id for part in parts) model_info.operation = operation model_info.name = '(' + operation.join(part.name for part in parts) + ')' model_info.filename = None model_info.title = 'Mixture model with ' + model_info.name model_info.description = model_info.title model_info.docs = model_info.title model_info.category = "custom" model_info.parameters = parameters model_info.random = random #model_info.single = any(part['single'] for part in parts) model_info.structure_factor = False model_info.variant_info = None #model_info.tests = [] #model_info.source = [] # Iq, Iqxy, form_volume, ER, VR and sesans # Remember the component info blocks so we can build the model model_info.composition = ('mixture', parts) return model_info class MixtureModel(KernelModel): def __init__(self, model_info, parts): # type: (ModelInfo, List[KernelModel]) -> None self.info = model_info self.parts = parts self.dtype = parts[0].dtype def make_kernel(self, q_vectors): # type: (List[np.ndarray]) -> MixtureKernel # Note: may be sending the q_vectors to the n times even though they # are only needed once. It would mess up modularity quite a bit to # handle this optimally, especially since there are many cases where # separate q vectors are needed (e.g., form in python and structure # in opencl; or both in opencl, but one in single precision and the # other in double precision). kernels = [part.make_kernel(q_vectors) for part in self.parts] return MixtureKernel(self.info, kernels) def release(self): # type: () -> None """ Free resources associated with the model. """ for part in self.parts: part.release() class MixtureKernel(Kernel): def __init__(self, model_info, kernels): # type: (ModelInfo, List[Kernel]) -> None self.dim = kernels[0].dim self.info = model_info self.kernels = kernels self.dtype = self.kernels[0].dtype self.operation = model_info.operation self.results = [] # type: List[np.ndarray] def __call__(self, call_details, values, cutoff, magnetic): # type: (CallDetails, np.ndarray, np.ndarry, float, bool) -> np.ndarray scale, background = values[0:2] total = 0.0 # remember the parts for plotting later self.results = [] # type: List[np.ndarray] parts = MixtureParts(self.info, self.kernels, call_details, values) for kernel, kernel_details, kernel_values in parts: #print("calling kernel", kernel.info.name) result = kernel(kernel_details, kernel_values, cutoff, magnetic) result = np.array(result).astype(kernel.dtype) # print(kernel.info.name, result) if self.operation == '+': total += result elif self.operation == '*': if np.all(total) == 0.0: total = result else: total *= result self.results.append(result) return scale*total + background def release(self): # type: () -> None for k in self.kernels: k.release() class MixtureParts(object): def __init__(self, model_info, kernels, call_details, values): # type: (ModelInfo, List[Kernel], CallDetails, np.ndarray) -> None self.model_info = model_info self.parts = model_info.composition[1] self.kernels = kernels self.call_details = call_details self.values = values self.spin_index = model_info.parameters.npars + 2 #call_details.show(values) def __iter__(self): # type: () -> PartIterable self.part_num = 0 self.par_index = 2 self.mag_index = self.spin_index + 3 return self def next(self): # type: () -> Tuple[List[Callable], CallDetails, np.ndarray] if self.part_num >= len(self.parts): raise StopIteration() info = self.parts[self.part_num] kernel = self.kernels[self.part_num] call_details = self._part_details(info, self.par_index) values = self._part_values(info, self.par_index, self.mag_index) values = values.astype(kernel.dtype) #call_details.show(values) self.part_num += 1 self.par_index += info.parameters.npars if self.model_info.operation == '+': self.par_index += 1 # Account for each constituent model's scale param self.mag_index += 3 * len(info.parameters.magnetism_index) return kernel, call_details, values def _part_details(self, info, par_index): # type: (ModelInfo, int) -> CallDetails full = self.call_details # par_index is index into values array of the current parameter, # which includes the initial scale and background parameters. # We want the index into the weight length/offset for each parameter. # Exclude the initial scale and background, so subtract two. If we're # building an addition model, each component has its own scale factor # which we need to skip when constructing the details for the kernel, so # add one, giving a net subtract one. diff = 1 if self.model_info.operation == '+' else 2 index = slice(par_index - diff, par_index - diff + info.parameters.npars) length = full.length[index] offset = full.offset[index] # The complete weight vector is being sent to each part so that # offsets don't need to be adjusted. part = make_details(info, length, offset, full.num_weights) return part def _part_values(self, info, par_index, mag_index): # type: (ModelInfo, int, int) -> np.ndarray # Set each constituent model's scale to 1 if this is a multiplication model scale = self.values[par_index] if self.model_info.operation == '+' else 1.0 diff = 1 if self.model_info.operation == '+' else 0 # Skip scale if addition model pars = self.values[par_index + diff:par_index + info.parameters.npars + diff] nmagnetic = len(info.parameters.magnetism_index) if nmagnetic: spin_state = self.values[self.spin_index:self.spin_index + 3] mag_index = self.values[mag_index:mag_index + 3 * nmagnetic] else: spin_state = [] mag_index = [] nvalues = self.model_info.parameters.nvalues nweights = self.call_details.num_weights weights = self.values[nvalues:nvalues+2*nweights] zero = self.values.dtype.type(0.) values = [[scale, zero], pars, spin_state, mag_index, weights] # Pad value array to a 32 value boundary spacer = (32 - sum(len(v) for v in values)%32)%32 values.append([zero]*spacer) values = np.hstack(values).astype(self.kernels[0].dtype) return values sasmodels/sasmodels/model_test.py000066400000000000000000000442071317715334700175750ustar00rootroot00000000000000# -*- coding: utf-8 -*- """ Run model unit tests. Usage:: python -m sasmodels.model_test [opencl|dll|opencl_and_dll] model1 model2 ... if model1 is 'all', then all except the remaining models will be tested Each model is tested using the default parameters at q=0.1, (qx, qy)=(0.1, 0.1), and the ER and VR are computed. The return values at these points are not considered. The test is only to verify that the models run to completion, and do not produce inf or NaN. Tests are defined with the *tests* attribute in the model.py file. *tests* is a list of individual tests to run, where each test consists of the parameter values for the test, the q-values and the expected results. For the effective radius test, the q-value should be 'ER'. For the VR test, the q-value should be 'VR'. For 1-D tests, either specify the q value or a list of q-values, and the corresponding I(q) value, or list of I(q) values. That is:: tests = [ [ {parameters}, q, I(q)], [ {parameters}, [q], [I(q)] ], [ {parameters}, [q1, q2, ...], [I(q1), I(q2), ...]], [ {parameters}, (qx, qy), I(qx, Iqy)], [ {parameters}, [(qx1, qy1), (qx2, qy2), ...], [I(qx1, qy1), I(qx2, qy2), ...]], [ {parameters}, 'ER', ER(pars) ], [ {parameters}, 'VR', VR(pars) ], ... ] Parameters are *key:value* pairs, where key is one of the parameters of the model and value is the value to use for the test. Any parameters not given in the parameter list will take on the default parameter value. Precision defaults to 5 digits (relative). """ from __future__ import print_function import sys import unittest try: from StringIO import StringIO except ImportError: # StringIO.StringIO renamed to io.StringIO in Python 3 # Note: io.StringIO exists in python 2, but using unicode instead of str from io import StringIO import numpy as np # type: ignore from . import core from .core import list_models, load_model_info, build_model from .direct_model import call_kernel, call_ER, call_VR from .exception import annotate_exception from .modelinfo import expand_pars try: from typing import List, Iterator, Callable except ImportError: pass else: from .modelinfo import ParameterTable, ParameterSet, TestCondition, ModelInfo from .kernel import KernelModel def make_suite(loaders, models): # type: (List[str], List[str]) -> unittest.TestSuite """ Construct the pyunit test suite. *loaders* is the list of kernel drivers to use, which is one of *["dll", "opencl"]*, *["dll"]* or *["opencl"]*. For python models, the python driver is always used. *models* is the list of models to test, or *["all"]* to test all models. """ ModelTestCase = _hide_model_case_from_nose() suite = unittest.TestSuite() if models[0] == 'all': skip = models[1:] models = list_models() else: skip = [] for model_name in models: if model_name in skip: continue model_info = load_model_info(model_name) #print('------') #print('found tests in', model_name) #print('------') # if ispy then use the dll loader to call pykernel # don't try to call cl kernel since it will not be # available in some environmentes. is_py = callable(model_info.Iq) # Some OpenCL drivers seem to be flaky, and are not producing the # expected result. Since we don't have known test values yet for # all of our models, we are instead going to compare the results # for the 'smoke test' (that is, evaluation at q=0.1 for the default # parameters just to see that the model runs to completion) between # the OpenCL and the DLL. To do this, we define a 'stash' which is # shared between OpenCL and DLL tests. This is just a list. If the # list is empty (which it will be when DLL runs, if the DLL runs # first), then the results are appended to the list. If the list # is not empty (which it will be when OpenCL runs second), the results # are compared to the results stored in the first element of the list. # This is a horrible stateful hack which only makes sense because the # test suite is thrown away after being run once. stash = [] if is_py: # kernel implemented in python test_name = "Model: %s, Kernel: python"%model_name test_method_name = "test_%s_python" % model_info.id test = ModelTestCase(test_name, model_info, test_method_name, platform="dll", # so that dtype="double", stash=stash) suite.addTest(test) else: # kernel implemented in C # test using dll if desired if 'dll' in loaders or not core.HAVE_OPENCL: test_name = "Model: %s, Kernel: dll"%model_name test_method_name = "test_%s_dll" % model_info.id test = ModelTestCase(test_name, model_info, test_method_name, platform="dll", dtype="double", stash=stash) suite.addTest(test) # test using opencl if desired and available if 'opencl' in loaders and core.HAVE_OPENCL: test_name = "Model: %s, Kernel: OpenCL"%model_name test_method_name = "test_%s_opencl" % model_info.id # Using dtype=None so that the models that are only # correct for double precision are not tested using # single precision. The choice is determined by the # presence of *single=False* in the model file. test = ModelTestCase(test_name, model_info, test_method_name, platform="ocl", dtype=None, stash=stash) #print("defining", test_name) suite.addTest(test) return suite def _hide_model_case_from_nose(): # type: () -> type class ModelTestCase(unittest.TestCase): """ Test suit for a particular model with a particular kernel driver. The test suite runs a simple smoke test to make sure the model functions, then runs the list of tests at the bottom of the model description file. """ def __init__(self, test_name, model_info, test_method_name, platform, dtype, stash): # type: (str, ModelInfo, str, str, DType, List[Any]) -> None self.test_name = test_name self.info = model_info self.platform = platform self.dtype = dtype self.stash = stash # container for the results of the first run setattr(self, test_method_name, self.run_all) unittest.TestCase.__init__(self, test_method_name) def run_all(self): # type: () -> None """ Run all the tests in the test suite, including smoke tests. """ smoke_tests = [ # test validity at reasonable values ({}, 0.1, None), ({}, (0.1, 0.1), None), # test validity at q = 0 #({}, 0.0, None), #({}, (0.0, 0.0), None), # test vector form ({}, [0.001, 0.01, 0.1], [None]*3), ({}, [(0.1, 0.1)]*2, [None]*2), # test that ER/VR will run if they exist ({}, 'ER', None), ({}, 'VR', None), ] tests = smoke_tests if self.info.tests is not None: tests += self.info.tests try: model = build_model(self.info, dtype=self.dtype, platform=self.platform) results = [self.run_one(model, test) for test in tests] if self.stash: for test, target, actual in zip(tests, self.stash[0], results): assert np.all(abs(target-actual) < 5e-5*abs(actual)),\ "GPU/CPU comparison expected %s but got %s for %s"%(target, actual, test[0]) else: self.stash.append(results) # Check for missing tests. Only do so for the "dll" tests # to reduce noise from both opencl and dll, and because # python kernels use platform="dll". if self.platform == "dll": missing = [] ## Uncomment the following to require test cases #missing = self._find_missing_tests() if missing: raise ValueError("Missing tests for "+", ".join(missing)) except: annotate_exception(self.test_name) raise def _find_missing_tests(self): # type: () -> None """make sure there are 1D, 2D, ER and VR tests as appropriate""" model_has_VR = callable(self.info.VR) model_has_ER = callable(self.info.ER) model_has_1D = True model_has_2D = any(p.type == 'orientation' for p in self.info.parameters.kernel_parameters) # Lists of tests that have a result that is not None single = [test for test in self.info.tests if not isinstance(test[2], list) and test[2] is not None] tests_has_VR = any(test[1] == 'VR' for test in single) tests_has_ER = any(test[1] == 'ER' for test in single) tests_has_1D_single = any(isinstance(test[1], float) for test in single) tests_has_2D_single = any(isinstance(test[1], tuple) for test in single) multiple = [test for test in self.info.tests if isinstance(test[2], list) and not all(result is None for result in test[2])] tests_has_1D_multiple = any(isinstance(test[1][0], float) for test in multiple) tests_has_2D_multiple = any(isinstance(test[1][0], tuple) for test in multiple) missing = [] if model_has_VR and not tests_has_VR: missing.append("VR") if model_has_ER and not tests_has_ER: missing.append("ER") if model_has_1D and not (tests_has_1D_single or tests_has_1D_multiple): missing.append("1D") if model_has_2D and not (tests_has_2D_single or tests_has_2D_multiple): missing.append("2D") return missing def run_one(self, model, test): # type: (KernelModel, TestCondition) -> None """Run a single test case.""" user_pars, x, y = test pars = expand_pars(self.info.parameters, user_pars) invalid = invalid_pars(self.info.parameters, pars) if invalid: raise ValueError("Unknown parameters in test: " + ", ".join(invalid)) if not isinstance(y, list): y = [y] if not isinstance(x, list): x = [x] self.assertEqual(len(y), len(x)) if x[0] == 'ER': actual = np.array([call_ER(model.info, pars)]) elif x[0] == 'VR': actual = np.array([call_VR(model.info, pars)]) elif isinstance(x[0], tuple): qx, qy = zip(*x) q_vectors = [np.array(qx), np.array(qy)] kernel = model.make_kernel(q_vectors) actual = call_kernel(kernel, pars) else: q_vectors = [np.array(x)] kernel = model.make_kernel(q_vectors) actual = call_kernel(kernel, pars) self.assertTrue(len(actual) > 0) self.assertEqual(len(y), len(actual)) for xi, yi, actual_yi in zip(x, y, actual): if yi is None: # smoke test --- make sure it runs and produces a value self.assertTrue(not np.isnan(actual_yi), 'invalid f(%s): %s' % (xi, actual_yi)) elif np.isnan(yi): self.assertTrue(np.isnan(actual_yi), 'f(%s): expected:%s; actual:%s' % (xi, yi, actual_yi)) else: # is_near does not work for infinite values, so also test # for exact values. Note that this will not self.assertTrue(yi == actual_yi or is_near(yi, actual_yi, 5), 'f(%s); expected:%s; actual:%s' % (xi, yi, actual_yi)) return actual return ModelTestCase def invalid_pars(partable, pars): # type: (ParameterTable, Dict[str, float]) """ Return a list of parameter names that are not part of the model. """ names = set(p.id for p in partable.call_parameters) invalid = [] for par in sorted(pars.keys()): parts = par.split('_pd') if len(parts) > 1 and parts[1] not in ("", "_n", "nsigma", "type"): invalid.append(par) continue if parts[0] not in names: invalid.append(par) return invalid def is_near(target, actual, digits=5): # type: (float, float, int) -> bool """ Returns true if *actual* is within *digits* significant digits of *target*. """ import math shift = 10**math.ceil(math.log10(abs(target))) return abs(target-actual)/shift < 1.5*10**-digits def run_one(model): # type: (str) -> str """ Run the tests for a single model, printing the results to stdout. *model* can by a python file, which is handy for checking user defined plugin models. """ # Note that running main() directly did not work from within the # wxPython pycrust console. Instead of the results appearing in the # window they were printed to the underlying console. from unittest.runner import TextTestResult, _WritelnDecorator # Build a object to capture and print the test results stream = _WritelnDecorator(StringIO()) # Add writeln() method to stream verbosity = 2 descriptions = True result = TextTestResult(stream, descriptions, verbosity) # Build a test suite containing just the model loaders = ['opencl'] if core.HAVE_OPENCL else ['dll'] models = [model] try: suite = make_suite(loaders, models) except Exception: import traceback stream.writeln(traceback.format_exc()) return # Run the test suite suite.run(result) # Print the failures and errors for _, tb in result.errors: stream.writeln(tb) for _, tb in result.failures: stream.writeln(tb) # Warn if there are no user defined tests. # Note: the test suite constructed above only has one test in it, which # runs through some smoke tests to make sure the model runs, then runs # through the input-output pairs given in the model definition file. To # check if any such pairs are defined, therefore, we just need to check if # they are in the first test of the test suite. We do this with an # iterator since we don't have direct access to the list of tests in the # test suite. for test in suite: if not test.info.tests: stream.writeln("Note: %s has no user defined tests."%model) break else: stream.writeln("Note: no test suite created --- this should never happen") output = stream.getvalue() stream.close() return output def main(*models): # type: (*str) -> int """ Run tests given is models. Returns 0 if success or 1 if any tests fail. """ try: from xmlrunner import XMLTestRunner as TestRunner test_args = {'output': 'logs'} except ImportError: from unittest import TextTestRunner as TestRunner test_args = {} if models and models[0] == '-v': verbosity = 2 models = models[1:] else: verbosity = 1 if models and models[0] == 'opencl': if not core.HAVE_OPENCL: print("opencl is not available") return 1 loaders = ['opencl'] models = models[1:] elif models and models[0] == 'dll': # TODO: test if compiler is available? loaders = ['dll'] models = models[1:] elif models and models[0] == 'opencl_and_dll': loaders = ['opencl', 'dll'] if core.HAVE_OPENCL else ['dll'] models = models[1:] else: loaders = ['opencl', 'dll'] if core.HAVE_OPENCL else ['dll'] if not models: print("""\ usage: python -m sasmodels.model_test [-v] [opencl|dll] model1 model2 ... If -v is included on the command line, then use verbose output. If neither opencl nor dll is specified, then models will be tested with both OpenCL and dll; the compute target is ignored for pure python models. If model1 is 'all', then all except the remaining models will be tested. """) return 1 runner = TestRunner(verbosity=verbosity, **test_args) result = runner.run(make_suite(loaders, models)) return 1 if result.failures or result.errors else 0 def model_tests(): # type: () -> Iterator[Callable[[], None]] """ Test runner visible to nosetests. Run "nosetests sasmodels" on the command line to invoke it. """ loaders = ['opencl', 'dll'] if core.HAVE_OPENCL else ['dll'] tests = make_suite(loaders, ['all']) for test_i in tests: # In order for nosetest to see the correct test name, need to set # the description attribute of the returned function. Since we # can't do this for the returned instance, wrap it in a lambda and # set the description on the lambda. Otherwise we could just do: # yield test_i.run_all L = lambda: test_i.run_all() L.description = test_i.test_name yield L if __name__ == "__main__": sys.exit(main(*sys.argv[1:])) sasmodels/sasmodels/modelinfo.py000066400000000000000000001245311317715334700174110ustar00rootroot00000000000000""" Model Info and Parameter Tables =============================== Defines :class:`ModelInfo` and :class:`ParameterTable` and the routines for manipulating them. In particular, :func:`make_model_info` converts a kernel module into the model info block as seen by the rest of the sasmodels library. """ from __future__ import print_function from copy import copy from os.path import abspath, basename, splitext import inspect import numpy as np # type: ignore # Optional typing try: from typing import Tuple, List, Union, Dict, Optional, Any, Callable, Sequence, Set except ImportError: pass else: Limits = Tuple[float, float] #LimitsOrChoice = Union[Limits, Tuple[Sequence[str]]] ParameterDef = Tuple[str, str, float, Limits, str, str] ParameterSetUser = Dict[str, Union[float, List[float]]] ParameterSet = Dict[str, float] TestInput = Union[str, float, List[float], Tuple[float, float], List[Tuple[float, float]]] TestValue = Union[float, List[float]] TestCondition = Tuple[ParameterSetUser, TestInput, TestValue] MAX_PD = 4 #: Maximum number of simultaneously polydisperse parameters # assumptions about common parameters exist throughout the code, such as: # (1) kernel functions Iq, Iqxy, form_volume, ... don't see them # (2) kernel drivers assume scale is par[0] and background is par[1] # (3) mixture models drop the background on components and replace the scale # with a scale that varies from [-inf, inf] # (4) product models drop the background and reassign scale # and maybe other places. # Note that scale and background cannot be coordinated parameters whose value # depends on the some polydisperse parameter with the current implementation COMMON_PARAMETERS = [ ("scale", "", 1, (0.0, np.inf), "", "Source intensity"), ("background", "1/cm", 1e-3, (-np.inf, np.inf), "", "Source background"), ] assert (len(COMMON_PARAMETERS) == 2 and COMMON_PARAMETERS[0][0] == "scale" and COMMON_PARAMETERS[1][0] == "background"), "don't change common parameters" def make_parameter_table(pars): # type: (List[ParameterDef]) -> ParameterTable """ Construct a parameter table from a list of parameter definitions. This is used by the module processor to convert the parameter block into the parameter table seen in the :class:`ModelInfo` for the module. """ processed = [] for p in pars: if not isinstance(p, (list, tuple)) or len(p) != 6: raise ValueError("Parameter should be [name, units, default, limits, type, desc], but got %r" %str(p)) processed.append(parse_parameter(*p)) partable = ParameterTable(processed) return partable def parse_parameter(name, units='', default=np.NaN, user_limits=None, ptype='', description=''): # type: (str, str, float, Sequence[Any], str, str) -> Parameter """ Parse an individual parameter from the parameter definition block. This does type and value checking on the definition, leading to early failure in the model loading process and easier debugging. """ # Parameter is a user facing class. Do robust type checking. if not isstr(name): raise ValueError("expected string for parameter name %r"%name) if not isstr(units): raise ValueError("expected units to be a string for %s"%name) # Process limits as [float, float] or [[str, str, ...]] choices = [] # type: List[str] if user_limits is None: limits = (-np.inf, np.inf) elif not isinstance(user_limits, (tuple, list)): raise ValueError("invalid limits for %s"%name) else: # if limits is [[str,...]], then this is a choice list field, # and limits are 1 to length of string list if isinstance(user_limits[0], (tuple, list)): choices = user_limits[0] limits = (0., len(choices)-1.) if not all(isstr(k) for k in choices): raise ValueError("choices must be strings for %s"%name) else: try: low, high = user_limits limits = (float(low), float(high)) except Exception: raise ValueError("invalid limits for %s: %r"%(name, user_limits)) if low >= high: raise ValueError("require lower limit < upper limit") # Process default value as float, making sure it is in range if not isinstance(default, (int, float)): raise ValueError("expected default %r to be a number for %s" % (default, name)) if default < limits[0] or default > limits[1]: raise ValueError("default value %r not in range for %s" % (default, name)) # Check for valid parameter type if ptype not in ("volume", "orientation", "sld", "magnetic", ""): raise ValueError("unexpected type %r for %s" % (ptype, name)) # Check for valid parameter description if not isstr(description): raise ValueError("expected description to be a string") # Parameter id for name[n] does not include [n] if "[" in name: if not name.endswith(']'): raise ValueError("Expected name[len] for vector parameter %s"%name) pid, ref = name[:-1].split('[', 1) ref = ref.strip() else: pid, ref = name, None # automatically identify sld types if ptype == '' and (pid.startswith('sld') or pid.endswith('sld')): ptype = 'sld' # Check if using a vector definition, name[k], as the parameter name if ref: if ref == '': raise ValueError("Need to specify vector length for %s"%name) try: length = int(ref) control = None except ValueError: length = None control = ref else: length = 1 control = None # Build the parameter parameter = Parameter(name=name, units=units, default=default, limits=limits, ptype=ptype, description=description) # TODO: need better control over whether a parameter is polydisperse parameter.polydisperse = ptype in ('orientation', 'volume') parameter.relative_pd = ptype == 'volume' parameter.choices = choices parameter.length = length parameter.length_control = control return parameter def expand_pars(partable, pars): # type: (ParameterTable, ParameterSetUser) -> ParameterSet """ Create demo parameter set from key-value pairs. *pars* are the key-value pairs to use for the parameters. Any parameters not specified in *pars* are set from the *partable* defaults. If *pars* references vector fields, such as thickness[n], then support different ways of assigning the demo values, including assigning a specific value (e.g., thickness3=50.0), assigning a new value to all (e.g., thickness=50.0) or assigning values using list notation. """ if pars is None: result = partable.defaults else: lookup = dict((p.id, p) for p in partable.kernel_parameters) result = partable.defaults.copy() scalars = dict((name, value) for name, value in pars.items() if name not in lookup or lookup[name].length == 1) vectors = dict((name, value) for name, value in pars.items() if name in lookup and lookup[name].length > 1) #print("lookup", lookup) #print("scalars", scalars) #print("vectors", vectors) if vectors: for name, value in vectors.items(): if np.isscalar(value): # support for the form # dict(thickness=0, thickness2=50) for k in range(1, lookup[name].length+1): key = name+str(k) if key not in scalars: scalars[key] = value else: # supoprt for the form # dict(thickness=[20,10,3]) for (k, v) in enumerate(value): scalars[name+str(k+1)] = v result.update(scalars) #print("expanded", result) return result def prefix_parameter(par, prefix): # type: (Parameter, str) -> Parameter """ Return a copy of the parameter with its name prefixed. """ new_par = copy(par) new_par.name = prefix + par.name new_par.id = prefix + par.id def suffix_parameter(par, suffix): # type: (Parameter, str) -> Parameter """ Return a copy of the parameter with its name prefixed. """ new_par = copy(par) # If name has the form x[n], replace with x_suffix[n] new_par.name = par.id + suffix + par.name[len(par.id):] new_par.id = par.id + suffix class Parameter(object): """ The available kernel parameters are defined as a list, with each parameter defined as a sublist with the following elements: *name* is the name that will be displayed to the user. Names should be lower case, with words separated by underscore. If acronyms are used, the whole acronym should be upper case. For vector parameters, the name will be followed by *[len]* where *len* is an integer length of the vector, or the name of the parameter which controls the length. The attribute *id* will be created from name without the length. *units* should be one of *degrees* for angles, *Ang* for lengths, *1e-6/Ang^2* for SLDs. *default value* will be the initial value for the model when it is selected, or when an initial value is not otherwise specified. *limits = [lb, ub]* are the hard limits on the parameter value, used to limit the polydispersity density function. In the fit, the parameter limits given to the fit are the limits on the central value of the parameter. If there is polydispersity, it will evaluate parameter values outside the fit limits, but not outside the hard limits specified in the model. If there are no limits, use +/-inf imported from numpy. *type* indicates how the parameter will be used. "volume" parameters will be used in all functions. "orientation" parameters will be used in *Iqxy* and *Imagnetic*. "magnetic* parameters will be used in *Imagnetic* only. If *type* is the empty string, the parameter will be used in all of *Iq*, *Iqxy* and *Imagnetic*. "sld" parameters can automatically be promoted to magnetic parameters, each of which will have a magnitude and a direction, which may be different from other sld parameters. The volume parameters are used for calls to form_volume within the kernel (required for volume normalization) and for calls to ER and VR for effective radius and volume ratio respectively. *description* is a short description of the parameter. This will be displayed in the parameter table and used as a tool tip for the parameter value in the user interface. Additional values can be set after the parameter is created: * *length* is the length of the field if it is a vector field * *length_control* is the parameter which sets the vector length * *is_control* is True if the parameter is a control parameter for a vector * *polydisperse* is true if the parameter accepts a polydispersity * *relative_pd* is true if that polydispersity is a portion of the value (so a 10% length dipsersity would use a polydispersity value of 0.1) rather than absolute dispersisity (such as an angle plus or minus 15 degrees). *choices* is the option names for a drop down list of options, as for example, might be used to set the value of a shape parameter. These values are set by :func:`make_parameter_table` and :func:`parse_parameter` therein. """ def __init__(self, name, units='', default=None, limits=(-np.inf, np.inf), ptype='', description=''): # type: (str, str, float, Limits, str, str) -> None self.id = name.split('[')[0].strip() # type: str self.name = name # type: str self.units = units # type: str self.default = default # type: float self.limits = limits # type: Limits self.type = ptype # type: str self.description = description # type: str # Length and length_control will be filled in once the complete # parameter table is available. self.length = 1 # type: int self.length_control = None # type: Optional[str] self.is_control = False # type: bool # TODO: need better control over whether a parameter is polydisperse self.polydisperse = False # type: bool self.relative_pd = False # type: bool # choices are also set externally. self.choices = [] # type: List[str] def as_definition(self): # type: () -> str """ Declare space for the variable in a parameter structure. For example, the parameter thickness with length 3 will return "double thickness[3];", with no spaces before and no new line character afterward. """ if self.length == 1: return "double %s;"%self.id else: return "double %s[%d];"%(self.id, self.length) def as_function_argument(self): # type: () -> str r""" Declare the variable as a function argument. For example, the parameter thickness with length 3 will return "double \*thickness", with no spaces before and no comma afterward. """ if self.length == 1: return "double %s"%self.id else: return "double *%s"%self.id def as_call_reference(self, prefix=""): # type: (str) -> str """ Return *prefix* + parameter name. For struct references, use "v." as the prefix. """ # Note: if the parameter is a struct type, then we will need to use # &prefix+id. For scalars and vectors we can just use prefix+id. return prefix + self.id def __str__(self): # type: () -> str return "<%s>"%self.name def __repr__(self): # type: () -> str return "P<%s>"%self.name class ParameterTable(object): """ ParameterTable manages the list of available parameters. There are a couple of complications which mean that the list of parameters for the kernel differs from the list of parameters that the user sees. (1) Common parameters. Scale and background are implicit to every model, but are not passed to the kernel. (2) Vector parameters. Vector parameters are passed to the kernel as a pointer to an array, e.g., thick[], but they are seen by the user as n separate parameters thick1, thick2, ... Therefore, the parameter table is organized by how it is expected to be used. The following information is needed to set up the kernel functions: * *kernel_parameters* is the list of parameters in the kernel parameter table, with vector parameter p declared as p[]. * *iq_parameters* is the list of parameters to the Iq(q, ...) function, with vector parameter p sent as p[]. * *iqxy_parameters* is the list of parameters to the Iqxy(qx, qy, ...) function, with vector parameter p sent as p[]. * *form_volume_parameters* is the list of parameters to the form_volume(...) function, with vector parameter p sent as p[]. Problem details, which sets up the polydispersity loops, requires the following: * *theta_offset* is the offset of the theta parameter in the kernel parameter table, with vector parameters counted as n individual parameters p1, p2, ..., or offset is -1 if there is no theta parameter. * *max_pd* is the maximum number of polydisperse parameters, with vector parameters counted as n individual parameters p1, p2, ... Note that this number is limited to sasmodels.modelinfo.MAX_PD. * *npars* is the total number of parameters to the kernel, with vector parameters counted as n individual parameters p1, p2, ... * *call_parameters* is the complete list of parameters to the kernel, including scale and background, with vector parameters recorded as individual parameters p1, p2, ... * *active_1d* is the set of names that may be polydisperse for 1d data * *active_2d* is the set of names that may be polydisperse for 2d data User parameters are the set of parameters visible to the user, including the scale and background parameters that the kernel does not see. User parameters don't use vector notation, and instead use p1, p2, ... """ # scale and background are implicit parameters COMMON = [Parameter(*p) for p in COMMON_PARAMETERS] def __init__(self, parameters): # type: (List[Parameter]) -> None self.kernel_parameters = parameters self._set_vector_lengths() self.npars = sum(p.length for p in self.kernel_parameters) self.nmagnetic = sum(p.length for p in self.kernel_parameters if p.type == 'sld') self.nvalues = 2 + self.npars if self.nmagnetic: self.nvalues += 3 + 3*self.nmagnetic self.call_parameters = self._get_call_parameters() self.defaults = self._get_defaults() #self._name_table= dict((p.id, p) for p in parameters) # Set the kernel parameters. Assumes background and scale are the # first two parameters in the parameter list, but these are not sent # to the underlying kernel functions. self.iq_parameters = [p for p in self.kernel_parameters if p.type not in ('orientation', 'magnetic')] self.iqxy_parameters = [p for p in self.kernel_parameters if p.type != 'magnetic'] self.form_volume_parameters = [p for p in self.kernel_parameters if p.type == 'volume'] # Theta offset offset = 0 for p in self.kernel_parameters: if p.name == 'theta': self.theta_offset = offset break offset += p.length else: self.theta_offset = -1 # number of polydisperse parameters num_pd = sum(p.length for p in self.kernel_parameters if p.polydisperse) # Don't use more polydisperse parameters than are available in the model self.max_pd = min(num_pd, MAX_PD) # true if has 2D parameters self.has_2d = any(p.type in ('orientation', 'magnetic') for p in self.kernel_parameters) self.magnetism_index = [k for k, p in enumerate(self.call_parameters) if p.id.startswith('M0:')] self.pd_1d = set(p.name for p in self.call_parameters if p.polydisperse and p.type not in ('orientation', 'magnetic')) self.pd_2d = set(p.name for p in self.call_parameters if p.polydisperse) def __getitem__(self, key): # Find the parameter definition for par in self.call_parameters: if par.name == key: break else: raise KeyError("unknown parameter %r"%key) return par def _set_vector_lengths(self): # type: () -> List[str] """ Walk the list of kernel parameters, setting the length field of the vector parameters from the upper limit of the reference parameter. This needs to be done once the entire parameter table is available since the reference may still be undefined when the parameter is initially created. Returns the list of control parameter names. Note: This modifies the underlying parameter object. """ # Sort out the length of the vector parameters such as thickness[n] for p in self.kernel_parameters: if p.length_control: for ref in self.kernel_parameters: if ref.id == p.length_control: break else: raise ValueError("no reference variable %r for %s" % (p.length_control, p.name)) ref.is_control = True ref.polydisperse = False low, high = ref.limits if int(low) != low or int(high) != high or low < 0 or high > 20: raise ValueError("expected limits on %s to be within [0, 20]" % ref.name) p.length = int(high) def _get_defaults(self): # type: () -> ParameterSet """ Get a list of parameter defaults from the parameters. Expands vector parameters into parameter id+number. """ # Construct default values, including vector defaults defaults = {} for p in self.call_parameters: if p.length == 1: defaults[p.id] = p.default else: for k in range(1, p.length+1): defaults["%s%d"%(p.id, k)] = p.default return defaults def _get_call_parameters(self): # type: () -> List[Parameter] full_list = self.COMMON[:] for p in self.kernel_parameters: if p.length == 1: full_list.append(p) else: for k in range(1, p.length+1): pk = Parameter(p.id+str(k), p.units, p.default, p.limits, p.type, p.description) pk.polydisperse = p.polydisperse pk.relative_pd = p.relative_pd pk.choices = p.choices full_list.append(pk) # Add the magnetic parameters to the end of the call parameter list. if self.nmagnetic > 0: full_list.extend([ Parameter('up:frac_i', '', 0., [0., 1.], 'magnetic', 'fraction of spin up incident'), Parameter('up:frac_f', '', 0., [0., 1.], 'magnetic', 'fraction of spin up final'), Parameter('up:angle', 'degress', 0., [0., 360.], 'magnetic', 'spin up angle'), ]) slds = [p for p in full_list if p.type == 'sld'] for p in slds: full_list.extend([ Parameter('M0:'+p.id, '1e-6/Ang^2', 0., [-np.inf, np.inf], 'magnetic', 'magnetic amplitude for '+p.description), Parameter('mtheta:'+p.id, 'degrees', 0., [-90., 90.], 'magnetic', 'magnetic latitude for '+p.description), Parameter('mphi:'+p.id, 'degrees', 0., [-180., 180.], 'magnetic', 'magnetic longitude for '+p.description), ]) #print("call parameters", full_list) return full_list def user_parameters(self, pars, is2d=True): # type: (Dict[str, float], bool) -> List[Parameter] """ Return the list of parameters for the given data type. Vector parameters are expanded in place. If multiple parameters share the same vector length, then the parameters will be interleaved in the result. The control parameters come first. For example, if the parameter table is ordered as:: sld_core sld_shell[num_shells] sld_solvent thickness[num_shells] num_shells and *pars[num_shells]=2* then the returned list will be:: num_shells scale background sld_core sld_shell1 thickness1 sld_shell2 thickness2 sld_solvent Note that shell/thickness pairs are grouped together in the result even though they were not grouped in the incoming table. The control parameter is always returned first since the GUI will want to set it early, and rerender the table when it is changed. Parameters marked as sld will automatically have a set of associated magnetic parameters (m0:p, mtheta:p, mphi:p), as well as polarization information (up:theta, up:frac_i, up:frac_f). """ # control parameters go first control = [p for p in self.kernel_parameters if p.is_control] # Gather entries such as name[n] into groups of the same n dependent = {} # type: Dict[str, List[Parameter]] dependent.update((p.id, []) for p in control) for p in self.kernel_parameters: if p.length_control is not None: dependent[p.length_control].append(p) # Gather entries such as name[4] into groups of the same length fixed_length = {} # type: Dict[int, List[Parameter]] for p in self.kernel_parameters: if p.length > 1 and p.length_control is None: fixed_length.setdefault(p.length, []).append(p) # Using the call_parameters table, we already have expanded forms # for each of the vector parameters; put them in a lookup table # Note: p.id and p.name are currently identical for the call parameters expanded_pars = dict((p.id, p) for p in self.call_parameters) def append_group(name): """add the named parameter, and related magnetic parameters if any""" result.append(expanded_pars[name]) if is2d: for tag in 'M0:', 'mtheta:', 'mphi:': if tag+name in expanded_pars: result.append(expanded_pars[tag+name]) # Gather the user parameters in order result = control + self.COMMON for p in self.kernel_parameters: if not is2d and p.type in ('orientation', 'magnetic'): pass elif p.is_control: pass # already added elif p.length_control is not None: table = dependent.get(p.length_control, []) if table: # look up length from incoming parameters table_length = int(pars.get(p.length_control, p.length)) del dependent[p.length_control] # first entry seen for k in range(1, table_length+1): for entry in table: append_group(entry.id+str(k)) else: pass # already processed all entries elif p.length > 1: table = fixed_length.get(p.length, []) if table: table_length = p.length del fixed_length[p.length] for k in range(1, table_length+1): for entry in table: append_group(entry.id+str(k)) else: pass # already processed all entries else: append_group(p.id) if is2d and 'up:angle' in expanded_pars: result.extend([ expanded_pars['up:frac_i'], expanded_pars['up:frac_f'], expanded_pars['up:angle'], ]) return result def isstr(x): # type: (Any) -> bool """ Return True if the object is a string. """ # TODO: 2-3 compatible tests for str, including unicode strings return isinstance(x, str) def _find_source_lines(model_info, kernel_module): """ Identify the location of the C source inside the model definition file. This code runs through the source of the kernel module looking for lines that start with 'Iq', 'Iqxy' or 'form_volume'. Clearly there are all sorts of reasons why this might not work (e.g., code commented out in a triple-quoted line block, code built using string concatenation, or code defined in the branch of an 'if' block), but it should work properly in the 95% case, and getting the incorrect line number will be harmless. """ # Check if we need line numbers at all if callable(model_info.Iq): return None if (model_info.Iq is None and model_info.Iqxy is None and model_info.Imagnetic is None and model_info.form_volume is None): return # find the defintion lines for the different code blocks try: source = inspect.getsource(kernel_module) except IOError: return for k, v in enumerate(source.split('\n')): if v.startswith('Imagnetic'): model_info._Imagnetic_line = k+1 elif v.startswith('Iqxy'): model_info._Iqxy_line = k+1 elif v.startswith('Iq'): model_info._Iq_line = k+1 elif v.startswith('form_volume'): model_info._form_volume_line = k+1 def make_model_info(kernel_module): # type: (module) -> ModelInfo """ Extract the model definition from the loaded kernel module. Fill in default values for parts of the module that are not provided. Note: vectorized Iq and Iqxy functions will be created for python models when the model is first called, not when the model is loaded. """ if hasattr(kernel_module, "model_info"): # Custom sum/multi models return kernel_module.model_info info = ModelInfo() #print("make parameter table", kernel_module.parameters) parameters = make_parameter_table(getattr(kernel_module, 'parameters', [])) demo = expand_pars(parameters, getattr(kernel_module, 'demo', None)) filename = abspath(kernel_module.__file__).replace('.pyc', '.py') kernel_id = splitext(basename(filename))[0] name = getattr(kernel_module, 'name', None) if name is None: name = " ".join(w.capitalize() for w in kernel_id.split('_')) info.id = kernel_id # string used to load the kernel info.filename = filename info.name = name info.title = getattr(kernel_module, 'title', name+" model") info.description = getattr(kernel_module, 'description', 'no description') info.parameters = parameters info.demo = demo info.composition = None info.docs = kernel_module.__doc__ info.category = getattr(kernel_module, 'category', None) info.structure_factor = getattr(kernel_module, 'structure_factor', False) info.profile_axes = getattr(kernel_module, 'profile_axes', ['x', 'y']) info.source = getattr(kernel_module, 'source', []) # TODO: check the structure of the tests info.tests = getattr(kernel_module, 'tests', []) info.ER = getattr(kernel_module, 'ER', None) # type: ignore info.VR = getattr(kernel_module, 'VR', None) # type: ignore info.form_volume = getattr(kernel_module, 'form_volume', None) # type: ignore info.Iq = getattr(kernel_module, 'Iq', None) # type: ignore info.Iqxy = getattr(kernel_module, 'Iqxy', None) # type: ignore info.Imagnetic = getattr(kernel_module, 'Imagnetic', None) # type: ignore info.profile = getattr(kernel_module, 'profile', None) # type: ignore info.sesans = getattr(kernel_module, 'sesans', None) # type: ignore # Default single and opencl to True for C models. Python models have callable Iq. info.opencl = getattr(kernel_module, 'opencl', not callable(info.Iq)) info.single = getattr(kernel_module, 'single', not callable(info.Iq)) info.random = getattr(kernel_module, 'random', None) # multiplicity info control_pars = [p.id for p in parameters.kernel_parameters if p.is_control] default_control = control_pars[0] if control_pars else None info.control = getattr(kernel_module, 'control', default_control) info.hidden = getattr(kernel_module, 'hidden', None) # type: ignore _find_source_lines(info, kernel_module) return info class ModelInfo(object): """ Interpret the model definition file, categorizing the parameters. The module can be loaded with a normal python import statement if you know which module you need, or with __import__('sasmodels.model.'+name) if the name is in a string. The structure should be mostly static, other than the delayed definition of *Iq* and *Iqxy* if they need to be defined. """ #: Full path to the file defining the kernel, if any. filename = None # type: Optional[str] #: Id of the kernel used to load it from the filesystem. id = None # type: str #: Display name of the model, which defaults to the model id but with #: capitalization of the parts so for example core_shell defaults to #: "Core Shell". name = None # type: str #: Short description of the model. title = None # type: str #: Long description of the model. description = None # type: str #: Model parameter table. Parameters are defined using a list of parameter #: definitions, each of which is contains parameter name, units, #: default value, limits, type and description. See :class:`Parameter` #: for details on the individual parameters. The parameters are gathered #: into a :class:`ParameterTable`, which provides various views into the #: parameter list. parameters = None # type: ParameterTable #: Demo parameters as a *parameter:value* map used as the default values #: for :mod:`compare`. Any parameters not set in *demo* will use the #: defaults from the parameter table. That means no polydispersity, and #: in the case of multiplicity models, a minimal model with no interesting #: scattering. demo = None # type: Dict[str, float] #: Composition is None if this is an independent model, or it is a #: tuple with comoposition type ('product' or 'misture') and a list of #: :class:`ModelInfo` blocks for the composed objects. This allows us #: to rebuild a complete mixture or product model from the info block. #: *composition* is not given in the model definition file, but instead #: arises when the model is constructed using names such as #: *sphere*hardsphere* or *cylinder+sphere*. composition = None # type: Optional[Tuple[str, List[ModelInfo]]] #: Name of the control parameter for a variant model such as :ref:`rpa`. #: The *control* parameter should appear in the parameter table, with #: limits defined as *[CASES]*, for case names such as #: *CASES = ["diblock copolymer", "triblock copolymer", ...]*. #: This should give *limits=[[case1, case2, ...]]*, but the #: model loader translates this to *limits=[0, len(CASES)-1]*, and adds #: *choices=CASES* to the :class:`Parameter` definition. Note that #: models can use a list of cases as a parameter without it being a #: control parameter. Either way, the parameter is sent to the model #: evaluator as *float(choice_num)*, where choices are numbered from 0. #: See also :attr:`hidden`. control = None # type: str #: Different variants require different parameters. In order to show #: just the parameters needed for the variant selected by :attr:`control`, #: you should provide a function *hidden(control) -> set(['a', 'b', ...])* #: indicating which parameters need to be hidden. For multiplicity #: models, you need to use the complete name of the parameter, including #: its number. So for example, if variant "a" uses only *sld1* and *sld2*, #: then *sld3*, *sld4* and *sld5* of multiplicity parameter *sld[5]* #: should be in the hidden set. hidden = None # type: Optional[Callable[[int], Set[str]]] #: Doc string from the top of the model file. This should be formatted #: using ReStructuredText format, with latex markup in ".. math" #: environments, or in dollar signs. This will be automatically #: extracted to a .rst file by :func:`generate.make_docs`, then #: converted to HTML or PDF by Sphinx. docs = None # type: str #: Location of the model description in the documentation. This takes the #: form of "section" or "section:subsection". So for example, #: :ref:`porod` uses *category="shape-independent"* so it is in the #: :ref:`shape-independent` section whereas #: :ref:`capped-cylinder` uses: *category="shape:cylinder"*, which puts #: it in the :ref:`shape-cylinder` section. category = None # type: Optional[str] #: True if the model can be computed accurately with single precision. #: This is True by default, but models such as :ref:`bcc-paracrystal` set #: it to False because they require double precision calculations. single = None # type: bool #: True if the model can be run as an opencl model. If for some reason #: the model cannot be run in opencl (e.g., because the model passes #: functions by reference), then set this to false. opencl = None # type: bool #: True if the model is a structure factor used to model the interaction #: between form factor models. This will default to False if it is not #: provided in the file. structure_factor = None # type: bool #: List of C source files used to define the model. The source files #: should define the *Iq* function, and possibly *Iqxy*, though a default #: *Iqxy = Iq(sqrt(qx**2+qy**2)* will be created if no *Iqxy* is provided. #: Files containing the most basic functions must appear first in the list, #: followed by the files that use those functions. Form factors are #: indicated by providing a :attr:`ER` function. source = None # type: List[str] #: The set of tests that must pass. The format of the tests is described #: in :mod:`model_test`. tests = None # type: List[TestCondition] #: Returns the effective radius of the model given its volume parameters. #: The presence of *ER* indicates that the model is a form factor model #: that may be used together with a structure factor to form an implicit #: multiplication model. #: #: The parameters to the *ER* function must be marked with type *volume*. #: in the parameter table. They will appear in the same order as they #: do in the table. The values passed to *ER* will be vectors, with one #: value for each polydispersity condition. For example, if the model #: is polydisperse over both length and radius, then both length and #: radius will have the same number of values in the vector, with one #: value for each *length X radius*. If only *radius* is polydisperse, #: then the value for *length* will be repeated once for each value of #: *radius*. The *ER* function should return one effective radius for #: each parameter set. Multiplicity parameters will be received as #: arrays, with one row per polydispersity condition. ER = None # type: Optional[Callable[[np.ndarray], np.ndarray]] #: Returns the occupied volume and the total volume for each parameter set. #: See :attr:`ER` for details on the parameters. VR = None # type: Optional[Callable[[np.ndarray], Tuple[np.ndarray, np.ndarray]]] #: Returns the form volume for python-based models. Form volume is needed #: for volume normalization in the polydispersity integral. If no #: parameters are *volume* parameters, then form volume is not needed. #: For C-based models, (with :attr:`sources` defined, or with :attr:`Iq` #: defined using a string containing C code), form_volume must also be #: C code, either defined as a string, or in the sources. form_volume = None # type: Union[None, str, Callable[[np.ndarray], float]] #: Returns *I(q, a, b, ...)* for parameters *a*, *b*, etc. defined #: by the parameter table. *Iq* can be defined as a python function, or #: as a C function. If it is defined in C, then set *Iq* to the body of #: the C function, including the return statement. This function takes #: values for *q* and each of the parameters as separate *double* values #: (which may be converted to float or long double by sasmodels). All #: source code files listed in :attr:`sources` will be loaded before the #: *Iq* function is defined. If *Iq* is not present, then sources should #: define *static double Iq(double q, double a, double b, ...)* which #: will return *I(q, a, b, ...)*. Multiplicity parameters are sent as #: pointers to doubles. Constants in floating point expressions should #: include the decimal point. See :mod:`generate` for more details. Iq = None # type: Union[None, str, Callable[[np.ndarray], np.ndarray]] #: Returns *I(qx, qy, a, b, ...)*. The interface follows :attr:`Iq`. Iqxy = None # type: Union[None, str, Callable[[np.ndarray], np.ndarray]] #: Returns *I(qx, qy, a, b, ...)*. The interface follows :attr:`Iq`. Imagnetic = None # type: Union[None, str, Callable[[np.ndarray], np.ndarray]] #: Returns a model profile curve *x, y*. If *profile* is defined, this #: curve will appear in response to the *Show* button in SasView. Use #: :attr:`profile_axes` to set the axis labels. Note that *y* values #: will be scaled by 1e6 before plotting. profile = None # type: Optional[Callable[[np.ndarray], None]] #: Axis labels for the :attr:`profile` plot. The default is *['x', 'y']*. #: Only the *x* component is used for now. profile_axes = None # type: Tuple[str, str] #: Returns *sesans(z, a, b, ...)* for models which can directly compute #: the SESANS correlation function. Note: not currently implemented. sesans = None # type: Optional[Callable[[np.ndarray], np.ndarray]] # line numbers within the python file for bits of C source, if defined # NB: some compilers fail with a "#line 0" directive, so default to 1. _Imagnetic_line = 1 _Iqxy_line = 1 _Iq_line = 1 _form_volume_line = 1 def __init__(self): # type: () -> None pass def get_hidden_parameters(self, control): """ Returns the set of hidden parameters for the model. *control* is the value of the control parameter. Note that multiplicity models have an implicit control parameter, which is the parameter that controls the multiplicity. """ if self.hidden is not None: hidden = self.hidden(control) else: controls = [p for p in self.parameters.kernel_parameters if p.is_control] if len(controls) != 1: raise ValueError("more than one control parameter") hidden = set(p.id+str(k) for p in self.parameters.kernel_parameters for k in range(control+1, p.length+1) if p.length > 1) return hidden sasmodels/sasmodels/models/000077500000000000000000000000001317715334700163405ustar00rootroot00000000000000sasmodels/sasmodels/models/__init__.py000066400000000000000000000000351317715334700204470ustar00rootroot00000000000000""" 1D Modeling for SAS """ sasmodels/sasmodels/models/_spherepy.py000066400000000000000000000076601317715334700207210ustar00rootroot00000000000000r""" For information about polarised and magnetic scattering, see the :doc:`magnetic help <../sasgui/perspectives/fitting/mag_help>` documentation. Definition ---------- The 1D scattering intensity is calculated in the following way (Guinier, 1955) .. math:: I(q) = \frac{\text{scale}}{V} \cdot \left[ 3V(\Delta\rho) \cdot \frac{\sin(qr) - qr\cos(qr))}{(qr)^3} \right]^2 + \text{background} where *scale* is a volume fraction, $V$ is the volume of the scatterer, $r$ is the radius of the sphere, *background* is the background level and *sld* and *sld_solvent* are the scattering length densities (SLDs) of the scatterer and the solvent respectively. Note that if your data is in absolute scale, the *scale* should represent the volume fraction (which is unitless) if you have a good fit. If not, it should represent the volume fraction times a factor (by which your data might need to be rescaled). The 2D scattering intensity is the same as above, regardless of the orientation of $\vec q$. Validation ---------- Validation of our code was done by comparing the output of the 1D model to the output of the software provided by the NIST (Kline, 2006). References ---------- A Guinier and G. Fournet, *Small-Angle Scattering of X-Rays*, John Wiley and Sons, New York, (1955) *2013/09/09 and 2014/01/06 - Description reviewed by S King and P Parker.* """ import numpy as np from numpy import pi, inf, sin, cos, sqrt, log name = " _sphere (python)" title = "PAK testing ideas for Spheres with uniform scattering length density" description = """\ P(q)=(scale/V)*[3V(sld-sld_solvent)*(sin(qr)-qr cos(qr)) /(qr)^3]^2 + background r: radius of sphere V: The volume of the scatter sld: the SLD of the sphere sld_solvent: the SLD of the solvent """ category = "shape:sphere" # ["name", "units", default, [lower, upper], "type","description"], parameters = [["sld", "1e-6/Ang^2", 1, [-inf, inf], "", "Layer scattering length density"], ["sld_solvent", "1e-6/Ang^2", 6, [-inf, inf], "", "Solvent scattering length density"], ["radius", "Ang", 50, [0, inf], "volume", "Sphere radius"], ] def form_volume(radius): return 1.333333333333333 * pi * radius ** 3 def Iq(q, sld, sld_solvent, radius): #print "q",q #print "sld,r",sld,sld_solvent,radius qr = q * radius sn, cn = sin(qr), cos(qr) ## The natural expression for the bessel function is the following: ## bes = 3 * (sn-qr*cn)/qr**3 if qr>0 else 1 ## however, to support vector q values we need to handle the conditional ## as a vector, which we do by first evaluating the full expression ## everywhere, then fixing it up where it is broken. We should probably ## set numpy to ignore the 0/0 error before we do though... bes = 3 * (sn - qr * cn) / qr ** 3 # may be 0/0 but we fix that next line bes[qr == 0] = 1 fq = bes * (sld - sld_solvent) * form_volume(radius) return 1.0e-4 * fq ** 2 Iq.vectorized = True # Iq accepts an array of q values def Iqxy(qx, qy, sld, sld_solvent, radius): return Iq(sqrt(qx ** 2 + qy ** 2), sld, sld_solvent, radius) Iqxy.vectorized = True # Iqxy accepts arrays of qx, qy values def sesans(z, sld, sld_solvent, radius): """ Calculate SESANS-correlation function for a solid sphere. Wim Bouwman after formulae Timofei Kruglov J.Appl.Cryst. 2003 article """ d = z / radius g = np.zeros_like(z) g[d == 0] = 1. low = ((d > 0) & (d < 2)) dlow = d[low] dlow2 = dlow ** 2 g[low] = sqrt(1 - dlow2 / 4.) * (1 + dlow2 / 8.) + dlow2 / 2.*(1 - dlow2 / 16.) * log(dlow / (2. + sqrt(4. - dlow2))) return g sesans.vectorized = True # sesans accepts an array of z values def ER(radius): return radius # VR defaults to 1.0 demo = dict(scale=1, background=0, sld=6, sld_solvent=1, radius=120, radius_pd=.2, radius_pd_n=45) sasmodels/sasmodels/models/adsorbed_layer.py000066400000000000000000000115411317715334700216730ustar00rootroot00000000000000r""" Definition ---------- This model describes the scattering from a layer of surfactant or polymer adsorbed on large, smooth, notionally spherical particles under the conditions that (i) the particles (cores) are contrast-matched to the dispersion medium, (ii) $S(Q) \sim 1$ (ie, the particle volume fraction is dilute), (iii) the particle radius is >> layer thickness (ie, the interface is locally flat), and (iv) scattering from excess unadsorbed adsorbate in the bulk medium is absent or has been corrected for. Unlike many other core-shell models, this model does not assume any form for the density distribution of the adsorbed species normal to the interface (cf, a core-shell model normally assumes the density distribution to be a homogeneous step-function). For comparison, if the thickness of a (traditional core-shell like) step function distribution is $t$, the second moment about the mean of the density distribution (ie, the distance of the centre-of-mass of the distribution from the interface), $\sigma = \sqrt{t^2/12}$. .. math:: I(q) = \text{scale} \cdot (\rho_\text{poly}-\rho_\text{solvent})^2 \left[ \frac{6\pi\phi_\text{core}}{Q^2} \frac{\Gamma^2}{\delta_\text{poly}^2R_\text{core}} \exp(-Q^2\sigma^2) \right] + \text{background} where *scale* is a scale factor, $\rho_\text{poly}$ is the sld of the polymer (or surfactant) layer, $\rho_\text{solv}$ is the sld of the solvent/medium and cores, $\phi_\text{core}$ is the volume fraction of the core particles, $\delta_\text{poly}$ is the bulk density of the polymer, $\Gamma$ is the adsorbed amount, and $\sigma$ is the second moment of the thickness distribution. Note that all parameters except $\sigma$ are correlated so fitting more than one of these parameters will generally fail. Also note that unlike other shape models, no volume normalization is applied to this model (the calculation is exact). The code for this model is based originally on a a fortran implementation by Steve King at ISIS in the SANDRA package c. 1990. References ---------- .. [#] S King, P Griffiths, J Hone, and T Cosgrove, *SANS from Adsorbed Polymer Layers*, *Macromol. Symp.*, 190 (2002) 33-42. Authorship and Verification ---------------------------- * **Author:** Jae-Hi Cho **Date:** pre 2010 * **Last Modified by:** Paul Kienzle **Date:** April 14, 2016 * **Last Reviewed by:** Steve King **Date:** March 18, 2016 """ from numpy import inf, pi, exp, errstate name = "adsorbed_layer" title = "Scattering from an adsorbed layer on particles" description = """ Evaluates the scattering from large particles with an adsorbed layer of surfactant or polymer, independent of the form of the density distribution. """ category = "shape:sphere" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type", "description"], parameters = [ ["second_moment", "Ang", 23.0, [0.0, inf], "", "Second moment of polymer distribution"], ["adsorbed_amount", "mg/m^2", 1.9, [0.0, inf], "", "Adsorbed amount of polymer"], ["density_shell", "g/cm^3", 0.7, [0.0, inf], "", "Bulk density of polymer in the shell"], ["radius", "Ang", 500.0, [0.0, inf], "", "Core particle radius"], ["volfraction", "None", 0.14, [0.0, inf], "", "Core particle volume fraction"], ["sld_shell", "1e-6/Ang^2", 1.5, [-inf, inf], "sld", "Polymer shell SLD"], ["sld_solvent", "1e-6/Ang^2", 6.3, [-inf, inf], "sld", "Solvent SLD"], ] # pylint: enable=bad-whitespace, line-too-long # NB: Scale and Background are implicit parameters on every model def Iq(q, second_moment, adsorbed_amount, density_shell, radius, volfraction, sld_shell, sld_solvent): with errstate(divide='ignore'): aa = ((sld_shell - sld_solvent)/density_shell * adsorbed_amount) / q bb = q * second_moment #scale by 10^-2 for units conversion to cm^-1 inten = 6.0e-02 * pi * volfraction * aa**2 * exp(-bb**2) / radius return inten Iq.vectorized = True # Iq accepts an array of q values def random(): # only care about the value of second_moment: # curve = scale * e**(-second_moment^2 q^2)/q^2 # scale = 6 pi/100 (contrast/density*absorbed_amount)^2 * Vf/radius # the remaining parameters can be randomly generated from zero to # twice the default value as done by default in compare.py import numpy as np pars = dict( scale=1, second_moment=10**np.random.uniform(1, 3), ) return pars # unit test values taken from SasView 3.1.2 tests = [ [{'scale': 1.0, 'second_moment': 23.0, 'adsorbed_amount': 1.9, 'density_shell': 0.7, 'radius': 500.0, 'volfraction': 0.14, 'sld_shell': 1.5, 'sld_solvent': 6.3, 'background': 0.0}, [0.0106939, 0.1], [73.741, 4.51684e-3]], ] # 2016-03-16 SMK converted from sasview, checked vs SANDRA # 2016-03-18 RKH some edits & renaming # 2016-04-14 PAK reformatting sasmodels/sasmodels/models/barbell.c000066400000000000000000000077101317715334700201140ustar00rootroot00000000000000double form_volume(double radius_bell, double radius, double length); double Iq(double q, double sld, double solvent_sld, double radius_bell, double radius, double length); double Iqxy(double qx, double qy, double sld, double solvent_sld, double radius_bell, double radius, double length, double theta, double phi); #define INVALID(v) (v.radius_bell < v.radius) //barbell kernel - same as dumbell static double _bell_kernel(double q, double h, double radius_bell, double half_length, double sin_alpha, double cos_alpha) { // translate a point in [-1,1] to a point in [lower,upper] const double upper = 1.0; const double lower = h/radius_bell; const double zm = 0.5*(upper-lower); const double zb = 0.5*(upper+lower); // cos term in integral is: // cos (q (R t - h + L/2) cos(alpha)) // so turn it into: // cos (m t + b) // where: // m = q R cos(alpha) // b = q(L/2-h) cos(alpha) const double m = q*radius_bell*cos_alpha; // cos argument slope const double b = q*(half_length-h)*cos_alpha; // cos argument intercept const double qrst = q*radius_bell*sin_alpha; // Q*R*sin(theta) double total = 0.0; for (int i = 0; i < 76; i++){ const double t = Gauss76Z[i]*zm + zb; const double radical = 1.0 - t*t; const double bj = sas_2J1x_x(qrst*sqrt(radical)); const double Fq = cos(m*t + b) * radical * bj; total += Gauss76Wt[i] * Fq; } // translate dx in [-1,1] to dx in [lower,upper] const double integral = total*zm; const double bell_fq = 2.0*M_PI*cube(radius_bell)*integral; return bell_fq; } static double _fq(double q, double h, double radius_bell, double radius, double half_length, double sin_alpha, double cos_alpha) { const double bell_fq = _bell_kernel(q, h, radius_bell, half_length, sin_alpha, cos_alpha); const double bj = sas_2J1x_x(q*radius*sin_alpha); const double si = sas_sinx_x(q*half_length*cos_alpha); const double cyl_fq = 2.0*M_PI*radius*radius*half_length*bj*si; const double Aq = bell_fq + cyl_fq; return Aq; } double form_volume(double radius_bell, double radius, double length) { // bell radius should never be less than radius when this is called const double hdist = sqrt(square(radius_bell) - square(radius)); const double p1 = 2.0/3.0*cube(radius_bell); const double p2 = square(radius_bell)*hdist; const double p3 = cube(hdist)/3.0; return M_PI*square(radius)*length + 2.0*M_PI*(p1+p2-p3); } double Iq(double q, double sld, double solvent_sld, double radius_bell, double radius, double length) { const double h = -sqrt(radius_bell*radius_bell - radius*radius); const double half_length = 0.5*length; // translate a point in [-1,1] to a point in [0, pi/2] const double zm = M_PI_4; const double zb = M_PI_4; double total = 0.0; for (int i = 0; i < 76; i++){ const double alpha= Gauss76Z[i]*zm + zb; double sin_alpha, cos_alpha; // slots to hold sincos function output SINCOS(alpha, sin_alpha, cos_alpha); const double Aq = _fq(q, h, radius_bell, radius, half_length, sin_alpha, cos_alpha); total += Gauss76Wt[i] * Aq * Aq * sin_alpha; } // translate dx in [-1,1] to dx in [lower,upper] const double form = total*zm; //Contrast const double s = (sld - solvent_sld); return 1.0e-4 * s * s * form; } double Iqxy(double qx, double qy, double sld, double solvent_sld, double radius_bell, double radius, double length, double theta, double phi) { double q, sin_alpha, cos_alpha; ORIENT_SYMMETRIC(qx, qy, theta, phi, q, sin_alpha, cos_alpha); const double h = -sqrt(square(radius_bell) - square(radius)); const double Aq = _fq(q, h, radius_bell, radius, 0.5*length, sin_alpha, cos_alpha); // Multiply by contrast^2 and convert to cm-1 const double s = (sld - solvent_sld); return 1.0e-4 * square(s * Aq); } sasmodels/sasmodels/models/barbell.py000066400000000000000000000133711317715334700203220ustar00rootroot00000000000000r""" Definition ---------- Calculates the scattering from a barbell-shaped cylinder. Like :ref:`capped-cylinder`, this is a sphereocylinder with spherical end caps that have a radius larger than that of the cylinder, but with the center of the end cap radius lying outside of the cylinder. See the diagram for the details of the geometry and restrictions on parameter values. .. figure:: img/barbell_geometry.jpg Barbell geometry, where $r$ is *radius*, $R$ is *radius_bell* and $L$ is *length*. Since the end cap radius $R \geq r$ and by definition for this geometry $h < 0$, $h$ is then defined by $r$ and $R$ as $h = - \sqrt{R^2 - r^2}$ The scattered intensity $I(q)$ is calculated as .. math:: I(q) = \frac{\Delta \rho^2}{V} \left where the amplitude $A(q,\alpha)$ with the rod axis at angle $\alpha$ to $q$ is given as .. math:: A(q) =&\ \pi r^2L \frac{\sin\left(\tfrac12 qL\cos\alpha\right)} {\tfrac12 qL\cos\alpha} \frac{2 J_1(qr\sin\alpha)}{qr\sin\alpha} \\ &\ + 4 \pi R^3 \int_{-h/R}^1 dt \cos\left[ q\cos\alpha \left(Rt + h + {\tfrac12} L\right)\right] \times (1-t^2) \frac{J_1\left[qR\sin\alpha \left(1-t^2\right)^{1/2}\right]} {qR\sin\alpha \left(1-t^2\right)^{1/2}} The $\left<\ldots\right>$ brackets denote an average of the structure over all orientations. $\left$ is then the form factor, $P(q)$. The scale factor is equivalent to the volume fraction of cylinders, each of volume, $V$. Contrast $\Delta\rho$ is the difference of scattering length densities of the cylinder and the surrounding solvent. The volume of the barbell is .. math:: V = \pi r_c^2 L + 2\pi\left(\tfrac23R^3 + R^2h-\tfrac13h^3\right) and its radius of gyration is .. math:: R_g^2 =&\ \left[ \tfrac{12}{5}R^5 + R^4\left(6h+\tfrac32 L\right) + R^2\left(4h^2 + L^2 + 4Lh\right) + R^2\left(3Lh^2 + \tfrac32 L^2h\right) \right. \\ &\ \left. + \tfrac25 h^5 - \tfrac12 Lh^4 - \tfrac12 L^2h^3 + \tfrac14 L^3r^2 + \tfrac32 Lr^4 \right] \left( 4R^3 6R^2h - 2h^3 + 3r^2L \right)^{-1} .. note:: The requirement that $R \geq r$ is not enforced in the model! It is up to you to restrict this during analysis. The 2D scattering intensity is calculated similar to the 2D cylinder model. .. figure:: img/cylinder_angle_definition.png Definition of the angles for oriented 2D barbells. References ---------- .. [#] H Kaya, *J. Appl. Cryst.*, 37 (2004) 37 223-230 .. [#] H Kaya and N R deSouza, *J. Appl. Cryst.*, 37 (2004) 508-509 (addenda and errata) Authorship and Verification ---------------------------- * **Author:** NIST IGOR/DANSE **Date:** pre 2010 * **Last Modified by:** Paul Butler **Date:** March 20, 2016 * **Last Reviewed by:** Richard Heenan **Date:** January 4, 2017 """ from numpy import inf, sin, cos, pi name = "barbell" title = "Cylinder with spherical end caps" description = """ Calculates the scattering from a barbell-shaped cylinder. That is a sphereocylinder with spherical end caps that have a radius larger than that of the cylinder and the center of the end cap radius lies outside of the cylinder. Note: As the length of cylinder(bar) -->0,it becomes a dumbbell. And when rad_bar = rad_bell, it is a spherocylinder. It must be that rad_bar <(=) rad_bell. """ category = "shape:cylinder" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type","description"], parameters = [["sld", "1e-6/Ang^2", 4, [-inf, inf], "sld", "Barbell scattering length density"], ["sld_solvent", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Solvent scattering length density"], ["radius_bell", "Ang", 40, [0, inf], "volume", "Spherical bell radius"], ["radius", "Ang", 20, [0, inf], "volume", "Cylindrical bar radius"], ["length", "Ang", 400, [0, inf], "volume", "Cylinder bar length"], ["theta", "degrees", 60, [-360, 360], "orientation", "Barbell axis to beam angle"], ["phi", "degrees", 60, [-360, 360], "orientation", "Rotation about beam"], ] # pylint: enable=bad-whitespace, line-too-long source = ["lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c", "barbell.c"] def random(): import numpy as np # TODO: increase volume range once problem with bell radius is fixed # The issue is that bell radii of more than about 200 fail at high q V = 10**np.random.uniform(7, 9) bar_volume = 10**np.random.uniform(-4, -1)*V bell_volume = V - bar_volume bell_radius = (bell_volume/6)**0.3333 # approximate min_bar = bar_volume/np.pi/bell_radius**2 bar_length = 10**np.random.uniform(0, 3)*min_bar bar_radius = np.sqrt(bar_volume/bar_length/np.pi) if bar_radius > bell_radius: bell_radius, bar_radius = bar_radius, bell_radius pars = dict( #background=0, radius_bell=bell_radius, radius=bar_radius, length=bar_length, ) return pars # parameters for demo demo = dict(scale=1, background=0, sld=6, sld_solvent=1, radius_bell=40, radius=20, length=400, theta=60, phi=60, radius_pd=.2, radius_pd_n=5, length_pd=.2, length_pd_n=5, theta_pd=15, theta_pd_n=0, phi_pd=15, phi_pd_n=0, ) q = 0.1 # april 6 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! qx = q*cos(pi/6.0) qy = q*sin(pi/6.0) tests = [[{}, 0.075, 25.5691260532], [{'theta':80., 'phi':10.}, (qx, qy), 3.04233067789], ] del qx, qy # not necessary to delete, but cleanersasmodels/sasmodels/models/bcc_paracrystal.c000066400000000000000000000074551317715334700216530ustar00rootroot00000000000000double form_volume(double radius); double Iq(double q,double dnn,double d_factor, double radius,double sld, double solvent_sld); double Iqxy(double qx, double qy, double dnn, double d_factor, double radius,double sld, double solvent_sld, double theta, double phi, double psi); double _BCC_Integrand(double q, double dnn, double d_factor, double theta, double phi); double _BCCeval(double Theta, double Phi, double temp1, double temp3); double _sphereform(double q, double radius, double sld, double solvent_sld); double _BCC_Integrand(double q, double dnn, double d_factor, double theta, double phi) { const double Da = d_factor*dnn; const double temp1 = q*q*Da*Da; const double temp3 = q*dnn; double retVal = _BCCeval(theta,phi,temp1,temp3)/(4.0*M_PI); return(retVal); } double _BCCeval(double Theta, double Phi, double temp1, double temp3) { double result; double sin_theta,cos_theta,sin_phi,cos_phi; SINCOS(Theta, sin_theta, cos_theta); SINCOS(Phi, sin_phi, cos_phi); const double temp6 = sin_theta; const double temp7 = sin_theta*cos_phi + sin_theta*sin_phi + cos_theta; const double temp8 = -sin_theta*cos_phi - sin_theta*sin_phi + cos_theta; const double temp9 = -sin_theta*cos_phi + sin_theta*sin_phi - cos_theta; const double temp10 = exp((-1.0/8.0)*temp1*(temp7*temp7 + temp8*temp8 + temp9*temp9)); result = cube(1.0 - (temp10*temp10))*temp6 / ( (1.0 - 2.0*temp10*cos(0.5*temp3*temp7) + temp10*temp10) * (1.0 - 2.0*temp10*cos(0.5*temp3*temp8) + temp10*temp10) * (1.0 - 2.0*temp10*cos(0.5*temp3*temp9) + temp10*temp10)); return (result); } double form_volume(double radius){ return sphere_volume(radius); } double Iq(double q, double dnn, double d_factor, double radius, double sld, double solvent_sld){ //Volume fraction calculated from lattice symmetry and sphere radius const double s1 = dnn/sqrt(0.75); const double latticescale = 2.0*sphere_volume(radius/s1); const double va = 0.0; const double vb = 2.0*M_PI; const double vaj = 0.0; const double vbj = M_PI; double summ = 0.0; double answer = 0.0; for(int i=0; i<150; i++) { //setup inner integral over the ellipsoidal cross-section double summj=0.0; const double zphi = ( Gauss150Z[i]*(vb-va) + va + vb )/2.0; //the outer dummy is phi for(int j=0;j<150;j++) { //20 gauss points for the inner integral double ztheta = ( Gauss150Z[j]*(vbj-vaj) + vaj + vbj )/2.0; //the inner dummy is theta double yyy = Gauss150Wt[j] * _BCC_Integrand(q,dnn,d_factor,ztheta,zphi); summj += yyy; } //now calculate the value of the inner integral double answer = (vbj-vaj)/2.0*summj; //now calculate outer integral summ = summ+(Gauss150Wt[i] * answer); } //final scaling is done at the end of the function, after the NT_FP64 case answer = (vb-va)/2.0*summ; answer = answer*sphere_form(q,radius,sld,solvent_sld)*latticescale; return answer; } double Iqxy(double qx, double qy, double dnn, double d_factor, double radius, double sld, double solvent_sld, double theta, double phi, double psi) { double q, zhat, yhat, xhat; ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); const double a1 = +xhat - zhat + yhat; const double a2 = +xhat + zhat - yhat; const double a3 = -xhat + zhat + yhat; const double qd = 0.5*q*dnn; const double arg = 0.5*square(qd*d_factor)*(a1*a1 + a2*a2 + a3*a3); const double tanh_qd = tanh(arg); const double cosh_qd = cosh(arg); const double Zq = tanh_qd/(1. - cos(qd*a1)/cosh_qd) * tanh_qd/(1. - cos(qd*a2)/cosh_qd) * tanh_qd/(1. - cos(qd*a3)/cosh_qd); const double Fq = sphere_form(q,radius,sld,solvent_sld)*Zq; //the occupied volume of the lattice const double lattice_scale = 2.0*sphere_volume(sqrt(0.75)*radius/dnn); return lattice_scale * Fq; }sasmodels/sasmodels/models/bcc_paracrystal.py000066400000000000000000000143501317715334700220510ustar00rootroot00000000000000r""" Definition ---------- Calculates the scattering from a **body-centered cubic lattice** with paracrystalline distortion. Thermal vibrations are considered to be negligible, and the size of the paracrystal is infinitely large. Paracrystalline distortion is assumed to be isotropic and characterized by a Gaussian distribution. The scattering intensity $I(q)$ is calculated as .. math:: I(q) = \frac{\text{scale}}{V_p} V_\text{lattice} P(q) Z(q) where *scale* is the volume fraction of spheres, $V_p$ is the volume of the primary particle, $V_\text{lattice}$ is a volume correction for the crystal structure, $P(q)$ is the form factor of the sphere (normalized), and $Z(q)$ is the paracrystalline structure factor for a body-centered cubic structure. Equation (1) of the 1990 reference\ [#CIT1990]_ is used to calculate $Z(q)$, using equations (29)-(31) from the 1987 paper\ [#CIT1987]_ for $Z1$, $Z2$, and $Z3$. The lattice correction (the occupied volume of the lattice) for a body-centered cubic structure of particles of radius $R$ and nearest neighbor separation $D$ is .. math:: V_\text{lattice} = \frac{16\pi}{3} \frac{R^3}{\left(D\sqrt{2}\right)^3} The distortion factor (one standard deviation) of the paracrystal is included in the calculation of $Z(q)$ .. math:: \Delta a = g D where $g$ is a fractional distortion based on the nearest neighbor distance. .. figure:: img/bcc_geometry.jpg Body-centered cubic lattice. For a crystal, diffraction peaks appear at reduced q-values given by .. math:: \frac{qD}{2\pi} = \sqrt{h^2 + k^2 + l^2} where for a body-centered cubic lattice, only reflections where $(h + k + l) = \text{even}$ are allowed and reflections where $(h + k + l) = \text{odd}$ are forbidden. Thus the peak positions correspond to (just the first 5) .. math:: \begin{array}{lccccc} q/q_o & 1 & \sqrt{2} & \sqrt{3} & \sqrt{4} & \sqrt{5} \\ \text{Indices} & (110) & (200) & (211) & (220) & (310) \\ \end{array} **NB**: The calculation of $Z(q)$ is a double numerical integral that must be carried out with a high density of points to properly capture the sharp peaks of the paracrystalline scattering. So be warned that the calculation is SLOW. Go get some coffee. Fitting of any experimental data must be resolution smeared for any meaningful fit. This makes a triple integral. Very, very slow. Go get lunch! This example dataset is produced using 200 data points, *qmin* = 0.001 |Ang^-1|, *qmax* = 0.1 |Ang^-1| and the above default values. The 2D (Anisotropic model) is based on the reference below where $I(q)$ is approximated for 1d scattering. Thus the scattering pattern for 2D may not be accurate. .. figure:: img/parallelepiped_angle_definition.png Orientation of the crystal with respect to the scattering plane, when $\theta = \phi = 0$ the $c$ axis is along the beam direction (the $z$ axis). References ---------- .. [#CIT1987] Hideki Matsuoka et. al. *Physical Review B*, 36 (1987) 1754-1765 (Original Paper) .. [#CIT1990] Hideki Matsuoka et. al. *Physical Review B*, 41 (1990) 3854 -3856 (Corrections to FCC and BCC lattice structure calculation) Authorship and Verification ---------------------------- * **Author:** NIST IGOR/DANSE **Date:** pre 2010 * **Last Modified by:** Paul Butler **Date:** September 29, 2016 * **Last Reviewed by:** Richard Heenan **Date:** March 21, 2016 """ from numpy import inf, pi name = "bcc_paracrystal" title = "Body-centred cubic lattic with paracrystalline distortion" description = """ Calculates the scattering from a **body-centered cubic lattice** with paracrystalline distortion. Thermal vibrations are considered to be negligible, and the size of the paracrystal is infinitely large. Paracrystalline distortion is assumed to be isotropic and characterized by a Gaussian distribution. """ category = "shape:paracrystal" #note - calculation requires double precision single = False # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type","description" ], parameters = [["dnn", "Ang", 220, [-inf, inf], "", "Nearest neighbour distance"], ["d_factor", "", 0.06, [-inf, inf], "", "Paracrystal distortion factor"], ["radius", "Ang", 40, [0, inf], "volume", "Particle radius"], ["sld", "1e-6/Ang^2", 4, [-inf, inf], "sld", "Particle scattering length density"], ["sld_solvent", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Solvent scattering length density"], ["theta", "degrees", 60, [-360, 360], "orientation", "c axis to beam angle"], ["phi", "degrees", 60, [-360, 360], "orientation", "rotation about beam"], ["psi", "degrees", 60, [-360, 360], "orientation", "rotation about c axis"] ] # pylint: enable=bad-whitespace, line-too-long source = ["lib/sas_3j1x_x.c", "lib/gauss150.c", "lib/sphere_form.c", "bcc_paracrystal.c"] def random(): import numpy as np # Define lattice spacing as a multiple of the particle radius # using the formulat a = 4 r/sqrt(3). Systems which are ordered # are probably mostly filled, so use a distribution which goes from # zero to one, but leaving 90% of them within 80% of the # maximum bcc packing. Lattice distortion values are empirically # useful between 0.01 and 0.7. Use an exponential distribution # in this range 'cuz its easy. radius = 10**np.random.uniform(1.3, 4) d_factor = 10**np.random.uniform(-2, -0.7) # sigma_d in 0.01-0.7 dnn_fraction = np.random.beta(a=10, b=1) dnn = radius*4/np.sqrt(3)/dnn_fraction pars = dict( #sld=1, sld_solvent=0, scale=1, background=1e-32, dnn=dnn, d_factor=d_factor, radius=radius, ) return pars # april 6 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! # add 2d test later q = 4.*pi/220. tests = [ [{}, [0.001, q, 0.215268], [1.46601394721, 2.85851284174, 0.00866710287078]], [{'theta': 20.0, 'phi': 30, 'psi': 40.0}, (-0.017, 0.035), 2082.20264399], [{'theta': 20.0, 'phi': 30, 'psi': 40.0}, (-0.081, 0.011), 0.436323144781], ] sasmodels/sasmodels/models/be_polyelectrolyte.py000066400000000000000000000173421317715334700226260ustar00rootroot00000000000000r""" Definition ---------- This model calculates the structure factor of a polyelectrolyte solution with the RPA expression derived by Borue and Erukhimovich\ [#Borue]_. Note however that the fitting procedure here does not follow the notation in that reference as 's' and 't' are **not** decoupled. Instead the scattering intensity $I(q)$ is calculated as .. math:: I(q) = K\frac{q^2+k^2}{4\pi L_b\alpha ^2} \frac{1}{1+r_{0}^2(q^2+k^2)(q^2-12hC_a/b^2)} + background k^2 = 4\pi L_b(2C_s + \alpha C_a) r_{0}^2 = \frac{1}{\alpha \sqrt{C_a} \left( b/\sqrt{48\pi L_b}\right)} where $K$ is the contrast factor for the polymer which is defined differently than in other models and is given in barns where $1 barn = 10^{-24} cm^2$. $K$ is defined as: .. math:: K = a^2 a = b_p - (v_p/v_s) b_s where $b_p$ and $b_s$ are sum of the scattering lengths of the atoms constituting the monomer of the polymer and the sum of the scattering lengths of the atoms constituting the solvent molecules respectively, and $v_p$ and $v_s$ are the partial molar volume of the polymer and the solvent respectively $L_b$ is the Bjerrum length(|Ang|) - **Note:** This parameter needs to be kept constant for a given solvent and temperature! $h$ is the virial parameter (|Ang^3|/mol) - **Note:** See [#Borue]_ for the correct interpretation of this parameter. It incorporates second and third virial coefficients and can be Negative. $b$ is the monomer length(|Ang|), $C_s$ is the concentration of monovalent salt(mol/L), $\alpha$ is the ionization degree (ionization degree : ratio of charged monomers to total number of monomers), $C_a$ is the polymer molar concentration(mol/L), and $background$ is the incoherent background. For 2D data the scattering intensity is calculated in the same way as 1D, where the $\vec q$ vector is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- .. [#Borue] V Y Borue, I Y Erukhimovich, *Macromolecules*, 21 (1988) 3240 .. [#] J F Joanny, L Leibler, *Journal de Physique*, 51 (1990) 545 .. [#] A Moussaid, F Schosseler, J P Munch, S Candau, *J. Journal de Physique II France*, 3 (1993) 573 .. [#] E Raphael, J F Joanny, *Europhysics Letters*, 11 (1990) 179 Authorship and Verification ---------------------------- * **Author:** NIST IGOR/DANSE **Date:** pre 2010 * **Last Modified by:** Paul Kienzle **Date:** July 24, 2016 * **Last Reviewed by:** Paul Butler and Richard Heenan **Date:** October 07, 2016 """ from numpy import inf, pi, sqrt name = "be_polyelectrolyte" title = "Polyelectrolyte with the RPA expression derived by Borue and Erukhimovich" description = """ Evaluate F(x) = K 1/(4 pi Lb (alpha)^(2)) (q^(2)+k2)/(1+(r02)^(2)) (q^(2)+k2) (q^(2)-(12 h C/b^(2))) has 3 internal parameters : The inverse Debye Length: K2 = 4 pi Lb (2 Cs+alpha C) r02 =1/alpha/Ca^(0.5) (B/(48 pi Lb)^(0.5)) Ca = 6.022136e-4 C """ category = "shape-independent" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type", "description"], parameters = [ ["contrast_factor", "barns", 10.0, [-inf, inf], "", "Contrast factor of the polymer"], ["bjerrum_length", "Ang", 7.1, [0, inf], "", "Bjerrum length"], ["virial_param", "Ang^3/mol", 12.0, [-inf, inf], "", "Virial parameter"], ["monomer_length", "Ang", 10.0, [0, inf], "", "Monomer length"], ["salt_concentration", "mol/L", 0.0, [-inf, inf], "", "Concentration of monovalent salt"], ["ionization_degree", "", 0.05, [0, inf], "", "Degree of ionization"], ["polymer_concentration", "mol/L", 0.7, [0, inf], "", "Polymer molar concentration"], ] # pylint: enable=bad-whitespace, line-too-long def Iq(q, contrast_factor=10.0, bjerrum_length=7.1, virial_param=12.0, monomer_length=10.0, salt_concentration=0.0, ionization_degree=0.05, polymer_concentration=0.7): """ :param q: Input q-value :param contrast_factor: Contrast factor of the polymer :param bjerrum_length: Bjerrum length :param virial_param: Virial parameter :param monomer_length: Monomer length :param salt_concentration: Concentration of monovalent salt :param ionization_degree: Degree of ionization :param polymer_concentration: Polymer molar concentration :return: 1-D intensity """ concentration = polymer_concentration * 6.022136e-4 k_square = 4.0 * pi * bjerrum_length * (2*salt_concentration + ionization_degree * concentration) r0_square = 1.0/ionization_degree/sqrt(concentration) * \ (monomer_length/sqrt((48.0*pi*bjerrum_length))) term1 = contrast_factor/(4.0 * pi * bjerrum_length * ionization_degree**2) * (q**2 + k_square) term2 = 1.0 + r0_square**2 * (q**2 + k_square) * \ (q**2 - (12.0 * virial_param * concentration/(monomer_length**2))) return term1/term2 Iq.vectorized = True # Iq accepts an array of q values def random(): import numpy as np # TODO: review random be_polyelectrolyte model generation pars = dict( scale=10000, #background=0, #polymer_concentration=0.7, polymer_concentration=np.random.beta(5, 3), # around 70% #salt_concentration=0.0, # keep salt concentration extremely low # and use explicit molar to match polymer concentration salt_concentration=np.random.beta(1, 100)*6.022136e-4, #contrast_factor=10.0, contrast_fact=np.random.uniform(1, 100), #bjerrum_length=7.1, bjerrum_length=np.random.uniform(1, 10), #virial_param=12.0, virial_param=np.random.uniform(-1000, 30), #monomer_length=10.0, monomer_length=10.0**(4*np.random.beta(1.5, 3)), #ionization_degree=0.05, ionization_degree=np.random.beta(1.5, 4), ) return pars demo = dict(scale=1, background=0.1, contrast_factor=10.0, bjerrum_length=7.1, virial_param=12.0, monomer_length=10.0, salt_concentration=0.0, ionization_degree=0.05, polymer_concentration=0.7) tests = [ # Accuracy tests based on content in test/utest_other_models.py [{'contrast_factor': 10.0, 'bjerrum_length': 7.1, 'virial_param': 12.0, 'monomer_length': 10.0, 'salt_concentration': 0.0, 'ionization_degree': 0.05, 'polymer_concentration': 0.7, 'background': 0.001, }, 0.001, 0.0948379], # Additional tests with larger range of parameters [{'contrast_factor': 10.0, 'bjerrum_length': 100.0, 'virial_param': 3.0, 'monomer_length': 1.0, 'salt_concentration': 10.0, 'ionization_degree': 2.0, 'polymer_concentration': 10.0, 'background': 0.0, }, 0.1, -3.75693800588], [{'contrast_factor': 10.0, 'bjerrum_length': 100.0, 'virial_param': 3.0, 'monomer_length': 1.0, 'salt_concentration': 10.0, 'ionization_degree': 2.0, 'polymer_concentration': 10.0, 'background': 100.0 }, 5.0, 100.029142149], [{'contrast_factor': 100.0, 'bjerrum_length': 10.0, 'virial_param': 180.0, 'monomer_length': 1.0, 'salt_concentration': 0.1, 'ionization_degree': 0.5, 'polymer_concentration': 0.1, 'background': 0.0, }, 200., 1.80664667511e-06], ] sasmodels/sasmodels/models/binary_hard_sphere.c000066400000000000000000000120051317715334700223320ustar00rootroot00000000000000double form_volume(void); double Iq(double q, double lg_radius, double sm_radius, double lg_vol_frac, double sm_vol_frac, double lg_sld, double sm_sld, double solvent_sld ); void calculate_psfs(double qval, double r2, double nf2, double aa, double phi, double *s11, double *s22, double *s12 ); double form_volume(void) { return 1.0; } double Iq(double q, double lg_radius, double sm_radius, double lg_vol_frac, double sm_vol_frac, double lg_sld, double sm_sld, double solvent_sld) { double r2,r1,nf2,phi,aa,rho2,rho1,rhos,inten; //my local names double psf11,psf12,psf22; double phi1,phi2,phr,a3; double v1,v2,n1,n2,qr1,qr2,b1,b2,sc1,sc2; r2 = lg_radius; r1 = sm_radius; phi2 = lg_vol_frac; phi1 = sm_vol_frac; rho2 = lg_sld; rho1 = sm_sld; rhos = solvent_sld; phi = phi1 + phi2; aa = r1/r2; //calculate the number fraction of larger spheres (eqn 2 in reference) a3=aa*aa*aa; phr=phi2/phi; nf2 = phr*a3/(1.0-phr+phr*a3); // calculate the PSF's here calculate_psfs(q,r2,nf2,aa,phi,&psf11,&psf22,&psf12); // /* do form factor calculations */ v1 = M_4PI_3*r1*r1*r1; v2 = M_4PI_3*r2*r2*r2; n1 = phi1/v1; n2 = phi2/v2; qr1 = r1*q; qr2 = r2*q; sc1 = sas_3j1x_x(qr1); sc2 = sas_3j1x_x(qr2); b1 = r1*r1*r1*(rho1-rhos)*M_4PI_3*sc1; b2 = r2*r2*r2*(rho2-rhos)*M_4PI_3*sc2; inten = n1*b1*b1*psf11; inten += sqrt(n1*n2)*2.0*b1*b2*psf12; inten += n2*b2*b2*psf22; ///* convert I(1/A) to (1/cm) */ inten *= 1.0e8; ///*convert rho^2 in 10^-6A to A*/ inten *= 1.0e-12; return(inten); } void calculate_psfs(double qval, double r2, double nf2, double aa, double phi, double *s11, double *s22, double *s12) { // variable qval,r2,nf2,aa,phi,&s11,&s22,&s12 // calculate constant terms double s2,v,a3,v1,v2,g11,g12,g22,wmv,wmv3,wmv4; double a1,a2i,a2,b1,b2,b12,gm1,gm12; double yy,ay,ay2,ay3,t1,t2,t3,f11,y2,y3,tt1,tt2,tt3; double c11,c22,c12,f12,f22,ttt1,ttt2,ttt3,ttt4,yl,y13; double t21,t22,t23,t31,t32,t33,t41,t42,yl3,wma3,y1; s2 = 2.0*r2; // s1 = aa*s2; why is this never used? check original paper? v = phi; a3 = aa*aa*aa; v1=((1.-nf2)*a3/(nf2+(1.-nf2)*a3))*v; v2=(nf2/(nf2+(1.-nf2)*a3))*v; g11=((1.+.5*v)+1.5*v2*(aa-1.))/(1.-v)/(1.-v); g22=((1.+.5*v)+1.5*v1*(1./aa-1.))/(1.-v)/(1.-v); g12=((1.+.5*v)+1.5*(1.-aa)*(v1-v2)/(1.+aa))/(1.-v)/(1.-v); wmv = 1/(1.-v); wmv3 = wmv*wmv*wmv; wmv4 = wmv*wmv3; a1=3.*wmv4*((v1+a3*v2)*(1.+v+v*v)-3.*v1*v2*(1.-aa)*(1.-aa)*(1.+v1+aa*(1.+v2))) + ((v1+a3*v2)*(1.+2.*v)+(1.+v+v*v)-3.*v1*v2*(1.-aa)*(1.-aa)-3.*v2*(1.-aa)*(1.-aa)*(1.+v1+aa*(1.+v2)))*wmv3; a2i=((v1+a3*v2)*(1.+v+v*v)-3.*v1*v2*(1.-aa)*(1.-aa)*(1.+v1+aa*(1.+v2)))*3*wmv4 + ((v1+a3*v2)*(1.+2.*v)+a3*(1.+v+v*v)-3.*v1*v2*(1.-aa)*(1.-aa)*aa-3.*v1*(1.-aa)*(1.-aa)*(1.+v1+aa*(1.+v2)))*wmv3; a2=a2i/a3; b1=-6.*(v1*g11*g11+.25*v2*(1.+aa)*(1.+aa)*aa*g12*g12); b2=-6.*(v2*g22*g22+.25*v1/a3*(1.+aa)*(1.+aa)*g12*g12); b12=-3.*aa*(1.+aa)*(v1*g11/aa/aa+v2*g22)*g12; gm1=(v1*a1+a3*v2*a2)*.5; gm12=2.*gm1*(1.-aa)/aa; //c //c calculate the direct correlation functions and print results //c // do 20 j=1,npts yy=qval*s2; //c calculate direct correlation functions //c ----c11 ay=aa*yy; ay2 = ay*ay; ay3 = ay*ay*ay; t1=a1*(sin(ay)-ay*cos(ay)); t2=b1*(2.*ay*sin(ay)-(ay2-2.)*cos(ay)-2.)/ay; t3=gm1*((4.*ay*ay2-24.*ay)*sin(ay)-(ay2*ay2-12.*ay2+24.)*cos(ay)+24.)/ay3; f11=24.*v1*(t1+t2+t3)/ay3; //c ------c22 y2=yy*yy; y3=yy*y2; tt1=a2*(sin(yy)-yy*cos(yy)); tt2=b2*(2.*yy*sin(yy)-(y2-2.)*cos(yy)-2.)/yy; tt3=gm1*((4.*y3-24.*yy)*sin(yy)-(y2*y2-12.*y2+24.)*cos(yy)+24.)/ay3; f22=24.*v2*(tt1+tt2+tt3)/y3; //c -----c12 yl=.5*yy*(1.-aa); yl3=yl*yl*yl; wma3 = (1.-aa)*(1.-aa)*(1.-aa); y1=aa*yy; y13 = y1*y1*y1; ttt1=3.*wma3*v*sqrt(nf2)*sqrt(1.-nf2)*a1*(sin(yl)-yl*cos(yl))/((nf2+(1.-nf2)*a3)*yl3); t21=b12*(2.*y1*cos(y1)+(y1*y1-2.)*sin(y1)); t22=gm12*((3.*y1*y1-6.)*cos(y1)+(y1*y1*y1-6.*y1)*sin(y1)+6.)/y1; t23=gm1*((4.*y13-24.*y1)*cos(y1)+(y13*y1-12.*y1*y1+24.)*sin(y1))/(y1*y1); t31=b12*(2.*y1*sin(y1)-(y1*y1-2.)*cos(y1)-2.); t32=gm12*((3.*y1*y1-6.)*sin(y1)-(y1*y1*y1-6.*y1)*cos(y1))/y1; t33=gm1*((4.*y13-24.*y1)*sin(y1)-(y13*y1-12.*y1*y1+24.)*cos(y1)+24.)/(y1*y1); t41=cos(yl)*((sin(y1)-y1*cos(y1))/(y1*y1) + (1.-aa)/(2.*aa)*(1.-cos(y1))/y1); t42=sin(yl)*((cos(y1)+y1*sin(y1)-1.)/(y1*y1) + (1.-aa)/(2.*aa)*sin(y1)/y1); ttt2=sin(yl)*(t21+t22+t23)/(y13*y1); ttt3=cos(yl)*(t31+t32+t33)/(y13*y1); ttt4=a1*(t41+t42)/y1; f12=ttt1+24.*v*sqrt(nf2)*sqrt(1.-nf2)*a3*(ttt2+ttt3+ttt4)/(nf2+(1.-nf2)*a3); c11=f11; c22=f22; c12=f12; *s11=1./(1.+c11-(c12)*c12/(1.+c22)); *s22=1./(1.+c22-(c12)*c12/(1.+c11)); *s12=-c12/((1.+c11)*(1.+c22)-(c12)*(c12)); return; } sasmodels/sasmodels/models/binary_hard_sphere.py000066400000000000000000000122271317715334700225460ustar00rootroot00000000000000r""" Definition ---------- The binary hard sphere model provides the scattering intensity, for binary mixture of hard spheres including hard sphere interaction between those particles, using rhw Percus-Yevick closure. The calculation is an exact multi-component solution that properly accounts for the 3 partial structure factors as follows: .. math:: I(q) = (1-x)f_1^2(q) S_{11}(q) + 2[x(1-x)]^{1/2} f_1(q)f_2(q)S_{12}(q) + x\,f_2^2(q)S_{22}(q) where $S_{ij}$ are the partial structure factors and $f_i$ are the scattering amplitudes of the particles. The subscript 1 is for the smaller particle and 2 is for the larger. The number fraction of the larger particle, ($x = n2/(n1+n2)$, where $n$ = the number density) is internally calculated based on the diameter ratio and the volume fractions. .. math:: :nowrap: \begin{align*} x &= \frac{(\phi_2 / \phi)\alpha^3}{(1-(\phi_2/\phi) + (\phi_2/\phi) \alpha^3)} \\ \phi &= \phi_1 + \phi_2 = \text{total volume fraction} \\ \alpha &= R_1/R_2 = \text{size ratio} \end{align*} The 2D scattering intensity is the same as 1D, regardless of the orientation of the *q* vector which is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} **NOTE 1:** The volume fractions and the scattering contrasts are loosely correlated, so holding as many parameters fixed to known values during fitting will improve the robustness of the fit. **NOTE 2:** Since the calculation uses the Percus-Yevick closure, all of the limitations of that closure relation apply here. Specifically, one should be wary of results for (total) volume fractions greater than approximately 40%. Depending on the size ratios or number fractions, the limit on total volume fraction may be lower. **NOTE 3:** The heavy arithmatic operations also mean that at present the function is poorly behaved at very low qr. In some cases very large qr may also be poorly behaved. These should however be outside any useful region of qr. The code for this model is based originally on a c-library implementation by the NIST Center for Neutron Research (Kline, 2006). See the references for details. References ---------- .. [#] N W Ashcroft and D C Langreth, *Physical Review*, 156 (1967) 685-692 [Errata found in *Phys. Rev.* 166 (1968) 934] .. [#] S R Kline, *J Appl. Cryst.*, 39 (2006) 895 Authorship and Verification ---------------------------- * **Author:** NIST IGOR/DANSE **Date:** pre 2010 * **Last Modified by:** Paul Butler **Date:** March 20, 2016 * **Last Reviewed by:** Paul Butler **Date:** March 20, 2016 """ from numpy import inf category = "shape:sphere" single = False # double precision only! name = "binary_hard_sphere" title = "binary mixture of hard spheres with hard sphere interactions." description = """Describes the scattering from a mixture of two distinct monodisperse, hard sphere particles. [Parameters]; radius_lg: large radius of binary hard sphere, radius_sm: small radius of binary hard sphere, volfraction_lg: volume fraction of large spheres, volfraction_sm: volume fraction of small spheres, sld_lg: large sphere scattering length density, sld_sm: small sphere scattering length density, sld_solvent: solvent scattering length density. """ # ["name", "units", default, [lower, upper], "type", "description"], parameters = [["radius_lg", "Ang", 100, [0, inf], "", "radius of large particle"], ["radius_sm", "Ang", 25, [0, inf], "", "radius of small particle"], ["volfraction_lg", "", 0.1, [0, 1], "", "volume fraction of large particle"], ["volfraction_sm", "", 0.2, [0, 1], "", "volume fraction of small particle"], ["sld_lg", "1e-6/Ang^2", 3.5, [-inf, inf], "sld", "scattering length density of large particle"], ["sld_sm", "1e-6/Ang^2", 0.5, [-inf, inf], "sld", "scattering length density of small particle"], ["sld_solvent", "1e-6/Ang^2", 6.36, [-inf, inf], "sld", "Solvent scattering length density"], ] source = ["lib/sas_3j1x_x.c", "binary_hard_sphere.c"] def random(): import numpy as np # TODO: binary_hard_sphere fails at low qr radius_lg = 10**np.random.uniform(2, 4.7) radius_sm = 10**np.random.uniform(2, 4.7) volfraction_lg = 10**np.random.uniform(-3, -0.3) volfraction_sm = 10**np.random.uniform(-3, -0.3) # TODO: Get slightly different results if large and small are swapped # modify the model so it doesn't care which is which if radius_lg < radius_sm: radius_lg, radius_sm = radius_sm, radius_lg volfraction_lg, volfraction_sm = volfraction_sm, volfraction_lg pars = dict( radius_lg=radius_lg, radius_sm=radius_sm, volfraction_lg=volfraction_lg, volfraction_sm=volfraction_sm, ) return pars # parameters for demo and documentation demo = dict(sld_lg=3.5, sld_sm=0.5, sld_solvent=6.36, radius_lg=100, radius_sm=20, volfraction_lg=0.1, volfraction_sm=0.2) # NOTE: test results taken from values returned by SasView 3.1.2 tests = [[{}, 0.001, 25.8927262013]] sasmodels/sasmodels/models/broad_peak.py000066400000000000000000000103011317715334700207740ustar00rootroot00000000000000r""" Definition ---------- This model calculates an empirical functional form for SAS data characterized by a broad scattering peak. Many SAS spectra are characterized by a broad peak even though they are from amorphous soft materials. For example, soft systems that show a SAS peak include copolymers, polyelectrolytes, multiphase systems, layered structures, etc. The d-spacing corresponding to the broad peak is a characteristic distance between the scattering inhomogeneities (such as in lamellar, cylindrical, or spherical morphologies, or for bicontinuous structures). The scattering intensity $I(q)$ is calculated as .. math:: I(q) = \frac{A}{q^n} + \frac{C}{1 + (|q - q_0|\xi)^m} + B Here the peak position is related to the d-spacing as $q_0 = 2\pi / d_0$. $A$ is the Porod law scale factor, $n$ the Porod exponent, $C$ is the Lorentzian scale factor, $m$ the exponent of $q$, $\xi$ the screening length, and $B$ the flat background. For 2D data the scattering intensity is calculated in the same way as 1D, where the $q$ vector is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- None. Authorship and Verification ---------------------------- * **Author:** NIST IGOR/DANSE **Date:** pre 2010 * **Last Modified by:** Paul kienle **Date:** July 24, 2016 * **Last Reviewed by:** Richard Heenan **Date:** March 21, 2016 """ from numpy import inf, errstate name = "broad_peak" title = "Broad Lorentzian type peak on top of a power law decay" description = """\ I(q) = scale_p/pow(q,exponent)+scale_l/ (1.0 + pow((fabs(q-q_peak)*length_l),exponent_l) )+ background List of default parameters: porod_scale = Porod term scaling porod_exp = Porod exponent lorentz_scale = Lorentzian term scaling lorentz_length = Lorentzian screening length [A] peak_pos = peak location [1/A] lorentz_exp = Lorentzian exponent background = Incoherent background""" category = "shape-independent" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type", "description"], parameters = [["porod_scale", "", 1.0e-05, [-inf, inf], "", "Power law scale factor"], ["porod_exp", "", 3.0, [-inf, inf], "", "Exponent of power law"], ["lorentz_scale", "", 10.0, [-inf, inf], "", "Scale factor for broad Lorentzian peak"], ["lorentz_length", "Ang", 50.0, [-inf, inf], "", "Lorentzian screening length"], ["peak_pos", "1/Ang", 0.1, [-inf, inf], "", "Peak position in q"], ["lorentz_exp", "", 2.0, [-inf, inf], "", "Exponent of Lorentz function"], ] # pylint: enable=bad-whitespace, line-too-long def Iq(q, porod_scale=1.0e-5, porod_exp=3.0, lorentz_scale=10.0, lorentz_length=50.0, peak_pos=0.1, lorentz_exp=2.0): """ :param q: Input q-value :param porod_scale: Power law scale factor :param porod_exp: Exponent of power law :param lorentz_scale: Scale factor for broad Lorentzian peak :param lorentz_length: Lorentzian screening length :param peak_pos: Peak position in q :param lorentz_exp: Exponent of Lorentz function :return: Calculated intensity """ z = abs(q - peak_pos) * lorentz_length with errstate(divide='ignore'): inten = (porod_scale / q ** porod_exp + lorentz_scale / (1 + z ** lorentz_exp)) return inten Iq.vectorized = True # Iq accepts an array of q values def random(): import numpy as np pars = dict( scale=1, porod_scale=10**np.random.uniform(-8, -5), porod_exp=np.random.uniform(1, 6), lorentz_scale=10**np.random.uniform(0.3, 6), lorentz_length=10**np.random.uniform(0, 2), peak_pos=10**np.random.uniform(-3, -1), lorentz_exp=np.random.uniform(1, 4), ) pars['lorentz_length'] /= pars['peak_pos'] pars['lorentz_scale'] *= pars['porod_scale'] / pars['peak_pos']**pars['porod_exp'] #pars['porod_scale'] = 0. return pars demo = dict(scale=1, background=0, porod_scale=1.0e-05, porod_exp=3, lorentz_scale=10, lorentz_length=50, peak_pos=0.1, lorentz_exp=2) sasmodels/sasmodels/models/capped_cylinder.c000066400000000000000000000120451317715334700216330ustar00rootroot00000000000000double form_volume(double radius, double radius_cap, double length); double Iq(double q, double sld, double solvent_sld, double radius, double radius_cap, double length); double Iqxy(double qx, double qy, double sld, double solvent_sld, double radius, double radius_cap, double length, double theta, double phi); #define INVALID(v) (v.radius_cap < v.radius) // Integral over a convex lens kernel for t in [h/R,1]. See the docs for // the definition of the function being integrated. // q is the magnitude of the q vector. // h is the length of the lens "inside" the cylinder. This negative wrt the // definition of h in the docs. // radius_cap is the radius of the lens // length is the cylinder length, or the separation between the lens halves // alpha is the angle of the cylinder wrt q. static double _cap_kernel(double q, double h, double radius_cap, double half_length, double sin_alpha, double cos_alpha) { // translate a point in [-1,1] to a point in [lower,upper] const double upper = 1.0; const double lower = h/radius_cap; // integral lower bound const double zm = 0.5*(upper-lower); const double zb = 0.5*(upper+lower); // cos term in integral is: // cos (q (R t - h + L/2) cos(alpha)) // so turn it into: // cos (m t + b) // where: // m = q R cos(alpha) // b = q(L/2-h) cos(alpha) const double m = q*radius_cap*cos_alpha; // cos argument slope const double b = q*(half_length-h)*cos_alpha; // cos argument intercept const double qrst = q*radius_cap*sin_alpha; // Q*R*sin(theta) double total = 0.0; for (int i=0; i<76 ;i++) { const double t = Gauss76Z[i]*zm + zb; const double radical = 1.0 - t*t; const double bj = sas_2J1x_x(qrst*sqrt(radical)); const double Fq = cos(m*t + b) * radical * bj; total += Gauss76Wt[i] * Fq; } // translate dx in [-1,1] to dx in [lower,upper] const double integral = total*zm; const double cap_Fq = 2.0*M_PI*cube(radius_cap)*integral; return cap_Fq; } static double _fq(double q, double h, double radius_cap, double radius, double half_length, double sin_alpha, double cos_alpha) { const double cap_Fq = _cap_kernel(q, h, radius_cap, half_length, sin_alpha, cos_alpha); const double bj = sas_2J1x_x(q*radius*sin_alpha); const double si = sas_sinx_x(q*half_length*cos_alpha); const double cyl_Fq = 2.0*M_PI*radius*radius*half_length*bj*si; const double Aq = cap_Fq + cyl_Fq; return Aq; } double form_volume(double radius, double radius_cap, double length) { // cap radius should never be less than radius when this is called // Note: volume V = 2*V_cap + V_cyl // // V_cyl = pi r_cyl^2 L // V_cap = 1/6 pi h_c (3 r_cyl^2 + h_c^2) = 1/3 pi h_c^2 (3 r_cap - h_c) // // The docs for capped cylinder give the volume as: // V = pi r^2 L + 2/3 pi (R-h)^2 (2R + h) // where r_cap=R and h = R - h_c. // // The first part is clearly V_cyl. The second part requires some work: // (R-h)^2 => h_c^2 // (2R+h) => 2R+ h_c-h_c + h => 2R + (R-h)-h_c + h => 3R-h_c // And so: // 2/3 pi (R-h)^2 (2R + h) => 2/3 pi h_c^2 (3 r_cap - h_c) // which is 2 V_cap, using the second form above. // // In this function we are going to use the first form of V_cap // // V = V_cyl + 2 V_cap // = pi r^2 L + pi hc (r^2 + hc^2/3) // = pi (r^2 (L+hc) + hc^3/3) const double hc = radius_cap - sqrt(radius_cap*radius_cap - radius*radius); return M_PI*(radius*radius*(length+hc) + hc*hc*hc/3.0); } double Iq(double q, double sld, double solvent_sld, double radius, double radius_cap, double length) { const double h = sqrt(radius_cap*radius_cap - radius*radius); const double half_length = 0.5*length; // translate a point in [-1,1] to a point in [0, pi/2] const double zm = M_PI_4; const double zb = M_PI_4; double total = 0.0; for (int i=0; i<76 ;i++) { const double alpha= Gauss76Z[i]*zm + zb; double sin_alpha, cos_alpha; // slots to hold sincos function output SINCOS(alpha, sin_alpha, cos_alpha); const double Aq = _fq(q, h, radius_cap, radius, half_length, sin_alpha, cos_alpha); // sin_alpha for spherical coord integration total += Gauss76Wt[i] * Aq * Aq * sin_alpha; } // translate dx in [-1,1] to dx in [lower,upper] const double form = total * zm; // Contrast const double s = (sld - solvent_sld); return 1.0e-4 * s * s * form; } double Iqxy(double qx, double qy, double sld, double solvent_sld, double radius, double radius_cap, double length, double theta, double phi) { double q, sin_alpha, cos_alpha; ORIENT_SYMMETRIC(qx, qy, theta, phi, q, sin_alpha, cos_alpha); const double h = sqrt(radius_cap*radius_cap - radius*radius); const double Aq = _fq(q, h, radius_cap, radius, 0.5*length, sin_alpha, cos_alpha); // Multiply by contrast^2 and convert to cm-1 const double s = (sld - solvent_sld); return 1.0e-4 * square(s * Aq); } sasmodels/sasmodels/models/capped_cylinder.py000066400000000000000000000153331317715334700220440ustar00rootroot00000000000000r""" Definitions ----------- Calculates the scattering from a cylinder with spherical section end-caps. Like :ref:`barbell`, this is a sphereocylinder with end caps that have a radius larger than that of the cylinder, but with the center of the end cap radius lying within the cylinder. This model simply becomes a convex lens when the length of the cylinder $L=0$. See the diagram for the details of the geometry and restrictions on parameter values. .. figure:: img/capped_cylinder_geometry.jpg Capped cylinder geometry, where $r$ is *radius*, $R$ is *bell_radius* and $L$ is *length*. Since the end cap radius $R \geq r$ and by definition for this geometry $h < 0$, $h$ is then defined by $r$ and $R$ as $h = - \sqrt{R^2 - r^2}$ The scattered intensity $I(q)$ is calculated as .. math:: I(q) = \frac{\Delta \rho^2}{V} \left where the amplitude $A(q,\alpha)$ with the rod axis at angle $\alpha$ to $q$ is given as .. math:: A(q) =&\ \pi r^2L \frac{\sin\left(\tfrac12 qL\cos\alpha\right)} {\tfrac12 qL\cos\alpha} \frac{2 J_1(qr\sin\alpha)}{qr\sin\alpha} \\ &\ + 4 \pi R^3 \int_{-h/R}^1 dt \cos\left[ q\cos\alpha \left(Rt + h + {\tfrac12} L\right)\right] \times (1-t^2) \frac{J_1\left[qR\sin\alpha \left(1-t^2\right)^{1/2}\right]} {qR\sin\alpha \left(1-t^2\right)^{1/2}} The $\left<\ldots\right>$ brackets denote an average of the structure over all orientations. $\left< A^2(q)\right>$ is then the form factor, $P(q)$. The scale factor is equivalent to the volume fraction of cylinders, each of volume, $V$. Contrast $\Delta\rho$ is the difference of scattering length densities of the cylinder and the surrounding solvent. The volume of the capped cylinder is (with $h$ as a positive value here) .. math:: V = \pi r_c^2 L + \tfrac{2\pi}{3}(R-h)^2(2R + h) and its radius of gyration is .. math:: R_g^2 =&\ \left[ \tfrac{12}{5}R^5 + R^4\left(6h+\tfrac32 L\right) + R^2\left(4h^2 + L^2 + 4Lh\right) + R^2\left(3Lh^2 + \tfrac32 L^2h\right) \right. \\ &\ \left. + \tfrac25 h^5 - \tfrac12 Lh^4 - \tfrac12 L^2h^3 + \tfrac14 L^3r^2 + \tfrac32 Lr^4 \right] \left( 4R^3 6R^2h - 2h^3 + 3r^2L \right)^{-1} .. note:: The requirement that $R \geq r$ is not enforced in the model! It is up to you to restrict this during analysis. The 2D scattering intensity is calculated similar to the 2D cylinder model. .. figure:: img/cylinder_angle_definition.png Definition of the angles for oriented 2D cylinders. References ---------- .. [#] H Kaya, *J. Appl. Cryst.*, 37 (2004) 223-230 .. [#] H Kaya and N-R deSouza, *J. Appl. Cryst.*, 37 (2004) 508-509 (addenda and errata) Authorship and Verification ---------------------------- * **Author:** NIST IGOR/DANSE **Date:** pre 2010 * **Last Modified by:** Paul Butler **Date:** September 30, 2016 * **Last Reviewed by:** Richard Heenan **Date:** January 4, 2017 """ from numpy import inf, sin, cos, pi name = "capped_cylinder" title = "Right circular cylinder with spherical end caps and uniform SLD" description = """That is, a sphereocylinder with end caps that have a radius larger than that of the cylinder and the center of the end cap radius lies within the cylinder. Note: As the length of cylinder -->0, it becomes a Convex Lens. It must be that radius <(=) radius_cap. [Parameters]; scale: volume fraction of spheres, background:incoherent background, radius: radius of the cylinder, length: length of the cylinder, radius_cap: radius of the semi-spherical cap, sld: SLD of the capped cylinder, sld_solvent: SLD of the solvent. """ category = "shape:cylinder" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type", "description"], parameters = [["sld", "1e-6/Ang^2", 4, [-inf, inf], "sld", "Cylinder scattering length density"], ["sld_solvent", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Solvent scattering length density"], ["radius", "Ang", 20, [0, inf], "volume", "Cylinder radius"], # TODO: use an expression for cap radius with fixed bounds. # The current form requires cap radius R bigger than cylinder radius r. # Could instead use R/r in [1,inf], r/R in [0,1], or the angle between # cylinder and cap in [0,90]. The problem is similar for the barbell # model. Propose r/R in [0,1] in both cases, with the model specifying # cylinder radius in the capped cylinder model and sphere radius in the # barbell model. This leads to the natural value of zero for no cap # in the capped cylinder, and zero for no bar in the barbell model. In # both models, one would be a pill. ["radius_cap", "Ang", 20, [0, inf], "volume", "Cap radius"], ["length", "Ang", 400, [0, inf], "volume", "Cylinder length"], ["theta", "degrees", 60, [-360, 360], "orientation", "cylinder axis to beam angle"], ["phi", "degrees", 60, [-360, 360], "orientation", "rotation about beam"], ] # pylint: enable=bad-whitespace, line-too-long source = ["lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c", "capped_cylinder.c"] def random(): import numpy as np # TODO: increase volume range once problem with bell radius is fixed # The issue is that bell radii of more than about 200 fail at high q V = 10**np.random.uniform(7, 9) bar_volume = 10**np.random.uniform(-4, -1)*V bell_volume = V - bar_volume bell_radius = (bell_volume/6)**0.3333 # approximate min_bar = bar_volume/np.pi/bell_radius**2 bar_length = 10**np.random.uniform(0, 3)*min_bar bar_radius = np.sqrt(bar_volume/bar_length/np.pi) if bar_radius > bell_radius: bell_radius, bar_radius = bar_radius, bell_radius pars = dict( #background=0, radius_cap=bell_radius, radius=bar_radius, length=bar_length, ) return pars demo = dict(scale=1, background=0, sld=6, sld_solvent=1, radius=260, radius_cap=290, length=290, theta=30, phi=15, radius_pd=.2, radius_pd_n=1, radius_cap_pd=.2, radius_cap_pd_n=1, length_pd=.2, length_pd_n=10, theta_pd=15, theta_pd_n=45, phi_pd=15, phi_pd_n=1) q = 0.1 # april 6 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! qx = q*cos(pi/6.0) qy = q*sin(pi/6.0) tests = [[{}, 0.075, 26.0698570695], [{'theta':80., 'phi':10.}, (qx, qy), 0.561811990502], ] del qx, qy # not necessary to delete, but cleanersasmodels/sasmodels/models/core_multi_shell.c000066400000000000000000000015611317715334700220400ustar00rootroot00000000000000 static double f_constant(double q, double r, double sld) { const double bes = sas_3j1x_x(q * r); const double vol = M_4PI_3 * cube(r); return sld * vol * bes; } static double form_volume(double core_radius, double fp_n, double thickness[]) { double r = core_radius; int n = (int)(fp_n+0.5); for (int i=0; i < n; i++) { r += thickness[i]; } return M_4PI_3 * cube(r); } static double Iq(double q, double core_sld, double core_radius, double solvent_sld, double fp_n, double sld[], double thickness[]) { const int n = (int)(fp_n+0.5); double f, r, last_sld; r = core_radius; last_sld = core_sld; f = 0.; for (int i=0; i`_ Authorship and Verification ---------------------------- * **Author:** NIST IGOR/DANSE **Date:** pre 2010 * **Last Modified by:** Paul Butler **Date:** September 30, 2016 * **Last Reviewed by:** Richard Heenan **Date:** January 4, 2017 """ from numpy import inf, sin, cos, pi name = "core_shell_bicelle" title = "Circular cylinder with a core-shell scattering length density profile.." description = """ P(q,alpha)= (scale/Vs)*f(q)^(2) + bkg, where: f(q)= Vt(sld_rim - sld_solvent)* sin[qLt.cos(alpha)/2] /[qLt.cos(alpha)/2]*J1(qRout.sin(alpha)) /[qRout.sin(alpha)]+ (sld_core-sld_face)*Vc*sin[qLcos(alpha)/2][[qL *cos(alpha)/2]*J1(qRc.sin(alpha)) /qRc.sin(alpha)]+ (sld_face-sld_rim)*(Vc+Vf)*sin[q(L+2.thick_face). cos(alpha)/2][[q(L+2.thick_face)*cos(alpha)/2]* J1(qRc.sin(alpha))/qRc.sin(alpha)] alpha:is the angle between the axis of the cylinder and the q-vector Vt = pi.(Rc + thick_rim)^2.Lt : total volume Vc = pi.Rc^2.L :the volume of the core Vf = 2.pi.Rc^2.thick_face Rc = radius: is the core radius L: the length of the core Lt = L + 2.thick_face: total length Rout = radius + thick_rim sld_core, sld_rim, sld_face:scattering length densities within the particle sld_solvent: the scattering length density of the solvent bkg: the background J1: the first order Bessel function theta: axis_theta of the cylinder phi: the axis_phi of the cylinder... """ category = "shape:cylinder" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type", "description"], parameters = [ ["radius", "Ang", 80, [0, inf], "volume", "Cylinder core radius"], ["thick_rim", "Ang", 10, [0, inf], "volume", "Rim shell thickness"], ["thick_face", "Ang", 10, [0, inf], "volume", "Cylinder face thickness"], ["length", "Ang", 50, [0, inf], "volume", "Cylinder length"], ["sld_core", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Cylinder core scattering length density"], ["sld_face", "1e-6/Ang^2", 4, [-inf, inf], "sld", "Cylinder face scattering length density"], ["sld_rim", "1e-6/Ang^2", 4, [-inf, inf], "sld", "Cylinder rim scattering length density"], ["sld_solvent", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Solvent scattering length density"], ["theta", "degrees", 90, [-360, 360], "orientation", "cylinder axis to beam angle"], ["phi", "degrees", 0, [-360, 360], "orientation", "rotation about beam"] ] # pylint: enable=bad-whitespace, line-too-long source = ["lib/sas_Si.c", "lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c", "core_shell_bicelle.c"] def random(): import numpy as np pars = dict( radius=10**np.random.uniform(1.3, 3), length=10**np.random.uniform(1.3, 4), thick_rim=10**np.random.uniform(0, 1.7), thick_face=10**np.random.uniform(0, 1.7), ) return pars demo = dict(scale=1, background=0, radius=20.0, thick_rim=10.0, thick_face=10.0, length=400.0, sld_core=1.0, sld_face=4.0, sld_rim=4.0, sld_solvent=1.0, theta=90, phi=0) q = 0.1 # april 6 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! qx = q*cos(pi/6.0) qy = q*sin(pi/6.0) tests = [[{}, 0.05, 7.4883545957], [{'theta':80., 'phi':10.}, (qx, qy), 2.81048892474 ] ] del qx, qy # not necessary to delete, but cleaner sasmodels/sasmodels/models/core_shell_bicelle_elliptical.c000066400000000000000000000110771317715334700245120ustar00rootroot00000000000000// NOTE that "length" here is the full height of the core! static double form_volume(double r_minor, double x_core, double thick_rim, double thick_face, double length) { return M_PI*(r_minor+thick_rim)*(r_minor*x_core+thick_rim)*(length+2.0*thick_face); } static double Iq(double q, double r_minor, double x_core, double thick_rim, double thick_face, double length, double rhoc, double rhoh, double rhor, double rhosolv) { double si1,si2,be1,be2; // core_shell_bicelle_elliptical, RKH Dec 2016, based on elliptical_cylinder and core_shell_bicelle // tested against limiting cases of cylinder, elliptical_cylinder, stacked_discs, and core_shell_bicelle // const double uplim = M_PI_4; const double halfheight = 0.5*length; //const double va = 0.0; //const double vb = 1.0; // inner integral limits //const double vaj=0.0; //const double vbj=M_PI; const double r_major = r_minor * x_core; const double r2A = 0.5*(square(r_major) + square(r_minor)); const double r2B = 0.5*(square(r_major) - square(r_minor)); const double dr1 = (rhoc-rhoh) *M_PI*r_minor*r_major*(2.0*halfheight);; const double dr2 = (rhor-rhosolv)*M_PI*(r_minor+thick_rim)*(r_major+thick_rim)*2.0*(halfheight+thick_face); const double dr3 = (rhoh-rhor) *M_PI*r_minor*r_major*2.0*(halfheight+thick_face); //const double vol1 = M_PI*r_minor*r_major*(2.0*halfheight); //const double vol2 = M_PI*(r_minor+thick_rim)*(r_major+thick_rim)*2.0*(halfheight+thick_face); //const double vol3 = M_PI*r_minor*r_major*2.0*(halfheight+thick_face); //initialize integral double outer_sum = 0.0; for(int i=0;i<76;i++) { //setup inner integral over the ellipsoidal cross-section // since we generate these lots of times, why not store them somewhere? //const double cos_alpha = ( Gauss76Z[i]*(vb-va) + va + vb )/2.0; const double cos_alpha = ( Gauss76Z[i] + 1.0 )/2.0; const double sin_alpha = sqrt(1.0 - cos_alpha*cos_alpha); double inner_sum=0; double sinarg1 = q*halfheight*cos_alpha; double sinarg2 = q*(halfheight+thick_face)*cos_alpha; si1 = sas_sinx_x(sinarg1); si2 = sas_sinx_x(sinarg2); for(int j=0;j<76;j++) { //76 gauss points for the inner integral (WAS 20 points,so this may make unecessarily slow, but playing safe) //const double beta = ( Gauss76Z[j]*(vbj-vaj) + vaj + vbj )/2.0; const double beta = ( Gauss76Z[j] +1.0)*M_PI_2; const double rr = sqrt(r2A - r2B*cos(beta)); double besarg1 = q*rr*sin_alpha; double besarg2 = q*(rr+thick_rim)*sin_alpha; be1 = sas_2J1x_x(besarg1); be2 = sas_2J1x_x(besarg2); inner_sum += Gauss76Wt[j] *square(dr1*si1*be1 + dr2*si2*be2 + dr3*si2*be1); } //now calculate outer integral outer_sum += Gauss76Wt[i] * inner_sum; } return outer_sum*2.5e-05; } static double Iqxy(double qx, double qy, double r_minor, double x_core, double thick_rim, double thick_face, double length, double rhoc, double rhoh, double rhor, double rhosolv, double theta, double phi, double psi) { // THIS NEEDS TESTING double q, xhat, yhat, zhat; ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); const double dr1 = rhoc-rhoh; const double dr2 = rhor-rhosolv; const double dr3 = rhoh-rhor; const double r_major = r_minor*x_core; const double halfheight = 0.5*length; const double vol1 = M_PI*r_minor*r_major*length; const double vol2 = M_PI*(r_minor+thick_rim)*(r_major+thick_rim)*2.0*(halfheight+thick_face); const double vol3 = M_PI*r_minor*r_major*2.0*(halfheight+thick_face); // Compute effective radius in rotated coordinates const double r_hat = sqrt(square(r_major*xhat) + square(r_minor*yhat)); const double rshell_hat = sqrt(square((r_major+thick_rim)*xhat) + square((r_minor+thick_rim)*yhat)); const double be1 = sas_2J1x_x( q*r_hat ); const double be2 = sas_2J1x_x( q*rshell_hat ); const double si1 = sas_sinx_x( q*halfheight*zhat ); const double si2 = sas_sinx_x( q*(halfheight + thick_face)*zhat ); const double Aq = square( vol1*dr1*si1*be1 + vol2*dr2*si2*be2 + vol3*dr3*si2*be1); return 1.0e-4 * Aq; } sasmodels/sasmodels/models/core_shell_bicelle_elliptical.py000066400000000000000000000172151317715334700247200ustar00rootroot00000000000000r""" Definition ---------- This model provides the form factor for an elliptical cylinder with a core-shell scattering length density profile. Thus this is a variation of the core-shell bicelle model, but with an elliptical cylinder for the core. Outer shells on the rims and flat ends may be of different thicknesses and scattering length densities. The form factor is normalized by the total particle volume. .. figure:: img/core_shell_bicelle_geometry.png Schematic cross-section of bicelle. Note however that the model here calculates for rectangular, not curved, rims as shown below. .. figure:: img/core_shell_bicelle_parameters.png Cross section of model used here. Users will have to decide how to distribute "heads" and "tails" between the rim, face and core regions in order to estimate appropriate starting parameters. Given the scattering length densities (sld) $\rho_c$, the core sld, $\rho_f$, the face sld, $\rho_r$, the rim sld and $\rho_s$ the solvent sld, the scattering length density variation along the bicelle axis is: .. math:: \rho(r) = \begin{cases} &\rho_c \text{ for } 0 \lt r \lt R; -L \lt z\lt L \\[1.5ex] &\rho_f \text{ for } 0 \lt r \lt R; -(L+2t) \lt z\lt -L; L \lt z\lt (L+2t) \\[1.5ex] &\rho_r\text{ for } 0 \lt r \lt R; -(L+2t) \lt z\lt -L; L \lt z\lt (L+2t) \end{cases} The form factor for the bicelle is calculated in cylindrical coordinates, where $\alpha$ is the angle between the $Q$ vector and the cylinder axis, and $\psi$ is the angle for the ellipsoidal cross section core, to give: .. math:: I(Q,\alpha,\psi) = \frac{\text{scale}}{V_t} \cdot F(Q,\alpha, \psi)^2 \cdot sin(\alpha) + \text{background} where a numerical integration of $F(Q,\alpha, \psi)^2 \cdot sin(\alpha)$ is carried out over \alpha and \psi for: .. math:: :nowrap: \begin{align*} F(Q,\alpha,\psi) = &\bigg[ (\rho_c - \rho_f) V_c \frac{2J_1(QR'sin \alpha)}{QR'sin\alpha}\frac{sin(QLcos\alpha/2)}{Q(L/2)cos\alpha} \\ &+(\rho_f - \rho_r) V_{c+f} \frac{2J_1(QR'sin\alpha)}{QR'sin\alpha}\frac{sin(Q(L/2+t_f)cos\alpha)}{Q(L/2+t_f)cos\alpha} \\ &+(\rho_r - \rho_s) V_t \frac{2J_1(Q(R'+t_r)sin\alpha)}{Q(R'+t_r)sin\alpha}\frac{sin(Q(L/2+t_f)cos\alpha)}{Q(L/2+t_f)cos\alpha} \bigg] \end{align*} where .. math:: R'=\frac{R}{\sqrt{2}}\sqrt{(1+X_{core}^{2}) + (1-X_{core}^{2})cos(\psi)} and $V_t = \pi.(R+t_r)(Xcore.R+t_r)^2.(L+2.t_f)$ is the total volume of the bicelle, $V_c = \pi.Xcore.R^2.L$ the volume of the core, $V_{c+f} = \pi.Xcore.R^2.(L+2.t_f)$ the volume of the core plus the volume of the faces, $R$ is the radius of the core, $Xcore$ is the axial ratio of the core, $L$ the length of the core, $t_f$ the thickness of the face, $t_r$ the thickness of the rim and $J_1$ the usual first order bessel function. The core has radii $R$ and $Xcore.R$ so is circular, as for the core_shell_bicelle model, for $Xcore$ =1. Note that you may need to limit the range of $Xcore$, especially if using the Monte-Carlo algorithm, as setting radius to $R/Xcore$ and axial ratio to $1/Xcore$ gives an equivalent solution! The output of the 1D scattering intensity function for randomly oriented bicelles is then given by integrating over all possible $\alpha$ and $\psi$. For oriented bicelles the *theta*, *phi* and *psi* orientation parameters will appear when fitting 2D data, see the :ref:`elliptical-cylinder` model for further information. .. figure:: img/elliptical_cylinder_angle_definition.png Definition of the angles for the oriented core_shell_bicelle_elliptical particles. References ---------- .. [#] Authorship and Verification ---------------------------- * **Author:** Richard Heenan **Date:** December 14, 2016 * **Last Modified by:** Richard Heenan **Date:** December 14, 2016 * **Last Reviewed by:** Richard Heenan BEWARE 2d data yet to be checked **Date:** December 14, 2016 """ from numpy import inf, sin, cos, pi name = "core_shell_bicelle_elliptical" title = "Elliptical cylinder with a core-shell scattering length density profile.." description = """ core_shell_bicelle_elliptical Elliptical cylinder core, optional shell on the two flat faces, and shell of uniform thickness on its rim (extending around the end faces). Please see full documentation for equations and further details. Involves a double numerical integral around the ellipsoid diameter and the angle of the cylinder axis to Q. Compare also the core_shell_bicelle and elliptical_cylinder models. """ category = "shape:cylinder" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type", "description"], parameters = [ ["radius", "Ang", 30, [0, inf], "volume", "Cylinder core radius"], ["x_core", "None", 3, [0, inf], "volume", "axial ratio of core, X = r_polar/r_equatorial"], ["thick_rim", "Ang", 8, [0, inf], "volume", "Rim shell thickness"], ["thick_face", "Ang", 14, [0, inf], "volume", "Cylinder face thickness"], ["length", "Ang", 50, [0, inf], "volume", "Cylinder length"], ["sld_core", "1e-6/Ang^2", 4, [-inf, inf], "sld", "Cylinder core scattering length density"], ["sld_face", "1e-6/Ang^2", 7, [-inf, inf], "sld", "Cylinder face scattering length density"], ["sld_rim", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Cylinder rim scattering length density"], ["sld_solvent", "1e-6/Ang^2", 6, [-inf, inf], "sld", "Solvent scattering length density"], ["theta", "degrees", 90.0, [-360, 360], "orientation", "cylinder axis to beam angle"], ["phi", "degrees", 0, [-360, 360], "orientation", "rotation about beam"], ["psi", "degrees", 0, [-360, 360], "orientation", "rotation about cylinder axis"] ] # pylint: enable=bad-whitespace, line-too-long source = ["lib/sas_Si.c", "lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c", "core_shell_bicelle_elliptical.c"] def random(): import numpy as np outer_major = 10**np.random.uniform(1, 4.7) outer_minor = 10**np.random.uniform(1, 4.7) # Use a distribution with a preference for thin shell or thin core, # limited by the minimum radius. Avoid core,shell radii < 1 min_radius = min(outer_major, outer_minor) thick_rim = np.random.beta(0.5, 0.5)*(min_radius-2) + 1 radius_major = outer_major - thick_rim radius_minor = outer_minor - thick_rim radius = radius_major x_core = radius_minor/radius_major outer_length = 10**np.random.uniform(1, 4.7) # Caps should be a small percentage of the total length, but at least one # angstrom long. Since outer length >= 10, the following will suffice thick_face = 10**np.random.uniform(-np.log10(outer_length), -1)*outer_length length = outer_length - thick_face pars = dict( radius=radius, x_core=x_core, thick_rim=thick_rim, thick_face=thick_face, length=length ) return pars q = 0.1 # april 6 2017, rkh added a 2d unit test, NOT READY YET pull #890 branch assume correct! qx = q*cos(pi/6.0) qy = q*sin(pi/6.0) tests = [ [{'radius': 30.0, 'x_core': 3.0, 'thick_rim':8.0, 'thick_face':14.0, 'length':50.0}, 'ER', 1], [{'radius': 30.0, 'x_core': 3.0, 'thick_rim':8.0, 'thick_face':14.0, 'length':50.0}, 'VR', 1], [{'radius': 30.0, 'x_core': 3.0, 'thick_rim':8.0, 'thick_face':14.0, 'length':50.0, 'sld_core':4.0, 'sld_face':7.0, 'sld_rim':1.0, 'sld_solvent':6.0, 'background':0.0}, 0.015, 286.540286], # [{'theta':80., 'phi':10.}, (qx, qy), 7.88866563001 ], ] del qx, qy # not necessary to delete, but cleaner sasmodels/sasmodels/models/core_shell_cylinder.c000066400000000000000000000053761317715334700225270ustar00rootroot00000000000000double form_volume(double radius, double thickness, double length); double Iq(double q, double core_sld, double shell_sld, double solvent_sld, double radius, double thickness, double length); double Iqxy(double qx, double qy, double core_sld, double shell_sld, double solvent_sld, double radius, double thickness, double length, double theta, double phi); // vd = volume * delta_rho // besarg = q * R * sin(alpha) // siarg = q * L/2 * cos(alpha) double _cyl(double vd, double besarg, double siarg); double _cyl(double vd, double besarg, double siarg) { return vd * sas_sinx_x(siarg) * sas_2J1x_x(besarg); } double form_volume(double radius, double thickness, double length) { return M_PI*(radius+thickness)*(radius+thickness)*(length+2.0*thickness); } double Iq(double q, double core_sld, double shell_sld, double solvent_sld, double radius, double thickness, double length) { // precalculate constants const double core_qr = q*radius; const double core_qh = q*0.5*length; const double core_vd = form_volume(radius,0,length) * (core_sld-shell_sld); const double shell_qr = q*(radius + thickness); const double shell_qh = q*(0.5*length + thickness); const double shell_vd = form_volume(radius,thickness,length) * (shell_sld-solvent_sld); double total = 0.0; // double lower=0, upper=M_PI_2; for (int i=0; i<76 ;i++) { // translate a point in [-1,1] to a point in [lower,upper] //const double alpha = ( Gauss76Z[i]*(upper-lower) + upper + lower )/2.0; double sn, cn; const double alpha = 0.5*(Gauss76Z[i]*M_PI_2 + M_PI_2); SINCOS(alpha, sn, cn); const double fq = _cyl(core_vd, core_qr*sn, core_qh*cn) + _cyl(shell_vd, shell_qr*sn, shell_qh*cn); total += Gauss76Wt[i] * fq * fq * sn; } // translate dx in [-1,1] to dx in [lower,upper] //const double form = (upper-lower)/2.0*total; return 1.0e-4 * total * M_PI_4; } double Iqxy(double qx, double qy, double core_sld, double shell_sld, double solvent_sld, double radius, double thickness, double length, double theta, double phi) { double q, sin_alpha, cos_alpha; ORIENT_SYMMETRIC(qx, qy, theta, phi, q, sin_alpha, cos_alpha); const double core_qr = q*radius; const double core_qh = q*0.5*length; const double core_vd = form_volume(radius,0,length) * (core_sld-shell_sld); const double shell_qr = q*(radius + thickness); const double shell_qh = q*(0.5*length + thickness); const double shell_vd = form_volume(radius,thickness,length) * (shell_sld-solvent_sld); const double fq = _cyl(core_vd, core_qr*sin_alpha, core_qh*cos_alpha) + _cyl(shell_vd, shell_qr*sin_alpha, shell_qh*cos_alpha); return 1.0e-4 * fq * fq; } sasmodels/sasmodels/models/core_shell_cylinder.py000066400000000000000000000142071317715334700227260ustar00rootroot00000000000000r""" Definition ---------- The output of the 2D scattering intensity function for oriented core-shell cylinders is given by (Kline, 2006 [#kline]_). The form factor is normalized by the particle volume. .. math:: I(q,\alpha) = \frac{\text{scale}}{V_s} F^2(q,\alpha).sin(\alpha) + \text{background} where .. math:: F(q,\alpha) = &\ (\rho_c - \rho_s) V_c \frac{\sin \left( q \tfrac12 L\cos\alpha \right)} {q \tfrac12 L\cos\alpha} \frac{2 J_1 \left( qR\sin\alpha \right)} {qR\sin\alpha} \\ &\ + (\rho_s - \rho_\text{solv}) V_s \frac{\sin \left( q \left(\tfrac12 L+T\right) \cos\alpha \right)} {q \left(\tfrac12 L +T \right) \cos\alpha} \frac{ 2 J_1 \left( q(R+T)\sin\alpha \right)} {q(R+T)\sin\alpha} and .. math:: V_s = \pi (R + T)^2 (L + 2T) and $\alpha$ is the angle between the axis of the cylinder and $\vec q$, $V_s$ is the volume of the outer shell (i.e. the total volume, including the shell), $V_c$ is the volume of the core, $L$ is the length of the core, $R$ is the radius of the core, $T$ is the thickness of the shell, $\rho_c$ is the scattering length density of the core, $\rho_s$ is the scattering length density of the shell, $\rho_\text{solv}$ is the scattering length density of the solvent, and *background* is the background level. The outer radius of the shell is given by $R+T$ and the total length of the outer shell is given by $L+2T$. $J1$ is the first order Bessel function. .. _core-shell-cylinder-geometry: .. figure:: img/core_shell_cylinder_geometry.jpg Core shell cylinder schematic. To provide easy access to the orientation of the core-shell cylinder, we define the axis of the cylinder using two angles $\theta$ and $\phi$. (see :ref:`cylinder model `) NB: The 2nd virial coefficient of the cylinder is calculated based on the radius and 2 length values, and used as the effective radius for $S(q)$ when $P(q) \cdot S(q)$ is applied. The $\theta$ and $\phi$ parameters are not used for the 1D output. Reference --------- .. [#] see, for example, Ian Livsey J. Chem. Soc., Faraday Trans. 2, 1987,83, 1445-1452 .. [#kline] S R Kline, *J Appl. Cryst.*, 39 (2006) 895 Authorship and Verification ---------------------------- * **Author:** NIST IGOR/DANSE **Date:** pre 2010 * **Last Modified by:** Paul Kienzle **Date:** Aug 8, 2016 * **Last Reviewed by:** Richard Heenan **Date:** March 18, 2016 """ from numpy import pi, inf, sin, cos name = "core_shell_cylinder" title = "Right circular cylinder with a core-shell scattering length density profile." description = """ P(q,alpha)= scale/Vs*f(q)^(2) + background, where: f(q)= 2(sld_core - solvant_sld) * Vc*sin[qLcos(alpha/2)] /[qLcos(alpha/2)]*J1(qRsin(alpha)) /[qRsin(alpha)]+2(sld_shell-sld_solvent) *Vs*sin[q(L+T)cos(alpha/2)][[q(L+T) *cos(alpha/2)]*J1(q(R+T)sin(alpha)) /q(R+T)sin(alpha)] alpha:is the angle between the axis of the cylinder and the q-vector Vs: the volume of the outer shell Vc: the volume of the core L: the length of the core sld_shell: the scattering length density of the shell sld_solvent: the scattering length density of the solvent background: the background T: the thickness R+T: is the outer radius L+2T: The total length of the outershell J1: the first order Bessel function theta: axis_theta of the cylinder phi: the axis_phi of the cylinder """ category = "shape:cylinder" # ["name", "units", default, [lower, upper], "type", "description"], parameters = [["sld_core", "1e-6/Ang^2", 4, [-inf, inf], "sld", "Cylinder core scattering length density"], ["sld_shell", "1e-6/Ang^2", 4, [-inf, inf], "sld", "Cylinder shell scattering length density"], ["sld_solvent", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Solvent scattering length density"], ["radius", "Ang", 20, [0, inf], "volume", "Cylinder core radius"], ["thickness", "Ang", 20, [0, inf], "volume", "Cylinder shell thickness"], ["length", "Ang", 400, [0, inf], "volume", "Cylinder length"], ["theta", "degrees", 60, [-360, 360], "orientation", "cylinder axis to beam angle"], ["phi", "degrees", 60, [-360, 360], "orientation", "rotation about beam"], ] source = ["lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c", "core_shell_cylinder.c"] def ER(radius, thickness, length): """ Returns the effective radius used in the S*P calculation """ radius = radius + thickness length = length + 2 * thickness ddd = 0.75 * radius * (2 * radius * length + (length + radius) * (length + pi * radius)) return 0.5 * (ddd) ** (1. / 3.) def VR(radius, thickness, length): """ Returns volume ratio """ whole = pi * (radius + thickness) ** 2 * (length + 2 * thickness) core = pi * radius ** 2 * length return whole, whole - core def random(): import numpy as np outer_radius = 10**np.random.uniform(1, 4.7) # Use a distribution with a preference for thin shell or thin core # Avoid core,shell radii < 1 radius = np.random.beta(0.5, 0.5)*(outer_radius-2) + 1 thickness = outer_radius - radius length = np.random.uniform(1, 4.7) pars = dict( radius=radius, thickness=thickness, length=length, ) return pars demo = dict(scale=1, background=0, sld_core=6, sld_shell=8, sld_solvent=1, radius=45, thickness=25, length=340, theta=30, phi=15, radius_pd=.2, radius_pd_n=1, length_pd=.2, length_pd_n=10, thickness_pd=.2, thickness_pd_n=10, theta_pd=15, theta_pd_n=45, phi_pd=15, phi_pd_n=1) q = 0.1 # april 6 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! qx = q*cos(pi/6.0) qy = q*sin(pi/6.0) tests = [[{}, 0.075, 10.8552692237], [{}, (qx, qy), 0.444618752741 ], ] del qx, qy # not necessary to delete, but cleaner sasmodels/sasmodels/models/core_shell_ellipsoid.c000066400000000000000000000105671317715334700227000ustar00rootroot00000000000000double form_volume(double radius_equat_core, double polar_core, double equat_shell, double polar_shell); double Iq(double q, double radius_equat_core, double x_core, double thick_shell, double x_polar_shell, double core_sld, double shell_sld, double solvent_sld); double Iqxy(double qx, double qy, double radius_equat_core, double x_core, double thick_shell, double x_polar_shell, double core_sld, double shell_sld, double solvent_sld, double theta, double phi); double form_volume(double radius_equat_core, double x_core, double thick_shell, double x_polar_shell) { const double equat_shell = radius_equat_core + thick_shell; const double polar_shell = radius_equat_core*x_core + thick_shell*x_polar_shell; double vol = M_4PI_3*equat_shell*equat_shell*polar_shell; return vol; } static double core_shell_ellipsoid_xt_kernel(double q, double radius_equat_core, double x_core, double thick_shell, double x_polar_shell, double core_sld, double shell_sld, double solvent_sld) { const double lolim = 0.0; const double uplim = 1.0; const double delpc = core_sld - shell_sld; //core - shell const double delps = shell_sld - solvent_sld; //shell - solvent const double polar_core = radius_equat_core*x_core; const double equat_shell = radius_equat_core + thick_shell; const double polar_shell = radius_equat_core*x_core + thick_shell*x_polar_shell; double summ = 0.0; //initialize intergral for(int i=0;i<76;i++) { double zi = 0.5*( Gauss76Z[i]*(uplim-lolim) + uplim + lolim ); double yyy = gfn4(zi, radius_equat_core, polar_core, equat_shell, polar_shell, delpc, delps, q); summ += Gauss76Wt[i] * yyy; } summ *= 0.5*(uplim-lolim); // convert to [cm-1] return 1.0e-4 * summ; } static double core_shell_ellipsoid_xt_kernel_2d(double qx, double qy, double radius_equat_core, double x_core, double thick_shell, double x_polar_shell, double core_sld, double shell_sld, double solvent_sld, double theta, double phi) { double q, sin_alpha, cos_alpha; ORIENT_SYMMETRIC(qx, qy, theta, phi, q, sin_alpha, cos_alpha); const double sldcs = core_sld - shell_sld; const double sldss = shell_sld- solvent_sld; const double polar_core = radius_equat_core*x_core; const double equat_shell = radius_equat_core + thick_shell; const double polar_shell = radius_equat_core*x_core + thick_shell*x_polar_shell; // Call the IGOR library function to get the kernel: // MUST use gfn4 not gf2 because of the def of params. double answer = gfn4(cos_alpha, radius_equat_core, polar_core, equat_shell, polar_shell, sldcs, sldss, q); //convert to [cm-1] answer *= 1.0e-4; return answer; } double Iq(double q, double radius_equat_core, double x_core, double thick_shell, double x_polar_shell, double core_sld, double shell_sld, double solvent_sld) { double intensity = core_shell_ellipsoid_xt_kernel(q, radius_equat_core, x_core, thick_shell, x_polar_shell, core_sld, shell_sld, solvent_sld); return intensity; } double Iqxy(double qx, double qy, double radius_equat_core, double x_core, double thick_shell, double x_polar_shell, double core_sld, double shell_sld, double solvent_sld, double theta, double phi) { double intensity = core_shell_ellipsoid_xt_kernel_2d(qx, qy, radius_equat_core, x_core, thick_shell, x_polar_shell, core_sld, shell_sld, solvent_sld, theta, phi); return intensity; } sasmodels/sasmodels/models/core_shell_ellipsoid.py000066400000000000000000000206121317715334700230760ustar00rootroot00000000000000r""" Definition ---------- Parameters for this model are the core axial ratio X and a shell thickness, which are more often what we would like to determine and makes the model better behaved, particularly when polydispersity is applied than the four independent radii used in the original parameterization of this model. .. figure:: img/core_shell_ellipsoid_geometry.png The geometric parameters of this model are shown in the diagram above, which shows (a) a cut through at the circular equator and (b) a cross section through the poles, of a prolate ellipsoid. When *X_core < 1* the core is oblate; when *X_core > 1* it is prolate. *X_core = 1* is a spherical core. For a fixed shell thickness *XpolarShell = 1*, to scale the shell thickness pro-rata with the radius set or constrain *XpolarShell = X_core*. When including an $S(q)$, the radius in $S(q)$ is calculated to be that of a sphere with the same 2nd virial coefficient of the outer surface of the ellipsoid. This may have some undesirable effects if the aspect ratio of the ellipsoid is large (ie, if $X << 1$ or $X >> 1$ ), when the $S(q)$ - which assumes spheres - will not in any case be valid. Generating a custom product model will enable separate effective volume fraction and effective radius in the $S(q)$. If SAS data are in absolute units, and the SLDs are correct, then scale should be the total volume fraction of the "outer particle". When $S(q)$ is introduced this moves to the $S(q)$ volume fraction, and scale should then be 1.0, or contain some other units conversion factor (for example, if you have SAXS data). The calculation of intensity follows that for the solid ellipsoid, but with separate terms for the core-shell and shell-solvent boundaries. .. math:: P(q,\alpha) = \frac{\text{scale}}{V} F^2(q,\alpha) + \text{background} where .. math:: :nowrap: \begin{align*} F(q,\alpha) = &f(q,radius\_equat\_core,radius\_equat\_core.x\_core,\alpha) \\ &+ f(q,radius\_equat\_core + thick\_shell,radius\_equat\_core.x\_core + thick\_shell.x\_polar\_shell,\alpha) \end{align*} where .. math:: f(q,R_e,R_p,\alpha) = \frac{3 \Delta \rho V (\sin[qr(R_p,R_e,\alpha)] - \cos[qr(R_p,R_e,\alpha)])} {[qr(R_p,R_e,\alpha)]^3} and .. math:: r(R_e,R_p,\alpha) = \left[ R_e^2 \sin^2 \alpha + R_p^2 \cos^2 \alpha \right]^{1/2} $\alpha$ is the angle between the axis of the ellipsoid and $\vec q$, $V = (4/3)\pi R_pR_e^2$ is the volume of the ellipsoid , $R_p$ is the polar radius along the rotational axis of the ellipsoid, $R_e$ is the equatorial radius perpendicular to the rotational axis of the ellipsoid and $\Delta \rho$ (contrast) is the scattering length density difference, either $(sld\_core - sld\_shell)$ or $(sld\_shell - sld\_solvent)$. For randomly oriented particles: .. math:: F^2(q)=\int_{0}^{\pi/2}{F^2(q,\alpha)\sin(\alpha)d\alpha} For oriented ellipsoids the *theta*, *phi* and *psi* orientation parameters will appear when fitting 2D data, see the :ref:`elliptical-cylinder` model for further information. References ---------- see for example: Kotlarchyk, M.; Chen, S.-H. J. Chem. Phys., 1983, 79, 2461. Berr, S. J. Phys. Chem., 1987, 91, 4760. Authorship and Verification ---------------------------- * **Author:** NIST IGOR/DANSE **Date:** pre 2010 * **Last Modified by:** Richard Heenan (reparametrised model) **Date:** 2015 * **Last Reviewed by:** Richard Heenan **Date:** October 6, 2016 """ from numpy import inf, sin, cos, pi name = "core_shell_ellipsoid" title = "Form factor for an spheroid ellipsoid particle with a core shell structure." description = """ [core_shell_ellipsoid] Calculates the form factor for an spheroid ellipsoid particle with a core_shell structure. The form factor is averaged over all possible orientations of the ellipsoid such that P(q) = scale*/Vol + bkg, where f is the single particle scattering amplitude. [Parameters]: radius_equat_core = equatorial radius of core, x_core = ratio of core polar/equatorial radii, thick_shell = equatorial radius of outer surface, x_polar_shell = ratio of polar shell thickness to equatorial shell thickness, sld_core = SLD_core sld_shell = SLD_shell sld_solvent = SLD_solvent background = Incoherent bkg scale =scale Note:It is the users' responsibility to ensure that shell radii are larger than core radii. oblate: polar radius < equatorial radius prolate : polar radius > equatorial radius - this new model will make this easier and polydispersity integrals more logical (as previously the shell could disappear). """ category = "shape:ellipsoid" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type", "description"], parameters = [ ["radius_equat_core","Ang", 20, [0, inf], "volume", "Equatorial radius of core"], ["x_core", "None", 3, [0, inf], "volume", "axial ratio of core, X = r_polar/r_equatorial"], ["thick_shell", "Ang", 30, [0, inf], "volume", "thickness of shell at equator"], ["x_polar_shell", "", 1, [0, inf], "volume", "ratio of thickness of shell at pole to that at equator"], ["sld_core", "1e-6/Ang^2", 2, [-inf, inf], "sld", "Core scattering length density"], ["sld_shell", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Shell scattering length density"], ["sld_solvent", "1e-6/Ang^2", 6.3, [-inf, inf], "sld", "Solvent scattering length density"], ["theta", "degrees", 0, [-360, 360], "orientation", "elipsoid axis to beam angle"], ["phi", "degrees", 0, [-360, 360], "orientation", "rotation about beam"], ] # pylint: enable=bad-whitespace, line-too-long source = ["lib/sas_3j1x_x.c", "lib/gfn.c", "lib/gauss76.c", "core_shell_ellipsoid.c"] def ER(radius_equat_core, x_core, thick_shell, x_polar_shell): """ Returns the effective radius used in the S*P calculation """ from .ellipsoid import ER as ellipsoid_ER polar_outer = radius_equat_core*x_core + thick_shell*x_polar_shell equat_outer = radius_equat_core + thick_shell return ellipsoid_ER(polar_outer, equat_outer) def random(): import numpy as np V = 10**np.random.uniform(5, 12) outer_polar = 10**np.random.uniform(1.3, 4) outer_equatorial = np.sqrt(V/outer_polar) # ignore 4/3 pi # Use a distribution with a preference for thin shell or thin core # Avoid core,shell radii < 1 thickness_polar = np.random.beta(0.5, 0.5)*(outer_polar-2) + 1 thickness_equatorial = np.random.beta(0.5, 0.5)*(outer_equatorial-2) + 1 radius_polar = outer_polar - thickness_polar radius_equatorial = outer_equatorial - thickness_equatorial x_core = radius_polar/radius_equatorial x_polar_shell = thickness_polar/thickness_equatorial pars = dict( #background=0, sld=0, sld_solvent=1, radius_equat_core=radius_equatorial, x_core=x_core, thick_shell=thickness_equatorial, x_polar_shell=x_polar_shell, ) return pars q = 0.1 # tests had in old coords theta=0, phi=0; new coords theta=90, phi=0 qx = q*cos(pi/6.0) qy = q*sin(pi/6.0) # 11Jan2017 RKH sorted tests after redefinition of angles tests = [ # Accuracy tests based on content in test/utest_coreshellellipsoidXTmodel.py [{'radius_equat_core': 200.0, 'x_core': 0.1, 'thick_shell': 50.0, 'x_polar_shell': 0.2, 'sld_core': 2.0, 'sld_shell': 1.0, 'sld_solvent': 6.3, 'background': 0.001, 'scale': 1.0, }, 1.0, 0.00189402], # Additional tests with larger range of parameters [{'background': 0.01}, 0.1, 11.6915], [{'radius_equat_core': 20.0, 'x_core': 200.0, 'thick_shell': 54.0, 'x_polar_shell': 3.0, 'sld_core': 20.0, 'sld_shell': 10.0, 'sld_solvent': 6.0, 'background': 0.0, 'scale': 1.0, }, 0.01, 8688.53], # 2D tests [{'background': 0.001, 'theta': 90.0, 'phi': 0.0, }, (0.4, 0.5), 0.00690673], [{'radius_equat_core': 20.0, 'x_core': 200.0, 'thick_shell': 54.0, 'x_polar_shell': 3.0, 'sld_core': 20.0, 'sld_shell': 10.0, 'sld_solvent': 6.0, 'background': 0.01, 'scale': 0.01, 'theta': 90.0, 'phi': 0.0, }, (qx, qy), 0.01000025], ] sasmodels/sasmodels/models/core_shell_parallelepiped.c000066400000000000000000000165611317715334700236770ustar00rootroot00000000000000double form_volume(double length_a, double length_b, double length_c, double thick_rim_a, double thick_rim_b, double thick_rim_c); double Iq(double q, double core_sld, double arim_sld, double brim_sld, double crim_sld, double solvent_sld, double length_a, double length_b, double length_c, double thick_rim_a, double thick_rim_b, double thick_rim_c); double Iqxy(double qx, double qy, double core_sld, double arim_sld, double brim_sld, double crim_sld, double solvent_sld, double length_a, double length_b, double length_c, double thick_rim_a, double thick_rim_b, double thick_rim_c, double theta, double phi, double psi); double form_volume(double length_a, double length_b, double length_c, double thick_rim_a, double thick_rim_b, double thick_rim_c) { //return length_a * length_b * length_c; return length_a * length_b * length_c + 2.0 * thick_rim_a * length_b * length_c + 2.0 * thick_rim_b * length_a * length_c + 2.0 * thick_rim_c * length_a * length_b; } double Iq(double q, double core_sld, double arim_sld, double brim_sld, double crim_sld, double solvent_sld, double length_a, double length_b, double length_c, double thick_rim_a, double thick_rim_b, double thick_rim_c) { // Code converted from functions CSPPKernel and CSParallelepiped in libCylinder.c_scaled // Did not understand the code completely, it should be rechecked (Miguel Gonzalez) //Code is rewritten,the code is compliant with Diva Singhs thesis now (Dirk Honecker) const double mu = 0.5 * q * length_b; //calculate volume before rescaling (in original code, but not used) //double vol = form_volume(length_a, length_b, length_c, thick_rim_a, thick_rim_b, thick_rim_c); //double vol = length_a * length_b * length_c + // 2.0 * thick_rim_a * length_b * length_c + // 2.0 * thick_rim_b * length_a * length_c + // 2.0 * thick_rim_c * length_a * length_b; // Scale sides by B const double a_scaled = length_a / length_b; const double c_scaled = length_c / length_b; double ta = a_scaled + 2.0*thick_rim_a/length_b; // incorrect ta = (a_scaled + 2.0*thick_rim_a)/length_b; double tb = 1+ 2.0*thick_rim_b/length_b; // incorrect tb = (a_scaled + 2.0*thick_rim_b)/length_b; double tc = c_scaled + 2.0*thick_rim_c/length_b; //not present double Vin = length_a * length_b * length_c; //double Vot = (length_a * length_b * length_c + // 2.0 * thick_rim_a * length_b * length_c + // 2.0 * length_a * thick_rim_b * length_c + // 2.0 * length_a * length_b * thick_rim_c); double V1 = (2.0 * thick_rim_a * length_b * length_c); // incorrect V1 (aa*bb*cc+2*ta*bb*cc) double V2 = (2.0 * length_a * thick_rim_b * length_c); // incorrect V2(aa*bb*cc+2*aa*tb*cc) double V3 = (2.0 * length_a * length_b * thick_rim_c); //not present double Vot = Vin + V1 + V2 + V3; // Scale factors (note that drC is not used later) const double drho0 = (core_sld-solvent_sld); const double drhoA = (arim_sld-solvent_sld); const double drhoB = (brim_sld-solvent_sld); const double drhoC = (crim_sld-solvent_sld); // incorrect const double drC_Vot = (crim_sld-solvent_sld)*Vot; // Precompute scale factors for combining cross terms from the shape const double scale23 = drhoA*V1; const double scale14 = drhoB*V2; const double scale24 = drhoC*V3; const double scale11 = drho0*Vin; const double scale12 = drho0*Vin - scale23 - scale14 - scale24; // outer integral (with gauss points), integration limits = 0, 1 double outer_total = 0; //initialize integral for( int i=0; i<76; i++) { double sigma = 0.5 * ( Gauss76Z[i] + 1.0 ); double mu_proj = mu * sqrt(1.0-sigma*sigma); // inner integral (with gauss points), integration limits = 0, 1 double inner_total = 0.0; double inner_total_crim = 0.0; for(int j=0; j<76; j++) { const double uu = 0.5 * ( Gauss76Z[j] + 1.0 ); double sin_uu, cos_uu; SINCOS(M_PI_2*uu, sin_uu, cos_uu); const double si1 = sas_sinx_x(mu_proj * sin_uu * a_scaled); const double si2 = sas_sinx_x(mu_proj * cos_uu ); const double si3 = sas_sinx_x(mu_proj * sin_uu * ta); const double si4 = sas_sinx_x(mu_proj * cos_uu * tb); // Expression in libCylinder.c (neither drC nor Vot are used) const double form = scale12*si1*si2 + scale23*si2*si3 + scale14*si1*si4; const double form_crim = scale11*si1*si2; // correct FF : sum of square of phase factors inner_total += Gauss76Wt[j] * form * form; inner_total_crim += Gauss76Wt[j] * form_crim * form_crim; } inner_total *= 0.5; inner_total_crim *= 0.5; // now sum up the outer integral const double si = sas_sinx_x(mu * c_scaled * sigma); const double si_crim = sas_sinx_x(mu * tc * sigma); outer_total += Gauss76Wt[i] * (inner_total * si * si + inner_total_crim * si_crim * si_crim); } outer_total *= 0.5; //convert from [1e-12 A-1] to [cm-1] return 1.0e-4 * outer_total; } double Iqxy(double qx, double qy, double core_sld, double arim_sld, double brim_sld, double crim_sld, double solvent_sld, double length_a, double length_b, double length_c, double thick_rim_a, double thick_rim_b, double thick_rim_c, double theta, double phi, double psi) { double q, zhat, yhat, xhat; ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); // cspkernel in csparallelepiped recoded here const double dr0 = core_sld-solvent_sld; const double drA = arim_sld-solvent_sld; const double drB = brim_sld-solvent_sld; const double drC = crim_sld-solvent_sld; double Vin = length_a * length_b * length_c; double V1 = 2.0 * thick_rim_a * length_b * length_c; // incorrect V1(aa*bb*cc+2*ta*bb*cc) double V2 = 2.0 * length_a * thick_rim_b * length_c; // incorrect V2(aa*bb*cc+2*aa*tb*cc) double V3 = 2.0 * length_a * length_b * thick_rim_c; // As for the 1D case, Vot is not used //double Vot = (length_a * length_b * length_c + // 2.0 * thick_rim_a * length_b * length_c + // 2.0 * length_a * thick_rim_b * length_c + // 2.0 * length_a * length_b * thick_rim_c); // The definitions of ta, tb, tc are not the same as in the 1D case because there is no // the scaling by B. double ta = length_a + 2.0*thick_rim_a; double tb = length_b + 2.0*thick_rim_b; double tc = length_c + 2.0*thick_rim_c; //handle arg=0 separately, as sin(t)/t -> 1 as t->0 double siA = sas_sinx_x(0.5*q*length_a*xhat); double siB = sas_sinx_x(0.5*q*length_b*yhat); double siC = sas_sinx_x(0.5*q*length_c*zhat); double siAt = sas_sinx_x(0.5*q*ta*xhat); double siBt = sas_sinx_x(0.5*q*tb*yhat); double siCt = sas_sinx_x(0.5*q*tc*zhat); // f uses Vin, V1, V2, and V3 and it seems to have more sense than the value computed // in the 1D code, but should be checked! double f = ( dr0*siA*siB*siC*Vin + drA*(siAt-siA)*siB*siC*V1 + drB*siA*(siBt-siB)*siC*V2 + drC*siA*siB*(siCt-siC)*V3); return 1.0e-4 * f * f; } sasmodels/sasmodels/models/core_shell_parallelepiped.py000066400000000000000000000211701317715334700240750ustar00rootroot00000000000000r""" Definition ---------- Calculates the form factor for a rectangular solid with a core-shell structure. The thickness and the scattering length density of the shell or "rim" can be different on each (pair) of faces. However at this time the 1D calculation does **NOT** actually calculate a c face rim despite the presence of the parameter. Some other aspects of the 1D calculation may be wrong. .. note:: This model was originally ported from NIST IGOR macros. However, it is not yet fully understood by the SasView developers and is currently under review. The form factor is normalized by the particle volume $V$ such that .. math:: I(q) = \text{scale}\frac{\langle f^2 \rangle}{V} + \text{background} where $\langle \ldots \rangle$ is an average over all possible orientations of the rectangular solid. The function calculated is the form factor of the rectangular solid below. The core of the solid is defined by the dimensions $A$, $B$, $C$ such that $A < B < C$. .. image:: img/core_shell_parallelepiped_geometry.jpg There are rectangular "slabs" of thickness $t_A$ that add to the $A$ dimension (on the $BC$ faces). There are similar slabs on the $AC$ $(=t_B)$ and $AB$ $(=t_C)$ faces. The projection in the $AB$ plane is then .. image:: img/core_shell_parallelepiped_projection.jpg The volume of the solid is .. math:: V = ABC + 2t_ABC + 2t_BAC + 2t_CAB **meaning that there are "gaps" at the corners of the solid.** Again note that $t_C = 0$ currently. The intensity calculated follows the :ref:`parallelepiped` model, with the core-shell intensity being calculated as the square of the sum of the amplitudes of the core and shell, in the same manner as a core-shell model. .. math:: F_{a}(Q,\alpha,\beta)= \left[\frac{\sin(\tfrac{1}{2}Q(L_A+2t_A)\sin\alpha \sin\beta)}{\tfrac{1}{2}Q(L_A+2t_A)\sin\alpha\sin\beta} - \frac{\sin(\tfrac{1}{2}QL_A\sin\alpha \sin\beta)}{\tfrac{1}{2}QL_A\sin\alpha \sin\beta} \right] \left[\frac{\sin(\tfrac{1}{2}QL_B\sin\alpha \sin\beta)}{\tfrac{1}{2}QL_B\sin\alpha \sin\beta} \right] \left[\frac{\sin(\tfrac{1}{2}QL_C\sin\alpha \sin\beta)}{\tfrac{1}{2}QL_C\sin\alpha \sin\beta} \right] .. note:: Why does t_B not appear in the above equation? For the calculation of the form factor to be valid, the sides of the solid MUST (perhaps not any more?) be chosen such that** $A < B < C$. If this inequality is not satisfied, the model will not report an error, but the calculation will not be correct and thus the result wrong. FITTING NOTES If the scale is set equal to the particle volume fraction, $\phi$, the returned value is the scattered intensity per unit volume, $I(q) = \phi P(q)$. However, **no interparticle interference effects are included in this calculation.** There are many parameters in this model. Hold as many fixed as possible with known values, or you will certainly end up at a solution that is unphysical. Constraints must be applied during fitting to ensure that the inequality $A < B < C$ is not violated. The calculation will not report an error, but the results will not be correct. The returned value is in units of |cm^-1|, on absolute scale. NB: The 2nd virial coefficient of the core_shell_parallelepiped is calculated based on the the averaged effective radius $(=\sqrt{(A+2t_A)(B+2t_B)/\pi})$ and length $(C+2t_C)$ values, after appropriately sorting the three dimensions to give an oblate or prolate particle, to give an effective radius, for $S(Q)$ when $P(Q) * S(Q)$ is applied. To provide easy access to the orientation of the parallelepiped, we define the axis of the cylinder using three angles $\theta$, $\phi$ and $\Psi$. (see :ref:`cylinder orientation `). The angle $\Psi$ is the rotational angle around the *long_c* axis against the $q$ plane. For example, $\Psi = 0$ when the *short_b* axis is parallel to the *x*-axis of the detector. .. figure:: img/parallelepiped_angle_definition.png Definition of the angles for oriented core-shell parallelepipeds. .. figure:: img/parallelepiped_angle_projection.png Examples of the angles for oriented core-shell parallelepipeds against the detector plane. References ---------- .. [#] P Mittelbach and G Porod, *Acta Physica Austriaca*, 14 (1961) 185-211 Equations (1), (13-14). (in German) .. [#] D Singh (2009). *Small angle scattering studies of self assembly in lipid mixtures*, John's Hopkins University Thesis (2009) 223-225. `Available from Proquest `_ Authorship and Verification ---------------------------- * **Author:** NIST IGOR/DANSE **Date:** pre 2010 * **Converted to sasmodels by:** Miguel Gonzales **Date:** February 26, 2016 * **Last Modified by:** Wojciech Potrzebowski **Date:** January 11, 2017 * **Currently Under review by:** Paul Butler """ import numpy as np from numpy import pi, inf, sqrt, cos, sin name = "core_shell_parallelepiped" title = "Rectangular solid with a core-shell structure." description = """ P(q)= """ category = "shape:parallelepiped" # ["name", "units", default, [lower, upper], "type","description"], parameters = [["sld_core", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Parallelepiped core scattering length density"], ["sld_a", "1e-6/Ang^2", 2, [-inf, inf], "sld", "Parallelepiped A rim scattering length density"], ["sld_b", "1e-6/Ang^2", 4, [-inf, inf], "sld", "Parallelepiped B rim scattering length density"], ["sld_c", "1e-6/Ang^2", 2, [-inf, inf], "sld", "Parallelepiped C rim scattering length density"], ["sld_solvent", "1e-6/Ang^2", 6, [-inf, inf], "sld", "Solvent scattering length density"], ["length_a", "Ang", 35, [0, inf], "volume", "Shorter side of the parallelepiped"], ["length_b", "Ang", 75, [0, inf], "volume", "Second side of the parallelepiped"], ["length_c", "Ang", 400, [0, inf], "volume", "Larger side of the parallelepiped"], ["thick_rim_a", "Ang", 10, [0, inf], "volume", "Thickness of A rim"], ["thick_rim_b", "Ang", 10, [0, inf], "volume", "Thickness of B rim"], ["thick_rim_c", "Ang", 10, [0, inf], "volume", "Thickness of C rim"], ["theta", "degrees", 0, [-360, 360], "orientation", "c axis to beam angle"], ["phi", "degrees", 0, [-360, 360], "orientation", "rotation about beam"], ["psi", "degrees", 0, [-360, 360], "orientation", "rotation about c axis"], ] source = ["lib/gauss76.c", "core_shell_parallelepiped.c"] def ER(length_a, length_b, length_c, thick_rim_a, thick_rim_b, thick_rim_c): """ Return equivalent radius (ER) """ # surface average radius (rough approximation) surf_rad = sqrt((length_a + 2.0*thick_rim_a) * (length_b + 2.0*thick_rim_b) / pi) height = length_c + 2.0*thick_rim_c ddd = 0.75 * surf_rad * (2 * surf_rad * height + (height + surf_rad) * (height + pi * surf_rad)) return 0.5 * (ddd) ** (1. / 3.) # VR defaults to 1.0 def random(): import numpy as np outer = 10**np.random.uniform(1, 4.7, size=3) thick = np.random.beta(0.5, 0.5, size=3)*(outer-2) + 1 length = outer - thick pars = dict( length_a=length[0], length_b=length[1], length_c=length[2], thick_rim_a=thick[0], thick_rim_b=thick[1], thick_rim_c=thick[2], ) return pars # parameters for demo demo = dict(scale=1, background=0.0, sld_core=1, sld_a=2, sld_b=4, sld_c=2, sld_solvent=6, length_a=35, length_b=75, length_c=400, thick_rim_a=10, thick_rim_b=10, thick_rim_c=10, theta=0, phi=0, psi=0, length_a_pd=0.1, length_a_pd_n=1, length_b_pd=0.1, length_b_pd_n=1, length_c_pd=0.1, length_c_pd_n=1, thick_rim_a_pd=0.1, thick_rim_a_pd_n=1, thick_rim_b_pd=0.1, thick_rim_b_pd_n=1, thick_rim_c_pd=0.1, thick_rim_c_pd_n=1, theta_pd=10, theta_pd_n=1, phi_pd=10, phi_pd_n=1, psi_pd=10, psi_pd_n=1) # rkh 7/4/17 add random unit test for 2d, note make all params different, 2d values not tested against other codes or models qx, qy = 0.2 * cos(pi/6.), 0.2 * sin(pi/6.) tests = [[{}, 0.2, 0.533149288477], [{}, [0.2], [0.533149288477]], [{'theta':10.0, 'phi':20.0}, (qx, qy), 0.0853299803222], [{'theta':10.0, 'phi':20.0}, [(qx, qy)], [0.0853299803222]], ] del qx, qy # not necessary to delete, but cleaner sasmodels/sasmodels/models/core_shell_sphere.c000066400000000000000000000012131317715334700221660ustar00rootroot00000000000000double form_volume(double radius, double thickness); double Iq(double q, double radius, double thickness, double core_sld, double shell_sld, double solvent_sld); double Iq(double q, double radius, double thickness, double core_sld, double shell_sld, double solvent_sld) { double intensity = core_shell_kernel(q, radius, thickness, core_sld, shell_sld, solvent_sld); return intensity; } double form_volume(double radius, double thickness) { return M_4PI_3 * cube(radius + thickness); } sasmodels/sasmodels/models/core_shell_sphere.py000066400000000000000000000104161317715334700224010ustar00rootroot00000000000000r""" .. _core_shell_sphere: This model provides the form factor, $P(q)$, for a spherical particle with a core-shell structure. The form factor is normalized by the particle volume. For information about polarised and magnetic scattering, see the :ref:`magnetism` documentation. Definition ---------- The 1D scattering intensity is calculated in the following way (Guinier, 1955) .. math:: P(q) = \frac{\text{scale}}{V} F^2(q) + \text{background} where .. math:: F^2(q) = \frac{3}{V_s}\left[ V_c(\rho_c-\rho_s)\frac{\sin(qr_c)-qr_c\cos(qr_c)}{(qr_c)^3} + V_s(\rho_s-\rho_\text{solv})\frac{\sin(qr_s)-qr_s\cos(qr_s)}{(qr_s)^3} \right] where $V_s$ is the volume of the whole particle, $V_c$ is the volume of the core, $r_s$ = $radius$ + $thickness$ is the radius of the particle, $r_c$ is the radius of the core, $\rho_c$ is the scattering length density of the core, $\rho_s$ is the scattering length density of the shell, $\rho_\text{solv}$, is the scattering length density of the solvent. The 2D scattering intensity is the same as $P(q)$ above, regardless of the orientation of the $q$ vector. NB: The outer most radius (ie, = radius + thickness) is used as the effective radius for $S(Q)$ when $P(Q) \cdot S(Q)$ is applied. References ---------- A Guinier and G Fournet, *Small-Angle Scattering of X-Rays*, John Wiley and Sons, New York, (1955) Validation ---------- Validation of our code was done by comparing the output of the 1D model to the output of the software provided by NIST (Kline, 2006). Figure 1 shows a comparison of the output of our model and the output of the NIST software. """ from numpy import pi, inf name = "core_shell_sphere" title = "Form factor for a monodisperse spherical particle with particle with a core-shell structure." description = """ F^2(q) = 3/V_s [V_c (sld_core-sld_shell) (sin(q*radius)-q*radius*cos(q*radius))/(q*radius)^3 + V_s (sld_shell-sld_solvent) (sin(q*r_s)-q*r_s*cos(q*r_s))/(q*r_s)^3] V_s: Volume of the sphere shell V_c: Volume of the sphere core r_s: Shell radius = radius + thickness """ category = "shape:sphere" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type","description"], parameters = [["radius", "Ang", 60.0, [0, inf], "volume", "Sphere core radius"], ["thickness", "Ang", 10.0, [0, inf], "volume", "Sphere shell thickness"], ["sld_core", "1e-6/Ang^2", 1.0, [-inf, inf], "sld", "core scattering length density"], ["sld_shell", "1e-6/Ang^2", 2.0, [-inf, inf], "sld", "shell scattering length density"], ["sld_solvent", "1e-6/Ang^2", 3.0, [-inf, inf], "sld", "Solvent scattering length density"]] # pylint: enable=bad-whitespace, line-too-long source = ["lib/sas_3j1x_x.c", "lib/core_shell.c", "core_shell_sphere.c"] demo = dict(scale=1, background=0, radius=60, thickness=10, sld_core=1.0, sld_shell=2.0, sld_solvent=0.0) def ER(radius, thickness): """ Equivalent radius @param radius: core radius @param thickness: shell thickness """ return radius + thickness def VR(radius, thickness): """ Volume ratio @param radius: core radius @param thickness: shell thickness """ return (1, 1) whole = 4.0/3.0 * pi * (radius + thickness)**3 core = 4.0/3.0 * pi * radius**3 return whole, whole - core def random(): import numpy as np outer_radius = 10**np.random.uniform(1.3, 4.3) # Use a distribution with a preference for thin shell or thin core # Avoid core,shell radii < 1 radius = np.random.beta(0.5, 0.5)*(outer_radius-2) + 1 thickness = outer_radius - radius pars = dict( radius=radius, thickness=thickness, ) return pars tests = [ [{'radius': 20.0, 'thickness': 10.0}, 'ER', 30.0], # TODO: VR test suppressed until we sort out new product model # and determine what to do with volume ratio. #[{'radius': 20.0, 'thickness': 10.0}, 'VR', 0.703703704], # The SasView test result was 0.00169, with a background of 0.001 [{'radius': 60.0, 'thickness': 10.0, 'sld_core': 1.0, 'sld_shell': 2.0, 'sld_solvent': 3.0, 'background': 0.0}, 0.4, 0.000698838], ] sasmodels/sasmodels/models/correlation_length.py000066400000000000000000000054721317715334700226040ustar00rootroot00000000000000#correlation length model # Note: model title and parameter table are inserted automatically r""" Definition ---------- The scattering intensity I(q) is calculated as .. math:: I(Q) = \frac{A}{Q^n} + \frac{C}{1 + (Q\xi)^m} + \text{background} The first term describes Porod scattering from clusters (exponent = $n$) and the second term is a Lorentzian function describing scattering from polymer chains (exponent = $m$). This second term characterizes the polymer/solvent interactions and therefore the thermodynamics. The two multiplicative factors $A$ and $C$, and the two exponents $n$ and $m$ are used as fitting parameters. (Respectively *porod_scale*, *lorentz_scale*, *porod_exp* and *lorentz_exp* in the parameter list.) The remaining parameter $\xi$ (*cor_length* in the parameter list) is a correlation length for the polymer chains. Note that when $m=2$ this functional form becomes the familiar Lorentzian function. Some interpretation of the values of $A$ and $C$ may be possible depending on the values of $m$ and $n$. For 2D data: The 2D scattering intensity is calculated in the same way as 1D, where the q vector is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- B Hammouda, D L Ho and S R Kline, Insight into Clustering in Poly(ethylene oxide) Solutions, Macromolecules, 37 (2004) 6932-6937 """ from numpy import inf, errstate name = "correlation_length" title = """Calculates an empirical functional form for SAS data characterized by a low-Q signal and a high-Q signal.""" description = """ """ category = "shape-independent" # pylint: disable=bad-continuation, line-too-long # ["name", "units", default, [lower, upper], "type","description"], parameters = [ ["lorentz_scale", "", 10.0, [0, inf], "", "Lorentzian Scaling Factor"], ["porod_scale", "", 1e-06, [0, inf], "", "Porod Scaling Factor"], ["cor_length", "Ang", 50.0, [0, inf], "", "Correlation length, xi, in Lorentzian"], ["porod_exp", "", 3.0, [0, inf], "", "Porod Exponent, n, in q^-n"], ["lorentz_exp", "1/Ang^2", 2.0, [0, inf], "", "Lorentzian Exponent, m, in 1/( 1 + (q.xi)^m)"], ] # pylint: enable=bad-continuation, line-too-long def Iq(q, lorentz_scale, porod_scale, cor_length, porod_exp, lorentz_exp): """ 1D calculation of the Correlation length model """ with errstate(divide='ignore'): porod = porod_scale / q**porod_exp lorentz = lorentz_scale / (1.0 + (q * cor_length)**lorentz_exp) inten = porod + lorentz return inten Iq.vectorized = True # parameters for demo demo = dict(lorentz_scale=10.0, porod_scale=1.0e-06, cor_length=50.0, porod_exp=3.0, lorentz_exp=2.0, background=0.1, ) tests = [[{}, 0.001, 1009.98], [{}, 0.150141, 0.175645], [{}, 0.442528, 0.0213957]] sasmodels/sasmodels/models/cylinder.c000066400000000000000000000041231317715334700203150ustar00rootroot00000000000000double form_volume(double radius, double length); double fq(double q, double sn, double cn,double radius, double length); double orient_avg_1D(double q, double radius, double length); double Iq(double q, double sld, double solvent_sld, double radius, double length); double Iqxy(double qx, double qy, double sld, double solvent_sld, double radius, double length, double theta, double phi); #define INVALID(v) (v.radius<0 || v.length<0) double form_volume(double radius, double length) { return M_PI*radius*radius*length; } double fq(double q, double sn, double cn, double radius, double length) { // precompute qr and qh to save time in the loop const double qr = q*radius; const double qh = q*0.5*length; return sas_2J1x_x(qr*sn) * sas_sinx_x(qh*cn); } double orient_avg_1D(double q, double radius, double length) { // translate a point in [-1,1] to a point in [0, pi/2] const double zm = M_PI_4; const double zb = M_PI_4; double total = 0.0; for (int i=0; i<76 ;i++) { const double alpha = Gauss76Z[i]*zm + zb; double sn, cn; // slots to hold sincos function output // alpha(theta,phi) the projection of the cylinder on the detector plane SINCOS(alpha, sn, cn); total += Gauss76Wt[i] * square( fq(q, sn, cn, radius, length) ) * sn; } // translate dx in [-1,1] to dx in [lower,upper] return total*zm; } double Iq(double q, double sld, double solvent_sld, double radius, double length) { const double s = (sld - solvent_sld) * form_volume(radius, length); return 1.0e-4 * s * s * orient_avg_1D(q, radius, length); } double Iqxy(double qx, double qy, double sld, double solvent_sld, double radius, double length, double theta, double phi) { double q, sin_alpha, cos_alpha; ORIENT_SYMMETRIC(qx, qy, theta, phi, q, sin_alpha, cos_alpha); //printf("sn: %g cn: %g\n", sin_alpha, cos_alpha); const double s = (sld-solvent_sld) * form_volume(radius, length); const double form = fq(q, sin_alpha, cos_alpha, radius, length); return 1.0e-4 * square(s * form); } sasmodels/sasmodels/models/cylinder.py000066400000000000000000000155451317715334700205350ustar00rootroot00000000000000# cylinder model # Note: model title and parameter table are inserted automatically r""" For information about polarised and magnetic scattering, see the :ref:`magnetism` documentation. Definition ---------- The output of the 2D scattering intensity function for oriented cylinders is given by (Guinier, 1955) .. math:: P(q,\alpha) = \frac{\text{scale}}{V} F^2(q,\alpha).sin(\alpha) + \text{background} where .. math:: F(q,\alpha) = 2 (\Delta \rho) V \frac{\sin \left(\tfrac12 qL\cos\alpha \right)} {\tfrac12 qL \cos \alpha} \frac{J_1 \left(q R \sin \alpha\right)}{q R \sin \alpha} and $\alpha$ is the angle between the axis of the cylinder and $\vec q$, $V =\pi R^2L$ is the volume of the cylinder, $L$ is the length of the cylinder, $R$ is the radius of the cylinder, and $\Delta\rho$ (contrast) is the scattering length density difference between the scatterer and the solvent. $J_1$ is the first order Bessel function. For randomly oriented particles: .. math:: F^2(q)=\int_{0}^{\pi/2}{F^2(q,\alpha)\sin(\alpha)d\alpha}=\int_{0}^{1}{F^2(q,u)du} Numerical integration is simplified by a change of variable to $u = cos(\alpha)$ with $sin(\alpha)=\sqrt{1-u^2}$. The output of the 1D scattering intensity function for randomly oriented cylinders is thus given by .. math:: P(q) = \frac{\text{scale}}{V} \int_0^{\pi/2} F^2(q,\alpha) \sin \alpha\ d\alpha + \text{background} NB: The 2nd virial coefficient of the cylinder is calculated based on the radius and length values, and used as the effective radius for $S(q)$ when $P(q) \cdot S(q)$ is applied. For oriented cylinders, we define the direction of the axis of the cylinder using two angles $\theta$ (note this is not the same as the scattering angle used in q) and $\phi$. Those angles are defined in :numref:`cylinder-angle-definition` . .. _cylinder-angle-definition: .. figure:: img/cylinder_angle_definition.png Definition of the $\theta$ and $\phi$ orientation angles for a cylinder relative to the beam line coordinates, plus an indication of their orientation distributions which are described as rotations about each of the perpendicular axes $\delta_1$ and $\delta_2$ in the frame of the cylinder itself, which when $\theta = \phi = 0$ are parallel to the $Y$ and $X$ axes. .. figure:: img/cylinder_angle_projection.png Examples for oriented cylinders. The $\theta$ and $\phi$ parameters to orient the cylinder only appear in the model when fitting 2d data. On introducing "Orientational Distribution" in the angles, "distribution of theta" and "distribution of phi" parameters will appear. These are actually rotations about the axes $\delta_1$ and $\delta_2$ of the cylinder, which when $\theta = \phi = 0$ are parallel to the $Y$ and $X$ axes of the instrument respectively. Some experimentation may be required to understand the 2d patterns fully. (Earlier implementations had numerical integration issues in some circumstances when orientation distributions passed through 90 degrees, such situations, with very broad distributions, should still be approached with care.) Validation ---------- Validation of the code was done by comparing the output of the 1D model to the output of the software provided by the NIST (Kline, 2006). The implementation of the intensity for fully oriented cylinders was done by averaging over a uniform distribution of orientations using .. math:: P(q) = \int_0^{\pi/2} d\phi \int_0^\pi p(\theta) P_0(q,\theta) \sin \theta\ d\theta where $p(\theta,\phi) = 1$ is the probability distribution for the orientation and $P_0(q,\theta)$ is the scattering intensity for the fully oriented system, and then comparing to the 1D result. References ---------- J. S. Pedersen, Adv. Colloid Interface Sci. 70, 171-210 (1997). G. Fournet, Bull. Soc. Fr. Mineral. Cristallogr. 74, 39-113 (1951). """ import numpy as np # type: ignore from numpy import pi, inf # type: ignore name = "cylinder" title = "Right circular cylinder with uniform scattering length density." description = """ f(q,alpha) = 2*(sld - sld_solvent)*V*sin(qLcos(alpha)/2)) /[qLcos(alpha)/2]*J1(qRsin(alpha))/[qRsin(alpha)] P(q,alpha)= scale/V*f(q,alpha)^(2)+background V: Volume of the cylinder R: Radius of the cylinder L: Length of the cylinder J1: The bessel function alpha: angle between the axis of the cylinder and the q-vector for 1D :the ouput is P(q)=scale/V*integral from pi/2 to zero of... f(q,alpha)^(2)*sin(alpha)*dalpha + background """ category = "shape:cylinder" # [ "name", "units", default, [lower, upper], "type", "description"], parameters = [["sld", "1e-6/Ang^2", 4, [-inf, inf], "sld", "Cylinder scattering length density"], ["sld_solvent", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Solvent scattering length density"], ["radius", "Ang", 20, [0, inf], "volume", "Cylinder radius"], ["length", "Ang", 400, [0, inf], "volume", "Cylinder length"], ["theta", "degrees", 60, [-360, 360], "orientation", "cylinder axis to beam angle"], ["phi", "degrees", 60, [-360, 360], "orientation", "rotation about beam"], ] source = ["lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c", "cylinder.c"] def ER(radius, length): """ Return equivalent radius (ER) """ ddd = 0.75 * radius * (2 * radius * length + (length + radius) * (length + pi * radius)) return 0.5 * (ddd) ** (1. / 3.) def random(): import numpy as np V = 10**np.random.uniform(5, 12) length = 10**np.random.uniform(-2, 2)*V**0.333 radius = np.sqrt(V/length/np.pi) pars = dict( #scale=1, #background=0, length=length, radius=radius, ) return pars # parameters for demo demo = dict(scale=1, background=0, sld=6, sld_solvent=1, radius=20, length=300, theta=60, phi=60, radius_pd=.2, radius_pd_n=9, length_pd=.2, length_pd_n=10, theta_pd=10, theta_pd_n=5, phi_pd=10, phi_pd_n=5) qx, qy = 0.2 * np.cos(2.5), 0.2 * np.sin(2.5) # After redefinition of angles, find new tests values. Was 10 10 in old coords tests = [[{}, 0.2, 0.042761386790780453], [{}, [0.2], [0.042761386790780453]], # new coords [{'theta':80.1534480601659, 'phi':10.1510817110481}, (qx, qy), 0.03514647218513852], [{'theta':80.1534480601659, 'phi':10.1510817110481}, [(qx, qy)], [0.03514647218513852]], # old coords [{'theta':10.0, 'phi':10.0}, (qx, qy), 0.03514647218513852], # [{'theta':10.0, 'phi':10.0}, [(qx, qy)], [0.03514647218513852]], ] del qx, qy # not necessary to delete, but cleaner # ADDED by: RKH ON: 18Mar2016 renamed sld's etcsasmodels/sasmodels/models/dab.py000066400000000000000000000041371317715334700174450ustar00rootroot00000000000000r""" Calculates the scattering from a randomly distributed, two-phase system based on the Debye-Anderson-Brumberger (DAB) model for such systems. The two-phase system is characterized by a single length scale, the correlation length, which is a measure of the average spacing between regions of phase 1 and phase 2. **The model also assumes smooth interfaces between the phases** and hence exhibits Porod behavior $(I \sim q^{-4})$ at large $q$, $(qL \gg 1)$. The DAB model is ostensibly a development of the earlier Debye-Bueche model. Definition ---------- .. math:: I(q) = \text{scale}\cdot\frac{L^3}{(1 + (q\cdot L)^2)^2} + \text{background} where scale is .. math:: \text{scale} = 8 \pi \phi (1-\phi) \Delta\rho^2 and the parameter $L$ is the correlation length. For 2D data the scattering intensity is calculated in the same way as 1D, where the $q$ vector is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- P Debye, H R Anderson, H Brumberger, *Scattering by an Inhomogeneous Solid. II. The Correlation Function and its Application*, *J. Appl. Phys.*, 28(6) (1957) 679 P Debye, A M Bueche, *Scattering by an Inhomogeneous Solid*, *J. Appl. Phys.*, 20 (1949) 518 *2013/09/09 - Description reviewed by King, S and Parker, P.* """ from numpy import inf name = "dab" title = "DAB (Debye Anderson Brumberger) Model" description = """\ F(q)= scale * L^3/(1 + (q*L)^2)^2 L: the correlation length """ category = "shape-independent" # ["name", "units", default, [lower, upper], "type", "description"], parameters = [["cor_length", "Ang", 50.0, [0, inf], "", "correlation length"], ] Iq = """ double numerator = cube(cor_length); double denominator = square(1 + square(q*cor_length)); return numerator / denominator ; """ def random(): import numpy as np pars = dict( scale=10**np.random.uniform(1, 4), cor_length=10**np.random.uniform(0.3, 3), #background = 0, ) pars['scale'] /= pars['cor_length']**3 return pars # ER defaults to 1.0 # VR defaults to 1.0 demo = dict(scale=1, background=0, cor_length=50) sasmodels/sasmodels/models/ellipsoid.c000066400000000000000000000043501317715334700204720ustar00rootroot00000000000000double form_volume(double radius_polar, double radius_equatorial); double Iq(double q, double sld, double sld_solvent, double radius_polar, double radius_equatorial); double Iqxy(double qx, double qy, double sld, double sld_solvent, double radius_polar, double radius_equatorial, double theta, double phi); double form_volume(double radius_polar, double radius_equatorial) { return M_4PI_3*radius_polar*radius_equatorial*radius_equatorial; } double Iq(double q, double sld, double sld_solvent, double radius_polar, double radius_equatorial) { // Using ratio v = Rp/Re, we can implement the form given in Guinier (1955) // i(h) = int_0^pi/2 Phi^2(h a sqrt(cos^2 + v^2 sin^2) cos dT // = int_0^pi/2 Phi^2(h a sqrt((1-sin^2) + v^2 sin^2) cos dT // = int_0^pi/2 Phi^2(h a sqrt(1 + sin^2(v^2-1)) cos dT // u-substitution of // u = sin, du = cos dT // i(h) = int_0^1 Phi^2(h a sqrt(1 + u^2(v^2-1)) du const double v_square_minus_one = square(radius_polar/radius_equatorial) - 1.0; // translate a point in [-1,1] to a point in [0, 1] // const double u = Gauss76Z[i]*(upper-lower)/2 + (upper+lower)/2; const double zm = 0.5; const double zb = 0.5; double total = 0.0; for (int i=0;i<76;i++) { const double u = Gauss76Z[i]*zm + zb; const double r = radius_equatorial*sqrt(1.0 + u*u*v_square_minus_one); const double f = sas_3j1x_x(q*r); total += Gauss76Wt[i] * f * f; } // translate dx in [-1,1] to dx in [lower,upper] const double form = total*zm; const double s = (sld - sld_solvent) * form_volume(radius_polar, radius_equatorial); return 1.0e-4 * s * s * form; } double Iqxy(double qx, double qy, double sld, double sld_solvent, double radius_polar, double radius_equatorial, double theta, double phi) { double q, sin_alpha, cos_alpha; ORIENT_SYMMETRIC(qx, qy, theta, phi, q, sin_alpha, cos_alpha); const double r = sqrt(square(radius_equatorial*sin_alpha) + square(radius_polar*cos_alpha)); const double f = sas_3j1x_x(q*r); const double s = (sld - sld_solvent) * form_volume(radius_polar, radius_equatorial); return 1.0e-4 * square(f * s); } sasmodels/sasmodels/models/ellipsoid.py000066400000000000000000000163671317715334700207130ustar00rootroot00000000000000# ellipsoid model # Note: model title and parameter table are inserted automatically r""" The form factor is normalized by the particle volume Definition ---------- The output of the 2D scattering intensity function for oriented ellipsoids is given by (Feigin, 1987) .. math:: P(q,\alpha) = \frac{\text{scale}}{V} F^2(q,\alpha) + \text{background} where .. math:: F(q,\alpha) = \Delta \rho V \frac{3(\sin qr - qr \cos qr)}{(qr)^3} for .. math:: r = \left[ R_e^2 \sin^2 \alpha + R_p^2 \cos^2 \alpha \right]^{1/2} $\alpha$ is the angle between the axis of the ellipsoid and $\vec q$, $V = (4/3)\pi R_pR_e^2$ is the volume of the ellipsoid, $R_p$ is the polar radius along the rotational axis of the ellipsoid, $R_e$ is the equatorial radius perpendicular to the rotational axis of the ellipsoid and $\Delta \rho$ (contrast) is the scattering length density difference between the scatterer and the solvent. For randomly oriented particles use the orientational average, .. math:: \langle F^2(q) \rangle = \int_{0}^{\pi/2}{F^2(q,\alpha)\sin(\alpha)\,d\alpha} computed via substitution of $u=\sin(\alpha)$, $du=\cos(\alpha)\,d\alpha$ as .. math:: \langle F^2(q) \rangle = \int_0^1{F^2(q, u)\,du} with .. math:: r = R_e \left[ 1 + u^2\left(R_p^2/R_e^2 - 1\right)\right]^{1/2} To provide easy access to the orientation of the ellipsoid, we define the rotation axis of the ellipsoid using two angles $\theta$ and $\phi$. These angles are defined in the :ref:`cylinder orientation figure `. For the ellipsoid, $\theta$ is the angle between the rotational axis and the $z$ -axis in the $xz$ plane followed by a rotation by $\phi$ in the $xy$ plane. NB: The 2nd virial coefficient of the solid ellipsoid is calculated based on the $R_p$ and $R_e$ values, and used as the effective radius for $S(q)$ when $P(q) \cdot S(q)$ is applied. The $\theta$ and $\phi$ parameters are not used for the 1D output. Validation ---------- Validation of the code was done by comparing the output of the 1D model to the output of the software provided by the NIST (Kline, 2006). The implementation of the intensity for fully oriented ellipsoids was validated by averaging the 2D output using a uniform distribution $p(\theta,\phi) = 1.0$ and comparing with the output of the 1D calculation. .. _ellipsoid-comparison-2d: .. figure:: img/ellipsoid_comparison_2d.jpg Comparison of the intensity for uniformly distributed ellipsoids calculated from our 2D model and the intensity from the NIST SANS analysis software. The parameters used were: *scale* = 1.0, *radius_polar* = 20 |Ang|, *radius_equatorial* = 400 |Ang|, *contrast* = 3e-6 |Ang^-2|, and *background* = 0.0 |cm^-1|. The discrepancy above $q$ = 0.3 |cm^-1| is due to the way the form factors are calculated in the c-library provided by NIST. A numerical integration has to be performed to obtain $P(q)$ for randomly oriented particles. The NIST software performs that integration with a 76-point Gaussian quadrature rule, which will become imprecise at high $q$ where the amplitude varies quickly as a function of $q$. The SasView result shown has been obtained by summing over 501 equidistant points. Our result was found to be stable over the range of $q$ shown for a number of points higher than 500. Model was also tested against the triaxial ellipsoid model with equal major and minor equatorial radii. It is also consistent with the cyclinder model with polar radius equal to length and equatorial radius equal to radius. References ---------- L A Feigin and D I Svergun. *Structure Analysis by Small-Angle X-Ray and Neutron Scattering*, Plenum Press, New York, 1987. A. Isihara. J. Chem. Phys. 18(1950) 1446-1449 Authorship and Verification ---------------------------- * **Author:** NIST IGOR/DANSE **Date:** pre 2010 * **Converted to sasmodels by:** Helen Park **Date:** July 9, 2014 * **Last Modified by:** Paul Kienzle **Date:** March 22, 2017 """ from __future__ import division from numpy import inf, sin, cos, pi name = "ellipsoid" title = "Ellipsoid of revolution with uniform scattering length density." description = """\ P(q.alpha)= scale*f(q)^2 + background, where f(q)= 3*(sld - sld_solvent)*V*[sin(q*r(Rp,Re,alpha)) -q*r*cos(qr(Rp,Re,alpha))] /[qr(Rp,Re,alpha)]^3" r(Rp,Re,alpha)= [Re^(2)*(sin(alpha))^2 + Rp^(2)*(cos(alpha))^2]^(1/2) sld: SLD of the ellipsoid sld_solvent: SLD of the solvent V: volume of the ellipsoid Rp: polar radius of the ellipsoid Re: equatorial radius of the ellipsoid """ category = "shape:ellipsoid" # ["name", "units", default, [lower, upper], "type","description"], parameters = [["sld", "1e-6/Ang^2", 4, [-inf, inf], "sld", "Ellipsoid scattering length density"], ["sld_solvent", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Solvent scattering length density"], ["radius_polar", "Ang", 20, [0, inf], "volume", "Polar radius"], ["radius_equatorial", "Ang", 400, [0, inf], "volume", "Equatorial radius"], ["theta", "degrees", 60, [-360, 360], "orientation", "ellipsoid axis to beam angle"], ["phi", "degrees", 60, [-360, 360], "orientation", "rotation about beam"], ] source = ["lib/sas_3j1x_x.c", "lib/gauss76.c", "ellipsoid.c"] def ER(radius_polar, radius_equatorial): import numpy as np # see equation (26) in A.Isihara, J.Chem.Phys. 18(1950)1446-1449 ee = np.empty_like(radius_polar) idx = radius_polar > radius_equatorial ee[idx] = (radius_polar[idx] ** 2 - radius_equatorial[idx] ** 2) / radius_polar[idx] ** 2 idx = radius_polar < radius_equatorial ee[idx] = (radius_equatorial[idx] ** 2 - radius_polar[idx] ** 2) / radius_equatorial[idx] ** 2 idx = radius_polar == radius_equatorial ee[idx] = 2 * radius_polar[idx] valid = (radius_polar * radius_equatorial != 0) bd = 1.0 - ee[valid] e1 = np.sqrt(ee[valid]) b1 = 1.0 + np.arcsin(e1) / (e1 * np.sqrt(bd)) bL = (1.0 + e1) / (1.0 - e1) b2 = 1.0 + bd / 2 / e1 * np.log(bL) delta = 0.75 * b1 * b2 ddd = np.zeros_like(radius_polar) ddd[valid] = 2.0 * (delta + 1.0) * radius_polar * radius_equatorial ** 2 return 0.5 * ddd ** (1.0 / 3.0) def random(): import numpy as np V = 10**np.random.uniform(5, 12) radius_polar = 10**np.random.uniform(1.3, 4) radius_equatorial = np.sqrt(V/radius_polar) # ignore 4/3 pi pars = dict( #background=0, sld=0, sld_solvent=1, radius_polar=radius_polar, radius_equatorial=radius_equatorial, ) return pars demo = dict(scale=1, background=0, sld=6, sld_solvent=1, radius_polar=50, radius_equatorial=30, theta=30, phi=15, radius_polar_pd=.2, radius_polar_pd_n=15, radius_equatorial_pd=.2, radius_equatorial_pd_n=15, theta_pd=15, theta_pd_n=45, phi_pd=15, phi_pd_n=1) q = 0.1 # april 6 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! qx = q*cos(pi/6.0) qy = q*sin(pi/6.0) tests = [[{}, 0.05, 54.8525847025], [{'theta':80., 'phi':10.}, (qx, qy), 1.74134670026 ], ] del qx, qy # not necessary to delete, but cleaner sasmodels/sasmodels/models/elliptical_cylinder.c000066400000000000000000000057141317715334700225260ustar00rootroot00000000000000double form_volume(double radius_minor, double r_ratio, double length); double Iq(double q, double radius_minor, double r_ratio, double length, double sld, double solvent_sld); double Iqxy(double qx, double qy, double radius_minor, double r_ratio, double length, double sld, double solvent_sld, double theta, double phi, double psi); double form_volume(double radius_minor, double r_ratio, double length) { return M_PI * radius_minor * radius_minor * r_ratio * length; } double Iq(double q, double radius_minor, double r_ratio, double length, double sld, double solvent_sld) { // orientational average limits const double va = 0.0; const double vb = 1.0; // inner integral limits const double vaj=0.0; const double vbj=M_PI; const double radius_major = r_ratio * radius_minor; const double rA = 0.5*(square(radius_major) + square(radius_minor)); const double rB = 0.5*(square(radius_major) - square(radius_minor)); //initialize integral double outer_sum = 0.0; for(int i=0;i<76;i++) { //setup inner integral over the ellipsoidal cross-section const double cos_val = ( Gauss76Z[i]*(vb-va) + va + vb )/2.0; const double sin_val = sqrt(1.0 - cos_val*cos_val); //const double arg = radius_minor*sin_val; double inner_sum=0; for(int j=0;j<20;j++) { //20 gauss points for the inner integral const double theta = ( Gauss20Z[j]*(vbj-vaj) + vaj + vbj )/2.0; const double r = sin_val*sqrt(rA - rB*cos(theta)); const double be = sas_2J1x_x(q*r); inner_sum += Gauss20Wt[j] * be * be; } //now calculate the value of the inner integral inner_sum *= 0.5*(vbj-vaj); //now calculate outer integral const double si = sas_sinx_x(q*0.5*length*cos_val); outer_sum += Gauss76Wt[i] * inner_sum * si * si; } outer_sum *= 0.5*(vb-va); //divide integral by Pi const double form = outer_sum/M_PI; // scale by contrast and volume, and convert to to 1/cm units const double vol = form_volume(radius_minor, r_ratio, length); const double delrho = sld - solvent_sld; return 1.0e-4*square(delrho*vol)*form; } double Iqxy(double qx, double qy, double radius_minor, double r_ratio, double length, double sld, double solvent_sld, double theta, double phi, double psi) { double q, xhat, yhat, zhat; ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); // Compute: r = sqrt((radius_major*cos_nu)^2 + (radius_minor*cos_mu)^2) // Given: radius_major = r_ratio * radius_minor const double r = radius_minor*sqrt(square(r_ratio*xhat) + square(yhat)); const double be = sas_2J1x_x(q*r); const double si = sas_sinx_x(q*zhat*0.5*length); const double Aq = be * si; const double delrho = sld - solvent_sld; const double vol = form_volume(radius_minor, r_ratio, length); return 1.0e-4 * square(delrho * vol * Aq); } sasmodels/sasmodels/models/elliptical_cylinder.py000066400000000000000000000164401317715334700227320ustar00rootroot00000000000000# pylint: disable=line-too-long r""" Definition for 2D (orientated system) ------------------------------------- The angles $\theta$ and $\phi$ define the orientation of the axis of the cylinder. The angle $\Psi$ is defined as the orientation of the major axis of the ellipse with respect to the vector $Q$. A gaussian polydispersity can be added to any of the orientation angles, and also for the minor radius and the ratio of the ellipse radii. .. figure:: img/elliptical_cylinder_geometry.png Elliptical cylinder geometry $a = r_\text{minor}$ and $\nu = r_\text{major} / r_\text{minor}$ is the *axis_ratio*. The function calculated is .. math:: I(\vec q)=\frac{1}{V_\text{cyl}}\int{d\psi}\int{d\phi}\int{ p(\theta,\phi,\psi)F^2(\vec q,\alpha,\psi)\sin(\alpha)d\alpha} with the functions .. math:: F(q,\alpha,\psi) = 2\frac{J_1(a)\sin(b)}{ab} where .. math:: a = qr'\sin(\alpha) b = q\frac{L}{2}\cos(\alpha) r'=\frac{r_{minor}}{\sqrt{2}}\sqrt{(1+\nu^{2}) + (1-\nu^{2})cos(\psi)} and the angle $\psi$ is defined as the orientation of the major axis of the ellipse with respect to the vector $\vec q$. The angle $\alpha$ is the angle between the axis of the cylinder and $\vec q$. Definition for 1D (no preferred orientation) -------------------------------------------- The form factor is averaged over all possible orientation before normalized by the particle volume .. math:: P(q) = \text{scale} / V To provide easy access to the orientation of the elliptical cylinder, we define the axis of the cylinder using two angles $\theta$, $\phi$ and $\Psi$ (see :ref:`cylinder orientation `). The angle $\Psi$ is the rotational angle around its own long_c axis. All angle parameters are valid and given only for 2D calculation; ie, an oriented system. .. figure:: img/elliptical_cylinder_angle_definition.png Definition of angles for oriented elliptical cylinder, where axis_ratio is drawn >1, and angle $\Psi$ is now a rotation around the axis of the cylinder. .. figure:: img/elliptical_cylinder_angle_projection.png Examples of the angles for oriented elliptical cylinders against the detector plane, with $\Psi$ = 0. The $\theta$ and $\phi$ parameters to orient the cylinder only appear in the model when fitting 2d data. On introducing "Orientational Distribution" in the angles, "distribution of theta" and "distribution of phi" parameters will appear. These are actually rotations about the axes $\delta_1$ and $\delta_2$ of the cylinder, the $b$ and $a$ axes of the cylinder cross section. (When $\theta = \phi = 0$ these are parallel to the $Y$ and $X$ axes of the instrument.) The third orientation distribution, in $\psi$, is about the $c$ axis of the particle. Some experimentation may be required to understand the 2d patterns fully. (Earlier implementations had numerical integration issues in some circumstances when orientation distributions passed through 90 degrees, such situations, with very broad distributions, should still be approached with care.) NB: The 2nd virial coefficient of the cylinder is calculated based on the averaged radius $(=\sqrt{r_\text{minor}^2 * \text{axis ratio}})$ and length values, and used as the effective radius for $S(Q)$ when $P(Q)*S(Q)$ is applied. Validation ---------- Validation of our code was done by comparing the output of the 1D calculation to the angular average of the output of the 2D calculation over all possible angles. In the 2D average, more binning in the angle $\phi$ is necessary to get the proper result. The following figure shows the results of the averaging by varying the number of angular bins. .. figure:: img/elliptical_cylinder_averaging.png The intensities averaged from 2D over different numbers of bins and angles. References ---------- L A Feigin and D I Svergun, *Structure Analysis by Small-Angle X-Ray and Neutron Scattering*, Plenum, New York, (1987) [see table 3.4] Authorship and Verification ---------------------------- * **Author:** * **Last Modified by:** * **Last Reviewed by:** Richard Heenan - corrected equation in docs **Date:** December 21, 2016 """ from numpy import pi, inf, sqrt, sin, cos name = "elliptical_cylinder" title = "Form factor for an elliptical cylinder." description = """ Form factor for an elliptical cylinder. See L A Feigin and D I Svergun, Structure Analysis by Small-Angle X-Ray and Neutron Scattering, Plenum, New York, (1987). """ category = "shape:cylinder" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type","description"], parameters = [["radius_minor", "Ang", 20.0, [0, inf], "volume", "Ellipse minor radius"], ["axis_ratio", "", 1.5, [1, inf], "volume", "Ratio of major radius over minor radius"], ["length", "Ang", 400.0, [1, inf], "volume", "Length of the cylinder"], ["sld", "1e-6/Ang^2", 4.0, [-inf, inf], "sld", "Cylinder scattering length density"], ["sld_solvent", "1e-6/Ang^2", 1.0, [-inf, inf], "sld", "Solvent scattering length density"], ["theta", "degrees", 90.0, [-360, 360], "orientation", "cylinder axis to beam angle"], ["phi", "degrees", 0, [-360, 360], "orientation", "rotation about beam"], ["psi", "degrees", 0, [-360, 360], "orientation", "rotation about cylinder axis"]] # pylint: enable=bad-whitespace, line-too-long source = ["lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c", "lib/gauss20.c", "elliptical_cylinder.c"] demo = dict(scale=1, background=0, radius_minor=100, axis_ratio=1.5, length=400.0, sld=4.0, sld_solvent=1.0, theta=10.0, phi=20, psi=30, theta_pd=10, phi_pd=2, psi_pd=3) def ER(radius_minor, axis_ratio, length): """ Equivalent radius @param radius_minor: Ellipse minor radius @param axis_ratio: Ratio of major radius over minor radius @param length: Length of the cylinder """ radius = sqrt(radius_minor * radius_minor * axis_ratio) ddd = 0.75 * radius * (2 * radius * length + (length + radius) * (length + pi * radius)) return 0.5 * (ddd) ** (1. / 3.) def random(): import numpy as np # V = pi * radius_major * radius_minor * length; V = 10**np.random.uniform(3, 9) length = 10**np.random.uniform(1, 3) axis_ratio = 10**np.random.uniform(0, 2) radius_minor = np.sqrt(V/length/axis_ratio) Vf = 10**np.random.uniform(-4, -2) pars = dict( #background=0, sld=0, sld_solvent=1, scale=1e9*Vf/V, length=length, radius_minor=radius_minor, axis_ratio=axis_ratio, ) return pars q = 0.1 # april 6 2017, rkh added a 2d unit test, NOT READY YET pull #890 branch assume correct! qx = q*cos(pi/6.0) qy = q*sin(pi/6.0) tests = [ [{'radius_minor': 20.0, 'axis_ratio': 1.5, 'length':400.0}, 'ER', 79.89245454155024], [{'radius_minor': 20.0, 'axis_ratio': 1.2, 'length':300.0}, 'VR', 1], # The SasView test result was 0.00169, with a background of 0.001 [{'radius_minor': 20.0, 'axis_ratio': 1.5, 'sld': 4.0, 'length':400.0, 'sld_solvent':1.0, 'background':0.0}, 0.001, 675.504402], # [{'theta':80., 'phi':10.}, (qx, qy), 7.88866563001 ], ] sasmodels/sasmodels/models/fcc_paracrystal.c000066400000000000000000000074101317715334700216460ustar00rootroot00000000000000double form_volume(double radius); double Iq(double q,double dnn,double d_factor, double radius,double sld, double solvent_sld); double Iqxy(double qx, double qy, double dnn, double d_factor, double radius,double sld, double solvent_sld, double theta, double phi, double psi); double _FCC_Integrand(double q, double dnn, double d_factor, double theta, double phi); double _FCCeval(double Theta, double Phi, double temp1, double temp3); double _FCC_Integrand(double q, double dnn, double d_factor, double theta, double phi) { const double Da = d_factor*dnn; const double temp1 = q*q*Da*Da; const double temp3 = q*dnn; double retVal = _FCCeval(theta,phi,temp1,temp3)/(4.0*M_PI); return(retVal); } double _FCCeval(double Theta, double Phi, double temp1, double temp3) { double result; double sin_theta,cos_theta,sin_phi,cos_phi; SINCOS(Theta, sin_theta, cos_theta); SINCOS(Phi, sin_phi, cos_phi); const double temp6 = sin_theta; const double temp7 = sin_theta*sin_phi + cos_theta; const double temp8 = -sin_theta*cos_phi + cos_theta; const double temp9 = -sin_theta*cos_phi + sin_theta*sin_phi; const double temp10 = exp((-1.0/8.0)*temp1*((temp7*temp7)+(temp8*temp8)+(temp9*temp9))); result = cube(1.0-(temp10*temp10))*temp6 / ( (1.0 - 2.0*temp10*cos(0.5*temp3*temp7) + temp10*temp10) * (1.0 - 2.0*temp10*cos(0.5*temp3*temp8) + temp10*temp10) * (1.0 - 2.0*temp10*cos(0.5*temp3*temp9) + temp10*temp10)); return (result); } double form_volume(double radius){ return sphere_volume(radius); } double Iq(double q, double dnn, double d_factor, double radius, double sld, double solvent_sld){ //Volume fraction calculated from lattice symmetry and sphere radius const double s1 = dnn*sqrt(2.0); const double latticescale = 4.0*sphere_volume(radius/s1); const double va = 0.0; const double vb = 2.0*M_PI; const double vaj = 0.0; const double vbj = M_PI; double summ = 0.0; double answer = 0.0; for(int i=0; i<150; i++) { //setup inner integral over the ellipsoidal cross-section double summj=0.0; const double zphi = ( Gauss150Z[i]*(vb-va) + va + vb )/2.0; //the outer dummy is phi for(int j=0;j<150;j++) { //20 gauss points for the inner integral double ztheta = ( Gauss150Z[j]*(vbj-vaj) + vaj + vbj )/2.0; //the inner dummy is theta double yyy = Gauss150Wt[j] * _FCC_Integrand(q,dnn,d_factor,ztheta,zphi); summj += yyy; } //now calculate the value of the inner integral double answer = (vbj-vaj)/2.0*summj; //now calculate outer integral summ = summ+(Gauss150Wt[i] * answer); } //final scaling is done at the end of the function, after the NT_FP64 case answer = (vb-va)/2.0*summ; answer = answer*sphere_form(q,radius,sld,solvent_sld)*latticescale; return answer; } double Iqxy(double qx, double qy, double dnn, double d_factor, double radius, double sld, double solvent_sld, double theta, double phi, double psi) { double q, zhat, yhat, xhat; ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); const double a1 = yhat + xhat; const double a2 = xhat + zhat; const double a3 = yhat + zhat; const double qd = 0.5*q*dnn; const double arg = 0.5*square(qd*d_factor)*(a1*a1 + a2*a2 + a3*a3); const double tanh_qd = tanh(arg); const double cosh_qd = cosh(arg); const double Zq = tanh_qd/(1. - cos(qd*a1)/cosh_qd) * tanh_qd/(1. - cos(qd*a2)/cosh_qd) * tanh_qd/(1. - cos(qd*a3)/cosh_qd); //if (isnan(Zq)) printf("q:(%g,%g) qd: %g a1: %g a2: %g a3: %g arg: %g\n", qx, qy, qd, a1, a2, a3, arg); const double Fq = sphere_form(q,radius,sld,solvent_sld)*Zq; //the occupied volume of the lattice const double lattice_scale = 4.0*sphere_volume(M_SQRT1_2*radius/dnn); return lattice_scale * Fq; } sasmodels/sasmodels/models/fcc_paracrystal.py000066400000000000000000000125141317715334700220550ustar00rootroot00000000000000#fcc paracrystal model #note model title and parameter table are automatically inserted #note - calculation requires double precision r""" Calculates the scattering from a **face-centered cubic lattice** with paracrystalline distortion. Thermal vibrations are considered to be negligible, and the size of the paracrystal is infinitely large. Paracrystalline distortion is assumed to be isotropic and characterized by a Gaussian distribution. Definition ---------- The scattering intensity $I(q)$ is calculated as .. math:: I(q) = \frac{\text{scale}}{V_p} V_\text{lattice} P(q) Z(q) where *scale* is the volume fraction of spheres, $V_p$ is the volume of the primary particle, $V_\text{lattice}$ is a volume correction for the crystal structure, $P(q)$ is the form factor of the sphere (normalized), and $Z(q)$ is the paracrystalline structure factor for a face-centered cubic structure. Equation (1) of the 1990 reference is used to calculate $Z(q)$, using equations (23)-(25) from the 1987 paper for $Z1$, $Z2$, and $Z3$. The lattice correction (the occupied volume of the lattice) for a face-centered cubic structure of particles of radius $R$ and nearest neighbor separation $D$ is .. math:: V_\text{lattice} = \frac{16\pi}{3}\frac{R^3}{\left(D\sqrt{2}\right)^3} The distortion factor (one standard deviation) of the paracrystal is included in the calculation of $Z(q)$ .. math:: \Delta a = gD where $g$ is a fractional distortion based on the nearest neighbor distance. .. figure:: img/fcc_geometry.jpg Face-centered cubic lattice. For a crystal, diffraction peaks appear at reduced q-values given by .. math:: \frac{qD}{2\pi} = \sqrt{h^2 + k^2 + l^2} where for a face-centered cubic lattice $h, k , l$ all odd or all even are allowed and reflections where $h, k, l$ are mixed odd/even are forbidden. Thus the peak positions correspond to (just the first 5) .. math:: \begin{array}{cccccc} q/q_0 & 1 & \sqrt{4/3} & \sqrt{8/3} & \sqrt{11/3} & \sqrt{4} \\ \text{Indices} & (111) & (200) & (220) & (311) & (222) \end{array} **NB**: The calculation of $Z(q)$ is a double numerical integral that must be carried out with a high density of points to properly capture the sharp peaks of the paracrystalline scattering. So be warned that the calculation is SLOW. Go get some coffee. Fitting of any experimental data must be resolution smeared for any meaningful fit. This makes a triple integral. Very, very slow. Go get lunch! The 2D (Anisotropic model) is based on the reference below where $I(q)$ is approximated for 1d scattering. Thus the scattering pattern for 2D may not be accurate. Note that we are not responsible for any incorrectness of the 2D model computation. .. figure:: img/parallelepiped_angle_definition.png Orientation of the crystal with respect to the scattering plane, when $\theta = \phi = 0$ the $c$ axis is along the beam direction (the $z$ axis). References ---------- Hideki Matsuoka et. al. *Physical Review B*, 36 (1987) 1754-1765 (Original Paper) Hideki Matsuoka et. al. *Physical Review B*, 41 (1990) 3854 -3856 (Corrections to FCC and BCC lattice structure calculation) """ from numpy import inf, pi name = "fcc_paracrystal" title = "Face-centred cubic lattic with paracrystalline distortion" description = """ Calculates the scattering from a **face-centered cubic lattice** with paracrystalline distortion. Thermal vibrations are considered to be negligible, and the size of the paracrystal is infinitely large. Paracrystalline distortion is assumed to be isotropic and characterized by a Gaussian distribution. """ category = "shape:paracrystal" single = False # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type","description"], parameters = [["dnn", "Ang", 220, [-inf, inf], "", "Nearest neighbour distance"], ["d_factor", "", 0.06, [-inf, inf], "", "Paracrystal distortion factor"], ["radius", "Ang", 40, [0, inf], "volume", "Particle radius"], ["sld", "1e-6/Ang^2", 4, [-inf, inf], "sld", "Particle scattering length density"], ["sld_solvent", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Solvent scattering length density"], ["theta", "degrees", 60, [-360, 360], "orientation", "c axis to beam angle"], ["phi", "degrees", 60, [-360, 360], "orientation", "rotation about beam"], ["psi", "degrees", 60, [-360, 360], "orientation", "rotation about c axis"] ] # pylint: enable=bad-whitespace, line-too-long source = ["lib/sas_3j1x_x.c", "lib/gauss150.c", "lib/sphere_form.c", "fcc_paracrystal.c"] def random(): import numpy as np # copied from bcc_paracrystal radius = 10**np.random.uniform(1.3, 4) d_factor = 10**np.random.uniform(-2, -0.7) # sigma_d in 0.01-0.7 dnn_fraction = np.random.beta(a=10, b=1) dnn = radius*4/np.sqrt(2)/dnn_fraction pars = dict( #sld=1, sld_solvent=0, scale=1, background=1e-32, dnn=dnn, d_factor=d_factor, radius=radius, ) return pars # april 10 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! q = 4.*pi/220. tests = [ [{}, [0.001, q, 0.215268], [0.275164706668, 5.7776842567, 0.00958167119232]], [{}, (-0.047, -0.007), 238.103096286], [{}, (0.053, 0.063), 0.863609587796], ] sasmodels/sasmodels/models/flexible_cylinder.c000066400000000000000000000007671317715334700222010ustar00rootroot00000000000000static double form_volume(double length, double kuhn_length, double radius) { return 1.0; } static double Iq(double q, double length, double kuhn_length, double radius, double sld, double solvent_sld) { const double contrast = sld - solvent_sld; const double cross_section = sas_2J1x_x(q*radius); const double volume = M_PI*radius*radius*length; const double flex = Sk_WR(q, length, kuhn_length); return 1.0e-4 * volume * square(contrast*cross_section) * flex; } sasmodels/sasmodels/models/flexible_cylinder.py000066400000000000000000000131671317715334700224050ustar00rootroot00000000000000r""" This model provides the form factor, $P(q)$, for a flexible cylinder where the form factor is normalized by the volume of the cylinder. **Inter-cylinder interactions are NOT provided for.** .. math:: P(q) = \text{scale} \left/V + \text{background} where the averaging $\left<\ldots\right>$ is applied only for the 1D calculation The 2D scattering intensity is the same as 1D, regardless of the orientation of the q vector which is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} Definitions ----------- .. figure:: img/flexible_cylinder_geometry.jpg The chain of contour length, $L$, (the total length) can be described as a chain of some number of locally stiff segments of length $l_p$, the persistence length (the length along the cylinder over which the flexible cylinder can be considered a rigid rod). The Kuhn length $(b = 2*l_p)$ is also used to describe the stiffness of a chain. The returned value is in units of $cm^{-1}$, on absolute scale. In the parameters, the sld and sld\_solvent represent the SLD of the cylinder and solvent respectively. Our model uses the form factor calculations implemented in a c-library provided by the NIST Center for Neutron Research (Kline, 2006). From the reference: 'Method 3 With Excluded Volume' is used. The model is a parametrization of simulations of a discrete representation of the worm-like chain model of Kratky and Porod applied in the pseudocontinuous limit. See equations (13,26-27) in the original reference for the details. References ---------- J S Pedersen and P Schurtenberger. *Scattering functions of semiflexible polymers with and without excluded volume effects.* Macromolecules, 29 (1996) 7602-7612 Correction of the formula can be found in W R Chen, P D Butler and L J Magid, *Incorporating Intermicellar Interactions in the Fitting of SANS Data from Cationic Wormlike Micelles.* Langmuir, 22(15) 2006 6539-6548 """ from numpy import inf name = "flexible_cylinder" title = "Flexible cylinder where the form factor is normalized by the volume" \ "of the cylinder." description = """Note : scale and contrast = (sld - sld_solvent) are both multiplicative factors in the model and are perfectly correlated. One or both of these parameters must be held fixed during model fitting. """ category = "shape:cylinder" single = False # double precision only! # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type", "description"], parameters = [ ["length", "Ang", 1000.0, [0, inf], "volume", "Length of the flexible cylinder"], ["kuhn_length", "Ang", 100.0, [0, inf], "volume", "Kuhn length of the flexible cylinder"], ["radius", "Ang", 20.0, [0, inf], "volume", "Radius of the flexible cylinder"], ["sld", "1e-6/Ang^2", 1.0, [-inf, inf], "sld", "Cylinder scattering length density"], ["sld_solvent", "1e-6/Ang^2", 6.3, [-inf, inf], "sld", "Solvent scattering length density"], ] # pylint: enable=bad-whitespace, line-too-long source = ["lib/polevl.c", "lib/sas_J1.c", "lib/wrc_cyl.c", "flexible_cylinder.c"] def random(): import numpy as np length = 10**np.random.uniform(2, 6) radius = 10**np.random.uniform(1, 3) kuhn_length = 10**np.random.uniform(-2, 0)*length pars = dict( length=length, radius=radius, kuhn_length=kuhn_length, ) return pars tests = [ # Accuracy tests based on content in test/utest_other_models.py [{'length': 1000.0, # test T1 'kuhn_length': 100.0, 'radius': 20.0, 'sld': 1.0, 'sld_solvent': 6.3, 'background': 0.0001, }, 0.001, 3509.2187], # Additional tests with larger range of parameters [{'length': 1000.0, # test T2 'kuhn_length': 100.0, 'radius': 20.0, 'sld': 1.0, 'sld_solvent': 6.3, 'background': 0.0001, }, 1.0, 0.000595345], [{'length': 10.0, # test T3 'kuhn_length': 800.0, 'radius': 2.0, 'sld': 6.0, 'sld_solvent': 12.3, 'background': 0.001, }, 0.1, 1.55228], [{'length': 100.0, # test T4 'kuhn_length': 800.0, 'radius': 50.0, 'sld': 0.1, 'sld_solvent': 5.1, 'background': 0.0, }, 1.0, 0.000938456] ] # There are a few branches in the code that ought to have test values: # # For length > 4 * kuhn_length # if length > 10 * kuhn_length then C is scaled by 3.06 (L/b)^(-0.44) # q*kuhn_length <= 3.1 => Sexv_new # dS/dQ < 0 has different behaviour from dS/dQ >= 0 # T2 q*kuhn_length > 3.1 => a_long # # For length <= 4 * kuhn_length # q*kuhn_length <= max(1.9/Rg_short, 3.0) => Sdebye((q*Rg)^2) # q*Rg < 0.5 uses Pade approx, q*Rg > 1.0 uses math lib # T3,T4 q*kuhn_length > max(1.9/Rg_short, 3.0) => a_short # # Note that the transitions between branches may be abrupt. You can see a # several percent change around length=10*kuhn_length and length=4*kuhn_length # using the following: # # sascomp flexible_cylinder -calc=double -sets=10 length=10*kuhn_length,10.000001*kuhn_length # sascomp flexible_cylinder -calc=double -sets=10 length=4*kuhn_length,4.000001*kuhn_length # # The transition between low q and high q around q*kuhn_length = 3 seems # to be good to 4 digits or better. This was tested by computing the value # on each branches near the transition point and reporting the relative error # for kuhn lengths of 10, 100 and 1000 and a variety of length:kuhn_length # ratios. sasmodels/sasmodels/models/flexible_cylinder_elliptical.c000066400000000000000000000036371317715334700244020ustar00rootroot00000000000000double form_volume(double length, double kuhn_length, double radius); double Iq(double q, double length, double kuhn_length, double radius, double axis_ratio, double sld, double solvent_sld); double flexible_cylinder_ex_kernel(double q, double length, double kuhn_length, double radius, double axis_ratio, double sld, double solvent_sld); double elliptical_crosssection(double q, double a, double b); double form_volume(double length, double kuhn_length, double radius) { return 1.0; } double elliptical_crosssection(double q, double a, double b) { double sum=0.0; for(int i=0;i/V + \text{background} where the averaging $\left<\ldots\right>$ is over all possible orientations of the flexible cylinder. The 2D scattering intensity is the same as 1D, regardless of the orientation of the q vector which is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} Definitions ----------- The function calculated in a similar way to that for the flexible_cylinder model from the reference given below using the author's "Method 3 With Excluded Volume". The model is a parameterization of simulations of a discrete representation of the worm-like chain model of Kratky and Porod applied in the pseudo-continuous limit. See equations (13, 26-27) in the original reference for the details. .. note:: There are several typos in the original reference that have been corrected by WRC. Details of the corrections are in the reference below. Most notably - Equation (13): the term $(1 - w(QR))$ should swap position with $w(QR)$ - Equations (23) and (24) are incorrect; WRC has entered these into Mathematica and solved analytically. The results were then converted to code. - Equation (27) should be $q0 = max(a3/sqrt(RgSquare),3)$ instead of $max(a3*b/sqrt(RgSquare),3)$ - The scattering function is negative for a range of parameter values and q-values that are experimentally accessible. A correction function has been added to give the proper behavior. .. figure:: img/flexible_cylinder_ex_geometry.jpg The chain of contour length, $L$, (the total length) can be described as a chain of some number of locally stiff segments of length $l_p$, the persistence length (the length along the cylinder over which the flexible cylinder can be considered a rigid rod). The Kuhn length $(b = 2*l_p)$ is also used to describe the stiffness of a chain. The cross section of the cylinder is elliptical, with minor radius $a$ . The major radius is larger, so of course, **the axis ratio (parameter 5) must be greater than one.** Simple constraints should be applied during curve fitting to maintain this inequality. The returned value is in units of $cm^{-1}$, on absolute scale. In the parameters, the $sld$ and $sld\_solvent$ represent the SLD of the chain/cylinder and solvent respectively. The *scale*, and the contrast are both multiplicative factors in the model and are perfectly correlated. One or both of these parameters must be held fixed during model fitting. **No inter-cylinder interference effects are included in this calculation.** References ---------- J S Pedersen and P Schurtenberger. *Scattering functions of semiflexible polymers with and without excluded volume effects.* Macromolecules, 29 (1996) 7602-7612 Correction of the formula can be found in W R Chen, P D Butler and L J Magid, *Incorporating Intermicellar Interactions in the Fitting of SANS Data from Cationic Wormlike Micelles.* Langmuir, 22(15) 2006 6539-6548 """ from numpy import inf name = "flexible_cylinder_elliptical" title = "Flexible cylinder wth an elliptical cross section and a uniform " \ "scattering length density." description = """Note : scale and contrast=sldCyl-sldSolv are both multiplicative factors in the model and are perfectly correlated. One or both of these parameters must be held fixed during model fitting. """ single = False category = "shape:cylinder" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type", "description"], parameters = [ ["length", "Ang", 1000.0, [0, inf], "volume", "Length of the flexible cylinder"], ["kuhn_length", "Ang", 100.0, [0, inf], "volume", "Kuhn length of the flexible cylinder"], ["radius", "Ang", 20.0, [1, inf], "volume", "Radius of the flexible cylinder"], ["axis_ratio", "", 1.5, [0, inf], "", "Axis_ratio (major_radius/minor_radius"], ["sld", "1e-6/Ang^2", 1.0, [-inf, inf], "sld", "Cylinder scattering length density"], ["sld_solvent", "1e-6/Ang^2", 6.3, [-inf, inf], "sld", "Solvent scattering length density"], ] # pylint: enable=bad-whitespace, line-too-long source = ["lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c", "lib/wrc_cyl.c", "flexible_cylinder_elliptical.c"] def random(): import numpy as np length = 10**np.random.uniform(2, 6) radius = 10**np.random.uniform(1, 3) axis_ratio = 10**np.random.uniform(-1, 1) kuhn_length = 10**np.random.uniform(-2, -0.7)*length # at least 10 segments pars = dict( length=length, radius=radius, axis_ratio=axis_ratio, kuhn_length=kuhn_length, ) return pars tests = [ # Accuracy tests based on content in test/utest_other_models.py # Currently fails in OCL # [{'length': 1000.0, # 'kuhn_length': 100.0, # 'radius': 20.0, # 'axis_ratio': 1.5, # 'sld': 1.0, # 'sld_solvent': 6.3, # 'background': 0.0001, # }, 0.001, 3509.2187], # Additional tests with larger range of parameters [{'length': 1000.0, 'kuhn_length': 100.0, 'radius': 20.0, 'axis_ratio': 1.5, 'sld': 1.0, 'sld_solvent': 6.3, 'background': 0.0001, }, 1.0, 0.00223819], [{'length': 10.0, 'kuhn_length': 800.0, 'radius': 2.0, 'axis_ratio': 0.5, 'sld': 6.0, 'sld_solvent': 12.3, 'background': 0.001, }, 0.1, 0.390281], [{'length': 100.0, 'kuhn_length': 800.0, 'radius': 50.0, 'axis_ratio': 4.5, 'sld': 0.1, 'sld_solvent': 5.1, 'background': 0.0, }, 1.0, 0.0016338264790] ] sasmodels/sasmodels/models/fractal.c000066400000000000000000000014171317715334700201230ustar00rootroot00000000000000#define INVALID(p) (p.fractal_dim < 0.0) static double form_volume(double radius) { return M_4PI_3 * cube(radius); } static double Iq(double q, double volfraction, double radius, double fractal_dim, double cor_length, double sld_block, double sld_solvent) { const double sq = fractal_sq(q, radius, fractal_dim, cor_length); //calculate P(q) for the spherical subunits const double pq = square(form_volume(radius) * (sld_block-sld_solvent) *sas_3j1x_x(q*radius)); // scale to units cm-1 sr-1 (assuming data on absolute scale) // convert I(1/A) to (1/cm) => 1e8 * I(q) // convert rho^2 in 10^-6 1/A to 1/A => 1e-12 * I(q) // combined: 1e-4 * I(q) return 1.e-4 * volfraction * sq * pq; } sasmodels/sasmodels/models/fractal.py000066400000000000000000000110021317715334700203200ustar00rootroot00000000000000r""" Definition ---------- This model calculates the scattering from fractal-like aggregates of spherical building blocks according the following equation: .. math:: I(q) = \phi\ V_\text{block} (\rho_\text{block} - \rho_\text{solvent})^2 P(q)S(q) + \text{background} where $\phi$ is The volume fraction of the spherical "building block" particles of radius $R_0$, $V_{block}$ is the volume of a single building block, $\rho_{solvent}$ is the scattering length density of the solvent, and $\rho_{block}$ is the scattering length density of the building blocks, and P(q), S(q) are the scattering from randomly distributed spherical particles (the building blocks) and the interference from such building blocks organized in a fractal-like clusters. P(q) and S(q) are calculated as: .. math:: P(q)&= F(qR_0)^2 \\ F(q)&= \frac{3 (\sin x - x \cos x)}{x^3} \\ V_\text{particle} &= \frac{4}{3}\ \pi R_0 \\ S(q) &= 1 + \frac{D_f\ \Gamma\!(D_f-1)}{[1+1/(q \xi)^2\ ]^{(D_f -1)/2}} \frac{\sin[(D_f-1) \tan^{-1}(q \xi) ]}{(q R_0)^{D_f}} where $\xi$ is the correlation length representing the cluster size and $D_f$ is the fractal dimension, representing the self similarity of the structure. Note that S(q) here goes negative if $D_f$ is too large, and the Gamma function diverges at $D_f=0$ and $D_f=1$. **Polydispersity on the radius is provided for.** For 2D data: The 2D scattering intensity is calculated in the same way as 1D, where the *q* vector is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- .. [#] J Teixeira, *J. Appl. Cryst.*, 21 (1988) 781-785 Authorship and Verification ---------------------------- * **Author:** NIST IGOR/DANSE **Date:** pre 2010 * **Converted to sasmodels by:** Paul Butler **Date:** March 19, 2016 * **Last Modified by:** Paul Butler **Date:** March 12, 2017 * **Last Reviewed by:** Paul Butler **Date:** March 12, 2017 """ from __future__ import division from numpy import inf name = "fractal" title = "Calculates the scattering from fractal-like aggregates of spheres \ following theTexiera reference." description = """ The scattering intensity is given by I(q) = scale * V * delta^(2) * P(q) * S(q) + background, where p(q)= F(q*radius)^(2) F(x) = 3*[sin(x)-x cos(x)]/x**3 delta = sld_block -sld_solv scale = scale * volfraction radius = Block radius sld_block = SDL block sld_solv = SDL solvent background = background and S(q) is the interference term between building blocks given in the full documentation and depending on the parameters fractal_dim = Fractal dimension cor_length = Correlation Length """ category = "shape-independent" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type","description"], parameters = [["volfraction", "", 0.05, [0.0, 1], "", "volume fraction of blocks"], ["radius", "Ang", 5.0, [0.0, inf], "volume", "radius of particles"], ["fractal_dim", "", 2.0, [0.0, 6.0], "", "fractal dimension"], ["cor_length", "Ang", 100.0, [0.0, inf], "", "cluster correlation length"], ["sld_block", "1e-6/Ang^2", 2.0, [-inf, inf], "sld", "scattering length density of particles"], ["sld_solvent", "1e-6/Ang^2", 6.4, [-inf, inf], "sld", "scattering length density of solvent"], ] # pylint: enable=bad-whitespace, line-too-long source = ["lib/sas_3j1x_x.c", "lib/sas_gamma.c", "lib/fractal_sq.c", "fractal.c"] def random(): import numpy as np radius = 10**np.random.uniform(0.7, 4) #radius = 5 cor_length = 10**np.random.uniform(0.7, 2)*radius #cor_length = 20*radius volfraction = 10**np.random.uniform(-3, -1) #volfraction = 0.05 fractal_dim = 2*np.random.beta(3, 4) + 1 #fractal_dim = 2 pars = dict( #background=0, sld_block=1, sld_solvent=0, volfraction=volfraction, radius=radius, cor_length=cor_length, fractal_dim=fractal_dim, ) return pars demo = dict(volfraction=0.05, radius=5.0, fractal_dim=2.0, cor_length=100.0, sld_block=2.0, sld_solvent=6.4) # NOTE: test results taken from values returned by SasView 3.1.2 tests = [ [{}, 0.0005, 40.4980069872], [{}, 0.234734468938, 0.0947143166058], [{}, 0.5, 0.0176878183458], ] sasmodels/sasmodels/models/fractal_core_shell.c000066400000000000000000000015041317715334700223170ustar00rootroot00000000000000static double form_volume(double radius, double thickness) { return M_4PI_3 * cube(radius + thickness); } static double Iq(double q, double radius, double thickness, double core_sld, double shell_sld, double solvent_sld, double volfraction, double fractal_dim, double cor_length) { //The radius for the building block of the core shell particle that is //needed by the Teixeira fractal S(q) is the radius of the whole particle. const double cs_radius = radius + thickness; const double sq = fractal_sq(q, cs_radius, fractal_dim, cor_length); const double pq = core_shell_kernel(q, radius, thickness, core_sld, shell_sld, solvent_sld); // Note: core_shell_kernel already performs the 1e-4 unit conversion return volfraction * sq * pq; } sasmodels/sasmodels/models/fractal_core_shell.py000066400000000000000000000137101317715334700225270ustar00rootroot00000000000000r""" Definition ---------- Calculates the scattering from a fractal structure with a primary building block of core-shell spheres, as opposed to just homogeneous spheres in the fractal model. It is an extension of the well known Teixeira\ [#teixeira]_ fractal model replacing the $P(q)$ of a solid sphere with that of a core-shell sphere. This model could find use for aggregates of coated particles, or aggregates of vesicles for example. .. math:: I(q) = P(q)S(q) + \text{background} Where $P(q)$ is the core-shell form factor and $S(q)$ is the Teixeira\ [#teixeira]_ fractal structure factor both of which are given again below: .. math:: P(q) &= \frac{\phi}{V_s}\left[3V_c(\rho_c-\rho_s) \frac{\sin(qr_c)-qr_c\cos(qr_c)}{(qr_c)^3}+ 3V_s(\rho_s-\rho_{solv}) \frac{\sin(qr_s)-qr_s\cos(qr_s)}{(qr_s)^3}\right]^2 \\ S(q) &= 1 + \frac{D_f\ \Gamma\!(D_f-1)}{[1+1/(q\xi)^2]^{(D_f-1)/2}} \frac{\sin[(D_f-1)\tan^{-1}(q\xi)]}{(qr_s)^{D_f}} where $\phi$ is the volume fraction of particles, $V_s$ is the volume of the whole particle, $V_c$ is the volume of the core, $\rho_c$, $\rho_s$, and $\rho_{solv}$ are the scattering length densities of the core, shell, and solvent respectively, $r_c$ and $r_s$ are the radius of the core and the radius of the whole particle respectively, $D_f$ is the fractal dimension, and $\xi$ the correlation length. Polydispersity of radius and thickness are also provided for. This model does not allow for anisotropy and thus the 2D scattering intensity is calculated in the same way as 1D, where the $q$ vector is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} Our model is derived from the form factor calculations implemented in IGOR macros by the NIST Center for Neutron Research\ [#Kline]_ References ---------- .. [#teixeira] J Teixeira, *J. Appl. Cryst.*, 21 (1988) 781-785 .. [#Kline] S R Kline, *J Appl. Cryst.*, 39 (2006) 895 Authorship and Verification ---------------------------- * **Author:** NIST IGOR/DANSE **Date:** pre 2010 * **Last Modified by:** Paul Butler and Paul Kienzle **on:** November 27, 2016 * **Last Reviewed by:** Paul Butler and Paul Kienzle **on:** November 27, 2016 """ from numpy import pi, inf name = "fractal_core_shell" title = "Scattering from a fractal structure formed from core shell spheres" description = """\ Model for fractal aggregates of core-shell primary particles. It is based on the Teixeira model for the S(q) of a fractal * P(q) for a core-shell sphere radius = the radius of the core thickness = thickness of the shell thick_layer = thickness of a layer sld_core = the SLD of the core sld_shell = the SLD of the shell sld_solvent = the SLD of the solvent volfraction = volume fraction of core-shell particles fractal_dim = fractal dimension cor_length = correlation length of the fractal like aggretates """ category = "shape-independent" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type","description"], parameters = [ ["radius", "Ang", 60.0, [0.0, inf], "volume", "Sphere core radius"], ["thickness", "Ang", 10.0, [0.0, inf], "volume", "Sphere shell thickness"], ["sld_core", "1e-6/Ang^2", 1.0, [-inf, inf], "sld", "Sphere core scattering length density"], ["sld_shell", "1e-6/Ang^2", 2.0, [-inf, inf], "sld", "Sphere shell scattering length density"], ["sld_solvent", "1e-6/Ang^2", 3.0, [-inf, inf], "sld", "Solvent scattering length density"], ["volfraction", "", 1.0, [0.0, inf], "", "Volume fraction of building block spheres"], ["fractal_dim", "", 2.0, [0.0, 6.0], "", "Fractal dimension"], ["cor_length", "Ang", 100.0, [0.0, inf], "", "Correlation length of fractal-like aggregates"], ] # pylint: enable=bad-whitespace, line-too-long source = ["lib/sas_3j1x_x.c", "lib/sas_gamma.c", "lib/core_shell.c", "lib/fractal_sq.c", "fractal_core_shell.c"] def random(): import numpy as np outer_radius = 10**np.random.uniform(0.7, 4) # Use a distribution with a preference for thin shell or thin core # Avoid core,shell radii < 1 thickness = np.random.beta(0.5, 0.5)*(outer_radius-2) + 1 radius = outer_radius - thickness cor_length = 10**np.random.uniform(0.7, 2)*outer_radius volfraction = 10**np.random.uniform(-3, -1) fractal_dim = 2*np.random.beta(3, 4) + 1 pars = dict( #background=0, sld_block=1, sld_solvent=0, volfraction=volfraction, radius=radius, cor_length=cor_length, fractal_dim=fractal_dim, ) return pars demo = dict(scale=0.05, background=0, radius=20, thickness=5, sld_core=3.5, sld_shell=1.0, sld_solvent=6.35, volfraction=0.05, fractal_dim=2.0, cor_length=100.0) def ER(radius, thickness): """ Equivalent radius @param radius: core radius @param thickness: shell thickness """ return radius + thickness def VR(radius, thickness): """ Volume ratio @param radius: core radius @param thickness: shell thickness """ whole = 4.0/3.0 * pi * (radius + thickness)**3 core = 4.0/3.0 * pi * radius**3 return whole, whole-core tests = [[{'radius': 20.0, 'thickness': 10.0}, 'ER', 30.0], [{'radius': 20.0, 'thickness': 10.0}, 'VR', 0.703703704]] # # The SasView test result was 0.00169, with a background of 0.001 # # They are however wrong as we now know. IGOR might be a more # # appropriate source. Otherwise will just have to assume this is now # # correct and self generate a correct answer for the future. Until we # # figure it out leave the tests commented out # [{'radius': 60.0, # 'thickness': 10.0, # 'sld_core': 1.0, # 'sld_shell': 2.0, # 'sld_solvent': 3.0, # 'background': 0.0 # }, 0.015211, 692.84]] sasmodels/sasmodels/models/fuzzy_sphere.py000066400000000000000000000102171317715334700214500ustar00rootroot00000000000000r""" For information about polarised and magnetic scattering, see the :ref:`magnetism` documentation. Definition ---------- The scattering intensity $I(q)$ is calculated as: .. math:: I(q) = \frac{\text{scale}}{V}(\Delta \rho)^2 A^2(q) S(q) + \text{background} where the amplitude $A(q)$ is given as the typical sphere scattering convoluted with a Gaussian to get a gradual drop-off in the scattering length density: .. math:: A(q) = \frac{3\left[\sin(qR) - qR \cos(qR)\right]}{(qR)^3} \exp\left(\frac{-(\sigma_\text{fuzzy}q)^2}{2}\right) Here $A(q)^2$ is the form factor, $P(q)$. The scale is equivalent to the volume fraction of spheres, each of volume, $V$. Contrast $(\Delta \rho)$ is the difference of scattering length densities of the sphere and the surrounding solvent. Poly-dispersion in radius and in fuzziness is provided for, though the fuzziness must be kept much smaller than the sphere radius for meaningful results. From the reference: The "fuzziness" of the interface is defined by the parameter $\sigma_\text{fuzzy}$. The particle radius $R$ represents the radius of the particle where the scattering length density profile decreased to 1/2 of the core density. $\sigma_\text{fuzzy}$ is the width of the smeared particle surface; i.e., the standard deviation from the average height of the fuzzy interface. The inner regions of the microgel that display a higher density are described by the radial box profile extending to a radius of approximately $R_\text{box} \sim R - 2 \sigma$. The profile approaches zero as $R_\text{sans} \sim R + 2\sigma$. For 2D data: The 2D scattering intensity is calculated in the same way as 1D, where the $q$ vector is defined as .. math:: q = \sqrt{{q_x}^2 + {q_y}^2} References ---------- M Stieger, J. S Pedersen, P Lindner, W Richtering, *Langmuir*, 20 (2004) 7283-7292 """ from numpy import inf name = "fuzzy_sphere" title = "Scattering from spherical particles with a fuzzy surface." description = """\ scale: scale factor times volume fraction, or just volume fraction for absolute scale data radius: radius of the solid sphere fuzziness = the standard deviation of the fuzzy interfacial thickness (ie., so-called interfacial roughness) sld: the SLD of the sphere solvend_sld: the SLD of the solvent background: incoherent background Note: By definition, this function works only when fuzziness << radius. """ category = "shape:sphere" # pylint: disable=bad-whitespace,line-too-long # ["name", "units", default, [lower, upper], "type","description"], parameters = [["sld", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Particle scattering length density"], ["sld_solvent", "1e-6/Ang^2", 3, [-inf, inf], "sld", "Solvent scattering length density"], ["radius", "Ang", 60, [0, inf], "volume", "Sphere radius"], ["fuzziness", "Ang", 10, [0, inf], "", "std deviation of Gaussian convolution for interface (must be << radius)"], ] # pylint: enable=bad-whitespace,line-too-long source = ["lib/sas_3j1x_x.c"] # No volume normalization despite having a volume parameter # This should perhaps be volume normalized? form_volume = """ return M_4PI_3*cube(radius); """ Iq = """ const double qr = q*radius; const double bes = sas_3j1x_x(qr); const double qf = q*fuzziness; const double fq = bes * (sld - sld_solvent) * form_volume(radius) * exp(-0.5*qf*qf); return 1.0e-4*fq*fq; """ def ER(radius): """ Return radius """ return radius # VR defaults to 1.0 def random(): import numpy as np radius = 10**np.random.uniform(1, 4.7) fuzziness = 10**np.random.uniform(-2, -0.5)*radius # 1% to 31% fuzziness pars = dict( radius=radius, fuzziness=fuzziness, ) return pars demo = dict(scale=1, background=0.001, sld=1, sld_solvent=3, radius=60, fuzziness=10, radius_pd=.2, radius_pd_n=45, fuzziness_pd=.2, fuzziness_pd_n=0) tests = [ # Accuracy tests based on content in test/utest_models_new1_3.py #[{'background': 0.001}, 1.0, 0.001], [{}, 0.00301005, 359.2315], ] sasmodels/sasmodels/models/gauss_lorentz_gel.py000066400000000000000000000117471317715334700224520ustar00rootroot00000000000000r""" This model calculates the scattering from a gel structure, but typically a physical rather than chemical network. It is modeled as a sum of a low-q exponential decay (which happens to give a functional form similar to Guinier scattering, so interpret with care) plus a Lorentzian at higher-q values. See also the gel_fit model. Definition ---------- The scattering intensity $I(q)$ is calculated as (Eqn. 5 from the reference) .. math:: I(q) = I_G(0) \exp(-q^2\Xi ^2/2) + I_L(0)/(1+q^2\xi^2) $\Xi$ is the length scale of the static correlations in the gel, which can be attributed to the "frozen-in" crosslinks. $\xi$ is the dynamic correlation length, which can be attributed to the fluctuating polymer chains between crosslinks. $I_G(0)$ and $I_L(0)$ are the scaling factors for each of these structures. Think carefully about how these map to your particular system! .. note:: The peaked structure at higher $q$ values (Figure 2 from the reference) is not reproduced by the model. Peaks can be introduced into the model by summing this model with the :ref:`gaussian-peak` model. For 2D data the scattering intensity is calculated in the same way as 1D, where the $q$ vector is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- G Evmenenko, E Theunissen, K Mortensen, H Reynaers, *Polymer*, 42 (2001) 2907-2913 """ from numpy import inf, exp name = "gauss_lorentz_gel" title = "Gauss Lorentz Gel model of scattering from a gel structure" description = """ Class that evaluates a GaussLorentzGel model. I(q) = scale_g*exp(- q^2*Z^2 / 2)+scale_l/(1+q^2*z^2) + background List of default parameters: scale_g = Gauss scale factor Z = Static correlation length scale_l = Lorentzian scale factor z = Dynamic correlation length background = Incoherent background """ category = "shape-independent" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type", "description"], parameters = [["gauss_scale", "", 100.0, [-inf, inf], "", "Gauss scale factor"], ["cor_length_static", "Ang", 100.0, [0, inf], "", "Static correlation length"], ["lorentz_scale", "", 50.0, [-inf, inf], "", "Lorentzian scale factor"], ["cor_length_dynamic", "Ang", 20.0, [0, inf], "", "Dynamic correlation length"], ] # pylint: enable=bad-whitespace, line-too-long def Iq(q, gauss_scale=100.0, cor_length_static=100.0, lorentz_scale=50.0, cor_length_dynamic=20.0): """ :param q: Input q-value :param gauss_scale: Gauss scale factor :param cor_length_static: Static correlation length :param lorentz_scale: Lorentzian scale factor :param cor_length_dynamic: Dynamic correlation length :return: 1-D intensity """ term1 = gauss_scale *\ exp(-1.0*q*q*cor_length_static*cor_length_static/2.0) term2 = lorentz_scale /\ (1.0+(q*cor_length_dynamic)*(q*cor_length_dynamic)) return term1 + term2 Iq.vectorized = True # Iq accepts an array of q values def random(): import numpy as np gauss_scale = 10**np.random.uniform(1, 3) lorentz_scale = 10**np.random.uniform(1, 3) cor_length_static = 10**np.random.uniform(0, 3) cor_length_dynamic = 10**np.random.uniform(0, 3) pars = dict( #background=0, scale=1, gauss_scale=gauss_scale, lorentz_scale=lorentz_scale, cor_length_static=cor_length_static, cor_length_dynamic=cor_length_dynamic, ) return pars demo = dict(scale=1, background=0.1, gauss_scale=100.0, cor_length_static=100.0, lorentz_scale=50.0, cor_length_dynamic=20.0) tests = [ # Accuracy tests based on content in test/utest_extra_models.py [{'gauss_scale': 100.0, 'cor_length_static': 100.0, 'lorentz_scale': 50.0, 'cor_length_dynamic': 20.0, }, 0.001, 149.482], [{'gauss_scale': 100.0, 'cor_length_static': 100.0, 'lorentz_scale': 50.0, 'cor_length_dynamic': 20.0, }, 0.105363, 9.1913], [{'gauss_scale': 100.0, 'cor_length_static': 100.0, 'lorentz_scale': 50.0, 'cor_length_dynamic': 20.0, }, 0.441623, 0.633811], # Additional tests with larger range of parameters [{'gauss_scale': 10.0, 'cor_length_static': 100.0, 'lorentz_scale': 3.0, 'cor_length_dynamic': 1.0, }, 0.1, 2.9712970297], [{'gauss_scale': 10.0, 'cor_length_static': 100.0, 'lorentz_scale': 3.0, 'cor_length_dynamic': 1.0, 'background': 100.0 }, 5.0, 100.116384615], [{'gauss_scale': 10.0, 'cor_length_static': 100.0, 'lorentz_scale': 3.0, 'cor_length_dynamic': 1.0, 'background': 0.0, }, 200., 7.49981250469e-05], ] sasmodels/sasmodels/models/gaussian_peak.py000066400000000000000000000030421317715334700215230ustar00rootroot00000000000000r""" Definition ---------- This model describes a Gaussian shaped peak on a flat background .. math:: I(q) = (\text{scale}) \exp\left[ -\tfrac12 (q-q_0)^2 / \sigma^2 \right] + \text{background} with the peak having height of *scale* centered at $q_0$ and having a standard deviation of $\sigma$. The FWHM (full-width half-maximum) is $2.354 \sigma$. For 2D data, scattering intensity is calculated in the same way as 1D, where the $q$ vector is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- None. """ from numpy import inf name = "gaussian_peak" title = "Gaussian shaped peak" description = """ Model describes a Gaussian shaped peak including a flat background Provide F(q) = scale*exp( -1/2 *[(q-peak_pos)/sigma]^2 )+ background """ category = "shape-independent" # ["name", "units", default, [lower, upper], "type","description"], parameters = [["peak_pos", "1/Ang", 0.05, [-inf, inf], "", "Peak position"], ["sigma", "1/Ang", 0.005, [0, inf], "", "Peak width (standard deviation)"], ] Iq = """ double scaled_dq = (q - peak_pos)/sigma; return exp(-0.5*scaled_dq*scaled_dq); //sqrt(2*M_PI*sigma*sigma); """ # VR defaults to 1.0 def random(): import numpy as np peak_pos = 10**np.random.uniform(-3, -1) sigma = 10**np.random.uniform(-1.3, -0.3)*peak_pos scale = 10**np.random.uniform(0, 4) pars = dict( #background=1e-8, scale=scale, peak_pos=peak_pos, sigam=sigma, ) return pars sasmodels/sasmodels/models/gel_fit.c000066400000000000000000000013061317715334700201150ustar00rootroot00000000000000static double Iq(double q, double guinier_scale, double lorentz_scale, double rg, double fractal_dim, double cor_length) { // Lorentzian Term ////////////////////////double a(x[i]*x[i]*zeta*zeta); double lorentzian_term = square(q*cor_length); lorentzian_term = 1.0 + ((fractal_dim + 1.0)/3.0)*lorentzian_term; lorentzian_term = pow(lorentzian_term, fractal_dim/2.0 ); // Exponential Term ////////////////////////double d(x[i]*x[i]*rg*rg); double exp_term = square(q*rg); exp_term = exp(-exp_term/3.0); // Scattering Law double result = lorentz_scale/lorentzian_term + guinier_scale*exp_term; return result; } sasmodels/sasmodels/models/gel_fit.py000066400000000000000000000066621317715334700203350ustar00rootroot00000000000000r""" *This model was implemented by an interested user!* Unlike a concentrated polymer solution, the fine-scale polymer distribution in a gel involves at least two characteristic length scales, a shorter correlation length ( $a1$ ) to describe the rapid fluctuations in the position of the polymer chains that ensure thermodynamic equilibrium, and a longer distance (denoted here as $a2$ ) needed to account for the static accumulations of polymer pinned down by junction points or clusters of such points. The latter is derived from a simple Guinier function. Compare also the gauss_lorentz_gel model. Definition ---------- The scattered intensity $I(q)$ is calculated as .. math:: I(Q) = I(0)_L \frac{1}{\left( 1+\left[ ((D+1/3)Q^2a_{1}^2 \right]\right)^{D/2}} + I(0)_G exp\left( -Q^2a_{2}^2\right) + B where .. math:: a_{2}^2 \approx \frac{R_{g}^2}{3} Note that the first term reduces to the Ornstein-Zernicke equation when $D = 2$; ie, when the Flory exponent is 0.5 (theta conditions). In gels with significant hydrogen bonding $D$ has been reported to be ~2.6 to 2.8. References ---------- Mitsuhiro Shibayama, Toyoichi Tanaka, Charles C Han, *J. Chem. Phys.* 1992, 97 (9), 6829-6841 Simon Mallam, Ferenc Horkay, Anne-Marie Hecht, Adrian R Rennie, Erik Geissler, *Macromolecules* 1991, 24, 543-548 """ from numpy import inf name = "gel_fit" title = "Fitting using fine-scale polymer distribution in a gel." description = """\ Structure factor for interacting particles: Shibayama-Geissler Two-Length Scale Fit for Gels (GelFit) Shibayama; Tanaka; Han J Chem Phys (1992), 97(9), 6829-6841 Mallam; Horkay; Hecht; Rennie; Geissler, Macromol (1991), 24, 543 """ category = "shape-independent" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type","description"], parameters = [["guinier_scale", "cm^-1", 1.7, [-inf, inf], "", "Guinier length scale"], ["lorentz_scale", "cm^-1", 3.5, [-inf, inf], "", "Lorentzian length scale"], ["rg", "Ang", 104.0, [2, inf], "", "Radius of gyration"], ["fractal_dim", "", 2.0, [0, inf], "", "Fractal exponent"], ["cor_length", "Ang", 16.0, [0, inf], "", "Correlation length"] ] # pylint: enable=bad-whitespace, line-too-long source = ["gel_fit.c"] def random(): import numpy as np guinier_scale = 10**np.random.uniform(1, 3) lorentz_scale = 10**np.random.uniform(1, 3) rg = 10**np.random.uniform(1, 5) fractal_dim = np.random.uniform(0, 6) cor_length = 10**np.random.uniform(0, 3) pars = dict( #background=0, scale=1, guinier_scale=guinier_scale, lorentz_scale=lorentz_scale, rg=rg, fractal_dim=fractal_dim, cor_length=cor_length ) return pars demo = dict(background=0.01, guinier_scale=1.7, lorentz_scale=3.5, rg=104, fractal_dim=2.0, cor_length=16.0) tests = [[{'guinier_scale': 1.0, 'lorentz_scale': 1.0, 'rg': 10.0, 'fractal_dim': 10.0, 'cor_length': 20.0, 'background': 0.0, }, 0.1, 0.716532], [{'guinier_scale': 4.0, 'lorentz_scale': 10.0, 'rg': 500.0, 'fractal_dim': 1.0, 'cor_length': 20.0, 'background': 20.0, }, 5.0, 20.1224653026], ] sasmodels/sasmodels/models/guinier.py000066400000000000000000000034301317715334700203540ustar00rootroot00000000000000r""" Definition ---------- This model fits the Guinier function .. math:: I(q) = \text{scale} \cdot \exp{\left[ \frac{-Q^2R_g^2}{3} \right]} + \text{background} to the data directly without any need for linearisation (*cf*. the usual plot of $\ln I(q)$ vs $q^2$\ ). Note that you may have to restrict the data range to include small q only, where the Guinier approximation actually applies. See also the guinier_porod model. For 2D data the scattering intensity is calculated in the same way as 1D, where the $q$ vector is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- A Guinier and G Fournet, *Small-Angle Scattering of X-Rays*, John Wiley & Sons, New York (1955) """ from numpy import inf name = "guinier" title = "" description = """ I(q) = scale.exp ( - rg^2 q^2 / 3.0 ) List of default parameters: scale = scale rg = Radius of gyration """ category = "shape-independent" # ["name", "units", default, [lower, upper], "type","description"], parameters = [["rg", "Ang", 60.0, [0, inf], "", "Radius of Gyration"]] Iq = """ double exponent = rg*rg*q*q/3.0; double value = exp(-exponent); return value; """ def random(): import numpy as np scale = 10**np.random.uniform(1, 4) # Note: compare.py has Rg cutoff of 1e-30 at q=1 for guinier, so use that # log_10 Ae^(-(q Rg)^2/3) = log_10(A) - (q Rg)^2/ (3 ln 10) > -30 # => log_10(A) > Rg^2/(3 ln 10) - 30 q_max = 1.0 rg_max = np.sqrt(90*np.log(10) + 3*np.log(scale))/q_max rg = 10**np.random.uniform(0, np.log10(rg_max)) pars = dict( #background=0, scale=scale, rg=rg, ) return pars # parameters for demo demo = dict(scale=1.0, rg=60.0) # parameters for unit tests tests = [[{'rg' : 31.5}, 0.005, 0.992756]] sasmodels/sasmodels/models/guinier_porod.py000066400000000000000000000102701317715334700215570ustar00rootroot00000000000000r""" Calculates the scattering for a generalized Guinier/power law object. This is an empirical model that can be used to determine the size and dimensionality of scattering objects, including asymmetric objects such as rods or platelets, and shapes intermediate between spheres and rods or between rods and platelets, and overcomes some of the deficiencies of the (Beaucage) Unified_Power_Rg model (see Hammouda, 2010). Definition ---------- The following functional form is used .. math:: I(q) = \begin{cases} \frac{G}{Q^s}\ \exp{\left[\frac{-Q^2R_g^2}{3-s} \right]} & Q \leq Q_1 \\ D / Q^m & Q \geq Q_1 \end{cases} This is based on the generalized Guinier law for such elongated objects (see the Glatter reference below). For 3D globular objects (such as spheres), $s = 0$ and one recovers the standard Guinier formula. For 2D symmetry (such as for rods) $s = 1$, and for 1D symmetry (such as for lamellae or platelets) $s = 2$. A dimensionality parameter ($3-s$) is thus defined, and is 3 for spherical objects, 2 for rods, and 1 for plates. Enforcing the continuity of the Guinier and Porod functions and their derivatives yields .. math:: Q_1 = \frac{1}{R_g} \sqrt{(m-s)(3-s)/2} and .. math:: D &= G \ \exp{ \left[ \frac{-Q_1^2 R_g^2}{3-s} \right]} \ Q_1^{m-s} &= \frac{G}{R_g^{m-s}} \ \exp \left[ -\frac{m-s}{2} \right] \left( \frac{(m-s)(3-s)}{2} \right)^{\frac{m-s}{2}} Note that the radius of gyration for a sphere of radius $R$ is given by $R_g = R \sqrt{3/5}$. For a cylinder of radius $R$ and length $L$, $R_g^2 = \frac{L^2}{12} + \frac{R^2}{2}$ from which the cross-sectional radius of gyration for a randomly oriented thin cylinder is $R_g = R/\sqrt{2}$ and the cross-sectional radius of gyration of a randomly oriented lamella of thickness $T$ is given by $R_g = T / \sqrt{12}$. For 2D data: The 2D scattering intensity is calculated in the same way as 1D, where the q vector is defined as .. math:: q = \sqrt{q_x^2+q_y^2} Reference --------- B Hammouda, *A new Guinier-Porod model, J. Appl. Cryst.*, (2010), 43, 716-719 B Hammouda, *Analysis of the Beaucage model, J. Appl. Cryst.*, (2010), 43, 1474-1478 """ from numpy import inf, sqrt, exp, errstate name = "guinier_porod" title = "Guinier-Porod function" description = """\ I(q) = scale/q^s* exp ( - R_g^2 q^2 / (3-s) ) for q<= ql = scale/q^porod_exp*exp((-ql^2*Rg^2)/(3-s))*ql^(porod_exp-s) for q>=ql where ql = sqrt((porod_exp-s)(3-s)/2)/Rg. List of parameters: scale = Guinier Scale s = Dimension Variable Rg = Radius of Gyration [A] porod_exp = Porod Exponent background = Background [1/cm]""" category = "shape-independent" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type","description"], parameters = [["rg", "Ang", 60.0, [0, inf], "", "Radius of gyration"], ["s", "", 1.0, [0, inf], "", "Dimension variable"], ["porod_exp", "", 3.0, [0, inf], "", "Porod exponent"]] # pylint: enable=bad-whitespace, line-too-long # pylint: disable=C0103 def Iq(q, rg, s, porod_exp): """ @param q: Input q-value """ n = 3.0 - s ms = 0.5*(porod_exp-s) # =(n-3+porod_exp)/2 # preallocate return value iq = 0.0*q # Take care of the singular points if rg <= 0.0 or ms <= 0.0: return iq # Do the calculation and return the function value idx = q < sqrt(n*ms)/rg with errstate(divide='ignore'): iq[idx] = q[idx]**-s * exp(-(q[idx]*rg)**2/n) iq[~idx] = q[~idx]**-porod_exp * (exp(-ms) * (n*ms/rg**2)**ms) return iq Iq.vectorized = True # Iq accepts an array of q values def random(): import numpy as np rg = 10**np.random.uniform(1, 5) s = np.random.uniform(0, 3) porod_exp = s + np.random.uniform(0, 3) pars = dict( #scale=1, background=0, rg=rg, s=s, porod_exp=porod_exp, ) return pars demo = dict(scale=1.5, background=0.5, rg=60, s=1.0, porod_exp=3.0) tests = [[{'scale': 1.5, 'background':0.5}, 0.04, 5.290096890253155]] sasmodels/sasmodels/models/hardsphere.py000066400000000000000000000156721317715334700210520ustar00rootroot00000000000000# Note: model title and parameter table are inserted automatically r"""Calculate the interparticle structure factor for monodisperse spherical particles interacting through hard sphere (excluded volume) interactions. May be a reasonable approximation for other shapes of particles that freely rotate, and for moderately polydisperse systems. Though strictly the maths needs to be modified (no \Beta(Q) correction yet in sasview). radius_effective is the effective hard sphere radius. volfraction is the volume fraction occupied by the spheres. In sasview the effective radius may be calculated from the parameters used in the form factor $P(q)$ that this $S(q)$ is combined with. For numerical stability the computation uses a Taylor series expansion at very small $qR$, there may be a very minor glitch at the transition point in some circumstances. The S(Q) uses the Percus-Yevick closure where the interparticle potential is .. math:: U(r) = \begin{cases} \infty & r < 2R \\ 0 & r \geq 2R \end{cases} where $r$ is the distance from the center of the sphere of a radius $R$. For a 2D plot, the wave transfer is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- J K Percus, J Yevick, *J. Phys. Rev.*, 110, (1958) 1 """ from numpy import inf name = "hardsphere" title = "Hard sphere structure factor, with Percus-Yevick closure" description = """\ [Hard sphere structure factor, with Percus-Yevick closure] Interparticle S(Q) for random, non-interacting spheres. May be a reasonable approximation for other shapes of particles that freely rotate, and for moderately polydisperse systems. Though strictly the maths needs to be modified - which sasview does not do yet. radius_effective is the hard sphere radius volfraction is the volume fraction occupied by the spheres. """ category = "structure-factor" structure_factor = True single = False # TODO: check # ["name", "units", default, [lower, upper], "type","description"], parameters = [["radius_effective", "Ang", 50.0, [0, inf], "volume", "effective radius of hard sphere"], ["volfraction", "", 0.2, [0, 0.74], "", "volume fraction of hard spheres"], ] # No volume normalization despite having a volume parameter # This should perhaps be volume normalized? form_volume = """ return 1.0; """ Iq = r""" double D,A,B,G,X,X2,X4,S,C,FF,HARDSPH; // these are c compiler instructions, can also put normal code inside the "if else" structure #if FLOAT_SIZE > 4 // double precision orig had 0.2, don't call the variable cutoff as PAK already has one called that! Must use UPPERCASE name please. // 0.05 better, 0.1 OK #define CUTOFFHS 0.05 #else // 0.1 bad, 0.2 OK, 0.3 good, 0.4 better, 0.8 no good #define CUTOFFHS 0.4 #endif if(fabs(radius_effective) < 1.E-12) { HARDSPH=1.0; //printf("HS1 %g: %g\n",q,HARDSPH); return(HARDSPH); } // removing use of pow(xxx,2) and rearranging the calcs of A, B & G cut ~40% off execution time ( 0.5 to 0.3 msec) X = 1.0/( 1.0 -volfraction); D= X*X; A= (1.+2.*volfraction)*D; A *=A; X=fabs(q*radius_effective*2.0); if(X < 5.E-06) { HARDSPH=1./A; //printf("HS2 %g: %g\n",q,HARDSPH); return(HARDSPH); } X2 =X*X; B = (1.0 +0.5*volfraction)*D; B *= B; B *= -6.*volfraction; G=0.5*volfraction*A; if(X < CUTOFFHS) { // RKH Feb 2016, use Taylor series expansion for small X // else no obvious way to rearrange the equations to avoid needing a very high number of significant figures. // Series expansion found using Mathematica software. Numerical test in .xls showed terms to X^2 are sufficient // for 5 or 6 significant figures, but I put the X^4 one in anyway //FF = 8*A +6*B + 4*G - (0.8*A +2.0*B/3.0 +0.5*G)*X2 +(A/35. +B/40. +G/50.)*X4; // refactoring the polynomial makes it very slightly faster (0.5 not 0.6 msec) //FF = 8*A +6*B + 4*G + ( -0.8*A -2.0*B/3.0 -0.5*G +(A/35. +B/40. +G/50.)*X2)*X2; FF = 8.0*A +6.0*B + 4.0*G + ( -0.8*A -B/1.5 -0.5*G +(A/35. +0.0125*B +0.02*G)*X2)*X2; // combining the terms makes things worse at smallest Q in single precision //FF = (8-0.8*X2)*A +(3.0-X2/3.)*2*B + (4+0.5*X2)*G +(A/35. +B/40. +G/50.)*X4; // note that G = -volfraction*A/2, combining this makes no further difference at smallest Q //FF = (8 +2.*volfraction + ( volfraction/4. -0.8 +(volfraction/100. -1./35.)*X2 )*X2 )*A + (3.0 -X2/3. +X4/40.)*2.*B; HARDSPH= 1./(1. + volfraction*FF ); //printf("HS3 %g: %g\n",q,HARDSPH); return(HARDSPH); } X4=X2*X2; SINCOS(X,S,C); // RKH Feb 2016, use version FISH code as is better than original sasview one at small Q in single precision, and more than twice as fast in double. //FF=A*(S-X*C)/X + B*(2.*X*S -(X2-2.)*C -2.)/X2 + G*( (4.*X2*X -24.*X)*S -(X4 -12.*X2 +24.)*C +24. )/X4; // refactoring the polynomial here & above makes it slightly faster FF= (( G*( (4.*X2 -24.)*X*S -(X4 -12.*X2 +24.)*C +24. )/X2 + B*(2.*X*S -(X2-2.)*C -2.) )/X + A*(S-X*C))/X ; HARDSPH= 1./(1. + 24.*volfraction*FF/X2 ); // changing /X and /X2 to *MX1 and *MX2, no significantg difference? //MX=1.0/X; //MX2=MX*MX; //FF= (( G*( (4.*X2 -24.)*X*S -(X4 -12.*X2 +24.)*C +24. )*MX2 + B*(2.*X*S -(X2-2.)*C -2.) )*MX + A*(S-X*C)) ; //HARDSPH= 1./(1. + 24.*volfraction*FF*MX2*MX ); // grouping the terms, was about same as sasmodels for single precision issues // FF=A*(S/X-C) + B*(2.*S/X - C +2.0*(C-1.0)/X2) + G*( (4./X -24./X3)*S -(1.0 -12./X2 +24./X4)*C +24./X4 ); // HARDSPH= 1./(1. + 24.*volfraction*FF/X2 ); // remove 1/X2 from final line, take more powers of X inside the brackets, stil bad // FF=A*(S/X3-C/X2) + B*(2.*S/X3 - C/X2 +2.0*(C-1.0)/X4) + G*( (4./X -24./X3)*S -(1.0 -12./X2 +24./X4)*C +24./X4 )/X2; // HARDSPH= 1./(1. + 24.*volfraction*FF ); //printf("HS4 %g: %g\n",q,HARDSPH); return(HARDSPH); """ def random(): import numpy as np pars = dict( scale=1, background=0, radius_effective=10**np.random.uniform(1, 4), volfraction=10**np.random.uniform(-2, 0), # high volume fraction ) return pars # ER defaults to 0.0 # VR defaults to 1.0 demo = dict(radius_effective=200, volfraction=0.2, radius_effective_pd=0.1, radius_effective_pd_n=40) # Q=0.001 is in the Taylor series, low Q part, so add Q=0.1, assuming double precision sasview is correct tests = [ [ {'scale': 1.0, 'background' : 0.0, 'radius_effective' : 50.0, 'volfraction' : 0.2, 'radius_effective_pd' : 0}, [0.001,0.1], [0.209128,0.930587]], ] # ADDED by: RKH ON: 16Mar2016 using equations from FISH as better than orig sasview, see notes above. Added Taylor expansions at small Q, sasmodels/sasmodels/models/hayter_msa.c000066400000000000000000000343271317715334700206510ustar00rootroot00000000000000// Hayter-Penfold (rescaled) MSA structure factor for screened Coulomb interactions // // C99 needs declarations of routines here double Iq(double QQ, double radius_effective, double zz, double VolFrac, double Temp, double csalt, double dialec); int sqcoef(int ir, double gMSAWave[]); int sqfun(int ix, int ir, double gMSAWave[]); double sqhcal(double qq, double gMSAWave[]); double Iq(double QQ, double radius_effective, double VolFrac, double zz, double Temp, double csalt, double dialec) { double gMSAWave[17]={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17}; double Elcharge=1.602189e-19; // electron charge in Coulombs (C) double kB=1.380662e-23; // Boltzman constant in J/K double FrSpPerm=8.85418782E-12; //Permittivity of free space in C^2/(N m^2) double SofQ, Qdiam, Vp, ss; double SIdiam, diam, Kappa, cs, IonSt; double Perm, Beta; double charge; int ierr; diam=2*radius_effective; //in A //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// //////////////////////////// convert to USEFUL inputs in SI units // //////////////////////////// NOTE: easiest to do EVERYTHING in SI units // //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// Beta=1.0/(kB*Temp); // in Joules^-1 Perm=dialec*FrSpPerm; //in C^2/(N m^2) charge=zz*Elcharge; //in Coulomb (C) SIdiam = diam*1.0E-10; //in m Vp=M_4PI_3*cube(SIdiam/2.0); //in m^3 cs=csalt*6.022E23*1.0E3; //# salt molecules/m^3 // Compute the derived values of : // Ionic strength IonSt (in C^2/m^3) // Kappa (Debye-Huckel screening length in m) // and gamma Exp(-k) // the zz*VolFrac/Vp is for the counterions from the micelle, assumed monovalent, the 2.0*cs if for added salt, assumed 1:1 electolyte IonSt=0.5 * Elcharge*Elcharge*(zz*VolFrac/Vp+2.0*cs); Kappa=sqrt(2*Beta*IonSt/Perm); //Kappa calc from Ionic strength // Kappa=2/SIdiam // Use to compare with HP paper gMSAWave[5]=Beta*charge*charge/(M_PI*Perm*SIdiam*square(2.0+Kappa*SIdiam)); // Finally set up dimensionless parameters Qdiam=QQ*diam; gMSAWave[6] = Kappa*SIdiam; gMSAWave[4] = VolFrac; //Function sqhpa(qq) {this is where Hayter-Penfold program began} // FIRST CALCULATE COUPLING ss=pow(gMSAWave[4],(1.0/3.0)); gMSAWave[9] = 2.0*ss*gMSAWave[5]*exp(gMSAWave[6]-gMSAWave[6]/ss); // CALCULATE COEFFICIENTS, CHECK ALL IS WELL // AND IF SO CALCULATE S(Q*SIG) ierr=0; ierr=sqcoef(ierr, gMSAWave); if (ierr>=0) { SofQ=sqhcal(Qdiam, gMSAWave); }else{ SofQ=NAN; // print "Error Level = ",ierr // print "Please report HPMSA problem with above error code" } return(SofQ); } ///////////////////////////////////////////////////////////// ///////////////////////////////////////////////////////////// // // // CALCULATES RESCALED VOLUME FRACTION AND CORRESPONDING // COEFFICIENTS FOR "SQHPA" // // JOHN B. HAYTER (I.L.L.) 14-SEP-81 // // ON EXIT: // // SETA IS THE RESCALED VOLUME FRACTION // SGEK IS THE RESCALED CONTACT POTENTIAL // SAK IS THE RESCALED SCREENING CONSTANT // A,B,C,F,U,V ARE THE MSA COEFFICIENTS // G1= G(1+) IS THE CONTACT VALUE OF G(R/SIG): // FOR THE GILLAN CONDITION, THE DIFFERENCE FROM // ZERO INDICATES THE COMPUTATIONAL ACCURACY. // // IR > 0: NORMAL EXIT, IR IS THE NUMBER OF ITERATIONS. // < 0: FAILED TO CONVERGE // int sqcoef(int ir, double gMSAWave[]) { int itm=40,ix,ig,ii; double acc=5.0E-6,del,e1,e2,f1,f2; // WAVE gMSAWave = $"root:HayPenMSA:gMSAWave" f1=0; //these were never properly initialized... f2=0; ig=1; if (gMSAWave[6]>=(1.0+8.0*gMSAWave[4])) { ig=0; gMSAWave[15]=gMSAWave[14]; gMSAWave[16]=gMSAWave[4]; ix=1; ir = sqfun(ix,ir,gMSAWave); gMSAWave[14]=gMSAWave[15]; gMSAWave[4]=gMSAWave[16]; if((ir<0.0) || (gMSAWave[14]>=0.0)) { return ir; } } gMSAWave[10]=fmin(gMSAWave[4],0.20); if ((ig!=1) || ( gMSAWave[9]>=0.15)) { ii=0; do { ii=ii+1; if(ii>itm) { ir=-1; return ir; } if (gMSAWave[10]<=0.0) { gMSAWave[10]=gMSAWave[4]/ii; } if(gMSAWave[10]>0.6) { gMSAWave[10] = 0.35/ii; } e1=gMSAWave[10]; gMSAWave[15]=f1; gMSAWave[16]=e1; ix=2; ir = sqfun(ix,ir,gMSAWave); f1=gMSAWave[15]; e1=gMSAWave[16]; e2=gMSAWave[10]*1.01; gMSAWave[15]=f2; gMSAWave[16]=e2; ix=2; ir = sqfun(ix,ir,gMSAWave); f2=gMSAWave[15]; e2=gMSAWave[16]; e2=e1-(e2-e1)*f1/(f2-f1); gMSAWave[10] = e2; del = fabs((e2-e1)/e1); } while (del>acc); gMSAWave[15]=gMSAWave[14]; gMSAWave[16]=e2; ix=4; ir = sqfun(ix,ir,gMSAWave); gMSAWave[14]=gMSAWave[15]; e2=gMSAWave[16]; ir=ii; if ((ig!=1) || (gMSAWave[10]>=gMSAWave[4])) { return ir; } } gMSAWave[15]=gMSAWave[14]; gMSAWave[16]=gMSAWave[4]; ix=3; ir = sqfun(ix,ir,gMSAWave); gMSAWave[14]=gMSAWave[15]; gMSAWave[4]=gMSAWave[16]; if ((ir>=0) && (gMSAWave[14]<0.0)) { ir=-3; } return ir; } int sqfun(int ix, int ir, double gMSAWave[]) { double acc=1.0e-6; double reta,eta2,eta21,eta22,eta3,eta32,eta2d,eta2d2,eta3d,eta6d,e12,e24,rgek; double rak,ak1,ak2,dak,dak2,dak4,d,d2,dd2,dd4,dd45,ex1,ex2,sk,ck,ckma,skma; double al1,al2,al3,al4,al5,al6,be1,be2,be3,vu1,vu2,vu3,vu4,vu5,ph1,ph2,ta1,ta2,ta3,ta4,ta5; double a1,a2,a3,b1,b2,b3,v1,v2,v3,p1,p2,p3,pp,pp1,pp2,p1p2,t1,t2,t3,um1,um2,um3,um4,um5,um6; double w0,w1,w2,w3,w4,w12,w13,w14,w15,w16,w24,w25,w26,w32,w34,w3425,w35,w3526,w36,w46,w56; double fa,fap,ca,e24g,pwk,qpw,pg,del,fun,fund,g24; int ii,ibig,itm=40; // WAVE gMSAWave = $"root:HayPenMSA:gMSAWave" a2=0; a3=0; b2=0; b3=0; v2=0; v3=0; p2=0; p3=0; // CALCULATE CONSTANTS; NOTATION IS HAYTER PENFOLD (1981) reta = gMSAWave[16]; eta2 = reta*reta; eta3 = eta2*reta; e12 = 12.0*reta; e24 = e12+e12; gMSAWave[13] = pow( (gMSAWave[4]/gMSAWave[16]),(1.0/3.0)); gMSAWave[12]=gMSAWave[6]/gMSAWave[13]; ibig=0; if (( gMSAWave[12]>15.0) && (ix==1)) { ibig=1; } gMSAWave[11] = gMSAWave[5]*gMSAWave[13]*exp(gMSAWave[6]- gMSAWave[12]); rgek = gMSAWave[11]; rak = gMSAWave[12]; ak2 = rak*rak; ak1 = 1.0+rak; dak2 = 1.0/ak2; dak4 = dak2*dak2; d = 1.0-reta; d2 = d*d; dak = d/rak; dd2 = 1.0/d2; dd4 = dd2*dd2; dd45 = dd4*2.0e-1; eta3d=3.0*reta; eta6d = eta3d+eta3d; eta32 = eta3+ eta3; eta2d = reta+2.0; eta2d2 = eta2d*eta2d; eta21 = 2.0*reta+1.0; eta22 = eta21*eta21; // ALPHA(I) al1 = -eta21*dak; al2 = (14.0*eta2-4.0*reta-1.0)*dak2; al3 = 36.0*eta2*dak4; // BETA(I) be1 = -(eta2+7.0*reta+1.0)*dak; be2 = 9.0*reta*(eta2+4.0*reta-2.0)*dak2; be3 = 12.0*reta*(2.0*eta2+8.0*reta-1.0)*dak4; // NU(I) vu1 = -(eta3+3.0*eta2+45.0*reta+5.0)*dak; vu2 = (eta32+3.0*eta2+42.0*reta-2.0e1)*dak2; vu3 = (eta32+3.0e1*reta-5.0)*dak4; vu4 = vu1+e24*rak*vu3; vu5 = eta6d*(vu2+4.0*vu3); // PHI(I) ph1 = eta6d/rak; ph2 = d-e12*dak2; // TAU(I) ta1 = (reta+5.0)/(5.0*rak); ta2 = eta2d*dak2; ta3 = -e12*rgek*(ta1+ta2); ta4 = eta3d*ak2*(ta1*ta1-ta2*ta2); ta5 = eta3d*(reta+8.0)*1.0e-1-2.0*eta22*dak2; // double PRECISION SINH(K), COSH(K) ex1 = exp(rak); ex2 = 0.0; if ( gMSAWave[12]<20.0) { ex2=exp(-rak); } sk=0.5*(ex1-ex2); ck = 0.5*(ex1+ex2); ckma = ck-1.0-rak*sk; skma = sk-rak*ck; // a(I) a1 = (e24*rgek*(al1+al2+ak1*al3)-eta22)*dd4; if (ibig==0) { a2 = e24*(al3*skma+al2*sk-al1*ck)*dd4; a3 = e24*(eta22*dak2-0.5*d2+al3*ckma-al1*sk+al2*ck)*dd4; } // b(I) b1 = (1.5*reta*eta2d2-e12*rgek*(be1+be2+ak1*be3))*dd4; if (ibig==0) { b2 = e12*(-be3*skma-be2*sk+be1*ck)*dd4; b3 = e12*(0.5*d2*eta2d-eta3d*eta2d2*dak2-be3*ckma+be1*sk-be2*ck)*dd4; } // V(I) v1 = (eta21*(eta2-2.0*reta+1.0e1)*2.5e-1-rgek*(vu4+vu5))*dd45; if (ibig==0) { v2 = (vu4*ck-vu5*sk)*dd45; v3 = ((eta3-6.0*eta2+5.0)*d-eta6d*(2.0*eta3-3.0*eta2+18.0*reta+1.0e1)*dak2+e24*vu3+vu4*sk-vu5*ck)*dd45; } // P(I) pp1 = ph1*ph1; pp2 = ph2*ph2; pp = pp1+pp2; p1p2 = ph1*ph2*2.0; p1 = (rgek*(pp1+pp2-p1p2)-0.5*eta2d)*dd2; if (ibig==0) { p2 = (pp*sk+p1p2*ck)*dd2; p3 = (pp*ck+p1p2*sk+pp1-pp2)*dd2; } // T(I) t1 = ta3+ta4*a1+ta5*b1; if (ibig!=0) { // VERY LARGE SCREENING: ASYMPTOTIC SOLUTION v3 = ((eta3-6.0*eta2+5.0)*d-eta6d*(2.0*eta3-3.0*eta2+18.0*reta+1.0e1)*dak2+e24*vu3)*dd45; t3 = ta4*a3+ta5*b3+e12*ta2 - 4.0e-1*reta*(reta+1.0e1)-1.0; p3 = (pp1-pp2)*dd2; b3 = e12*(0.5*d2*eta2d-eta3d*eta2d2*dak2+be3)*dd4; a3 = e24*(eta22*dak2-0.5*d2-al3)*dd4; um6 = t3*a3-e12*v3*v3; um5 = t1*a3+a1*t3-e24*v1*v3; um4 = t1*a1-e12*v1*v1; al6 = e12*p3*p3; al5 = e24*p1*p3-b3-b3-ak2; al4 = e12*p1*p1-b1-b1; w56 = um5*al6-al5*um6; w46 = um4*al6-al4*um6; fa = -w46/w56; ca = -fa; gMSAWave[3] = fa; gMSAWave[2] = ca; gMSAWave[1] = b1+b3*fa; gMSAWave[0] = a1+a3*fa; gMSAWave[8] = v1+v3*fa; gMSAWave[14] = -(p1+p3*fa); gMSAWave[15] = gMSAWave[14]; if (fabs(gMSAWave[15])<1.0e-3) { gMSAWave[15] = 0.0; } gMSAWave[10] = gMSAWave[16]; } else { t2 = ta4*a2+ta5*b2+e12*(ta1*ck-ta2*sk); t3 = ta4*a3+ta5*b3+e12*(ta1*sk-ta2*(ck-1.0))-4.0e-1*reta*(reta+1.0e1)-1.0; // MU(i) um1 = t2*a2-e12*v2*v2; um2 = t1*a2+t2*a1-e24*v1*v2; um3 = t2*a3+t3*a2-e24*v2*v3; um4 = t1*a1-e12*v1*v1; um5 = t1*a3+t3*a1-e24*v1*v3; um6 = t3*a3-e12*v3*v3; // GILLAN CONDITION ? // // YES - G(X=1+) = 0 // // COEFFICIENTS AND FUNCTION VALUE // if ((ix==1) || (ix==3)) { // NO - CALCULATE REMAINING COEFFICIENTS. // LAMBDA(I) al1 = e12*p2*p2; al2 = e24*p1*p2-b2-b2; al3 = e24*p2*p3; al4 = e12*p1*p1-b1-b1; al5 = e24*p1*p3-b3-b3-ak2; al6 = e12*p3*p3; // OMEGA(I) w16 = um1*al6-al1*um6; w15 = um1*al5-al1*um5; w14 = um1*al4-al1*um4; w13 = um1*al3-al1*um3; w12 = um1*al2-al1*um2; w26 = um2*al6-al2*um6; w25 = um2*al5-al2*um5; w24 = um2*al4-al2*um4; w36 = um3*al6-al3*um6; w35 = um3*al5-al3*um5; w34 = um3*al4-al3*um4; w32 = um3*al2-al3*um2; // w46 = um4*al6-al4*um6; w56 = um5*al6-al5*um6; w3526 = w35+w26; w3425 = w34+w25; // QUARTIC COEFFICIENTS w4 = w16*w16-w13*w36; w3 = 2.0*w16*w15-w13*w3526-w12*w36; w2 = w15*w15+2.0*w16*w14-w13*w3425-w12*w3526; w1 = 2.0*w15*w14-w13*w24-w12*w3425; w0 = w14*w14-w12*w24; // ESTIMATE THE STARTING VALUE OF f if (ix==1) { // LARGE K fap = (w14-w34-w46)/(w12-w15+w35-w26+w56-w32); } else { // ASSUME NOT TOO FAR FROM GILLAN CONDITION. // IF BOTH RGEK AND RAK ARE SMALL, USE P-W ESTIMATE. gMSAWave[14]=0.5*eta2d*dd2*exp(-rgek); if (( gMSAWave[11]<=2.0) && ( gMSAWave[11]>=0.0) && ( gMSAWave[12]<=1.0)) { e24g = e24*rgek*exp(rak); pwk = sqrt(e24g); qpw = (1.0-sqrt(1.0+2.0*d2*d*pwk/eta22))*eta21/d; gMSAWave[14] = -qpw*qpw/e24+0.5*eta2d*dd2; } pg = p1+gMSAWave[14]; ca = ak2*pg+2.0*(b3*pg-b1*p3)+e12*gMSAWave[14]*gMSAWave[14]*p3; ca = -ca/(ak2*p2+2.0*(b3*p2-b2*p3)); fap = -(pg+p2*ca)/p3; } // AND REFINE IT ACCORDING TO NEWTON ii=0; do { ii = ii+1; if (ii>itm) { // FAILED TO CONVERGE IN ITM ITERATIONS ir=-2; return (ir); } fa = fap; fun = w0+(w1+(w2+(w3+w4*fa)*fa)*fa)*fa; fund = w1+(2.0*w2+(3.0*w3+4.0*w4*fa)*fa)*fa; fap = fa-fun/fund; del=fabs((fap-fa)/fa); } while (del>acc); ir = ir+ii; fa = fap; ca = -(w16*fa*fa+w15*fa+w14)/(w13*fa+w12); gMSAWave[14] = -(p1+p2*ca+p3*fa); gMSAWave[15] = gMSAWave[14]; if (fabs(gMSAWave[15])<1.0e-3) { gMSAWave[15] = 0.0; } gMSAWave[10] = gMSAWave[16]; } else { ca = ak2*p1+2.0*(b3*p1-b1*p3); ca = -ca/(ak2*p2+2.0*(b3*p2-b2*p3)); fa = -(p1+p2*ca)/p3; if (ix==2) { gMSAWave[15] = um1*ca*ca+(um2+um3*fa)*ca+um4+um5*fa+um6*fa*fa; } if (ix==4) { gMSAWave[15] = -(p1+p2*ca+p3*fa); } } gMSAWave[3] = fa; gMSAWave[2] = ca; gMSAWave[1] = b1+b2*ca+b3*fa; gMSAWave[0] = a1+a2*ca+a3*fa; gMSAWave[8] = (v1+v2*ca+v3*fa)/gMSAWave[0]; } g24 = e24*rgek*ex1; gMSAWave[7] = (rak*ak2*ca-g24)/(ak2*g24); return (ir); } double sqhcal(double qq, double gMSAWave[]) { double SofQ,etaz,akz,gekz,e24,x1,x2,ck,sk,ak2,qk,q2k,qk2,qk3,qqk,sink,cosk,asink,qcosk,aqk,inter; // WAVE gMSAWave = $"root:HayPenMSA:gMSAWave" etaz = gMSAWave[10]; akz = gMSAWave[12]; gekz = gMSAWave[11]; e24 = 24.0*etaz; x1 = exp(akz); x2 = 0.0; if ( gMSAWave[12]<20.0) { x2 = exp(-akz); } ck = 0.5*(x1+x2); sk = 0.5*(x1-x2); ak2 = akz*akz; qk = qq/gMSAWave[13]; q2k = qk*qk; if (qk<=1.0e-08) { SofQ = -1.0/gMSAWave[0]; } else { // this rescales Q.sigma = 2.Q.Radius, so is hard to predict the value to test the function if (qk<=0.01) { // try Taylor series expansion at small qk (RKH Feb 2016, with help from Mathematica), // transition point may need to depend on precision of cpu used and ALAS on the values of some of the parameters ! // note have adsorbed a factor 24 from SofQ= // needs thorough test over wide range of parameter space! // there seem to be some rounding issues here in single precision, must use double aqk = gMSAWave[0]*(8.0+2.0*etaz) + 6*gMSAWave[1] -12.0*gMSAWave[3] -24*(gekz*(1.0+akz) -ck*akz*gMSAWave[2] +gMSAWave[3]*(ck-1.0) +(gMSAWave[2]-gMSAWave[3]*akz)*sk )/ak2 +q2k*( -(gMSAWave[0]*(48.0+15.0*etaz) +40.0*gMSAWave[1])/60.0 +gMSAWave[3] +(4.0/ak2)*(gekz*(9.0+7.0*akz) +ck*(9.0*gMSAWave[3] -7.0*gMSAWave[2]*akz) +sk*(9.0*gMSAWave[2] -7.0*gMSAWave[3]*akz)) ); SofQ = 1.0/(1.0-gMSAWave[10]*aqk); } else { qk2 = 1.0/q2k; qk3 = qk2/qk; qqk = 1.0/(qk*(q2k+ak2)); SINCOS(qk,sink,cosk); asink = akz*sink; qcosk = qk*cosk; aqk = gMSAWave[0]*(sink-qcosk); aqk=aqk+gMSAWave[1]*((2.0*qk2-1.0)*qcosk+2.0*sink-2.0/qk); inter=24.0*qk3+4.0*(1.0-6.0*qk2)*sink; aqk=(aqk+0.5*etaz*gMSAWave[0]*(inter-(1.0-12.0*qk2+24.0*qk2*qk2)*qcosk))*qk3; aqk=aqk +gMSAWave[2]*(ck*asink-sk*qcosk)*qqk; aqk=aqk +gMSAWave[3]*(sk*asink-qk*(ck*cosk-1.0))*qqk; aqk=aqk +gMSAWave[3]*(cosk-1.0)*qk2; aqk=aqk -gekz*(asink+qcosk)*qqk; SofQ = 1.0/(1.0 -e24*aqk); } } return (SofQ); } sasmodels/sasmodels/models/hayter_msa.py000066400000000000000000000131771317715334700210570ustar00rootroot00000000000000# Note: model title and parameter table are inserted automatically r""" This calculates the structure factor (the Fourier transform of the pair correlation function $g(r)$) for a system of charged, spheroidal objects in a dielectric medium. When combined with an appropriate form factor (such as sphere, core+shell, ellipsoid, etc), this allows for inclusion of the interparticle interference effects due to screened coulomb repulsion between charged particles. **This routine only works for charged particles**. If the charge is set to zero the routine may self-destruct! For non-charged particles use a hard sphere potential. The salt concentration is used to compute the ionic strength of the solution which in turn is used to compute the Debye screening length. At present there is no provision for entering the ionic strength directly nor for use of any multivalent salts, though it should be possible to simulate the effect of this by increasing the salt concentration. The counterions are also assumed to be monovalent. In sasview the effective radius may be calculated from the parameters used in the form factor $P(q)$ that this $S(q)$ is combined with. The computation uses a Taylor series expansion at very small rescaled $qR$, to avoid some serious rounding error issues, this may result in a minor artefact in the transition region under some circumstances. For 2D data, the scattering intensity is calculated in the same way as 1D, where the $q$ vector is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- J B Hayter and J Penfold, *Molecular Physics*, 42 (1981) 109-118 J P Hansen and J B Hayter, *Molecular Physics*, 46 (1982) 651-656 """ from numpy import inf category = "structure-factor" structure_factor = True single = False # double precision only! # dp[0] = 2.0*radius_effective(); # dp[1] = fabs(charge()); # dp[2] = volfraction(); # dp[3] = temperature(); # dp[4] = concentration_salt(); # dp[5] = dielectconst(); name = "hayter_msa" title = "Hayter-Penfold rescaled MSA, charged sphere, interparticle S(Q) structure factor" description = """\ [Hayter-Penfold RMSA charged sphere interparticle S(Q) structure factor] Interparticle structure factor S(Q)for a charged hard spheres. Routine takes absolute value of charge, use HardSphere if charge goes to zero. In sasview the effective radius and volume fraction may be calculated from the parameters used in P(Q). """ # pylint: disable=bad-whitespace, line-too-long # [ "name", "units", default, [lower, upper], "type", "description" ], parameters = [ ["radius_effective", "Ang", 20.75, [0, inf], "volume", "effective radius of charged sphere"], ["volfraction", "None", 0.0192, [0, 0.74], "", "volume fraction of spheres"], ["charge", "e", 19.0, [0, 200], "", "charge on sphere (in electrons)"], ["temperature", "K", 318.16, [0, 450], "", "temperature, in Kelvin, for Debye length calculation"], ["concentration_salt", "M", 0.0, [0, inf], "", "conc of salt, moles/litre, 1:1 electolyte, for Debye length"], ["dielectconst", "None", 71.08, [-inf, inf], "", "dielectric constant (relative permittivity) of solvent, default water, for Debye length"] ] # pylint: enable=bad-whitespace, line-too-long source = ["hayter_msa.c"] # No volume normalization despite having a volume parameter # This should perhaps be volume normalized? form_volume = """ return 1.0; """ # ER defaults to 0.0 # VR defaults to 1.0 def random(): import numpy as np # TODO: too many failures for random hayter_msa parameters pars = dict( scale=1, background=0, radius_effective=10**np.random.uniform(1, 4.7), volfraction=10**np.random.uniform(-2, 0), # high volume fraction charge=min(int(10**np.random.uniform(0, 1.3)+0.5), 200), temperature=10**np.random.uniform(0, np.log10(450)), # max T = 450 #concentration_salt=10**np.random.uniform(-3, 1), dialectconst=10**np.random.uniform(0, 6), #charge=10, #temperature=318.16, concentration_salt=0.0, #dielectconst=71.08, ) return pars # default parameter set, use compare.sh -midQ -linear # note the calculation varies in different limiting cases so a wide range of # parameters will be required for a thorough test! # odd that the default st has concentration_salt zero demo = dict(radius_effective=20.75, charge=19.0, volfraction=0.0192, temperature=318.16, concentration_salt=0.05, dielectconst=71.08, radius_effective_pd=0.1, radius_effective_pd_n=40) # # attempt to use same values as old sasview unit test at Q=.001 was 0.0712928, # then add lots new ones assuming values from new model are OK, need some # low Q values to test the small Q Taylor expansion tests = [ [{'scale': 1.0, 'background': 0.0, 'radius_effective': 20.75, 'charge': 19.0, 'volfraction': 0.0192, 'temperature': 298.0, 'concentration_salt': 0, 'dielectconst': 78.0, 'radius_effective_pd': 0}, [0.00001, 0.0010, 0.01, 0.075], [0.0711646, 0.0712928, 0.0847006, 1.07150]], [{'scale': 1.0, 'background': 0.0, 'radius_effective': 20.75, 'charge': 19.0, 'volfraction': 0.0192, 'temperature': 298.0, 'concentration_salt': 0.05, 'dielectconst': 78.0, 'radius_effective_pd': 0.1, 'radius_effective_pd_n': 40}, [0.00001, 0.0010, 0.01, 0.075], [0.450272, 0.450420, 0.465116, 1.039625]] ] # ADDED by: RKH ON: 16Mar2016 converted from sasview, new Taylor expansion at smallest rescaled Q sasmodels/sasmodels/models/hollow_cylinder.c000066400000000000000000000050731317715334700217060ustar00rootroot00000000000000double form_volume(double radius, double thickness, double length); double Iq(double q, double radius, double thickness, double length, double sld, double solvent_sld); double Iqxy(double qx, double qy, double radius, double thickness, double length, double sld, double solvent_sld, double theta, double phi); //#define INVALID(v) (v.radius_core >= v.radius) // From Igor library static double _hollow_cylinder_scaling(double integrand, double delrho, double volume) { return 1.0e-4 * square(volume * delrho) * integrand; } static double _hollow_cylinder_kernel(double q, double radius, double thickness, double length, double sin_val, double cos_val) { const double qs = q*sin_val; const double lam1 = sas_2J1x_x((radius+thickness)*qs); const double lam2 = sas_2J1x_x(radius*qs); const double gamma_sq = square(radius/(radius+thickness)); //Note: lim_{thickness -> 0} psi = sas_J0(radius*qs) //Note: lim_{radius -> 0} psi = sas_2J1x_x(thickness*qs) const double psi = (lam1 - gamma_sq*lam2)/(1.0 - gamma_sq); //SRK 10/19/00 const double t2 = sas_sinx_x(0.5*q*length*cos_val); return psi*t2; } double form_volume(double radius, double thickness, double length) { double v_shell = M_PI*length*(square(radius+thickness) - radius*radius); return v_shell; } double Iq(double q, double radius, double thickness, double length, double sld, double solvent_sld) { const double lower = 0.0; const double upper = 1.0; //limits of numerical integral double summ = 0.0; //initialize intergral for (int i=0;i<76;i++) { const double cos_val = 0.5*( Gauss76Z[i] * (upper-lower) + lower + upper ); const double sin_val = sqrt(1.0 - cos_val*cos_val); const double inter = _hollow_cylinder_kernel(q, radius, thickness, length, sin_val, cos_val); summ += Gauss76Wt[i] * inter * inter; } const double Aq = 0.5*summ*(upper-lower); const double volume = form_volume(radius, thickness, length); return _hollow_cylinder_scaling(Aq, solvent_sld - sld, volume); } double Iqxy(double qx, double qy, double radius, double thickness, double length, double sld, double solvent_sld, double theta, double phi) { double q, sin_alpha, cos_alpha; ORIENT_SYMMETRIC(qx, qy, theta, phi, q, sin_alpha, cos_alpha); const double Aq = _hollow_cylinder_kernel(q, radius, thickness, length, sin_alpha, cos_alpha); const double vol = form_volume(radius, thickness, length); return _hollow_cylinder_scaling(Aq*Aq, solvent_sld-sld, vol); } sasmodels/sasmodels/models/hollow_cylinder.py000066400000000000000000000127131317715334700221130ustar00rootroot00000000000000r""" This model provides the form factor, $P(q)$, for a monodisperse hollow right angle circular cylinder (rigid tube) where the form factor is normalized by the volume of the tube (i.e. not by the external volume). .. math:: P(q) = \text{scale} \left/V_\text{shell} + \text{background} where the averaging $\left<\ldots\right>$ is applied only for the 1D calculation. The inside and outside of the hollow cylinder are assumed have the same SLD. Definition ---------- The 1D scattering intensity is calculated in the following way (Guinier, 1955) .. math:: P(q) &= (\text{scale})V_\text{shell}\Delta\rho^2 \int_0^{1}\Psi^2 \left[q_z, R_\text{outer}(1-x^2)^{1/2}, R_\text{core}(1-x^2)^{1/2}\right] \left[\frac{\sin(qHx)}{qHx}\right]^2 dx \\ \Psi[q,y,z] &= \frac{1}{1-\gamma^2} \left[ \Lambda(qy) - \gamma^2\Lambda(qz) \right] \\ \Lambda(a) &= 2 J_1(a) / a \\ \gamma &= R_\text{core} / R_\text{outer} \\ V_\text{shell} &= \pi \left(R_\text{outer}^2 - R_\text{core}^2 \right)L \\ J_1(x) &= (\sin(x)-x\cdot \cos(x)) / x^2 where *scale* is a scale factor, $H = L/2$ and $J_1$ is the 1st order Bessel function. **NB**: The 2nd virial coefficient of the cylinder is calculated based on the outer radius and full length, which give an the effective radius for structure factor $S(q)$ when $P(q) \cdot S(q)$ is applied. In the parameters,the *radius* is $R_\text{core}$ while *thickness* is $R_\text{outer} - R_\text{core}$. To provide easy access to the orientation of the core-shell cylinder, we define the axis of the cylinder using two angles $\theta$ and $\phi$ (see :ref:`cylinder model `). References ---------- L A Feigin and D I Svergun, *Structure Analysis by Small-Angle X-Ray and Neutron Scattering*, Plenum Press, New York, (1987) Authorship and Verification ---------------------------- * **Author:** NIST IGOR/DANSE **Date:** pre 2010 * **Last Modified by:** Richard Heenan **Date:** October 06, 2016 (reparametrised to use thickness, not outer radius) * **Last Reviewed by:** Richard Heenan **Date:** October 06, 2016 """ from numpy import pi, inf, sin, cos name = "hollow_cylinder" title = "" description = """ P(q) = scale*/Vol + background, where f is the scattering amplitude. radius = the radius of core thickness = the thickness of shell length = the total length of the cylinder sld = SLD of the shell sld_solvent = SLD of the solvent background = incoherent background """ category = "shape:cylinder" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type","description"], parameters = [ ["radius", "Ang", 20.0, [0, inf], "volume", "Cylinder core radius"], ["thickness", "Ang", 10.0, [0, inf], "volume", "Cylinder wall thickness"], ["length", "Ang", 400.0, [0, inf], "volume", "Cylinder total length"], ["sld", "1e-6/Ang^2", 6.3, [-inf, inf], "sld", "Cylinder sld"], ["sld_solvent", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Solvent sld"], ["theta", "degrees", 90, [-360, 360], "orientation", "Cylinder axis to beam angle"], ["phi", "degrees", 0, [-360, 360], "orientation", "Rotation about beam"], ] # pylint: enable=bad-whitespace, line-too-long source = ["lib/polevl.c", "lib/sas_J1.c", "lib/gauss76.c", "hollow_cylinder.c"] # pylint: disable=W0613 def ER(radius, thickness, length): """ :param radius: Cylinder core radius :param thickness: Cylinder wall thickness :param length: Cylinder length :return: Effective radius """ router = radius + thickness if router == 0 or length == 0: return 0.0 len1 = router len2 = length/2.0 term1 = len1*len1*2.0*len2/2.0 term2 = 1.0 + (len2/len1)*(1.0 + 1/len2/2.0)*(1.0 + pi*len1/len2/2.0) ddd = 3.0*term1*term2 diam = pow(ddd, (1.0/3.0)) return diam def VR(radius, thickness, length): """ :param radius: Cylinder radius :param thickness: Cylinder wall thickness :param length: Cylinder length :return: Volf ratio for P(q)*S(q) """ router = radius + thickness vol_core = pi*radius*radius*length vol_total = pi*router*router*length vol_shell = vol_total - vol_core return vol_shell, vol_total def random(): import numpy as np length = 10**np.random.uniform(1, 4.7) outer_radius = 10**np.random.uniform(1, 4.7) # Use a distribution with a preference for thin shell or thin core # Avoid core,shell radii < 1 thickness = np.random.beta(0.5, 0.5)*(outer_radius-2) + 1 radius = outer_radius - thickness pars = dict( length=length, radius=radius, thickness=thickness, ) return pars # parameters for demo demo = dict(scale=1.0, background=0.0, length=400.0, radius=20.0, thickness=10, sld=6.3, sld_solvent=1, theta=90, phi=0, thickness_pd=0.2, thickness_pd_n=9, length_pd=.2, length_pd_n=10, radius_pd=.2, radius_pd_n=9, theta_pd=10, theta_pd_n=5, ) q = 0.1 # april 6 2017, rkh added a 2d unit test, assume correct! qx = q*cos(pi/6.0) qy = q*sin(pi/6.0) # Parameters for unit tests tests = [ [{}, 0.00005, 1764.926], [{}, 'VR', 1.8], [{}, 0.001, 1756.76], [{}, (qx, qy), 2.36885476192 ], ] del qx, qy # not necessary to delete, but cleaner sasmodels/sasmodels/models/hollow_rectangular_prism.c000066400000000000000000000063711317715334700236200ustar00rootroot00000000000000double form_volume(double length_a, double b2a_ratio, double c2a_ratio, double thickness); double Iq(double q, double sld, double solvent_sld, double length_a, double b2a_ratio, double c2a_ratio, double thickness); double form_volume(double length_a, double b2a_ratio, double c2a_ratio, double thickness) { double length_b = length_a * b2a_ratio; double length_c = length_a * c2a_ratio; double a_core = length_a - 2.0*thickness; double b_core = length_b - 2.0*thickness; double c_core = length_c - 2.0*thickness; double vol_core = a_core * b_core * c_core; double vol_total = length_a * length_b * length_c; double vol_shell = vol_total - vol_core; return vol_shell; } double Iq(double q, double sld, double solvent_sld, double length_a, double b2a_ratio, double c2a_ratio, double thickness) { const double length_b = length_a * b2a_ratio; const double length_c = length_a * c2a_ratio; const double a_half = 0.5 * length_a; const double b_half = 0.5 * length_b; const double c_half = 0.5 * length_c; const double vol_total = length_a * length_b * length_c; const double vol_core = 8.0 * (a_half-thickness) * (b_half-thickness) * (c_half-thickness); //Integration limits to use in Gaussian quadrature const double v1a = 0.0; const double v1b = M_PI_2; //theta integration limits const double v2a = 0.0; const double v2b = M_PI_2; //phi integration limits double outer_sum = 0.0; for(int i=0; i<76; i++) { const double theta = 0.5 * ( Gauss76Z[i]*(v1b-v1a) + v1a + v1b ); double sin_theta, cos_theta; SINCOS(theta, sin_theta, cos_theta); const double termC1 = sas_sinx_x(q * c_half * cos(theta)); const double termC2 = sas_sinx_x(q * (c_half-thickness)*cos(theta)); double inner_sum = 0.0; for(int j=0; j<76; j++) { const double phi = 0.5 * ( Gauss76Z[j]*(v2b-v2a) + v2a + v2b ); double sin_phi, cos_phi; SINCOS(phi, sin_phi, cos_phi); // Amplitude AP from eqn. (13), rewritten to avoid round-off effects when arg=0 const double termA1 = sas_sinx_x(q * a_half * sin_theta * sin_phi); const double termA2 = sas_sinx_x(q * (a_half-thickness) * sin_theta * sin_phi); const double termB1 = sas_sinx_x(q * b_half * sin_theta * cos_phi); const double termB2 = sas_sinx_x(q * (b_half-thickness) * sin_theta * cos_phi); const double AP1 = vol_total * termA1 * termB1 * termC1; const double AP2 = vol_core * termA2 * termB2 * termC2; inner_sum += Gauss76Wt[j] * square(AP1-AP2); } inner_sum *= 0.5 * (v2b-v2a); outer_sum += Gauss76Wt[i] * inner_sum * sin(theta); } outer_sum *= 0.5*(v1b-v1a); // Normalize as in Eqn. (15) without the volume factor (as cancels with (V*DelRho)^2 normalization) // The factor 2 is due to the different theta integration limit (pi/2 instead of pi) const double form = outer_sum/M_PI_2; // Multiply by contrast^2. Factor corresponding to volume^2 cancels with previous normalization. const double delrho = sld - solvent_sld; // Convert from [1e-12 A-1] to [cm-1] return 1.0e-4 * delrho * delrho * form; } sasmodels/sasmodels/models/hollow_rectangular_prism.py000066400000000000000000000143721317715334700240260ustar00rootroot00000000000000# rectangular_prism model # Note: model title and parameter table are inserted automatically r""" This model provides the form factor, $P(q)$, for a hollow rectangular parallelepiped with a wall of thickness $\Delta$. It computes only the 1D scattering, not the 2D. Definition ---------- The 1D scattering intensity for this model is calculated by forming the difference of the amplitudes of two massive parallelepipeds differing in their outermost dimensions in each direction by the same length increment $2\Delta$ (Nayuk, 2012). As in the case of the massive parallelepiped model (:ref:`rectangular-prism`), the scattering amplitude is computed for a particular orientation of the parallelepiped with respect to the scattering vector and then averaged over all possible orientations, giving .. math:: P(q) = \frac{1}{V^2} \frac{2}{\pi} \times \, \int_0^{\frac{\pi}{2}} \, \int_0^{\frac{\pi}{2}} A_{P\Delta}^2(q) \, \sin\theta \, d\theta \, d\phi where $\theta$ is the angle between the $z$ axis and the longest axis of the parallelepiped, $\phi$ is the angle between the scattering vector (lying in the $xy$ plane) and the $y$ axis, and .. math:: :nowrap: \begin{align*} A_{P\Delta}(q) & = A B C \left[\frac{\sin \bigl( q \frac{C}{2} \cos\theta \bigr)} {\left( q \frac{C}{2} \cos\theta \right)} \right] \left[\frac{\sin \bigl( q \frac{A}{2} \sin\theta \sin\phi \bigr)} {\left( q \frac{A}{2} \sin\theta \sin\phi \right)}\right] \left[\frac{\sin \bigl( q \frac{B}{2} \sin\theta \cos\phi \bigr)} {\left( q \frac{B}{2} \sin\theta \cos\phi \right)}\right] \\ & - 8 \left(\frac{A}{2}-\Delta\right) \left(\frac{B}{2}-\Delta\right) \left(\frac{C}{2}-\Delta\right) \left[ \frac{\sin \bigl[ q \bigl(\frac{C}{2}-\Delta\bigr) \cos\theta \bigr]} {q \bigl(\frac{C}{2}-\Delta\bigr) \cos\theta} \right] \left[ \frac{\sin \bigl[ q \bigl(\frac{A}{2}-\Delta\bigr) \sin\theta \sin\phi \bigr]} {q \bigl(\frac{A}{2}-\Delta\bigr) \sin\theta \sin\phi} \right] \left[ \frac{\sin \bigl[ q \bigl(\frac{B}{2}-\Delta\bigr) \sin\theta \cos\phi \bigr]} {q \bigl(\frac{B}{2}-\Delta\bigr) \sin\theta \cos\phi} \right] \end{align*} where $A$, $B$ and $C$ are the external sides of the parallelepiped fulfilling $A \le B \le C$, and the volume $V$ of the parallelepiped is .. math:: V = A B C \, - \, (A - 2\Delta) (B - 2\Delta) (C - 2\Delta) The 1D scattering intensity is then calculated as .. math:: I(q) = \text{scale} \times V \times (\rho_\text{p} - \rho_\text{solvent})^2 \times P(q) + \text{background} where $\rho_\text{p}$ is the scattering length of the parallelepiped, $\rho_\text{solvent}$ is the scattering length of the solvent, and (if the data are in absolute units) *scale* represents the volume fraction (which is unitless). **The 2D scattering intensity is not computed by this model.** Validation ---------- Validation of the code was conducted by qualitatively comparing the output of the 1D model to the curves shown in (Nayuk, 2012). References ---------- R Nayuk and K Huber, *Z. Phys. Chem.*, 226 (2012) 837-854 """ from numpy import pi, inf, sqrt name = "hollow_rectangular_prism" title = "Hollow rectangular parallelepiped with uniform scattering length density." description = """ I(q)= scale*V*(sld - sld_solvent)^2*P(q,theta,phi)+background P(q,theta,phi) = (2/pi/V^2) * double integral from 0 to pi/2 of ... (AP1-AP2)^2(q)*sin(theta)*dtheta*dphi AP1 = S(q*C*cos(theta)/2) * S(q*A*sin(theta)*sin(phi)/2) * S(q*B*sin(theta)*cos(phi)/2) AP2 = S(q*C'*cos(theta)) * S(q*A'*sin(theta)*sin(phi)) * S(q*B'*sin(theta)*cos(phi)) C' = (C/2-thickness) B' = (B/2-thickness) A' = (A/2-thickness) S(x) = sin(x)/x """ category = "shape:parallelepiped" # ["name", "units", default, [lower, upper], "type","description"], parameters = [["sld", "1e-6/Ang^2", 6.3, [-inf, inf], "sld", "Parallelepiped scattering length density"], ["sld_solvent", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Solvent scattering length density"], ["length_a", "Ang", 35, [0, inf], "volume", "Shorter side of the parallelepiped"], ["b2a_ratio", "Ang", 1, [0, inf], "volume", "Ratio sides b/a"], ["c2a_ratio", "Ang", 1, [0, inf], "volume", "Ratio sides c/a"], ["thickness", "Ang", 1, [0, inf], "volume", "Thickness of parallelepiped"], ] source = ["lib/gauss76.c", "hollow_rectangular_prism.c"] def ER(length_a, b2a_ratio, c2a_ratio, thickness): """ Return equivalent radius (ER) thickness parameter not used """ b_side = length_a * b2a_ratio c_side = length_a * c2a_ratio # surface average radius (rough approximation) surf_rad = sqrt(length_a * b_side / pi) ddd = 0.75 * surf_rad * (2 * surf_rad * c_side + (c_side + surf_rad) * (c_side + pi * surf_rad)) return 0.5 * (ddd) ** (1. / 3.) def VR(length_a, b2a_ratio, c2a_ratio, thickness): """ Return shell volume and total volume """ b_side = length_a * b2a_ratio c_side = length_a * c2a_ratio a_core = length_a - 2.0*thickness b_core = b_side - 2.0*thickness c_core = c_side - 2.0*thickness vol_core = a_core * b_core * c_core vol_total = length_a * b_side * c_side vol_shell = vol_total - vol_core return vol_total, vol_shell def random(): import numpy as np a, b, c = 10**np.random.uniform(1, 4.7, size=3) # Thickness is limited to 1/2 the smallest dimension # Use a distribution with a preference for thin shell or thin core # Avoid core,shell radii < 1 min_dim = 0.5*min(a, b, c) thickness = np.random.beta(0.5, 0.5)*(min_dim-2) + 1 #print(a, b, c, thickness, thickness/min_dim) pars = dict( length_a=a, b2a_ratio=b/a, c2a_ratio=c/a, thickness=thickness, ) return pars # parameters for demo demo = dict(scale=1, background=0, sld=6.3, sld_solvent=1.0, length_a=35, b2a_ratio=1, c2a_ratio=1, thickness=1, length_a_pd=0.1, length_a_pd_n=10, b2a_ratio_pd=0.1, b2a_ratio_pd_n=1, c2a_ratio_pd=0.1, c2a_ratio_pd_n=1) tests = [[{}, 0.2, 0.76687283098], [{}, [0.2], [0.76687283098]], ] sasmodels/sasmodels/models/hollow_rectangular_prism_thin_walls.c000066400000000000000000000056001317715334700260360ustar00rootroot00000000000000double form_volume(double length_a, double b2a_ratio, double c2a_ratio); double Iq(double q, double sld, double solvent_sld, double length_a, double b2a_ratio, double c2a_ratio); double form_volume(double length_a, double b2a_ratio, double c2a_ratio) { double length_b = length_a * b2a_ratio; double length_c = length_a * c2a_ratio; double vol_shell = 2.0 * (length_a*length_b + length_a*length_c + length_b*length_c); return vol_shell; } double Iq(double q, double sld, double solvent_sld, double length_a, double b2a_ratio, double c2a_ratio) { const double length_b = length_a * b2a_ratio; const double length_c = length_a * c2a_ratio; const double a_half = 0.5 * length_a; const double b_half = 0.5 * length_b; const double c_half = 0.5 * length_c; //Integration limits to use in Gaussian quadrature const double v1a = 0.0; const double v1b = M_PI_2; //theta integration limits const double v2a = 0.0; const double v2b = M_PI_2; //phi integration limits double outer_sum = 0.0; for(int i=0; i<76; i++) { const double theta = 0.5 * ( Gauss76Z[i]*(v1b-v1a) + v1a + v1b ); double sin_theta, cos_theta; double sin_c, cos_c; SINCOS(theta, sin_theta, cos_theta); SINCOS(q*c_half*cos_theta, sin_c, cos_c); // To check potential problems if denominator goes to zero here !!! const double termAL_theta = 8.0 * cos_c / (q*q*sin_theta*sin_theta); const double termAT_theta = 8.0 * sin_c / (q*q*sin_theta*cos_theta); double inner_sum = 0.0; for(int j=0; j<76; j++) { const double phi = 0.5 * ( Gauss76Z[j]*(v2b-v2a) + v2a + v2b ); double sin_phi, cos_phi; double sin_a, cos_a; double sin_b, cos_b; SINCOS(phi, sin_phi, cos_phi); SINCOS(q*a_half*sin_theta*sin_phi, sin_a, cos_a); SINCOS(q*b_half*sin_theta*cos_phi, sin_b, cos_b); // Amplitude AL from eqn. (7c) const double AL = termAL_theta * sin_a*sin_b / (sin_phi*cos_phi); // Amplitude AT from eqn. (9) const double AT = termAT_theta * ( cos_a*sin_b/cos_phi + cos_b*sin_a/sin_phi ); inner_sum += Gauss76Wt[j] * square(AL+AT); } inner_sum *= 0.5 * (v2b-v2a); outer_sum += Gauss76Wt[i] * inner_sum * sin_theta; } outer_sum *= 0.5*(v1b-v1a); // Normalize as in Eqn. (15) without the volume factor (as cancels with (V*DelRho)^2 normalization) // The factor 2 is due to the different theta integration limit (pi/2 instead of pi) double answer = outer_sum/M_PI_2; // Multiply by contrast^2. Factor corresponding to volume^2 cancels with previous normalization. answer *= square(sld-solvent_sld); // Convert from [1e-12 A-1] to [cm-1] answer *= 1.0e-4; return answer; } sasmodels/sasmodels/models/hollow_rectangular_prism_thin_walls.py000066400000000000000000000115421317715334700262460ustar00rootroot00000000000000# rectangular_prism model # Note: model title and parameter table are inserted automatically r""" This model provides the form factor, $P(q)$, for a hollow rectangular prism with infinitely thin walls. It computes only the 1D scattering, not the 2D. Definition ---------- The 1D scattering intensity for this model is calculated according to the equations given by Nayuk and Huber (Nayuk, 2012). Assuming a hollow parallelepiped with infinitely thin walls, edge lengths $A \le B \le C$ and presenting an orientation with respect to the scattering vector given by $\theta$ and $\phi$, where $\theta$ is the angle between the $z$ axis and the longest axis of the parallelepiped $C$, and $\phi$ is the angle between the scattering vector (lying in the $xy$ plane) and the $y$ axis, the form factor is given by .. math:: P(q) = \frac{1}{V^2} \frac{2}{\pi} \int_0^{\frac{\pi}{2}} \int_0^{\frac{\pi}{2}} [A_L(q)+A_T(q)]^2 \sin\theta\,d\theta\,d\phi where .. math:: V &= 2AB + 2AC + 2BC \\ A_L(q) &= 8 \times \frac{ \sin \left( \tfrac{1}{2} q A \sin\phi \sin\theta \right) \sin \left( \tfrac{1}{2} q B \cos\phi \sin\theta \right) \cos \left( \tfrac{1}{2} q C \cos\theta \right) }{q^2 \, \sin^2\theta \, \sin\phi \cos\phi} \\ A_T(q) &= A_F(q) \times \frac{2\,\sin \left( \tfrac{1}{2} q C \cos\theta \right)}{q\,\cos\theta} and .. math:: A_F(q) = 4 \frac{ \cos \left( \tfrac{1}{2} q A \sin\phi \sin\theta \right) \sin \left( \tfrac{1}{2} q B \cos\phi \sin\theta \right) } {q \, \cos\phi \, \sin\theta} + 4 \frac{ \sin \left( \tfrac{1}{2} q A \sin\phi \sin\theta \right) \cos \left( \tfrac{1}{2} q B \cos\phi \sin\theta \right) } {q \, \sin\phi \, \sin\theta} The 1D scattering intensity is then calculated as .. math:: I(q) = \text{scale} \times V \times (\rho_\text{p} - \rho_\text{solvent})^2 \times P(q) where $V$ is the volume of the rectangular prism, $\rho_\text{p}$ is the scattering length of the parallelepiped, $\rho_\text{solvent}$ is the scattering length of the solvent, and (if the data are in absolute units) *scale* represents the volume fraction (which is unitless). **The 2D scattering intensity is not computed by this model.** Validation ---------- Validation of the code was conducted by qualitatively comparing the output of the 1D model to the curves shown in (Nayuk, 2012). References ---------- R Nayuk and K Huber, *Z. Phys. Chem.*, 226 (2012) 837-854 """ from numpy import pi, inf, sqrt name = "hollow_rectangular_prism_thin_walls" title = "Hollow rectangular parallelepiped with thin walls." description = """ I(q)= scale*V*(sld - sld_solvent)^2*P(q)+background with P(q) being the form factor corresponding to a hollow rectangular parallelepiped with infinitely thin walls. """ category = "shape:parallelepiped" # ["name", "units", default, [lower, upper], "type","description"], parameters = [["sld", "1e-6/Ang^2", 6.3, [-inf, inf], "sld", "Parallelepiped scattering length density"], ["sld_solvent", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Solvent scattering length density"], ["length_a", "Ang", 35, [0, inf], "volume", "Shorter side of the parallelepiped"], ["b2a_ratio", "Ang", 1, [0, inf], "volume", "Ratio sides b/a"], ["c2a_ratio", "Ang", 1, [0, inf], "volume", "Ratio sides c/a"], ] source = ["lib/gauss76.c", "hollow_rectangular_prism_thin_walls.c"] def ER(length_a, b2a_ratio, c2a_ratio): """ Return equivalent radius (ER) """ b_side = length_a * b2a_ratio c_side = length_a * c2a_ratio # surface average radius (rough approximation) surf_rad = sqrt(length_a * b_side / pi) ddd = 0.75 * surf_rad * (2 * surf_rad * c_side + (c_side + surf_rad) * (c_side + pi * surf_rad)) return 0.5 * (ddd) ** (1. / 3.) def VR(length_a, b2a_ratio, c2a_ratio): """ Return shell volume and total volume """ b_side = length_a * b2a_ratio c_side = length_a * c2a_ratio vol_total = length_a * b_side * c_side vol_shell = 2.0 * (length_a*b_side + length_a*c_side + b_side*c_side) return vol_shell, vol_total def random(): import numpy as np a, b, c = 10**np.random.uniform(1, 4.7, size=3) pars = dict( length_a=a, b2a_ratio=b/a, c2a_ratio=c/a, ) return pars # parameters for demo demo = dict(scale=1, background=0, sld=6.3, sld_solvent=1.0, length_a=35, b2a_ratio=1, c2a_ratio=1, length_a_pd=0.1, length_a_pd_n=10, b2a_ratio_pd=0.1, b2a_ratio_pd_n=1, c2a_ratio_pd=0.1, c2a_ratio_pd_n=1) tests = [[{}, 0.2, 0.837719188592], [{}, [0.2], [0.837719188592]], ] sasmodels/sasmodels/models/img/000077500000000000000000000000001317715334700171145ustar00rootroot00000000000000sasmodels/sasmodels/models/img/barbell_geometry.jpg000066400000000000000000000204701317715334700231370ustar00rootroot00000000000000JFIF``C    $.' 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Definition ---------- The scattering intensity $I(q)$ for dilute, randomly oriented, "infinitely large" sheets or lamellae is .. math:: I(q) = \text{scale}\frac{2\pi P(q)}{q^2\delta} + \text{background} The form factor is .. math:: P(q) = \frac{2\Delta\rho^2}{q^2}(1-\cos(q\delta)) = \frac{4\Delta\rho^2}{q^2}\sin^2\left(\frac{q\delta}{2}\right) where $\delta$ is the total layer thickness and $\Delta\rho$ is the scattering length density difference. This is the limiting form for a spherical shell of infinitely large radius. Note that the division by $\delta$ means that $scale$ in sasview is the volume fraction of sheet, $\phi = S\delta$ where $S$ is the area of sheet per unit volume. $S$ is half the Porod surface area per unit volume of a thicker layer (as that would include both faces of the sheet). The 2D scattering intensity is calculated in the same way as 1D, where the $q$ vector is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- F Nallet, R Laversanne, and D Roux, J. Phys. II France, 3, (1993) 487-502 also in J. Phys. Chem. B, 105, (2001) 11081-11088 """ from numpy import inf name = "lamellar" title = "Lyotropic lamellar phase with uniform SLD and random distribution" description = """\ [Dilute Lamellar Form Factor](from a lyotropic lamellar phase) I(q)= 2*pi*P(q)/(delta *q^(2)), where P(q)=2*(contrast/q)^(2)*(1-cos(q*delta))^(2)) thickness = layer thickness sld = layer scattering length density sld_solvent = solvent scattering length density background = incoherent background scale = scale factor """ category = "shape:lamellae" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type","description"], parameters = [ ["thickness", "Ang", 50, [0, inf], "volume", "total layer thickness" ], ["sld", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Layer scattering length density" ], ["sld_solvent", "1e-6/Ang^2", 6, [-inf, inf], "sld", "Solvent scattering length density" ], ] # pylint: enable=bad-whitespace, line-too-long # No volume normalization despite having a volume parameter # This should perhaps be volume normalized? - it is! form_volume = """ return 1.0; """ Iq = """ const double sub = sld - sld_solvent; const double qsq = q*q; // Original expression //return 4.0e-4*M_PI*sub*sub/qsq * (1.0-cos(q*thickness)) / (thickness*qsq); // const double alpha = fmod(q*thickness+0.1, 2.0*M_PI)-0.1; // Use small angle fix 1-cos(theta) = 2 sin^2(theta/2) const double sinq2 = sin(0.5*q*thickness); return 4.0e-4*M_PI*sub*sub/qsq * 2.0*sinq2*sinq2 / (thickness*qsq); """ def random(): import numpy as np thickness = 10**np.random.uniform(1, 4) pars = dict( thickness=thickness, ) return pars # ER defaults to 0.0 # VR defaults to 1.0 demo = dict(scale=1, background=0, sld=6, sld_solvent=1, thickness=40, thickness_pd=0.2, thickness_pd_n=40) tests = [ [ {'scale': 1.0, 'background': 0.0, 'thickness': 50.0, 'sld': 1.0, 'sld_solvent': 6.3, 'thickness_pd': 0.0}, [0.001], [882289.54309]] ] # ADDED by: converted by PAK? (or RKH?) ON: 16Mar2016 - RKH adding unit tests from sasview to early 2015 conversion # [(qx1, qy1), (qx2, qy2), ...], [I(qx1,qy1), I(qx2,qy2), ...]], sasmodels/sasmodels/models/lamellar_hg.py000066400000000000000000000101001317715334700211510ustar00rootroot00000000000000# Note: model title and parameter table are inserted automatically r""" This model provides the scattering intensity, $I(q)$, for a lyotropic lamellar phase where a random distribution in solution are assumed. The SLD of the head region is taken to be different from the SLD of the tail region. Definition ---------- The scattering intensity $I(q)$ is .. math:: I(q) = 2\pi\frac{\text{scale}}{2(\delta_H + \delta_T)} P(q) \frac{1}{q^2} The form factor $P(q)$ is .. math:: P(q) = \frac{4}{q^2} \left\lbrace \Delta \rho_H \left[\sin[q(\delta_H + \delta_T)\ - \sin(q\delta_T)\right] + \Delta\rho_T\sin(q\delta_T) \right\rbrace^2 where $\delta_T$ is *length_tail*, $\delta_H$ is *length_head*, $\Delta\rho_H$ is the head contrast (*sld_head* $-$ *sld_solvent*), and $\Delta\rho_T$ is tail contrast (*sld* $-$ *sld_solvent*). The total thickness of the lamellar sheet is $\delta_H + \delta_T + \delta_T + \delta_H$. Note that in a non aqueous solvent the chemical "head" group may be the "Tail region" and vice-versa. The 2D scattering intensity is calculated in the same way as 1D, where the $q$ vector is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- F Nallet, R Laversanne, and D Roux, J. Phys. II France, 3, (1993) 487-502 also in J. Phys. Chem. B, 105, (2001) 11081-11088 *2014/04/17 - Description reviewed by S King and P Butler.* """ from numpy import inf name = "lamellar_hg" title = "Random lamellar phase with Head and Tail Groups" description = """\ [Random lamellar phase with Head and Tail Groups] I(q)= 2*pi*P(q)/(2(H+T)*q^(2)), where P(q)= see manual layer thickness =(H+T+T+H) = 2(Head+Tail) sld = Tail scattering length density sld_head = Head scattering length density sld_solvent = solvent scattering length density background = incoherent background scale = scale factor """ category = "shape:lamellae" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type","description"], parameters = [["length_tail", "Ang", 15, [0, inf], "volume", "Tail thickness ( total = H+T+T+H)"], ["length_head", "Ang", 10, [0, inf], "volume", "Head thickness"], ["sld", "1e-6/Ang^2", 0.4, [-inf,inf], "sld", "Tail scattering length density"], ["sld_head", "1e-6/Ang^2", 3.0, [-inf,inf], "sld", "Head scattering length density"], ["sld_solvent", "1e-6/Ang^2", 6, [-inf,inf], "sld", "Solvent scattering length density"]] # pylint: enable=bad-whitespace, line-too-long # No volume normalization despite having a volume parameter # This should perhaps be volume normalized? form_volume = """ return 1.0; """ Iq = """ const double qsq = q*q; const double drh = sld_head - sld_solvent; const double drt = sld - sld_solvent; //correction 13FEB06 by L.Porcar const double qT = q*length_tail; double Pq, inten; Pq = drh*(sin(q*(length_head+length_tail))-sin(qT)) + drt*sin(qT); Pq *= Pq; Pq *= 4.0/(qsq); inten = 2.0e-4*M_PI*Pq/qsq; // normalize by the bilayer thickness inten /= 2.0*(length_head+length_tail); return inten; """ def random(): import numpy as np thickness = 10**np.random.uniform(1, 4) length_head = thickness * np.random.uniform(0, 1) length_tail = thickness - length_head pars = dict( length_head=length_head, length_tail=length_tail, ) return pars # ER defaults to 0.0 # VR defaults to 1.0 demo = dict(scale=1, background=0, length_tail=15, length_head=10, sld=0.4, sld_head=3.0, sld_solvent=6.0, length_tail_pd=0.2, length_tail_pd_n=40, length_head_pd=0.01, length_head_pd_n=40) # tests = [ [{'scale': 1.0, 'background': 0.0, 'length_tail': 15.0, 'length_head': 10.0, 'sld': 0.4, 'sld_head': 3.0, 'sld_solvent': 6.0}, [0.001], [653143.9209]], ] # ADDED by: RKH ON: 18Mar2016 converted from sasview previously, now renaming everything & sorting the docs sasmodels/sasmodels/models/lamellar_hg_stack_caille.c000066400000000000000000000032641317715334700234560ustar00rootroot00000000000000/* LamellarCailleHG kernel - allows for name changes of passed parameters ... Maths identical to LamellarCaille apart from the line for P(Q) */ static double Iq(double qval, double length_tail, double length_head, double fp_Nlayers, double dd, double Cp, double tail_sld, double head_sld, double solvent_sld) { int Nlayers = (int)(fp_Nlayers+0.5); //cast to an integer for the loop double inten,Pq,Sq,alpha,temp,t2; //double dQ, dQDefault, t1, t3; // from wikipedia 0.577215664901532860606512090082402431042159335 const double Euler = 0.577215664901533; // Euler's constant, increased sig figs for new models Feb 2015 //dQDefault = 0.0; //[=] 1/A, q-resolution, default value //dQ = dQDefault; // REMOVED UNUSED dQ calculations for new models Feb 2015 Pq = (head_sld-solvent_sld)*(sin(qval*(length_head+length_tail))-sin(qval*length_tail)) + (tail_sld-solvent_sld)*sin(qval*length_tail); Pq *= Pq; Pq *= 4.0/(qval*qval); Sq = 0.0; for(int ii=1; ii < Nlayers; ii++) { temp = 0.0; alpha = Cp/4.0/M_PI/M_PI*(log(M_PI*ii) + Euler); //t1 = 2.0*dQ*dQ*dd*dd*alpha; t2 = 2.0*qval*qval*dd*dd*alpha; //t3 = dQ*dQ*dd*dd*ii*ii; temp = 1.0-(double)ii/(double)Nlayers; //temp *= cos(dd*qval*ii/(1.0+t1)); temp *= cos(dd*qval*ii); //if (temp < 0) printf("q=%g: ii=%d, cos(dd*q*ii)=cos(%g) < 0\n",qval,ii,dd*qval*ii); //temp *= exp(-1.0*(t2 + t3)/(2.0*(1.0+t1)) ); temp *= exp(-t2/2.0); //temp /= sqrt(1.0+t1); Sq += temp; } Sq *= 2.0; Sq += 1.0; //if (Sq < 0) printf("q=%g: S(q) =%g\n", qval, Sq); inten = 2.0*M_PI*Pq*Sq/(dd*qval*qval); inten *= 1.0e-04; // 1/A to 1/cm return inten; } sasmodels/sasmodels/models/lamellar_hg_stack_caille.py000066400000000000000000000121571317715334700236650ustar00rootroot00000000000000# Note: model title and parameter table are inserted automatically r""" This model provides the scattering intensity, $I(q) = P(q)S(q)$, for a lamellar phase where a random distribution in solution are assumed. Here a Caille $S(q)$ is used for the lamellar stacks. The scattering intensity $I(q)$ is .. math:: I(q) = 2 \pi \frac{P(q)S(q)}{q^2\delta } The form factor $P(q)$ is .. math:: P(q) = \frac{4}{q^2}\big\{ \Delta\rho_H \left[\sin[q(\delta_H + \delta_T)] - \sin(q\delta_T)\right] + \Delta\rho_T\sin(q\delta_T)\big\}^2 and the structure factor $S(q)$ is .. math:: S(q) = 1 + 2 \sum_1^{N-1}\left(1-\frac{n}{N}\right) \cos(qdn)\exp\left(-\frac{2q^2d^2\alpha(n)}{2}\right) where .. math:: :nowrap: \begin{align*} \alpha(n) &= \frac{\eta_{cp}}{4\pi^2} \left(\ln(\pi n)+\gamma_E\right) && \\ \gamma_E &= 0.5772156649 && \text{Euler's constant} \\ \eta_{cp} &= \frac{q_o^2k_B T}{8\pi\sqrt{K\overline{B}}} && \text{Caille constant} \end{align*} $\delta_T$ is the tail length (or *length_tail*), $\delta_H$ is the head thickness (or *length_head*), $\Delta\rho_H$ is SLD(headgroup) - SLD(solvent), and $\Delta\rho_T$ is SLD(tail) - SLD(headgroup). Here $d$ is (repeat) spacing, $K$ is smectic bending elasticity, $B$ is compression modulus, and $N$ is the number of lamellar plates (*Nlayers*). NB: **When the Caille parameter is greater than approximately 0.8 to 1.0, the assumptions of the model are incorrect.** And due to a complication of the model function, users are responsible for making sure that all the assumptions are handled accurately (see the original reference below for more details). Non-integer numbers of stacks are calculated as a linear combination of results for the next lower and higher values. Be aware that the computations may be very slow. The 2D scattering intensity is calculated in the same way as 1D, where the $q$ vector is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- F Nallet, R Laversanne, and D Roux, J. Phys. II France, 3, (1993) 487-502 also in J. Phys. Chem. B, 105, (2001) 11081-11088 """ from numpy import inf name = "lamellar_hg_stack_caille" title = "Random lamellar head/tail/tail/head sheet with Caille structure factor" description = """\ [Random lamellar phase with Caille structure factor] randomly oriented stacks of infinite sheets with Caille S(Q), having polydisperse spacing. layer thickness =(H+T+T+H) = 2(Head+Tail) sld = Tail scattering length density sld_head = Head scattering length density sld_solvent = solvent scattering length density background = incoherent background scale = scale factor """ category = "shape:lamellae" single = False # TODO: check parameters = [ # [ "name", "units", default, [lower, upper], "type", # "description" ], ["length_tail", "Ang", 10, [0, inf], "volume", "Tail thickness"], ["length_head", "Ang", 2, [0, inf], "volume", "head thickness"], ["Nlayers", "", 30, [1, inf], "", "Number of layers"], ["d_spacing", "Ang", 40., [0.0, inf], "volume", "lamellar d-spacing of Caille S(Q)"], ["Caille_parameter", "", 0.001, [0.0, 0.8], "", "Caille parameter"], ["sld", "1e-6/Ang^2", 0.4, [-inf, inf], "sld", "Tail scattering length density"], ["sld_head", "1e-6/Ang^2", 2.0, [-inf, inf], "sld", "Head scattering length density"], ["sld_solvent", "1e-6/Ang^2", 6, [-inf, inf], "sld", "Solvent scattering length density"], ] source = ["lamellar_hg_stack_caille.c"] # No volume normalization despite having a volume parameter # This should perhaps be volume normalized? form_volume = """ return 1.0; """ # ER defaults to 0.0 # VR defaults to 1.0 def random(): import numpy as np total_thickness = 10**np.random.uniform(2, 4.7) Nlayers = np.random.randint(2, 200) d_spacing = total_thickness / Nlayers thickness = d_spacing * np.random.uniform(0, 1) length_head = thickness * np.random.uniform(0, 1) length_tail = thickness - length_head Caille_parameter = np.random.uniform(0, 0.8) pars = dict( length_head=length_head, length_tail=length_tail, Nlayers=Nlayers, d_spacing=d_spacing, Caille_parameter=Caille_parameter, ) return pars demo = dict( scale=1, background=0, Nlayers=20, d_spacing=200., Caille_parameter=0.05, length_tail=15, length_head=10, #sld=-1, sld_head=4.0, sld_solvent=6.0, sld=-1, sld_head=4.1, sld_solvent=6.0, length_tail_pd=0.1, length_tail_pd_n=20, length_head_pd=0.05, length_head_pd_n=30, d_spacing_pd=0.2, d_spacing_pd_n=40, ) # tests = [[{'scale': 1.0, 'background': 0.0, 'length_tail': 10.0, 'length_head': 2.0, 'Nlayers': 30.0, 'd_spacing': 40., 'Caille_parameter': 0.001, 'sld': 0.4, 'sld_head': 2.0, 'sld_solvent': 6.0, 'length_tail_pd': 0.0, 'length_head_pd': 0.0, 'd_spacing_pd': 0.0}, [0.001], [6838238.571488]]] # ADDED by: RKH ON: 18Mar2016 converted from sasview previously, now renaming everything & sorting the docs sasmodels/sasmodels/models/lamellar_stack_caille.c000066400000000000000000000026041317715334700227750ustar00rootroot00000000000000/* LamellarCaille kernel - allows for name changes of passed parameters ... */ static double Iq(double qval, double del, double fp_Nlayers, double dd, double Cp, double sld, double solvent_sld) { int Nlayers = (int)(fp_Nlayers+0.5); //cast to an integer for the loop double contr; //local variables of coefficient wave double inten,Pq,Sq,alpha,temp,t2; //double dQ, dQDefault, t1, t3; // from wikipedia 0.577215664901532860606512090082402431042159335 const double Euler = 0.577215664901533; // Euler's constant, increased sig figs for new models Feb 2015 //dQDefault = 0.0; //[=] 1/A, q-resolution, default value //dQ = dQDefault; // REMOVED UNUSED dQ calculations for new models Feb 2015 contr = sld - solvent_sld; Pq = 2.0*contr*contr/qval/qval*(1.0-cos(qval*del)); Sq = 0.0; for (int ii=1; ii < Nlayers; ii++) { temp = 0.0; alpha = Cp/4.0/M_PI/M_PI*(log(M_PI*ii) + Euler); //t1 = 2.0*dQ*dQ*dd*dd*alpha; t2 = 2.0*qval*qval*dd*dd*alpha; //t3 = dQ*dQ*dd*dd*ii*ii; temp = 1.0 - (double)ii / (double)Nlayers; //temp *= cos(dd*qval*ii/(1.0+t1)); temp *= cos(dd*qval*ii); //temp *= exp(-1.0*(t2 + t3)/(2.0*(1.0+t1)) ); temp *= exp(-t2/2.0); //temp /= sqrt(1.0+t1); Sq += temp; } Sq *= 2.0; Sq += 1.0; inten = 2.0*M_PI*Pq*Sq/(dd*qval*qval); inten *= 1.0e-04; // 1/A to 1/cm return(inten); } sasmodels/sasmodels/models/lamellar_stack_caille.py000066400000000000000000000105161317715334700232040ustar00rootroot00000000000000r""" This model provides the scattering intensity, $I(q) = P(q) S(q)$, for a lamellar phase where a random distribution in solution are assumed. Here a Caille $S(q)$ is used for the lamellar stacks. Definition ---------- The scattering intensity $I(q)$ is .. math:: I(q) = 2\pi \frac{P(q)S(q)}{q^2\delta } The form factor is .. math:: P(q) = \frac{2\Delta\rho^2}{q^2}\left(1-\cos q\delta \right) and the structure factor is .. math:: S(q) = 1 + 2 \sum_1^{N-1}\left(1-\frac{n}{N}\right) \cos(qdn)\exp\left(-\frac{2q^2d^2\alpha(n)}{2}\right) where .. math:: :nowrap: \begin{align*} \alpha(n) &= \frac{\eta_{cp}}{4\pi^2} \left(\ln(\pi n)+\gamma_E\right) && \\ \gamma_E &= 0.5772156649 && \text{Euler's constant} \\ \eta_{cp} &= \frac{q_o^2k_B T}{8\pi\sqrt{K\overline{B}}} && \text{Caille constant} \end{align*} Here $d$ = (repeat) d_spacing, $\delta$ = bilayer thickness, the contrast $\Delta\rho$ = SLD(headgroup) - SLD(solvent), $K$ = smectic bending elasticity, $B$ = compression modulus, and $N$ = number of lamellar plates (*n_plates*). NB: **When the Caille parameter is greater than approximately 0.8 to 1.0, the assumptions of the model are incorrect.** And due to a complication of the model function, users are responsible for making sure that all the assumptions are handled accurately (see the original reference below for more details). Non-integer numbers of stacks are calculated as a linear combination of results for the next lower and higher values. The 2D scattering intensity is calculated in the same way as 1D, where the $q$ vector is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- F Nallet, R Laversanne, and D Roux, J. Phys. II France, 3, (1993) 487-502 also in J. Phys. Chem. B, 105, (2001) 11081-11088 """ from numpy import inf name = "lamellar_stack_caille" title = "Random lamellar sheet with Caille structure factor" description = """\ [Random lamellar phase with Caille structure factor] randomly oriented stacks of infinite sheets with Caille S(Q), having polydisperse spacing. sld = sheet scattering length density sld_solvent = solvent scattering length density background = incoherent background scale = scale factor """ category = "shape:lamellae" single = False # TODO: check # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type","description"], parameters = [ ["thickness", "Ang", 30.0, [0, inf], "volume", "sheet thickness"], ["Nlayers", "", 20, [1, inf], "", "Number of layers"], ["d_spacing", "Ang", 400., [0.0,inf], "volume", "lamellar d-spacing of Caille S(Q)"], ["Caille_parameter", "1/Ang^2", 0.1, [0.0,0.8], "", "Caille parameter"], ["sld", "1e-6/Ang^2", 6.3, [-inf,inf], "sld", "layer scattering length density"], ["sld_solvent", "1e-6/Ang^2", 1.0, [-inf,inf], "sld", "Solvent scattering length density"], ] # pylint: enable=bad-whitespace, line-too-long source = ["lamellar_stack_caille.c"] def random(): import numpy as np total_thickness = 10**np.random.uniform(2, 4.7) Nlayers = np.random.randint(2, 200) d_spacing = total_thickness / Nlayers thickness = d_spacing * np.random.uniform(0, 1) Caille_parameter = np.random.uniform(0, 0.8) pars = dict( thickness=thickness, Nlayers=Nlayers, d_spacing=d_spacing, Caille_parameter=Caille_parameter, ) return pars # No volume normalization despite having a volume parameter # This should perhaps be volume normalized? form_volume = """ return 1.0; """ # ER defaults to 0.0 # VR defaults to 1.0 demo = dict(scale=1, background=0, thickness=67., Nlayers=3.75, d_spacing=200., Caille_parameter=0.268, sld=1.0, sld_solvent=6.34, thickness_pd=0.1, thickness_pd_n=100, d_spacing_pd=0.05, d_spacing_pd_n=40) # tests = [ [{'scale': 1.0, 'background': 0.0, 'thickness': 30., 'Nlayers': 20.0, 'd_spacing': 400., 'Caille_parameter': 0.1, 'sld': 6.3, 'sld_solvent': 1.0, 'thickness_pd': 0.0, 'd_spacing_pd': 0.0}, [0.001], [28895.13397]] ] # ADDED by: RKH ON: 18Mar2016 converted from sasview previously, now renaming everything & sorting the docs sasmodels/sasmodels/models/lamellar_stack_paracrystal.c000066400000000000000000000037551317715334700241010ustar00rootroot00000000000000/* Lamellar_ParaCrystal - Pedersen's model */ double paraCryst_sn(double ww, double qval, double davg, int Nlayers, double an); double paraCryst_an(double ww, double qval, double davg, int Nlayers); static double Iq(double qval, double th, double fp_Nlayers, double davg, double pd, double sld, double solvent_sld) { //get the fractional part of Nlayers, to determine the "mixing" of N's int n1 = (int)(fp_Nlayers); //truncate towards zero int n2 = n1 + 1; const double xn = (double)n2 - fp_Nlayers; //fractional contribution of n1 const double ww = exp(-0.5*square(qval*pd*davg)); //calculate the n1 contribution double Znq,Snq,an; an = paraCryst_an(ww,qval,davg,n1); Snq = paraCryst_sn(ww,qval,davg,n1,an); Znq = xn*Snq; //calculate the n2 contribution an = paraCryst_an(ww,qval,davg,n2); Snq = paraCryst_sn(ww,qval,davg,n2,an); Znq += (1.0-xn)*Snq; //and the independent contribution Znq += (1.0-ww*ww)/(1.0+ww*ww-2.0*ww*cos(qval*davg)); //the limit when Nlayers approaches infinity // Zq = (1-ww^2)/(1+ww^2-2*ww*cos(qval*davg)) const double xi = th/2.0; //use 1/2 the bilayer thickness const double Pbil = square(sas_sinx_x(qval*xi)); const double contr = sld - solvent_sld; const double inten = 2.0*M_PI*contr*contr*Pbil*Znq/(qval*qval); //printf("q=%.7e wwm1=%g ww=%.5e an=% 12.5e Snq=% 12.5e Znq=% 12.5e Pbil=% 12.5e\n",qval,wwm1,ww,an,Snq,Znq,Pbil); return 1.0e-4*inten; } // functions for the lamellar paracrystal model double paraCryst_sn(double ww, double qval, double davg, int Nlayers, double an) { double Snq; Snq = an/( (double)Nlayers*square(1.0+ww*ww-2.0*ww*cos(qval*davg)) ); return Snq; } double paraCryst_an(double ww, double qval, double davg, int Nlayers) { double an; an = 4.0*ww*ww - 2.0*(ww*ww*ww+ww)*cos(qval*davg); an -= 4.0*pow(ww,(Nlayers+2))*cos((double)Nlayers*qval*davg); an += 2.0*pow(ww,(Nlayers+3))*cos((double)(Nlayers-1)*qval*davg); an += 2.0*pow(ww,(Nlayers+1))*cos((double)(Nlayers+1)*qval*davg); return an; } sasmodels/sasmodels/models/lamellar_stack_paracrystal.py000066400000000000000000000114761317715334700243060ustar00rootroot00000000000000# Note: model title and parameter table are inserted automatically r""" This model calculates the scattering from a stack of repeating lamellar structures. The stacks of lamellae (infinite in lateral dimension) are treated as a paracrystal to account for the repeating spacing. The repeat distance is further characterized by a Gaussian polydispersity. **This model can be used for large multilamellar vesicles.** Definition ---------- In the equations below, - *scale* is used instead of the mass per area of the bilayer $\Gamma_m$ (this corresponds to the volume fraction of the material in the bilayer, *not* the total excluded volume of the paracrystal), - *sld* $-$ *sld_solvent* is the contrast $\Delta \rho$, - *thickness* is the layer thickness $t$, - *Nlayers* is the number of layers $N$, - *d_spacing* is the average distance between adjacent layers $\langle D \rangle$, and - *sigma_d* is the relative standard deviation of the Gaussian layer distance distribution $\sigma_D / \langle D \rangle$. The scattering intensity $I(q)$ is calculated as .. math:: I(q) = 2\pi\Delta\rho^2\Gamma_m\frac{P_\text{bil}(q)}{q^2} Z_N(q) The form factor of the bilayer is approximated as the cross section of an infinite, planar bilayer of thickness $t$ (compare the equations for the lamellar model). .. math:: P_\text{bil}(q) = \left(\frac{\sin(qt/2)}{qt/2}\right)^2 $Z_N(q)$ describes the interference effects for aggregates consisting of more than one bilayer. The equations used are (3-5) from the Bergstrom reference: .. math:: Z_N(q) = \frac{1 - w^2}{1 + w^2 - 2w \cos(q \langle D \rangle)} + x_N S_N + (1 - x_N) S_{N+1} where .. math:: S_N(q) = \frac{a_N}{N}[1 + w^2 - 2 w \cos(q \langle D \rangle)]^2 and .. math:: a_N &= 4w^2 - 2(w^3 + w) \cos(q \langle D \rangle) \\ &\quad - 4w^{N+2}\cos(Nq \langle D \rangle) + 2 w^{N+3}\cos[(N-1)q \langle D \rangle] + 2w^{N+1}\cos[(N+1)q \langle D \rangle] for the layer spacing distribution $w = \exp(-\sigma_D^2 q^2/2)$. Non-integer numbers of stacks are calculated as a linear combination of the lower and higher values .. math:: N_L = x_N N + (1 - x_N)(N+1) The 2D scattering intensity is the same as 1D, regardless of the orientation of the $q$ vector which is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} Reference --------- M Bergstrom, J S Pedersen, P Schurtenberger, S U Egelhaaf, *J. Phys. Chem. B*, 103 (1999) 9888-9897 """ from numpy import inf name = "lamellar_stack_paracrystal" title = "Random lamellar sheet with paracrystal structure factor" description = """\ [Random lamellar phase with paracrystal structure factor] randomly oriented stacks of infinite sheets with paracrytal S(Q), having polydisperse spacing. sld = sheet scattering length density sld_solvent = solvent scattering length density background = incoherent background scale = scale factor """ category = "shape:lamellae" single = False # ["name", "units", default, [lower, upper], "type","description"], parameters = [["thickness", "Ang", 33.0, [0, inf], "volume", "sheet thickness"], ["Nlayers", "", 20, [1, inf], "", "Number of layers"], ["d_spacing", "Ang", 250., [0.0, inf], "", "lamellar spacing of paracrystal stack"], ["sigma_d", "Ang", 0.0, [0.0, inf], "", "Sigma (polydispersity) of the lamellar spacing"], ["sld", "1e-6/Ang^2", 1.0, [-inf, inf], "sld", "layer scattering length density"], ["sld_solvent", "1e-6/Ang^2", 6.34, [-inf, inf], "sld", "Solvent scattering length density"], ] source = ["lamellar_stack_paracrystal.c"] form_volume = """ return 1.0; """ def random(): import numpy as np total_thickness = 10**np.random.uniform(2, 4.7) Nlayers = np.random.randint(2, 200) d_spacing = total_thickness / Nlayers thickness = d_spacing * np.random.uniform(0, 1) # Let polydispersity peak around 15%; 95% < 0.4; max=100% sigma_d = np.random.beta(1.5, 7) pars = dict( thickness=thickness, Nlayers=Nlayers, d_spacing=d_spacing, sigma_d=sigma_d, ) return pars # ER defaults to 0.0 # VR defaults to 1.0 demo = dict(scale=1, background=0, thickness=33, Nlayers=20, d_spacing=250, sigma_d=0.2, sld=1.0, sld_solvent=6.34, thickness_pd=0.2, thickness_pd_n=40) # tests = [ [{'scale': 1.0, 'background': 0.0, 'thickness': 33.,'Nlayers': 20.0, 'd_spacing': 250., 'sigma_d': 0.2, 'sld': 1.0, 'sld_solvent': 6.34, 'thickness_pd': 0.0, 'thickness_pd_n': 40 }, [0.001, 0.215268], [21829.3, 0.00487686]], ] # ADDED by: RKH ON: 18Mar2016 converted from sasview previously, now renaming everything & sorting the docs sasmodels/sasmodels/models/lib/000077500000000000000000000000001317715334700171065ustar00rootroot00000000000000sasmodels/sasmodels/models/lib/core_shell.c000066400000000000000000000021071317715334700213710ustar00rootroot00000000000000/******************************************************************* core_shell_kernel Form factor used in core_shell and fractal_core_shell ********************************************************************/ static double core_shell_kernel(double q, double radius, double thickness, double core_sld, double shell_sld, double solvent_sld) { // Core first, then add in shell const double core_qr = q * radius; const double core_contrast = core_sld - shell_sld; const double core_bes = sas_3j1x_x(core_qr); const double core_volume = M_4PI_3 * cube(radius); double f = core_volume * core_bes * core_contrast; // Now the shell const double shell_qr = q * (radius + thickness); const double shell_contrast = shell_sld - solvent_sld; const double shell_bes = sas_3j1x_x(shell_qr); const double shell_volume = M_4PI_3 * cube(radius + thickness); f += shell_volume * shell_bes * shell_contrast; return f * f * 1.0e-4; }sasmodels/sasmodels/models/lib/fractal_sq.c000066400000000000000000000021731317715334700213740ustar00rootroot00000000000000static double fractal_sq(double q, double radius, double fractal_dim, double cor_length) { //calculate S(q), using Teixeira, Eq(15) // mathematica query to check limiting conditions: // lim x->0 of [ x gamma(x-1) sin(arctan(q c (x-1))) (q r)^(-x) (1 + 1/(q c)^2)^((1-x)/2) ] // Note: gamma(x) may be unreliable for x<0, so the gamma(D-1) is risky. // We instead transform D*gamma(D-1) into gamma(D+1)/(D-1). double term; if (q == 0.) { const double D = fractal_dim; term = pow(cor_length/radius, D)*sas_gamma(D+1.); } else if (fractal_dim == 0.) { term = 1.0; } else if (fractal_dim == 1.) { term = atan(q*cor_length)/(q*radius); } else { // q>0, D>0 const double D = fractal_dim; const double Dm1 = fractal_dim - 1.0; // Note: for large Dm1, sin(Dm1*atan(q*cor_length) can go negative const double t1 = sas_gamma(D+1.)/Dm1*sin(Dm1*atan(q*cor_length)); const double t2 = pow(q*radius, -D); const double t3 = pow(1.0 + 1.0/square(q*cor_length), -0.5*Dm1); term = t1 * t2 * t3; } return 1.0 + term; } sasmodels/sasmodels/models/lib/gauss150.c000066400000000000000000000160531317715334700206270ustar00rootroot00000000000000/* * GaussWeights.c * SANSAnalysis * * Created by Andrew Jackson on 4/23/07. * Copyright 2007 __MyCompanyName__. All rights reserved. * */ // Gaussians constant double Gauss150Z[150]={ -0.9998723404457334, -0.9993274305065947, -0.9983473449340834, -0.9969322929775997, -0.9950828645255290, -0.9927998590434373, -0.9900842691660192, -0.9869372772712794, -0.9833602541697529, -0.9793547582425894, -0.9749225346595943, -0.9700655145738374, -0.9647858142586956, -0.9590857341746905, -0.9529677579610971, -0.9464345513503147, -0.9394889610042837, -0.9321340132728527, -0.9243729128743136, -0.9162090414984952, -0.9076459563329236, -0.8986873885126239, -0.8893372414942055, -0.8795995893549102, -0.8694786750173527, -0.8589789084007133, -0.8481048644991847, -0.8368612813885015, -0.8252530581614230, -0.8132852527930605, -0.8009630799369827, -0.7882919086530552, -0.7752772600680049, -0.7619248049697269, -0.7482403613363824, -0.7342298918013638, -0.7198995010552305, -0.7052554331857488, -0.6903040689571928, -0.6750519230300931, -0.6595056411226444, -0.6436719971150083, -0.6275578900977726, -0.6111703413658551, -0.5945164913591590, -0.5776035965513142, -0.5604390262878617, -0.5430302595752546, -0.5253848818220803, -0.5075105815339176, -0.4894151469632753, -0.4711064627160663, -0.4525925063160997, -0.4338813447290861, -0.4149811308476706, -0.3959000999390257, -0.3766465660565522, -0.3572289184172501, -0.3376556177463400, -0.3179351925907259, -0.2980762356029071, -0.2780873997969574, -0.2579773947782034, -0.2377549829482451, -0.2174289756869712, -0.1970082295132342, -0.1765016422258567, -0.1559181490266516, -0.1352667186271445, -0.1145563493406956, -0.0937960651617229, -0.0729949118337358, -0.0521619529078925, -0.0313062657937972, -0.0104369378042598, 0.0104369378042598, 0.0313062657937972, 0.0521619529078925, 0.0729949118337358, 0.0937960651617229, 0.1145563493406956, 0.1352667186271445, 0.1559181490266516, 0.1765016422258567, 0.1970082295132342, 0.2174289756869712, 0.2377549829482451, 0.2579773947782034, 0.2780873997969574, 0.2980762356029071, 0.3179351925907259, 0.3376556177463400, 0.3572289184172501, 0.3766465660565522, 0.3959000999390257, 0.4149811308476706, 0.4338813447290861, 0.4525925063160997, 0.4711064627160663, 0.4894151469632753, 0.5075105815339176, 0.5253848818220803, 0.5430302595752546, 0.5604390262878617, 0.5776035965513142, 0.5945164913591590, 0.6111703413658551, 0.6275578900977726, 0.6436719971150083, 0.6595056411226444, 0.6750519230300931, 0.6903040689571928, 0.7052554331857488, 0.7198995010552305, 0.7342298918013638, 0.7482403613363824, 0.7619248049697269, 0.7752772600680049, 0.7882919086530552, 0.8009630799369827, 0.8132852527930605, 0.8252530581614230, 0.8368612813885015, 0.8481048644991847, 0.8589789084007133, 0.8694786750173527, 0.8795995893549102, 0.8893372414942055, 0.8986873885126239, 0.9076459563329236, 0.9162090414984952, 0.9243729128743136, 0.9321340132728527, 0.9394889610042837, 0.9464345513503147, 0.9529677579610971, 0.9590857341746905, 0.9647858142586956, 0.9700655145738374, 0.9749225346595943, 0.9793547582425894, 0.9833602541697529, 0.9869372772712794, 0.9900842691660192, 0.9927998590434373, 0.9950828645255290, 0.9969322929775997, 0.9983473449340834, 0.9993274305065947, 0.9998723404457334 }; constant double Gauss150Wt[150]={ 0.0003276086705538, 0.0007624720924706, 0.0011976474864367, 0.0016323569986067, 0.0020663664924131, 0.0024994789888943, 0.0029315036836558, 0.0033622516236779, 0.0037915348363451, 0.0042191661429919, 0.0046449591497966, 0.0050687282939456, 0.0054902889094487, 0.0059094573005900, 0.0063260508184704, 0.0067398879387430, 0.0071507883396855, 0.0075585729801782, 0.0079630641773633, 0.0083640856838475, 0.0087614627643580, 0.0091550222717888, 0.0095445927225849, 0.0099300043714212, 0.0103110892851360, 0.0106876814158841, 0.0110596166734735, 0.0114267329968529, 0.0117888704247183, 0.0121458711652067, 0.0124975796646449, 0.0128438426753249, 0.0131845093222756, 0.0135194311690004, 0.0138484622795371, 0.0141714592928592, 0.0144882814685445, 0.0147987907597169, 0.0151028518701744, 0.0154003323133401, 0.0156911024699895, 0.0159750356447283, 0.0162520081211971, 0.0165218992159766, 0.0167845913311726, 0.0170399700056559, 0.0172879239649355, 0.0175283451696437, 0.0177611288626114, 0.0179861736145128, 0.0182033813680609, 0.0184126574807331, 0.0186139107660094, 0.0188070535331042, 0.0189920016251754, 0.0191686744559934, 0.0193369950450545, 0.0194968900511231, 0.0196482898041878, 0.0197911283358190, 0.0199253434079123, 0.0200508765398072, 0.0201676730337687, 0.0202756819988200, 0.0203748563729175, 0.0204651529434560, 0.0205465323660984, 0.0206189591819181, 0.0206824018328499, 0.0207368326754401, 0.0207822279928917, 0.0208185680053983, 0.0208458368787627, 0.0208640227312962, 0.0208731176389954, 0.0208731176389954, 0.0208640227312962, 0.0208458368787627, 0.0208185680053983, 0.0207822279928917, 0.0207368326754401, 0.0206824018328499, 0.0206189591819181, 0.0205465323660984, 0.0204651529434560, 0.0203748563729175, 0.0202756819988200, 0.0201676730337687, 0.0200508765398072, 0.0199253434079123, 0.0197911283358190, 0.0196482898041878, 0.0194968900511231, 0.0193369950450545, 0.0191686744559934, 0.0189920016251754, 0.0188070535331042, 0.0186139107660094, 0.0184126574807331, 0.0182033813680609, 0.0179861736145128, 0.0177611288626114, 0.0175283451696437, 0.0172879239649355, 0.0170399700056559, 0.0167845913311726, 0.0165218992159766, 0.0162520081211971, 0.0159750356447283, 0.0156911024699895, 0.0154003323133401, 0.0151028518701744, 0.0147987907597169, 0.0144882814685445, 0.0141714592928592, 0.0138484622795371, 0.0135194311690004, 0.0131845093222756, 0.0128438426753249, 0.0124975796646449, 0.0121458711652067, 0.0117888704247183, 0.0114267329968529, 0.0110596166734735, 0.0106876814158841, 0.0103110892851360, 0.0099300043714212, 0.0095445927225849, 0.0091550222717888, 0.0087614627643580, 0.0083640856838475, 0.0079630641773633, 0.0075585729801782, 0.0071507883396855, 0.0067398879387430, 0.0063260508184704, 0.0059094573005900, 0.0054902889094487, 0.0050687282939456, 0.0046449591497966, 0.0042191661429919, 0.0037915348363451, 0.0033622516236779, 0.0029315036836558, 0.0024994789888943, 0.0020663664924131, 0.0016323569986067, 0.0011976474864367, 0.0007624720924706, 0.0003276086705538 }; sasmodels/sasmodels/models/lib/gauss20.c000066400000000000000000000017571317715334700205500ustar00rootroot00000000000000/* * GaussWeights.c * SANSAnalysis * * Created by Andrew Jackson on 4/23/07. * Copyright 2007 __MyCompanyName__. All rights reserved. * */ // Gaussians constant double Gauss20Wt[20]={ .0176140071391521, .0406014298003869, .0626720483341091, .0832767415767047, .10193011981724, .118194531961518, .131688638449177, .142096109318382, .149172986472604, .152753387130726, .152753387130726, .149172986472604, .142096109318382, .131688638449177, .118194531961518, .10193011981724, .0832767415767047, .0626720483341091, .0406014298003869, .0176140071391521 }; constant double Gauss20Z[20]={ -.993128599185095, -.963971927277914, -.912234428251326, -.839116971822219, -.746331906460151, -.636053680726515, -.510867001950827, -.37370608871542, -.227785851141645, -.076526521133497, .0765265211334973, .227785851141645, .37370608871542, .510867001950827, .636053680726515, .746331906460151, .839116971822219, .912234428251326, .963971927277914, .993128599185095 }; sasmodels/sasmodels/models/lib/gauss76.c000066400000000000000000000065001317715334700205520ustar00rootroot00000000000000/* * GaussWeights.c * SANSAnalysis * * Created by Andrew Jackson on 4/23/07. * Copyright 2007 __MyCompanyName__. All rights reserved. * */ #define N_POINTS_76 76 // Gaussians constant double Gauss76Wt[N_POINTS_76]={ .00126779163408536, //0 .00294910295364247, .00462793522803742, .00629918049732845, .00795984747723973, .00960710541471375, .0112381685696677, .0128502838475101, .0144407317482767, .0160068299122486, .0175459372914742, //10 .0190554584671906, .020532847967908, .0219756145344162, .0233813253070112, .0247476099206597, .026072164497986, .0273527555318275, .028587223650054, .029773487255905, .0309095460374916, //20 .0319934843404216, .0330234743977917, .0339977794120564, .0349147564835508, .0357728593807139, .0365706411473296, .0373067565423816, .0379799643084053, .0385891292645067, .0391332242205184, //30 .0396113317090621, .0400226455325968, .040366472122844, .0406422317102947, .0408494593018285, .040987805464794, .0410570369162294, .0410570369162294, .040987805464794, .0408494593018285, //40 .0406422317102947, .040366472122844, .0400226455325968, .0396113317090621, .0391332242205184, .0385891292645067, .0379799643084053, .0373067565423816, .0365706411473296, .0357728593807139, //50 .0349147564835508, .0339977794120564, .0330234743977917, .0319934843404216, .0309095460374916, .029773487255905, .028587223650054, .0273527555318275, .026072164497986, .0247476099206597, //60 .0233813253070112, .0219756145344162, .020532847967908, .0190554584671906, .0175459372914742, .0160068299122486, .0144407317482767, .0128502838475101, .0112381685696677, .00960710541471375, //70 .00795984747723973, .00629918049732845, .00462793522803742, .00294910295364247, .00126779163408536 //75 (indexed from 0) }; constant double Gauss76Z[N_POINTS_76]={ -.999505948362153, //0 -.997397786355355, -.993608772723527, -.988144453359837, -.981013938975656, -.972229228520377, -.961805126758768, -.949759207710896, -.936111781934811, -.92088586125215, -.904107119545567, //10 -.885803849292083, -.866006913771982, -.844749694983342, -.822068037328975, -.7980001871612, -.77258672828181, -.74587051350361, -.717896592387704, -.688712135277641, -.658366353758143, //20 -.626910417672267, -.594397368836793, -.560882031601237, -.526420920401243, -.491072144462194, -.454895309813726, -.417951418780327, -.380302767117504, -.342012838966962, -.303146199807908, //30 -.263768387584994, -.223945802196474, -.183745593528914, -.143235548227268, -.102483975391227, -.0615595913906112, -.0205314039939986, .0205314039939986, .0615595913906112, .102483975391227, //40 .143235548227268, .183745593528914, .223945802196474, .263768387584994, .303146199807908, .342012838966962, .380302767117504, .417951418780327, .454895309813726, .491072144462194, //50 .526420920401243, .560882031601237, .594397368836793, .626910417672267, .658366353758143, .688712135277641, .717896592387704, .74587051350361, .77258672828181, .7980001871612, //60 .822068037328975, .844749694983342, .866006913771982, .885803849292083, .904107119545567, .92088586125215, .936111781934811, .949759207710896, .961805126758768, .972229228520377, //70 .981013938975656, .988144453359837, .993608772723527, .997397786355355, .999505948362153 //75 }; sasmodels/sasmodels/models/lib/gfn.c000066400000000000000000000025071317715334700200300ustar00rootroot00000000000000// // FUNCTION gfn4: CONTAINS F(Q,A,B,MU)**2 AS GIVEN // BY (53) & (58-59) IN CHEN AND // KOTLARCHYK REFERENCE // // // function gfn4 for oblate ellipsoids double gfn4(double xx, double crmaj, double crmin, double trmaj, double trmin, double delpc, double delps, double qq); double gfn4(double xx, double crmaj, double crmin, double trmaj, double trmin, double delpc, double delps, double qq) { // local variables const double aa = crmaj; const double bb = crmin; const double u2 = (bb*bb*xx*xx + aa*aa*(1.0-xx*xx)); const double uq = sqrt(u2)*qq; // changing to more accurate sph_j1c since the following inexplicably fails on Radeon Nano. //const double siq = (uq == 0.0 ? 1.0 : 3.0*(sin(uq)/uq/uq - cos(uq)/uq)/uq); const double siq = sas_3j1x_x(uq); const double vc = M_4PI_3*aa*aa*bb; const double gfnc = siq*vc*delpc; const double ut2 = (trmin*trmin*xx*xx + trmaj*trmaj*(1.0-xx*xx)); const double ut= sqrt(ut2)*qq; const double vt = M_4PI_3*trmaj*trmaj*trmin; //const double sit = (ut == 0.0 ? 1.0 : 3.0*(sin(ut)/ut/ut - cos(ut)/ut)/ut); const double sit = sas_3j1x_x(ut); const double gfnt = sit*vt*delps; const double tgfn = gfnc + gfnt; const double result = tgfn*tgfn; return result; } sasmodels/sasmodels/models/lib/polevl.c000066400000000000000000000032731317715334700205600ustar00rootroot00000000000000/* polevl.c * p1evl.c * * Evaluate polynomial * * * * SYNOPSIS: * * int N; * double x, y, coef[N+1], polevl[]; * * y = polevl( x, coef, N ); * * * * DESCRIPTION: * * Evaluates polynomial of degree N: * * 2 N * y = C + C x + C x +...+ C x * 0 1 2 N * * Coefficients are stored in reverse order: * * coef[0] = C , ..., coef[N] = C . * N 0 * * The function p1evl() assumes that C_N = 1.0 and is * omitted from the array. Its calling arguments are * otherwise the same as polevl(). * * * SPEED: * * In the interest of speed, there are no checks for out * of bounds arithmetic. This routine is used by most of * the functions in the library. Depending on available * equipment features, the user may wish to rewrite the * program in microcode or assembly language. * */ /* Cephes Math Library Release 2.1: December, 1988 Copyright 1984, 1987, 1988 by Stephen L. Moshier Direct inquiries to 30 Frost Street, Cambridge, MA 02140 */ double polevl( double x, constant double *coef, int N ); double polevl( double x, constant double *coef, int N ) { int i = 0; double ans = coef[i]; while (i < N) { i++; ans = ans * x + coef[i]; } return ans; } /* p1evl() */ /* N * Evaluate polynomial when coefficient of x is 1.0. * Otherwise same as polevl. */ double p1evl( double x, constant double *coef, int N ); double p1evl( double x, constant double *coef, int N ) { int i=0; double ans = x+coef[i]; while (i < N-1) { i++; ans = ans*x + coef[i]; } return ans; }sasmodels/sasmodels/models/lib/sas_3j1x_x.c000066400000000000000000000036261317715334700212430ustar00rootroot00000000000000/** * Spherical Bessel function 3*j1(x)/x * * Used for low q to avoid cancellation error. * Note that the values differ from sasview ~ 5e-12 rather than 5e-14, but * in this case it is likely cancellation errors in the original expression * using double precision that are the source. */ double sas_3j1x_x(double q); // The choice of the number of terms in the series and the cutoff value for // switching between series and direct calculation depends on the numeric // precision. // // Point where direct calculation reaches machine precision: // // single machine precision eps 3e-8 at qr=1.1 ** // double machine precision eps 4e-16 at qr=1.1 // // Point where Taylor series reaches machine precision (eps), where taylor // series matches direct calculation (cross) and the error at that point: // // prec n eps cross error // single 3 0.28 0.4 6.2e-7 // single 4 0.68 0.7 2.3e-7 // single 5 1.18 1.2 7.5e-8 // double 3 0.01 0.03 2.3e-13 // double 4 0.06 0.1 3.1e-14 // double 5 0.16 0.2 5.0e-15 // // ** Note: relative error on single precision starts increase on the direct // method at qr=1.1, rising from 3e-8 to 5e-5 by qr=1e3. This should be // safe for the sans range, with objects of 100 nm supported to a q of 0.1 // while maintaining 5 digits of precision. For usans/sesans, the objects // are larger but the q is smaller, so again it should be fine. // // See explore/sph_j1c.py for code to explore these ranges. // Use 4th order series #if FLOAT_SIZE>4 #define SPH_J1C_CUTOFF 0.1 #else #define SPH_J1C_CUTOFF 0.7 #endif double sas_3j1x_x(double q) { // 2017-05-18 PAK - support negative q if (fabs(q) < SPH_J1C_CUTOFF) { const double q2 = q*q; return (1.0 + q2*(-3./30. + q2*(3./840. + q2*(-3./45360.))));// + q2*(3./3991680.))))); } else { double sin_q, cos_q; SINCOS(q, sin_q, cos_q); return 3.0*(sin_q/q - cos_q)/(q*q); } } sasmodels/sasmodels/models/lib/sas_J0.c000066400000000000000000000140561317715334700203770ustar00rootroot00000000000000/* j0.c * * Bessel function of order zero * * * * SYNOPSIS: * * double x, y, j0(); * * y = j0( x ); * * * * DESCRIPTION: * * Returns Bessel function of order zero of the argument. * * The domain is divided into the intervals [0, 5] and * (5, infinity). In the first interval the following rational * approximation is used: * * * 2 2 * (w - r ) (w - r ) P (w) / Q (w) * 1 2 3 8 * * 2 * where w = x and the two r's are zeros of the function. * * In the second interval, the Hankel asymptotic expansion * is employed with two rational functions of degree 6/6 * and 7/7. * * * * ACCURACY: * * Absolute error: * arithmetic domain # trials peak rms * DEC 0, 30 10000 4.4e-17 6.3e-18 * IEEE 0, 30 60000 4.2e-16 1.1e-16 * */ /* Cephes Math Library Release 2.8: June, 2000 Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier */ /* Note: all coefficients satisfy the relative error criterion * except YP, YQ which are designed for absolute error. */ #if FLOAT_SIZE>4 //Cephes double precission double cephes_j0(double x); constant double PPJ0[8] = { 7.96936729297347051624E-4, 8.28352392107440799803E-2, 1.23953371646414299388E0, 5.44725003058768775090E0, 8.74716500199817011941E0, 5.30324038235394892183E0, 9.99999999999999997821E-1, 0.0 }; constant double PQJ0[8] = { 9.24408810558863637013E-4, 8.56288474354474431428E-2, 1.25352743901058953537E0, 5.47097740330417105182E0, 8.76190883237069594232E0, 5.30605288235394617618E0, 1.00000000000000000218E0, 0.0 }; constant double QPJ0[8] = { -1.13663838898469149931E-2, -1.28252718670509318512E0, -1.95539544257735972385E1, -9.32060152123768231369E1, -1.77681167980488050595E2, -1.47077505154951170175E2, -5.14105326766599330220E1, -6.05014350600728481186E0, }; constant double QQJ0[8] = { /* 1.00000000000000000000E0,*/ 6.43178256118178023184E1, 8.56430025976980587198E2, 3.88240183605401609683E3, 7.24046774195652478189E3, 5.93072701187316984827E3, 2.06209331660327847417E3, 2.42005740240291393179E2, }; constant double YPJ0[8] = { 1.55924367855235737965E4, -1.46639295903971606143E7, 5.43526477051876500413E9, -9.82136065717911466409E11, 8.75906394395366999549E13, -3.46628303384729719441E15, 4.42733268572569800351E16, -1.84950800436986690637E16, }; constant double YQJ0[7] = { /* 1.00000000000000000000E0,*/ 1.04128353664259848412E3, 6.26107330137134956842E5, 2.68919633393814121987E8, 8.64002487103935000337E10, 2.02979612750105546709E13, 3.17157752842975028269E15, 2.50596256172653059228E17, }; constant double RPJ0[8] = { -4.79443220978201773821E9, 1.95617491946556577543E12, -2.49248344360967716204E14, 9.70862251047306323952E15, 0.0, 0.0, 0.0, 0.0 }; constant double RQJ0[8] = { /* 1.00000000000000000000E0,*/ 4.99563147152651017219E2, 1.73785401676374683123E5, 4.84409658339962045305E7, 1.11855537045356834862E10, 2.11277520115489217587E12, 3.10518229857422583814E14, 3.18121955943204943306E16, 1.71086294081043136091E18, }; double cephes_j0(double x) { double w, z, p, q, xn; //const double TWOOPI = 6.36619772367581343075535E-1; const double SQ2OPI = 7.9788456080286535587989E-1; const double PIO4 = 7.85398163397448309616E-1; const double DR1 = 5.78318596294678452118E0; const double DR2 = 3.04712623436620863991E1; if( x < 0 ) x = -x; if( x <= 5.0 ) { z = x * x; if( x < 1.0e-5 ) return( 1.0 - z/4.0 ); p = (z - DR1) * (z - DR2); p = p * polevl( z, RPJ0, 3)/p1evl( z, RQJ0, 8 ); return( p ); } w = 5.0/x; q = 25.0/(x*x); p = polevl( q, PPJ0, 6)/polevl( q, PQJ0, 6 ); q = polevl( q, QPJ0, 7)/p1evl( q, QQJ0, 7 ); xn = x - PIO4; double sn, cn; SINCOS(xn, sn, cn); p = p * cn - w * q * sn; return( p * SQ2OPI / sqrt(x) ); } #else //Cephes single precission float cephes_j0f(float x); constant float MOJ0[8] = { -6.838999669318810E-002, 1.864949361379502E-001, -2.145007480346739E-001, 1.197549369473540E-001, -3.560281861530129E-003, -4.969382655296620E-002, -3.355424622293709E-006, 7.978845717621440E-001 }; constant float PHJ0[8] = { 3.242077816988247E+001, -3.630592630518434E+001, 1.756221482109099E+001, -4.974978466280903E+000, 1.001973420681837E+000, -1.939906941791308E-001, 6.490598792654666E-002, -1.249992184872738E-001 }; constant float JPJ0[8] = { -6.068350350393235E-008, 6.388945720783375E-006, -3.969646342510940E-004, 1.332913422519003E-002, -1.729150680240724E-001, 0.0, 0.0, 0.0 }; float cephes_j0f(float x) { float xx, w, z, p, q, xn; //const double YZ1 = 0.43221455686510834878; //const double YZ2 = 22.401876406482861405; //const double YZ3 = 64.130620282338755553; const float DR1 = 5.78318596294678452118; const float PIO4F = 0.7853981633974483096; if( x < 0 ) xx = -x; else xx = x; // 2017-05-18 PAK - support negative x if( xx <= 2.0 ) { z = xx * xx; if( xx < 1.0e-3 ) return( 1.0 - 0.25*z ); p = (z-DR1) * polevl( z, JPJ0, 4); return( p ); } q = 1.0/xx; w = sqrt(q); p = w * polevl( q, MOJ0, 7); w = q*q; xn = q * polevl( w, PHJ0, 7) - PIO4F; p = p * cos(xn + xx); return(p); } #endif #if FLOAT_SIZE>4 #define sas_J0 cephes_j0 #else #define sas_J0 cephes_j0f #endif sasmodels/sasmodels/models/lib/sas_J1.c000066400000000000000000000135111317715334700203730ustar00rootroot00000000000000/* j1.c * * Bessel function of order one * * * * SYNOPSIS: * * double x, y, j1(); * * y = j1( x ); * * * * DESCRIPTION: * * Returns Bessel function of order one of the argument. * * The domain is divided into the intervals [0, 8] and * (8, infinity). In the first interval a 24 term Chebyshev * expansion is used. In the second, the asymptotic * trigonometric representation is employed using two * rational functions of degree 5/5. * * * * ACCURACY: * * Absolute error: * arithmetic domain # trials peak rms * DEC 0, 30 10000 4.0e-17 1.1e-17 * IEEE 0, 30 30000 2.6e-16 1.1e-16 * * */ /* Cephes Math Library Release 2.8: June, 2000 Copyright 1984, 1987, 1989, 2000 by Stephen L. Moshier */ #if FLOAT_SIZE>4 //Cephes double pression function double cephes_j1(double x); constant double RPJ1[8] = { -8.99971225705559398224E8, 4.52228297998194034323E11, -7.27494245221818276015E13, 3.68295732863852883286E15, 0.0, 0.0, 0.0, 0.0 }; constant double RQJ1[8] = { 6.20836478118054335476E2, 2.56987256757748830383E5, 8.35146791431949253037E7, 2.21511595479792499675E10, 4.74914122079991414898E12, 7.84369607876235854894E14, 8.95222336184627338078E16, 5.32278620332680085395E18 }; constant double PPJ1[8] = { 7.62125616208173112003E-4, 7.31397056940917570436E-2, 1.12719608129684925192E0, 5.11207951146807644818E0, 8.42404590141772420927E0, 5.21451598682361504063E0, 1.00000000000000000254E0, 0.0} ; constant double PQJ1[8] = { 5.71323128072548699714E-4, 6.88455908754495404082E-2, 1.10514232634061696926E0, 5.07386386128601488557E0, 8.39985554327604159757E0, 5.20982848682361821619E0, 9.99999999999999997461E-1, 0.0 }; constant double QPJ1[8] = { 5.10862594750176621635E-2, 4.98213872951233449420E0, 7.58238284132545283818E1, 3.66779609360150777800E2, 7.10856304998926107277E2, 5.97489612400613639965E2, 2.11688757100572135698E2, 2.52070205858023719784E1 }; constant double QQJ1[8] = { 7.42373277035675149943E1, 1.05644886038262816351E3, 4.98641058337653607651E3, 9.56231892404756170795E3, 7.99704160447350683650E3, 2.82619278517639096600E3, 3.36093607810698293419E2, 0.0 }; double cephes_j1(double x) { double w, z, p, q, abs_x, sign_x; const double Z1 = 1.46819706421238932572E1; const double Z2 = 4.92184563216946036703E1; // 2017-05-18 PAK - mathematica and mpmath use J1(-x) = -J1(x) if (x < 0) { abs_x = -x; sign_x = -1.0; } else { abs_x = x; sign_x = 1.0; } if( abs_x <= 5.0 ) { z = abs_x * abs_x; w = polevl( z, RPJ1, 3 ) / p1evl( z, RQJ1, 8 ); w = w * abs_x * (z - Z1) * (z - Z2); return( sign_x * w ); } w = 5.0/abs_x; z = w * w; p = polevl( z, PPJ1, 6)/polevl( z, PQJ1, 6 ); q = polevl( z, QPJ1, 7)/p1evl( z, QQJ1, 7 ); // 2017-05-19 PAK improve accuracy using trig identies // original: // const double THPIO4 = 2.35619449019234492885; // const double SQ2OPI = 0.79788456080286535588; // double sin_xn, cos_xn; // SINCOS(abs_x - THPIO4, sin_xn, cos_xn); // p = p * cos_xn - w * q * sin_xn; // return( sign_x * p * SQ2OPI / sqrt(abs_x) ); // expanding p*cos(a - 3 pi/4) - wq sin(a - 3 pi/4) // [ p(sin(a) - cos(a)) + wq(sin(a) + cos(a)) / sqrt(2) // note that sqrt(1/2) * sqrt(2/pi) = sqrt(1/pi) const double SQRT1_PI = 0.56418958354775628; double sin_x, cos_x; SINCOS(abs_x, sin_x, cos_x); p = p*(sin_x - cos_x) + w*q*(sin_x + cos_x); return( sign_x * p * SQRT1_PI / sqrt(abs_x) ); } #else //Single precission version of cephes float cephes_j1f(float x); constant float JPJ1[8] = { -4.878788132172128E-009, 6.009061827883699E-007, -4.541343896997497E-005, 1.937383947804541E-003, -3.405537384615824E-002, 0.0, 0.0, 0.0 }; constant float MO1J1[8] = { 6.913942741265801E-002, -2.284801500053359E-001, 3.138238455499697E-001, -2.102302420403875E-001, 5.435364690523026E-003, 1.493389585089498E-001, 4.976029650847191E-006, 7.978845453073848E-001 }; constant float PH1J1[8] = { -4.497014141919556E+001, 5.073465654089319E+001, -2.485774108720340E+001, 7.222973196770240E+000, -1.544842782180211E+000, 3.503787691653334E-001, -1.637986776941202E-001, 3.749989509080821E-001 }; float cephes_j1f(float xx) { float x, w, z, p, q, xn; const float Z1 = 1.46819706421238932572E1; // 2017-05-18 PAK - mathematica and mpmath use J1(-x) = -J1(x) x = xx; if( x < 0 ) x = -xx; if( x <= 2.0 ) { z = x * x; p = (z-Z1) * x * polevl( z, JPJ1, 4 ); return( xx < 0. ? -p : p ); } q = 1.0/x; w = sqrt(q); p = w * polevl( q, MO1J1, 7); w = q*q; // 2017-05-19 PAK improve accuracy using trig identies // original: // const float THPIO4F = 2.35619449019234492885; /* 3*pi/4 */ // xn = q * polevl( w, PH1J1, 7) - THPIO4F; // p = p * cos(xn + x); // return( xx < 0. ? -p : p ); // expanding cos(a + b - 3 pi/4) is // [sin(a)sin(b) + sin(a)cos(b) + cos(a)sin(b)-cos(a)cos(b)] / sqrt(2) xn = q * polevl( w, PH1J1, 7); float cos_xn, sin_xn; float cos_x, sin_x; SINCOS(xn, sin_xn, cos_xn); // about xn and 1 SINCOS(x, sin_x, cos_x); p *= M_SQRT1_2*(sin_xn*(sin_x+cos_x) + cos_xn*(sin_x-cos_x)); return( xx < 0. ? -p : p ); } #endif #if FLOAT_SIZE>4 #define sas_J1 cephes_j1 #else #define sas_J1 cephes_j1f #endif //Finally J1c function that equals 2*J1(x)/x double sas_2J1x_x(double x); double sas_2J1x_x(double x) { return (x != 0.0 ) ? 2.0*sas_J1(x)/x : 1.0; }sasmodels/sasmodels/models/lib/sas_JN.c000066400000000000000000000072331317715334700204340ustar00rootroot00000000000000/* jn.c * * Bessel function of integer order * * * * SYNOPSIS: * * int n; * double x, y, jn(); * * y = jn( n, x ); * * * * DESCRIPTION: * * Returns Bessel function of order n, where n is a * (possibly negative) integer. * * The ratio of jn(x) to j0(x) is computed by backward * recurrence. First the ratio jn/jn-1 is found by a * continued fraction expansion. Then the recurrence * relating successive orders is applied until j0 or j1 is * reached. * * If n = 0 or 1 the routine for j0 or j1 is called * directly. * * * * ACCURACY: * * Absolute error: * arithmetic range # trials peak rms * DEC 0, 30 5500 6.9e-17 9.3e-18 * IEEE 0, 30 5000 4.4e-16 7.9e-17 * * * Not suitable for large n or x. Use jv() instead. * */ /* jn.c Cephes Math Library Release 2.8: June, 2000 Copyright 1984, 1987, 2000 by Stephen L. Moshier */ #if FLOAT_SIZE > 4 double cephes_jn( int n, double x ); double cephes_jn( int n, double x ) { // PAK: seems to be machine epsilon/2 const double MACHEP = 1.11022302462515654042E-16; double pkm2, pkm1, pk, xk, r, ans; int k, sign; if( n < 0 ) { n = -n; if( (n & 1) == 0 ) /* -1**n */ sign = 1; else sign = -1; } else { sign = 1; } if( x < 0.0 ) { if( n & 1 ) sign = -sign; x = -x; } if( n == 0 ) return( sign * cephes_j0(x) ); if( n == 1 ) return( sign * cephes_j1(x) ); if( n == 2 ) return( sign * (2.0 * cephes_j1(x) / x - cephes_j0(x)) ); if( x < MACHEP ) return( 0.0 ); k = 53; pk = 2 * (n + k); ans = pk; xk = x * x; do { pk -= 2.0; ans = pk - (xk/ans); } while( --k > 0 ); /* backward recurrence */ pk = 1.0; ans = x/ans; pkm1 = 1.0/ans; k = n-1; r = 2 * k; do { pkm2 = (pkm1 * r - pk * x) / x; pk = pkm1; pkm1 = pkm2; r -= 2.0; } while( --k > 0 ); if( fabs(pk) > fabs(pkm1) ) ans = cephes_j1(x)/pk; else ans = cephes_j0(x)/pkm1; return( sign * ans ); } #else float cephes_jnf(int n, float x); float cephes_jnf(int n, float x) { // PAK: seems to be machine epsilon/2 const double MACHEP = 5.9604645e-08; float pkm2, pkm1, pk, xk, r, ans; int k, sign; if( n < 0 ) { n = -n; if( (n & 1) == 0 ) /* -1**n */ sign = 1; else sign = -1; } else { sign = 1; } if( x < 0.0 ) { if( n & 1 ) sign = -sign; x = -x; } if( n == 0 ) return( sign * cephes_j0f(x) ); if( n == 1 ) return( sign * cephes_j1f(x) ); if( n == 2 ) return( sign * (2.0 * cephes_j1f(x) / x - cephes_j0f(x)) ); if( x < MACHEP ) return( 0.0 ); k = 24; pk = 2 * (n + k); ans = pk; xk = x * x; do { pk -= 2.0; ans = pk - (xk/ans); } while( --k > 0 ); /* backward recurrence */ pk = 1.0; const float xinv = 1.0/x; pkm1 = ans * xinv; k = n-1; r = (float )(2 * k); do { pkm2 = (pkm1 * r - pk * x) * xinv; pk = pkm1; pkm1 = pkm2; r -= 2.0; } while( --k > 0 ); r = pk; if( r < 0 ) r = -r; ans = pkm1; if( ans < 0 ) ans = -ans; if( r > ans ) /* if( fabs(pk) > fabs(pkm1) ) */ ans = sign * cephes_j1f(x)/pk; else ans = sign * cephes_j0f(x)/pkm1; return( ans ); } #endif #if FLOAT_SIZE>4 #define sas_JN cephes_jn #else #define sas_JN cephes_jnf #endif sasmodels/sasmodels/models/lib/sas_Si.c000066400000000000000000000015251317715334700204760ustar00rootroot00000000000000// integral of sin(x)/x Taylor series approximated to w/i 0.1% double sas_Si(double x); double sas_Si(double x) { if (x >= M_PI*6.2/4.0) { const double xxinv = 1./(x*x); // Explicitly writing factorial values triples the speed of the calculation const double out_cos = (((-720.*xxinv + 24.)*xxinv - 2.)*xxinv + 1.)/x; const double out_sin = (((-5040.*xxinv + 120.)*xxinv - 6.)*xxinv + 1)*xxinv; double sin_x, cos_x; SINCOS(x, sin_x, cos_x); return M_PI_2 - cos_x*out_cos - sin_x*out_sin; } else { const double xx = x*x; // Explicitly writing factorial values triples the speed of the calculation return (((((-1./439084800.*xx + 1./3265920.)*xx - 1./35280.)*xx + 1./600.)*xx - 1./18.)*xx + 1.)*x; } } sasmodels/sasmodels/models/lib/sas_erf.c000066400000000000000000000155251317715334700207040ustar00rootroot00000000000000 /* * Cephes Math Library Release 2.2: June, 1992 * Copyright 1984, 1987, 1988, 1992 by Stephen L. Moshier * Direct inquiries to 30 Frost Street, Cambridge, MA 02140 */ /* * * Error function * * * * SYNOPSIS: * * double x, y, erf(); * * y = erf( x ); * * * * DESCRIPTION: * * The integral is * * x * - * 2 | | 2 * erf(x) = -------- | exp( - t ) dt. * sqrt(pi) | | * - * 0 * * For 0 <= |x| < 1, erf(x) = x * P4(x**2)/Q5(x**2); otherwise * erf(x) = 1 - erfc(x). * * * * ACCURACY: * * Relative error: * arithmetic domain # trials peak rms * IEEE 0,1 30000 3.7e-16 1.0e-16 * */ /* * * Complementary error function * * * * SYNOPSIS: * * double x, y, erfc(); * * y = erfc( x ); * * * * DESCRIPTION: * * * 1 - erf(x) = * * inf. * - * 2 | | 2 * erfc(x) = -------- | exp( - t ) dt * sqrt(pi) | | * - * x * * * For small x, erfc(x) = 1 - erf(x); otherwise rational * approximations are computed. * * * * ACCURACY: * * Relative error: * arithmetic domain # trials peak rms * IEEE 0,26.6417 30000 5.7e-14 1.5e-14 */ #ifdef NEED_ERF #if FLOAT_SIZE>4 // DOUBLE_PRECISION double cephes_erf(double x); double cephes_erfc(double a); constant double PD[] = { 2.46196981473530512524E-10, 5.64189564831068821977E-1, 7.46321056442269912687E0, 4.86371970985681366614E1, 1.96520832956077098242E2, 5.26445194995477358631E2, 9.34528527171957607540E2, 1.02755188689515710272E3, 5.57535335369399327526E2 }; constant double QD[] = { /* 1.00000000000000000000E0, */ 1.32281951154744992508E1, 8.67072140885989742329E1, 3.54937778887819891062E2, 9.75708501743205489753E2, 1.82390916687909736289E3, 2.24633760818710981792E3, 1.65666309194161350182E3, 5.57535340817727675546E2 }; constant double RD[] = { 5.64189583547755073984E-1, 1.27536670759978104416E0, 5.01905042251180477414E0, 6.16021097993053585195E0, 7.40974269950448939160E0, 2.97886665372100240670E0 }; constant double SD[] = { /* 1.00000000000000000000E0, */ 2.26052863220117276590E0, 9.39603524938001434673E0, 1.20489539808096656605E1, 1.70814450747565897222E1, 9.60896809063285878198E0, 3.36907645100081516050E0 }; constant double TD[] = { 9.60497373987051638749E0, 9.00260197203842689217E1, 2.23200534594684319226E3, 7.00332514112805075473E3, 5.55923013010394962768E4 }; constant double UD[] = { /* 1.00000000000000000000E0, */ 3.35617141647503099647E1, 5.21357949780152679795E2, 4.59432382970980127987E3, 2.26290000613890934246E4, 4.92673942608635921086E4 }; double cephes_erfc(double a) { double MAXLOG = 88.72283905206835; double p, q, x, y, z; x = fabs(a); if (x < 1.0) { // The line below causes problems on the GPU, so inline // the erf function instead and z < 1.0. //return (1.0 - cephes_erf(a)); // 2017-05-18 PAK - use erf(a) rather than erf(|a|) z = a * a; y = a * polevl(z, TD, 4) / p1evl(z, UD, 5); return 1.0 - y; } z = -a * a; if (z < -MAXLOG) { if (a < 0) return (2.0); else return (0.0); } z = exp(z); if (x < 8.0) { p = polevl(x, PD, 8); q = p1evl(x, QD, 8); } else { p = polevl(x, RD, 5); q = p1evl(x, SD, 6); } y = (z * p) / q; if (a < 0) y = 2.0 - y; if (y == 0.0) { if (a < 0) return (2.0); else return (0.0); } return y; } double cephes_erf(double x) { double y, z; if (fabs(x) > 1.0) return (1.0 - cephes_erfc(x)); z = x * x; y = x * polevl(z, TD, 4) / p1evl(z, UD, 5); return y; } #else // SINGLE PRECISION float cephes_erff(float x); float cephes_erfcf(float a); /* erfc(x) = exp(-x^2) P(1/x), 1 < x < 2 */ constant float PF[] = { 2.326819970068386E-002, -1.387039388740657E-001, 3.687424674597105E-001, -5.824733027278666E-001, 6.210004621745983E-001, -4.944515323274145E-001, 3.404879937665872E-001, -2.741127028184656E-001, 5.638259427386472E-001 }; /* erfc(x) = exp(-x^2) 1/x P(1/x^2), 2 < x < 14 */ constant float RF[] = { -1.047766399936249E+001, 1.297719955372516E+001, -7.495518717768503E+000, 2.921019019210786E+000, -1.015265279202700E+000, 4.218463358204948E-001, -2.820767439740514E-001, 5.641895067754075E-001 }; /* erf(x) = x P(x^2), 0 < x < 1 */ constant float TF[] = { 7.853861353153693E-005, -8.010193625184903E-004, 5.188327685732524E-003, -2.685381193529856E-002, 1.128358514861418E-001, -3.761262582423300E-001, 1.128379165726710E+000 }; float cephes_erfcf(float a) { float MAXLOG = 88.72283905206835; float p, q, x, y, z; /*if (a < 0.0) x = -a; else x = a;*/ // TODO: tinycc does not support fabsf x = fabs(a); if (x < 1.0) { //The line below is a troublemaker for GPU, so sas_erf function //is explicit here for the case < 1.0 //return (1.0 - sas_erf(a)); // 2017-05-18 PAK - use erf(a) rather than erf(|a|) z = a * a; y = a * polevl( z, TF, 6 ); return 1.0 - y; } z = -a * a; if (z < -MAXLOG) { if (a < 0) return (2.0); else return (0.0); } z = expf(z); q=1.0/x; y=q*q; if( x < 2.0 ) { p = polevl( y, PF, 8 ); } else { p = polevl( y, RF, 7 ); } y = z * q * p; if (a < 0) y = 2.0 - y; if (y == 0.0) { if (a < 0) return (2.0); else return (0.0); } return y; } float cephes_erff(float x) { float y, z; // TODO: tinycc does not support fabsf if (fabs(x) > 1.0) return (1.0 - cephes_erfcf(x)); z = x * x; y = x * polevl( z, TF, 6 ); return y; } #endif // SINGLE_PRECISION #if FLOAT_SIZE>4 //static double sas_erf(double x) { return erf(x); } //static double sas_erfc(double x) { return erfc(x); } #define sas_erf cephes_erf #define sas_erfc cephes_erfc #else #define sas_erf cephes_erff #define sas_erfc cephes_erfcf #endif #else // !NEED_ERF #if FLOAT_SIZE>4 //static double sas_erf(double x) { return erf(x); } //static double sas_erfc(double x) { return erfc(x); } #define sas_erf erf #define sas_erfc erfc #else #define sas_erf erff #define sas_erfc erfcf #endif #endif // !NEED_ERF sasmodels/sasmodels/models/lib/sas_gamma.c000066400000000000000000000056711317715334700212130ustar00rootroot00000000000000/* The wrapper for gamma function from OpenCL and standard libraries The OpenCL gamma function fails miserably on values lower than 1.0 while works fine on larger values. We use gamma definition Gamma(t + 1) = t * Gamma(t) to compute to function for values lower than 1.0. Namely Gamma(t) = 1/t * Gamma(t + 1) For t < 0, we use Gamma(t) = pi / ( Gamma(1 - t) * sin(pi * t) ) */ #if defined(NEED_TGAMMA) static double cephes_stirf(double x) { const double MAXSTIR=143.01608; const double SQTPI=2.50662827463100050242E0; double y, w, v; w = 1.0 / x; w = (((( 7.87311395793093628397E-4*w - 2.29549961613378126380E-4)*w - 2.68132617805781232825E-3)*w + 3.47222221605458667310E-3)*w + 8.33333333333482257126E-2)*w + 1.0; y = exp(x); if (x > MAXSTIR) { /* Avoid overflow in pow() */ v = pow(x, 0.5 * x - 0.25); y = v * (v / y); } else { y = pow(x, x - 0.5) / y; } y = SQTPI * y * w; return(y); } static double tgamma(double x) { double p, q, z; int sgngam; int i; sgngam = 1; if (isnan(x)) return(x); q = fabs(x); if (q > 33.0) { if (x < 0.0) { p = floor(q); if (p == q) { return (NAN); } i = p; if ((i & 1) == 0) sgngam = -1; z = q - p; if (z > 0.5) { p += 1.0; z = q - p; } z = q * sin(M_PI * z); if (z == 0.0) { return(NAN); } z = fabs(z); z = M_PI / (z * cephes_stirf(q)); } else { z = cephes_stirf(x); } return(sgngam * z); } z = 1.0; while (x >= 3.0) { x -= 1.0; z *= x; } while (x < 0.0) { if (x > -1.E-9) goto small; z /= x; x += 1.0; } while (x < 2.0) { if (x < 1.e-9) goto small; z /= x; x += 1.0; } if (x == 2.0) return(z); x -= 2.0; p = ((((( +1.60119522476751861407E-4*x + 1.19135147006586384913E-3)*x + 1.04213797561761569935E-2)*x + 4.76367800457137231464E-2)*x + 2.07448227648435975150E-1)*x + 4.94214826801497100753E-1)*x + 9.99999999999999996796E-1; q = (((((( -2.31581873324120129819E-5*x + 5.39605580493303397842E-4)*x - 4.45641913851797240494E-3)*x + 1.18139785222060435552E-2)*x + 3.58236398605498653373E-2)*x - 2.34591795718243348568E-1)*x + 7.14304917030273074085E-2)*x + 1.00000000000000000320E0; return(z * p / q); small: if (x == 0.0) { return (NAN); } else return(z / ((1.0 + 0.5772156649015329 * x) * x)); } #endif // NEED_TGAMMA inline double sas_gamma(double x) { // Note: the builtin tgamma can give slow and unreliable results for x<1. // The following transform extends it to zero and to negative values. // It should return NaN for zero and negative integers but doesn't. // The accuracy is okay but not wonderful for negative numbers, maybe // one or two digits lost in the calculation. If higher accuracy is // needed, you could test the following loop: // double norm = 1.; // while (x<1.) { norm*=x; x+=1.; } // return tgamma(x)/norm; return (x<0. ? M_PI/tgamma(1.-x)/sin(M_PI*x) : tgamma(x+1)/x); } sasmodels/sasmodels/models/lib/sphere_form.c000066400000000000000000000006531317715334700215670ustar00rootroot00000000000000double sphere_volume(double radius); double sphere_form(double q, double radius, double sld, double solvent_sld); double sphere_volume(double radius) { return M_4PI_3*cube(radius); } double sphere_form(double q, double radius, double sld, double solvent_sld) { const double fq = sphere_volume(radius) * sas_3j1x_x(q*radius); const double contrast = (sld - solvent_sld); return 1.0e-4*square(contrast * fq); } sasmodels/sasmodels/models/lib/wrc_cyl.c000066400000000000000000000160541317715334700207220ustar00rootroot00000000000000/* Functions for WRC implementation of flexible cylinders */ static double Rgsquare(double L, double b) { const double x = L/b; // Use Horner's method to evaluate Pedersen eq 15: // alpha^2 = [1.0 + (x/3.12)^2 + (x/8.67)^3] ^ (0.176/3) const double alphasq = pow(1.0 + x*x*(1.027284681130835e-01 + 1.534414548417740e-03*x), 5.866666666666667e-02); return alphasq*L*b/6.0; } static double Rgsquareshort(double L, double b) { const double r = b/L; // = 1/n_b in Pedersen ref. return Rgsquare(L, b) * (1.0 + r*(-1.5 + r*(1.5 + r*0.75*expm1(-2.0/r)))); } static double w_WR(double x) { // Pedersen eq. 16: // w = [1 + tanh((x-C4)/C5)]/2 const double C4 = 1.523; const double C5 = 0.1477; return 0.5 + 0.5*tanh((x - C4)/C5); } static double Sdebye(double qsq) { #if FLOAT_SIZE>4 # define DEBYE_CUTOFF 0.25 // 1e-15 error #else # define DEBYE_CUTOFF 1.0 // 4e-7 error #endif if (qsq < DEBYE_CUTOFF) { const double x = qsq; // mathematica: PadeApproximant[2*Exp[-x^2] + x^2-1)/x^4, {x, 0, 8}] const double A1=1./15., A2=1./60, A3=0., A4=1./75600.; const double B1=2./5., B2=1./15., B3=1./180., B4=1./5040.; return ((((A4*x + A3)*x + A2)*x + A1)*x + 1.) / ((((B4*x + B3)*x + B2)*x + B1)*x + 1.); } else { return 2.*(expm1(-qsq) + qsq)/(qsq*qsq); } } static double a_long(double q, double L, double b/*, double p1, double p2, double q0*/) { const double p1 = 4.12; const double p2 = 4.42; const double q0 = 3.1; // Constants C1, ..., C5 derived from least squares fit (Pedersen, eq 13,16) const double C1 = 1.22; const double C2 = 0.4288; const double C3 = -1.651; const double C4 = 1.523; const double C5 = 0.1477; const double miu = 0.585; const double C = (L/b>10.0 ? 3.06*pow(L/b, -0.44) : 1.0); //printf("branch B-%d q=%g L=%g b=%g\n", C==1.0, q, L, b); const double r2 = Rgsquare(L,b); const double r = sqrt(r2); const double qr_b = q0*r/b; const double qr_b_sq = qr_b*qr_b; const double qr_b_4 = qr_b_sq*qr_b_sq; const double qr_b_miu = pow(qr_b, -1.0/miu); const double em1_qr_b_sq = expm1(-qr_b_sq); const double sech2 = 1.0/square(cosh((qr_b-C4)/C5)); const double w = w_WR(qr_b); const double t1 = pow(q0, 1.0 + p1 + p2)/(b*(p1-p2)); const double t2 = C/(15.0*L) * ( + 14.0*b*b*em1_qr_b_sq/(q0*qr_b_sq) + 2.0*q0*r2*exp(-qr_b_sq)*(11.0 + 7.0/qr_b_sq)); const double t11 = ((C3*qr_b_miu + C2)*qr_b_miu + C1)*qr_b_miu; const double t3 = r*sech2/(2.*C5)*t11; const double t4 = r*(em1_qr_b_sq + qr_b_sq)*sech2 / (C5*qr_b_4); const double t5 = -4.0*r*qr_b*em1_qr_b_sq/qr_b_4 * (1.0 - w); const double t10 = 2.0*(em1_qr_b_sq + qr_b_sq)/qr_b_4 * (1.0 - w); //=Sdebye*(1-w) const double t6 = 4.0*b/q0 * t10; const double t7 = r*((-3.0*C3*qr_b_miu -2.0*C2)*qr_b_miu -1.0*C1)*qr_b_miu/(miu*qr_b); const double t9 = C*b/L * (4.0 - exp(-qr_b_sq) * (11.0 + 7.0/qr_b_sq) + 7.0/qr_b_sq)/15.0; const double t12 = b*b*M_PI/(L*q0*q0) + t2 + t3 - t4 + t5 - t6 + t7*w; const double t13 = -b*M_PI/(L*q0) + t9 + t10 + t11*w; const double a1 = pow(q0,p1)*t13 - t1*pow(q0,-p2)*(t12 + b*p1/q0*t13); const double a2 = t1*pow(q0,-p1)*(t12 + b*p1/q0*t13); const double ans = a1*pow(q*b, -p1) + a2*pow(q*b, -p2) + M_PI/(q*L); return ans; } static double _short(double r2, double exp_qr_b, double L, double b, double p1short, double p2short, double q0) { const double qr2 = q0*q0 * r2; const double b3 = b*b*b; const double q0p = pow(q0, -4.0 + p1short); double yy = 1.0/(L*r2*r2) * b/exp_qr_b*q0p * (8.0*b3*L - 8.0*b3*exp_qr_b*L + 2.0*b3*exp_qr_b*L*p2short - 2.0*b*exp_qr_b*L*p2short*qr2 + 4.0*b*exp_qr_b*L*qr2 - 2.0*b3*L*p2short + 4.0*b*L*qr2 - M_PI*exp_qr_b*qr2*q0*r2 + M_PI*exp_qr_b*p2short*qr2*q0*r2); return yy; } static double a_short(double qp, double L, double b /*double p1short, double p2short*/, double q0) { const double p1short = 5.36; const double p2short = 5.62; const double r2 = Rgsquareshort(L,b); const double exp_qr_b = exp(r2*square(q0/b)); const double pdiff = p1short - p2short; const double a1 = _short(r2,exp_qr_b,L,b,p1short,p2short,q0)/pdiff; const double a2= -_short(r2,exp_qr_b,L,b,p2short,p1short,q0)/pdiff; const double ans = a1*pow(qp*b, -p1short) + a2*pow(qp*b, -p2short) + M_PI/(qp*L); return ans; } static double Sexv(double q, double L, double b) { // Pedersen eq 13, corrected by Chen eq A.5, swapping w and 1-w const double C1=1.22; const double C2=0.4288; const double C3=-1.651; const double miu = 0.585; const double qr = q*sqrt(Rgsquare(L,b)); const double qr_miu = pow(qr, -1.0/miu); const double w = w_WR(qr); const double t10 = Sdebye(qr*qr)*(1.0 - w); const double t11 = ((C3*qr_miu + C2)*qr_miu + C1)*qr_miu; return t10 + w*t11; } // Modified by Yun on Oct. 15, static double Sexv_new(double q, double L, double b) { const double qr = q*sqrt(Rgsquare(L,b)); const double qr2 = qr*qr; const double C = (L/b > 10.0) ? 3.06*pow(L/b, -0.44) : 1.0; const double t9 = C*b/L * (4.0 - exp(-qr2) * (11.0 + 7.0/qr2) + 7.0/qr2)/15.0; const double Sexv_orig = Sexv(q, L, b); // calculating the derivative to decide on the correction (cutoff) term? // Note: this is modified from WRs original code const double del=1.05; const double qdel = (Sexv(q*del,L,b) - Sexv_orig)/(q*(del - 1.0)); if (qdel < 0) { //printf("branch A1-%d q=%g L=%g b=%g\n", C==1.0, q, L, b); return t9 + Sexv_orig; } else { //printf("branch A2-%d q=%g L=%g b=%g\n", C==1.0, q, L, b); const double w = w_WR(qr); const double t10 = Sdebye(qr*qr)*(1.0 - w); return t9 + t10; } } static double Sk_WR(double q, double L, double b) { const double Rg_short = sqrt(Rgsquareshort(L, b)); double q0short = fmax(1.9/Rg_short, 3.0); double ans; if( L > 4*b ) { // L > 4*b : Longer Chains if (q*b <= 3.1) { ans = Sexv_new(q, L, b); } else { //q(i)*b > 3.1 ans = a_long(q, L, b /*, p1, p2, q0*/); } } else { // L <= 4*b : Shorter Chains if (q*b <= q0short) { // q*b <= fmax(1.9/Rg_short, 3) //printf("branch C-%d q=%g L=%g b=%g\n", square(q*Rg_short) b < 2.37 // L/b == 2 => b < 1.36 // L/b == 3 => b < 1.00 // L/b == 4 => b < 0.816 // 2017-10-01 pkienzle: moved low q approximation into Sdebye() ans = Sdebye(square(q*Rg_short)); } else { // q*b > max(1.9/Rg_short, 3) //printf("branch D q=%g L=%g b=%g\n", q, L, b); ans = a_short(q, L, b /*, p1short, p2short*/, q0short); } } return ans; } sasmodels/sasmodels/models/line.py000066400000000000000000000047521317715334700176510ustar00rootroot00000000000000r""" This model calculates intensity using simple linear function Definition ---------- The scattering intensity $I(q)$ is calculated as .. math:: I(q) = \text{scale} (A + B \cdot q) + \text{background} .. note:: For 2D plots intensity has different definition than other shape independent models .. math:: I(q) = \text{scale} (I(qx) \cdot I(qy)) + \text{background} References ---------- None. """ from numpy import inf name = "line" title = "Line model" description = """\ I(q) = A + B*q List of default parameters: A = intercept B = slope """ category = "shape-independent" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type", "description"], parameters = [["intercept", "1/cm", 1.0, [-inf, inf], "", "intercept in linear model"], ["slope", "Ang/cm", 1.0, [-inf, inf], "", "slope in linear model"], ] # pylint: enable=bad-whitespace, line-too-long def Iq(q, intercept, slope): """ :param q: Input q-value :param intercept: Intrecept in linear model :param slope: Slope in linear model :return: Calculated Intensity """ inten = intercept + slope*q return inten Iq.vectorized = True # Iq accepts an array of q values def Iqxy(qx, qy, *args): """ :param qx: Input q_x-value :param qy: Input q_y-value :param args: Remaining arguments :return: 2D-Intensity """ # TODO: SasView documents 2D intensity as Iq(qx)*Iq(qy), but returns Iq(qy) # Note: SasView.run([r, theta]) does return Iq(qx)*Iq(qy) return Iq(qx, *args)*Iq(qy, *args) Iqxy.vectorized = True # Iqxy accepts an array of qx qy values def random(): import numpy as np scale = 10**np.random.uniform(0, 3) slope = np.random.uniform(-1, 1)*1e2 offset = 1e-5 + (0 if slope > 0 else -slope) intercept = 10**np.random.uniform(0, 1) + offset pars = dict( #background=0, scale=scale, slope=slope, intercept=intercept, ) return pars tests = [ [{'intercept': 1.0, 'slope': 1.0, }, 1.0, 2.001], [{'intercept': 1.0, 'slope': 1.0, }, 0.0, 1.001], [{'intercept': 1.0, 'slope': 1.0, }, 0.4, 1.401], [{'intercept': 1.0, 'slope': 1.0, }, 1.3, 2.301], [{'intercept': 1.0, 'slope': 1.0, }, 0.5, 1.501], [{'intercept': 1.0, 'slope': 1.0, }, [0.4, 0.5], [1.401, 1.501]], [{'intercept': 1.0, 'slope': 1.0, 'background': 0.0, }, (1.3, 1.57), 5.911], ] sasmodels/sasmodels/models/linear_pearls.c000066400000000000000000000040411317715334700213230ustar00rootroot00000000000000double form_volume(double radius, double num_pearls); double Iq(double q, double radius, double edge_sep, double fp_num_pearls, double pearl_sld, double solvent_sld); double linear_pearls_kernel(double q, double radius, double edge_sep, int num_pearls, double pearl_sld, double solvent_sld); double form_volume(double radius, double fp_num_pearls) { int num_pearls = (int)(fp_num_pearls + 0.5); // Pearl volume double pearl_vol = M_4PI_3 * cube(radius); // Return total volume return num_pearls * pearl_vol;; } double linear_pearls_kernel(double q, double radius, double edge_sep, int num_pearls, double pearl_sld, double solvent_sld) { //relative sld double contrast_pearl = pearl_sld - solvent_sld; //each volume double pearl_vol = M_4PI_3 * cube(radius); //total volume double tot_vol = num_pearls * pearl_vol; //mass double m_s = contrast_pearl * pearl_vol; //center to center distance between the neighboring pearls double separation = edge_sep + 2.0 * radius; //sine functions of a pearl double psi = sas_3j1x_x(q * radius); // N pearls interaction terms double structure_factor = (double)num_pearls; for(int num=1; num1 [gamma(D-1) sin((D-1) a)] = a // lim q->0 [sin((D-1) atan(q c))/q] = (D-1) c // lim q,D->0,1 [gamma(D-1) sin((D-1)atan(q c))/q] = c double sq; if (q > 0. && fractal_dim_mass > 1.) { const double Dm1 = fractal_dim_mass - 1.0; const double t1 = sas_gamma(Dm1)*sin(Dm1*atan(q*cutoff_length)); const double t2 = pow(cutoff_length, Dm1); const double t3 = pow(1.0 + square(q*cutoff_length), -0.5*Dm1); sq = t1 * t2 * t3 / q; } else if (q > 0.) { sq = atan(q*cutoff_length)/q; } else if (fractal_dim_mass > 1.) { const double D = fractal_dim_mass; sq = pow(cutoff_length, D) * sas_gamma(D); } else { sq = cutoff_length; } return pq * sq; } sasmodels/sasmodels/models/mass_fractal.py000066400000000000000000000073501317715334700213560ustar00rootroot00000000000000r""" Calculates the scattering from fractal-like aggregates based on the Mildner reference. Definition ---------- The scattering intensity $I(q)$ is calculated as .. math:: I(q) = scale \times P(q)S(q) + background .. math:: P(q) = F(qR)^2 .. math:: F(x) = \frac{3\left[sin(x)-xcos(x)\right]}{x^3} .. math:: S(q) = \frac{\Gamma(D_m-1)\zeta^{D_m-1}}{\left[1+(q\zeta)^2 \right]^{(D_m-1)/2}} \frac{sin\left[(D_m - 1) tan^{-1}(q\zeta) \right]}{q} .. math:: scale = scale\_factor \times NV^2(\rho_\text{particle} - \rho_\text{solvent})^2 .. math:: V = \frac{4}{3}\pi R^3 where $R$ is the radius of the building block, $D_m$ is the **mass** fractal dimension, $\zeta$ is the cut-off length, $\rho_\text{solvent}$ is the scattering length density of the solvent, and $\rho_\text{particle}$ is the scattering length density of particles. .. note:: The mass fractal dimension ( $D_m$ ) is only valid if $1 < mass\_dim < 6$. It is also only valid over a limited $q$ range (see the reference for details). References ---------- D Mildner and P Hall, *J. Phys. D: Appl. Phys.*, 19 (1986) 1535-1545 Equation(9) """ from numpy import inf name = "mass_fractal" title = "Mass Fractal model" description = """ The scattering intensity I(x) = scale*P(x)*S(x) + background, where scale = scale_factor * V * delta^(2) p(x)= F(x*radius)^(2) F(x) = 3*[sin(x)-x cos(x)]/x**3 S(x) = [(gamma(Dm-1)*colength^(Dm-1)*[1+(x^2*colength^2)]^((1-Dm)/2) * sin[(Dm-1)*arctan(x*colength)])/x] where delta = sldParticle -sldSolv. radius = Particle radius fractal_dim_mass = Mass fractal dimension cutoff_length = Cut-off length background = background Ref.:Mildner, Hall,J Phys D Appl Phys(1986), 9, 1535-1545 Note I: This model is valid for 1 6.) static double Iq(double q, double fractal_dim_mass, double fractal_dim_surf, double rg_cluster, double rg_primary) { //computation const double Dm = 0.5*fractal_dim_mass; const double Dt = 0.5*(6.0 - (fractal_dim_mass + fractal_dim_surf)); const double t1 = Dm==0. ? 1.0 : pow(1.0 + square(q*rg_cluster)/(3.0*Dm), -Dm); const double t2 = Dt==0. ? 1.0 : pow(1.0 + square(q*rg_primary)/(3.0*Dt), -Dt); const double form = t1*t2; return form; } sasmodels/sasmodels/models/mass_surface_fractal.py000066400000000000000000000115441317715334700230660ustar00rootroot00000000000000r""" A number of natural and commercial processes form high-surface area materials as a result of the vapour-phase aggregation of primary particles. Examples of such materials include soots, aerosols, and fume or pyrogenic silicas. These are all characterised by cluster mass distributions (sometimes also cluster size distributions) and internal surfaces that are fractal in nature. The scattering from such materials displays two distinct breaks in log-log representation, corresponding to the radius-of-gyration of the primary particles, $rg$, and the radius-of-gyration of the clusters (aggregates), $Rg$. Between these boundaries the scattering follows a power law related to the mass fractal dimension, $Dm$, whilst above the high-Q boundary the scattering follows a power law related to the surface fractal dimension of the primary particles, $Ds$. Definition ---------- The scattered intensity I(q) is calculated using a modified Ornstein-Zernicke equation .. math:: I(q) = scale \times P(q) + background \\ P(q) = \left\{ \left[ 1+(q^2a)\right]^{D_m/2} \times \left[ 1+(q^2b)\right]^{(6-D_s-D_m)/2} \right\}^{-1} \\ a = R_{g}^2/(3D_m/2) \\ b = r_{g}^2/[-3(D_s+D_m-6)/2] \\ scale = scale\_factor \times NV^2 (\rho_{particle} - \rho_{solvent})^2 where $R_g$ is the size of the cluster, $r_g$ is the size of the primary particle, $D_s$ is the surface fractal dimension, $D_m$ is the mass fractal dimension, $\rho_{solvent}$ is the scattering length density of the solvent, and $\rho_{particle}$ is the scattering length density of particles. .. note:: The surface ( $D_s$ ) and mass ( $D_m$ ) fractal dimensions are only valid if $0 < surface\_dim < 6$ , $0 < mass\_dim < 6$ , and $(surface\_dim + mass\_dim ) < 6$ . References ---------- P Schmidt, *J Appl. Cryst.*, 24 (1991) 414-435 Equation(19) A J Hurd, D W Schaefer, J E Martin, *Phys. Rev. A*, 35 (1987) 2361-2364 Equation(2) """ from numpy import inf name = "mass_surface_fractal" title = "Mass Surface Fractal model" description = """ The scattering intensity I(x) = scale*P(x)*S(x) + background, where p(x)= {[1+(x^2*a)]^(Dm/2) * [1+(x^2*b)]^(6-Ds-Dm)/2}^(-1) a = Rg^2/(3*Dm/2) b = rg^2/(3*(6-Ds-Dm)/2) scale = scale factor * N*Volume^2*contrast^2 fractal_dim_mass = Dm (mass fractal dimension) fractal_dim_surf = Ds rg_cluster = Rg rg_primary = rg background = background Ref: Schmidt, J Appl Cryst, eq(19), (1991), 24, 414-435 Hurd, Schaefer, Martin, Phys Rev A, eq(2),(1987),35, 2361-2364 Note that 0 < Ds< 6 and 0 < Dm < 6. """ category = "shape-independent" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type","description"], parameters = [ ["fractal_dim_mass", "", 1.8, [0.0, 6.0], "", "Mass fractal dimension"], ["fractal_dim_surf", "", 2.3, [0.0, 6.0], "", "Surface fractal dimension"], ["rg_cluster", "Ang", 86.7, [0.0, inf], "", "Cluster radius of gyration"], ["rg_primary", "Ang", 4000., [0.0, inf], "", "Primary particle radius of gyration"], ] # pylint: enable=bad-whitespace, line-too-long source = ["mass_surface_fractal.c"] def random(): import numpy as np fractal_dim = np.random.uniform(0, 6) surface_portion = np.random.uniform(0, 1) fractal_dim_surf = fractal_dim*surface_portion fractal_dim_mass = fractal_dim - fractal_dim_surf rg_cluster = 10**np.random.uniform(1, 5) rg_primary = rg_cluster*10**np.random.uniform(-4, -1) scale = 10**np.random.uniform(2, 5) pars = dict( #background=0, scale=scale, fractal_dim_mass=fractal_dim_mass, fractal_dim_surf=fractal_dim_surf, rg_cluster=rg_cluster, rg_primary=rg_primary, ) return pars demo = dict(scale=1, background=0, fractal_dim_mass=1.8, fractal_dim_surf=2.3, rg_cluster=86.7, rg_primary=4000.0) tests = [ # Accuracy tests based on content in test/utest_other_models.py [{'fractal_dim_mass': 1.8, 'fractal_dim_surf': 2.3, 'rg_cluster': 86.7, 'rg_primary': 4000.0, 'background': 0.0, }, 0.05, 1.77537e-05], # Additional tests with larger range of parameters [{'fractal_dim_mass': 3.3, 'fractal_dim_surf': 1.0, 'rg_cluster': 90.0, 'rg_primary': 4000.0, }, 0.001, 0.18562699016], [{'fractal_dim_mass': 1.3, 'fractal_dim_surf': 1.0, 'rg_cluster': 90.0, 'rg_primary': 2000.0, 'background': 0.8, }, 0.001, 1.16539753641], [{'fractal_dim_mass': 2.3, 'fractal_dim_surf': 1.0, 'rg_cluster': 90.0, 'rg_primary': 1000.0, 'scale': 10.0, 'background': 0.0, }, 0.051, 0.000169548800377], ] sasmodels/sasmodels/models/mono_gauss_coil.py000066400000000000000000000057311317715334700221000ustar00rootroot00000000000000#mono_gauss_coil model #conversion of DebyeModel.py #converted by Steve King, Mar 2016 r""" This Debye Gaussian coil model strictly describes the scattering from *monodisperse* polymer chains in theta solvents or polymer melts, conditions under which the distances between segments follow a Gaussian distribution. Provided the number of segments is large (ie, high molecular weight polymers) the single-chain form factor P(Q) is that described by Debye (1947). To describe the scattering from *polydisperse* polymer chains see the :ref:`poly-gauss-coil` model. Definition ---------- .. math:: I(q) = \text{scale} \cdot I_0 \cdot P(q) + \text{background} where .. math:: I_0 &= \phi_\text{poly} \cdot V \cdot (\rho_\text{poly} - \rho_\text{solv})^2 \\ P(q) &= 2 [\exp(-Z) + Z - 1] / Z^2 \\ Z &= (q R_g)^2 \\ V &= M / (N_A \delta) Here, $\phi_\text{poly}$ is the volume fraction of polymer, $V$ is the volume of a polymer coil, *M* is the molecular weight of the polymer, $N_A$ is Avogadro's Number, $\delta$ is the bulk density of the polymer, $\rho_\text{poly}$ is the sld of the polymer, $\rho\text{solv}$ is the sld of the solvent, and $R_g$ is the radius of gyration of the polymer coil. The 2D scattering intensity is calculated in the same way as the 1D, but where the *q* vector is redefined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- P Debye, *J. Phys. Colloid. Chem.*, 51 (1947) 18. R J Roe, *Methods of X-Ray and Neutron Scattering in Polymer Science*, Oxford University Press, New York (2000). http://www.ncnr.nist.gov/staff/hammouda/distance_learning/chapter_28.pdf """ from numpy import inf, exp, errstate name = "mono_gauss_coil" title = "Scattering from monodisperse polymer coils" description = """ Evaluates the scattering from monodisperse polymer chains. """ category = "shape-independent" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type", "description"], parameters = [ ["i_zero", "1/cm", 70.0, [0.0, inf], "", "Intensity at q=0"], ["rg", "Ang", 75.0, [0.0, inf], "", "Radius of gyration"], ] # pylint: enable=bad-whitespace, line-too-long # NB: Scale and Background are implicit parameters on every model def Iq(q, i_zero, rg): # pylint: disable = missing-docstring z = (q * rg)**2 with errstate(invalid='ignore'): inten = (i_zero * 2.0) * (exp(-z) + z - 1.0)/z**2 inten[q == 0] = i_zero return inten Iq.vectorized = True # Iq accepts an array of q values def random(): import numpy as np rg = 10**np.random.uniform(0, 4) #rg = 1e3 pars = dict( #scale=1, background=0, i_zero=1e7, # i_zero is a simple scale rg=rg, ) return pars demo = dict(scale=1.0, i_zero=70.0, rg=75.0, background=0.0) # these unit test values taken from SasView 3.1.2 tests = [ [{'scale': 1.0, 'i_zero': 70.0, 'rg': 75.0, 'background': 0.0}, [0.0106939, 0.469418], [57.1241, 0.112859]], ] sasmodels/sasmodels/models/multilayer_vesicle.c000066400000000000000000000033351317715334700224110ustar00rootroot00000000000000static double form_volume(double radius, double thick_shell, double thick_solvent, double fp_n_shells) { int n_shells = (int)(fp_n_shells + 0.5); double R_N = radius + n_shells*(thick_shell+thick_solvent) - thick_solvent; return M_4PI_3*cube(R_N); } static double multilayer_vesicle_kernel(double q, double volfraction, double radius, double thick_shell, double thick_solvent, double sld_solvent, double sld, int n_shells) { //calculate with a loop, two shells at a time int ii = 0; double fval = 0.0; double voli = 0.0; const double sldi = sld_solvent-sld; do { double ri = radius + (double)ii*(thick_shell + thick_solvent); // layer 1 voli = M_4PI_3*ri*ri*ri; fval += voli*sldi*sas_3j1x_x(ri*q); ri += thick_shell; // layer 2 voli = M_4PI_3*ri*ri*ri; fval -= voli*sldi*sas_3j1x_x(ri*q); //do 2 layers at a time ii++; } while(ii <= n_shells-1); //change to make 0 < n_shells < 2 correspond to //unilamellar vesicles (C. Glinka, 11/24/03) return 1.0e-4*volfraction*fval*fval; // Volume normalization happens in caller } static double Iq(double q, double volfraction, double radius, double thick_shell, double thick_solvent, double sld_solvent, double sld, double fp_n_shells) { int n_shells = (int)(fp_n_shells + 0.5); return multilayer_vesicle_kernel(q, volfraction, radius, thick_shell, thick_solvent, sld_solvent, sld, n_shells); } sasmodels/sasmodels/models/multilayer_vesicle.py000066400000000000000000000165361317715334700226260ustar00rootroot00000000000000r""" Definition ---------- This model is a trivial extension of the core_shell_sphere function where the core is filled with solvent and is surrounded by $N$ shells of material (such as lipids) interleaved with $N - 1$ layers of solvent. For $N = 1$, this returns the same as the vesicle model, except for the normalisation, which here is to outermost volume. The shell thicknesses and SLD are constant for all shells as expected for a multilayer vesicle. .. figure:: img/multi_shell_geometry.jpg Geometry of the multilayer_vesicle model. See the :ref:`core-shell-sphere` model for more documentation. The 1D scattering intensity is calculated in the following way (Guinier, 1955) .. math:: P(q) = \text{scale} \cdot \frac{\phi}{V(R_N)} F^2(q) + \text{background} where .. math:: F(q) = (\rho_\text{shell}-\rho_\text{solv}) \sum_{i=1}^{N} \left[ 3V(r_i)\frac{\sin(qr_i) - qr_i\cos(qr_i)}{(qr_i)^3} - 3V(R_i)\frac{\sin(qR_i) - qR_i\cos(qR_i)}{(qR_i)^3} \right] for .. math:: r_i &= r_c + (i-1)(t_s + t_w) \text{ solvent radius before shell } i \\ R_i &= r_i + t_s \text{ shell radius for shell } i $\phi$ is the volume fraction of particles, $V(r)$ is the volume of a sphere of radius $r$, $r_c$ is the radius of the core, $t_s$ is the thickness of the shell, $t_w$ is the thickness of the solvent layer between the shells, $\rho_\text{shell}$ is the scattering length density of a shell, and $\rho_\text{solv}$ is the scattering length density of the solvent. USAGE NOTES * The outer-most shell radius $R_N$ is used as the effective radius for $P(Q)$ when $P(Q) * S(Q)$ is applied. calculations rather slow. * The number of shells is always rounded to an integer value as a non interger number of layers is not physical. * Thus Polydispersity should only be applied to number of shells **VERY CAREFULLY**. A possible legitimate use would be for mixed systems in which some vesicles have 1 shell, some have 2, etc. A polydispersity on $N$ can be used to model the data by using the "array distriubtion" feature. First create a file such as *shell_dist.txt* containing the relative portion of each vesicle size:: 1 20 2 4 3 1 Turn on polydispersity and select an array distribution for the *n_shells* parameter. Choose the above *shell_dist.txt* file, and the model will be computed with 80% 1-shell vesicles, 16% 2-shell vesicles and 4% 3-shell vesicles. * This is a highly non-linear, highly oscillatory (especially around the q-values that correspond to the repeat distance of the layers), model function complicated by the fact that the number of water/shell pairs must physically be an integer value, although the optimization treats it as a floating point value. Thus it may be that the resolution interpolation is not sufficiently fine grained in certain cases. Please report any such occurences to the SasView team. Generally, for the best possible experience: - Start with the best possible guess - Using a priori knowledge, hold as many parameters fixed as possible - if N=1, tw (water thickness) must by definition be zero. Both N and tw should be fixed during fitting. - If N>1, use constraints to keep N > 1 - Because N only really moves in integer steps, it may get "stuck" if the optimizer step size is too small so care should be taken If you experience problems with this please contact the SasView team and let them know the issue preferably with example data and model which fail to converge. The 2D scattering intensity is the same as 1D, regardless of the orientation of the q vector which is defined as: .. math:: q = \sqrt{q_x^2 + q_y^2} For information about polarised and magnetic scattering, see the :ref:`magnetism` documentation. References ---------- .. [#] B Cabane, *Small Angle Scattering Methods*, in *Surfactant Solutions: New Methods of Investigation*, Ch.2, Surfactant Science Series Vol. 22, Ed. R Zana and M Dekker, New York, (1987). Authorship and Verification ---------------------------- * **Author:** NIST IGOR/DANSE **Date:** pre 2010 * **Converted to sasmodels by:** Piotr Rozyczko **Date:** Feb 24, 2016 * **Last Modified by:** Paul Kienzle **Date:** Feb 7, 2017 * **Last Reviewed by:** Paul Butler **Date:** March 12, 2017 """ from numpy import inf name = "multilayer_vesicle" title = "P(Q) for a Multi-lamellar vesicle" description = """ multilayer_vesicle model parameters; scale : scale factor for abs intensity if needed else 1.0 volfraction: volume fraction radius : Core radius of the multishell thick_shell: shell thickness thick_solvent: water thickness sld_solvent: solvent scattering length density sld: shell scattering length density n_shells:number of "shell plus solvent" layer pairs background: incoherent background """ category = "shape:sphere" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type","description"], parameters = [ ["volfraction", "", 0.05, [0.0, 1], "", "volume fraction of vesicles"], ["radius", "Ang", 60.0, [0.0, inf], "volume", "radius of solvent filled core"], ["thick_shell", "Ang", 10.0, [0.0, inf], "volume", "thickness of one shell"], ["thick_solvent", "Ang", 10.0, [0.0, inf], "volume", "solvent thickness between shells"], ["sld_solvent", "1e-6/Ang^2", 6.4, [-inf, inf], "sld", "solvent scattering length density"], ["sld", "1e-6/Ang^2", 0.4, [-inf, inf], "sld", "Shell scattering length density"], ["n_shells", "", 2.0, [1.0, inf], "volume", "Number of shell plus solvent layer pairs"], ] # pylint: enable=bad-whitespace, line-too-long # TODO: proposed syntax for specifying which parameters can be polydisperse #polydispersity = ["radius", "thick_shell"] source = ["lib/sas_3j1x_x.c", "multilayer_vesicle.c"] def ER(radius, thick_shell, thick_solvent, n_shells): n_shells = int(n_shells+0.5) return radius + n_shells * (thick_shell + thick_solvent) - thick_solvent def random(): import numpy as np volfraction = 10**np.random.uniform(-3, -0.5) # scale from 0.1% to 30% radius = 10**np.random.uniform(0, 2.5) # core less than 300 A total_thick = 10**np.random.uniform(2, 4) # up to 10000 A of shells # random number of shells, with shell+solvent thickness > 10 A n_shells = int(10**np.random.uniform(0, np.log10(total_thick)-1)+0.5) # split total shell thickness with preference for shell over solvent; # make sure that shell thickness is at least 1 A one_thick = total_thick/n_shells thick_solvent = 10**np.random.uniform(-2, 0)*(one_thick - 1) thick_shell = one_thick - thick_solvent pars = dict( scale=1, volfraction=volfraction, radius=radius, thick_shell=thick_shell, thick_solvent=thick_solvent, n_shells=n_shells, ) return pars tests = [ # Accuracy tests based on content in test/utest_other_models.py [{'radius': 60.0, 'thick_shell': 10.0, 'thick_solvent': 10.0, 'sld_solvent': 6.4, 'sld': 0.4, 'n_shells': 2.0, 'scale': 1.0, 'background': 0.001, }, 0.001, 122.1405], [{'volfraction': 1.0, 'radius': 60.0, 'thick_shell': 10.0, 'thick_solvent': 10.0, 'sld_solvent': 6.4, 'sld': 0.4, 'n_shells': 2.0, 'scale': 1.0, 'background': 0.001, }, (0.001, 0.30903), 1.61873], ] sasmodels/sasmodels/models/onion.c000066400000000000000000000033531317715334700176320ustar00rootroot00000000000000 static double f_exp(double q, double r, double sld_in, double sld_out, double thickness, double A, double side) { const double vol = M_4PI_3 * cube(r); const double qr = q * r; const double bes = sas_3j1x_x(qr); const double alpha = A * r/thickness; double result; if (qr == 0.0) { result = 1.0; } else if (fabs(A) > 0.0) { const double qrsq = qr * qr; const double alphasq = alpha * alpha; const double sumsq = alphasq + qrsq; double sinqr, cosqr; SINCOS(qr, sinqr, cosqr); const double t1 = (alphasq - qrsq)*sinqr/qr - 2.0*alpha*cosqr; const double t2 = alpha*sinqr/qr - cosqr; const double fun = -3.0*(t1/sumsq - t2)/sumsq; const double slope = (sld_out - sld_in)/expm1(A); const double contrast = slope*exp(A*side); result = contrast*fun + (sld_in-slope)*bes; } else { result = sld_in*bes; } return vol * result; } static double form_volume(double radius_core, double n_shells, double thickness[]) { int n = (int)(n_shells+0.5); double r = radius_core; for (int i=0; i < n; i++) { r += thickness[i]; } return M_4PI_3*cube(r); } static double Iq(double q, double sld_core, double radius_core, double sld_solvent, double n_shells, double sld_in[], double sld_out[], double thickness[], double A[]) { int n = (int)(n_shells+0.5); double r_out = radius_core; double f = f_exp(q, r_out, sld_core, 0.0, 0.0, 0.0, 0.0); for (int i=0; i < n; i++){ const double r_in = r_out; r_out += thickness[i]; f -= f_exp(q, r_in, sld_in[i], sld_out[i], thickness[i], A[i], 0.0); f += f_exp(q, r_out, sld_in[i], sld_out[i], thickness[i], A[i], 1.0); } f -= f_exp(q, r_out, sld_solvent, 0.0, 0.0, 0.0, 0.0); const double f2 = f * f * 1.0e-4; return f2; } sasmodels/sasmodels/models/onion.py000066400000000000000000000266711317715334700200500ustar00rootroot00000000000000r""" This model provides the form factor, $P(q)$, for a multi-shell sphere where the scattering length density (SLD) of each shell is described by an exponential, linear, or constant function. The form factor is normalized by the volume of the sphere where the SLD is not identical to the SLD of the solvent. We currently provide up to 9 shells with this model. NB: *radius* represents the core radius $r_0$ and *thickness[k]* represents the thickness of the shell, $r_{k+1} - r_k$. Definition ---------- The 1D scattering intensity is calculated in the following way .. math:: P(q) = [f]^2 / V_\text{particle} where .. math:: :nowrap: \begin{align*} f &= f_\text{core} + \left(\sum_{\text{shell}=1}^N f_\text{shell}\right) + f_\text{solvent} \end{align*} The shells are spherically symmetric with particle density $\rho(r)$ and constant SLD within the core and solvent, so .. math:: :nowrap: \begin{align*} f_\text{core} &= 4\pi\int_0^{r_\text{core}} \rho_\text{core} \frac{\sin(qr)}{qr}\, r^2\,\mathrm{d}r &= 3\rho_\text{core} V(r_\text{core}) \frac{j_1(qr_\text{core})}{qr_\text{core}} \\ f_\text{shell} &= 4\pi\int_{r_{\text{shell}-1}}^{r_\text{shell}} \rho_\text{shell}(r)\frac{\sin(qr)}{qr}\,r^2\,\mathrm{d}r \\ f_\text{solvent} &= 4\pi\int_{r_N}^\infty \rho_\text{solvent}\frac{\sin(qr)}{qr}\,r^2\,\mathrm{d}r &= -3\rho_\text{solvent}V(r_N)\frac{j_1(q r_N)}{q r_N} \end{align*} where the spherical bessel function $j_1$ is .. math:: j_1(x) = \frac{\sin(x)}{x^2} - \frac{\cos(x)}{x} and the volume is $V(r) = \frac{4\pi}{3}r^3$. The volume of the particle is determined by the radius of the outer shell, so $V_\text{particle} = V(r_N)$. Now lets consider the SLD of a shell defined by .. math:: \rho_\text{shell}(r) = \begin{cases} B\exp\left(A(r-r_{\text{shell}-1})/\Delta t_\text{shell}\right) + C & \mbox{for } A \neq 0 \\ \rho_\text{in} = \text{constant} & \mbox{for } A = 0 \end{cases} An example of a possible SLD profile is shown below where $\rho_\text{in}$ and $\Delta t_\text{shell}$ stand for the SLD of the inner side of the $k^\text{th}$ shell and the thickness of the $k^\text{th}$ shell in the equation above, respectively. For $A > 0$, .. math:: f_\text{shell} &= 4 \pi \int_{r_{\text{shell}-1}}^{r_\text{shell}} \left[ B\exp \left(A (r - r_{\text{shell}-1}) / \Delta t_\text{shell} \right) + C \right] \frac{\sin(qr)}{qr}\,r^2\,\mathrm{d}r \\ &= 3BV(r_\text{shell}) e^A h(\alpha_\text{out},\beta_\text{out}) - 3BV(r_{\text{shell}-1}) h(\alpha_\text{in},\beta_\text{in}) + 3CV(r_{\text{shell}}) \frac{j_1(\beta_\text{out})}{\beta_\text{out}} - 3CV(r_{\text{shell}-1}) \frac{j_1(\beta_\text{in})}{\beta_\text{in}} for .. math:: :nowrap: \begin{align*} B&=\frac{\rho_\text{out} - \rho_\text{in}}{e^A-1} & C &= \frac{\rho_\text{in}e^A - \rho_\text{out}}{e^A-1} \\ \alpha_\text{in} &= A\frac{r_{\text{shell}-1}}{\Delta t_\text{shell}} & \alpha_\text{out} &= A\frac{r_\text{shell}}{\Delta t_\text{shell}} \\ \beta_\text{in} &= qr_{\text{shell}-1} & \beta_\text{out} &= qr_\text{shell} \\ \end{align*} where $h$ is .. math:: h(x,y) = \frac{x \sin(y) - y\cos(y)}{(x^2+y^2)y} - \frac{(x^2-y^2)\sin(y) - 2xy\cos(y)}{(x^2+y^2)^2y} For $A \sim 0$, e.g., $A = -0.0001$, this function converges to that of the linear SLD profile with $\rho_\text{shell}(r) \approx A(r-r_{\text{shell}-1})/\Delta t_\text{shell})+B$, so this case is equivalent to .. math:: :nowrap: \begin{align*} f_\text{shell} &= 3 V(r_\text{shell}) \frac{\Delta\rho_\text{shell}}{\Delta t_\text{shell}} \left[\frac{ 2 \cos(qr_\text{out}) + qr_\text{out} \sin(qr_\text{out}) }{ (qr_\text{out})^4 }\right] \\ &{} -3 V(r_\text{shell}) \frac{\Delta\rho_\text{shell}}{\Delta t_\text{shell}} \left[\frac{ 2\cos(qr_\text{in}) +qr_\text{in}\sin(qr_\text{in}) }{ (qr_\text{in})^4 }\right] \\ &{} +3\rho_\text{out}V(r_\text{shell}) \frac{j_1(qr_\text{out})}{qr_\text{out}} -3\rho_\text{in}V(r_{\text{shell}-1}) \frac{j_1(qr_\text{in})}{qr_\text{in}} \end{align*} For $A = 0$, the exponential function has no dependence on the radius (so that $\rho_\text{out}$ is ignored in this case) and becomes flat. We set the constant to $\rho_\text{in}$ for convenience, and thus the form factor contributed by the shells is .. math:: f_\text{shell} = 3\rho_\text{in}V(r_\text{shell}) \frac{j_1(qr_\text{out})}{qr_\text{out}} - 3\rho_\text{in}V(r_{\text{shell}-1}) \frac{j_1(qr_\text{in})}{qr_\text{in}} .. figure:: img/onion_geometry.png Example of an onion model profile. The 2D scattering intensity is the same as $P(q)$ above, regardless of the orientation of the $q$ vector which is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} NB: The outer most radius is used as the effective radius for $S(q)$ when $P(q) S(q)$ is applied. References ---------- L A Feigin and D I Svergun, *Structure Analysis by Small-Angle X-Ray and Neutron Scattering*, Plenum Press, New York, 1987. """ # # Give a polynomial $\rho(r) = Ar^3 + Br^2 + Cr + D$ for density, # # .. math:: # # f = 4 \pi \int_a^b \rho(r) \sin(qr)/(qr) \mathrm{d}r = h(b) - h(a) # # where # # .. math:: # # h(r) = \frac{4 \pi}{q^6}\left[ # (q^3(4Ar^3 + 3Br^2 + 2Cr + D) - q(24Ar + 6B)) \sin(qr) # - (q^4(Ar^4 + Br^3 + Cr^2 + Dr) - q^2(12Ar^2 + 6Br + 2C) + 24A) \cos(qr) # \right] # # Use the monotonic spline to get the polynomial coefficients for each shell. # # Order 0 # # .. math:: # # h(r) = \frac{4 \pi}{q^3} \left[ # - \cos(qr) (Ar) q # + \sin(qr) (A) # \right] # # Order 1 # # .. math:: # # h(r) = \frac{4 \pi}{q^4} \left[ # - \cos(qr) ( Ar^2 + Br) q^2 # + \sin(qr) ( Ar + B ) q # + \cos(qr) (2A ) # \right] # # Order 2 # # .. math:: # h(r) = \frac{4 \pi}{q^5} \left[ # - \cos(qr) ( Ar^3 + Br^2 + Cr) q^3 # + \sin(qr) (3Ar^2 + 2Br + C ) q^2 # + \cos(qr) (6Ar + 2B ) q # - \sin(qr) (6A ) # # Order 3 # # h(r) = \frac{4 \pi}{q^6}\left[ # - \cos(qr) ( Ar^4 + Br^3 + Cr^2 + Dr) q^4 # + \sin(qr) ( 4Ar^3 + 3Br^2 + 2Cr + D ) q^3 # + \cos(qr) (12Ar^2 + 6Br + 2C ) q^2 # - \sin(qr) (24Ar + 6B ) q # - \cos(qr) (24A ) # \right] # # Order p # # h(r) = \frac{4 \pi}{q^{2}} # \sum_{k=0}^p -\frac{d^k\cos(qr)}{dr^k} \frac{d^k r\rho(r)}{dr^k} (qr)^{-k} # # Given the equation # # f = sum_(k=0)^(n-1) h_k(r_(k+1)) - h_k(r_k) # # we can rearrange the terms so that # # f = sum_0^(n-1) h_k(r_(k+1)) - sum_0^(n-1) h_k(r_k) # = sum_1^n h_(k-1)(r_k) - sum_0^(n-1) h_k(r_k) # = h_(n-1)(r_n) - h_0(r_0) + sum_1^(n-1) [h_(k-1)(r_k) - h_k(r_k)] # = h_(n-1)(r_n) - h_0(r_0) - sum_1^(n-1) h_(Delta k)(r_k) # # where # # h_(Delta k)(r) = h(Delta rho_k, r) # # for # # Delta rho_k = (A_k-A_(k-1)) r^p + (B_k-B_(k-1)) r^(p-1) + ... # # Using l'H\^opital's Rule 6 times on the order 3 polynomial, # # lim_(q->0) h(r) = (140D r^3 + 180C r^4 + 144B r^5 + 120A r^6)/720 # from __future__ import division import numpy as np from numpy import inf, nan from math import fabs, exp, expm1 name = "onion" title = "Onion shell model with constant, linear or exponential density" description = """\ Form factor of mutishells normalized by the volume. Here each shell is described by an exponential function; I) For A_shell != 0, f(r) = B*exp(A_shell*(r-r_in)/thick_shell)+C where B=(sld_out-sld_in)/(exp(A_shell)-1) C=sld_in-B. Note that in the above case, the function becomes a linear function as A_shell --> 0+ or 0-. II) For the exact point of A_shell == 0, f(r) = sld_in ,i.e., it crosses over flat function Note that the 'sld_out' becaomes NULL in this case. background:background, rad_core0: radius of sphere(core) thick_shell#:the thickness of the shell# sld_core0: the SLD of the sphere sld_solv: the SLD of the solvent sld_shell: the SLD of the shell# A_shell#: the coefficient in the exponential function """ category = "shape:sphere" # TODO: n is a volume parameter that is not polydisperse # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type","description"], parameters = [ ["sld_core", "1e-6/Ang^2", 1.0, [-inf, inf], "sld", "Core scattering length density"], ["radius_core", "Ang", 200., [0, inf], "volume", "Radius of the core"], ["sld_solvent", "1e-6/Ang^2", 6.4, [-inf, inf], "sld", "Solvent scattering length density"], ["n_shells", "", 1, [0, 10], "volume", "number of shells"], ["sld_in[n_shells]", "1e-6/Ang^2", 1.7, [-inf, inf], "sld", "scattering length density at the inner radius of shell k"], ["sld_out[n_shells]", "1e-6/Ang^2", 2.0, [-inf, inf], "sld", "scattering length density at the outer radius of shell k"], ["thickness[n_shells]", "Ang", 40., [0, inf], "volume", "Thickness of shell k"], ["A[n_shells]", "", 1.0, [-inf, inf], "", "Decay rate of shell k"], ] # pylint: enable=bad-whitespace, line-too-long source = ["lib/sas_3j1x_x.c", "onion.c"] single = False profile_axes = ['Radius (A)', 'SLD (1e-6/A^2)'] def profile(sld_core, radius_core, sld_solvent, n_shells, sld_in, sld_out, thickness, A): """ Returns shape profile with x=radius, y=SLD. """ n_shells = int(n_shells+0.5) total_radius = 1.25*(sum(thickness[:n_shells]) + radius_core + 1) dz = total_radius/400 # 400 points for a smooth plot z = [] rho = [] # add in the core z.append(0) rho.append(sld_core) z.append(radius_core) rho.append(sld_core) # add in the shells for k in range(int(n_shells)): # Left side of each shells z_current = z[-1] z.append(z_current) rho.append(sld_in[k]) if fabs(A[k]) < 1.0e-16: # flat shell z.append(z_current + thickness[k]) rho.append(sld_in[k]) else: # exponential shell # num_steps must be at least 1, so use floor()+1 rather than ceil # to protect against a thickness0. num_steps = np.floor(thickness[k]/dz) + 1 slope = (sld_out[k] - sld_in[k]) / expm1(A[k]) const = (sld_in[k] - slope) for z_shell in np.linspace(0, thickness[k], num_steps+1): z.append(z_current+z_shell) rho.append(slope*exp(A[k]*z_shell/thickness[k]) + const) # add in the solvent z.append(z[-1]) rho.append(sld_solvent) z.append(total_radius) rho.append(sld_solvent) return np.asarray(z), np.asarray(rho) def ER(radius_core, n_shells, thickness): """Effective radius""" n = int(n_shells[0]+0.5) return np.sum(thickness[:n], axis=0) + radius_core demo = { "sld_solvent": 2.2, "sld_core": 1.0, "radius_core": 100, "n_shells": 4, "sld_in": [0.5, 1.5, 0.9, 2.0], "sld_out": [nan, 0.9, 1.2, 1.6], "thickness": [50, 75, 150, 75], "A": [0, -1, 1e-4, 1], # Could also specify them individually as # "A1": 0, "A2": -1, "A3": 1e-4, "A4": 1, #"radius_core_pd_n": 10, #"radius_core_pd": 0.4, #"thickness4_pd_n": 10, #"thickness4_pd": 0.4, } sasmodels/sasmodels/models/parallelepiped.c000066400000000000000000000052061317715334700214720ustar00rootroot00000000000000double form_volume(double length_a, double length_b, double length_c); double Iq(double q, double sld, double solvent_sld, double length_a, double length_b, double length_c); double Iqxy(double qx, double qy, double sld, double solvent_sld, double length_a, double length_b, double length_c, double theta, double phi, double psi); double form_volume(double length_a, double length_b, double length_c) { return length_a * length_b * length_c; } double Iq(double q, double sld, double solvent_sld, double length_a, double length_b, double length_c) { const double mu = 0.5 * q * length_b; // Scale sides by B const double a_scaled = length_a / length_b; const double c_scaled = length_c / length_b; // outer integral (with gauss points), integration limits = 0, 1 double outer_total = 0; //initialize integral for( int i=0; i<76; i++) { const double sigma = 0.5 * ( Gauss76Z[i] + 1.0 ); const double mu_proj = mu * sqrt(1.0-sigma*sigma); // inner integral (with gauss points), integration limits = 0, 1 // corresponding to angles from 0 to pi/2. double inner_total = 0.0; for(int j=0; j<76; j++) { const double uu = 0.5 * ( Gauss76Z[j] + 1.0 ); double sin_uu, cos_uu; SINCOS(M_PI_2*uu, sin_uu, cos_uu); const double si1 = sas_sinx_x(mu_proj * sin_uu * a_scaled); const double si2 = sas_sinx_x(mu_proj * cos_uu); inner_total += Gauss76Wt[j] * square(si1 * si2); } inner_total *= 0.5; const double si = sas_sinx_x(mu * c_scaled * sigma); outer_total += Gauss76Wt[i] * inner_total * si * si; } outer_total *= 0.5; // Multiply by contrast^2 and convert from [1e-12 A-1] to [cm-1] const double V = form_volume(length_a, length_b, length_c); const double drho = (sld-solvent_sld); return 1.0e-4 * square(drho * V) * outer_total; } double Iqxy(double qx, double qy, double sld, double solvent_sld, double length_a, double length_b, double length_c, double theta, double phi, double psi) { double q, xhat, yhat, zhat; ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); const double siA = sas_sinx_x(0.5*length_a*q*xhat); const double siB = sas_sinx_x(0.5*length_b*q*yhat); const double siC = sas_sinx_x(0.5*length_c*q*zhat); const double V = form_volume(length_a, length_b, length_c); const double drho = (sld - solvent_sld); const double form = V * drho * siA * siB * siC; // Square and convert from [1e-12 A-1] to [cm-1] return 1.0e-4 * form * form; } sasmodels/sasmodels/models/parallelepiped.py000066400000000000000000000246331317715334700217050ustar00rootroot00000000000000# parallelepiped model # Note: model title and parameter table are inserted automatically r""" The form factor is normalized by the particle volume. For information about polarised and magnetic scattering, see the :ref:`magnetism` documentation. Definition ---------- This model calculates the scattering from a rectangular parallelepiped (\:numref:`parallelepiped-image`\). If you need to apply polydispersity, see also :ref:`rectangular-prism`. .. _parallelepiped-image: .. figure:: img/parallelepiped_geometry.jpg Parallelepiped with the corresponding definition of sides. The three dimensions of the parallelepiped (strictly here a cuboid) may be given in *any* size order. To avoid multiple fit solutions, especially with Monte-Carlo fit methods, it may be advisable to restrict their ranges. There may be a number of closely similar "best fits", so some trial and error, or fixing of some dimensions at expected values, may help. The 1D scattering intensity $I(q)$ is calculated as: .. Comment by Miguel Gonzalez: I am modifying the original text because I find the notation a little bit confusing. I think that in most textbooks/papers, the notation P(Q) is used for the form factor (adim, P(Q=0)=1), although F(q) seems also to be used. But here (as for many other models), P(q) is used to represent the scattering intensity (in cm-1 normally). It would be good to agree on a common notation. .. math:: I(q) = \frac{\text{scale}}{V} (\Delta\rho \cdot V)^2 \left< P(q, \alpha) \right> + \text{background} where the volume $V = A B C$, the contrast is defined as $\Delta\rho = \rho_\text{p} - \rho_\text{solvent}$, $P(q, \alpha)$ is the form factor corresponding to a parallelepiped oriented at an angle $\alpha$ (angle between the long axis C and $\vec q$), and the averaging $\left<\ldots\right>$ is applied over all orientations. Assuming $a = A/B < 1$, $b = B /B = 1$, and $c = C/B > 1$, the form factor is given by (Mittelbach and Porod, 1961) .. math:: P(q, \alpha) = \int_0^1 \phi_Q\left(\mu \sqrt{1-\sigma^2},a\right) \left[S(\mu c \sigma/2)\right]^2 d\sigma with .. math:: \phi_Q(\mu,a) &= \int_0^1 \left\{S\left[\frac{\mu}{2}\cos\left(\frac{\pi}{2}u\right)\right] S\left[\frac{\mu a}{2}\sin\left(\frac{\pi}{2}u\right)\right] \right\}^2 du \\ S(x) &= \frac{\sin x}{x} \\ \mu &= qB The scattering intensity per unit volume is returned in units of |cm^-1|. NB: The 2nd virial coefficient of the parallelepiped is calculated based on the averaged effective radius, after appropriately sorting the three dimensions, to give an oblate or prolate particle, $(=\sqrt{AB/\pi})$ and length $(= C)$ values, and used as the effective radius for $S(q)$ when $P(q) \cdot S(q)$ is applied. To provide easy access to the orientation of the parallelepiped, we define three angles $\theta$, $\phi$ and $\Psi$. The definition of $\theta$ and $\phi$ is the same as for the cylinder model (see also figures below). .. Comment by Miguel Gonzalez: The following text has been commented because I think there are two mistakes. Psi is the rotational angle around C (but I cannot understand what it means against the q plane) and psi=0 corresponds to a||x and b||y. The angle $\Psi$ is the rotational angle around the $C$ axis against the $q$ plane. For example, $\Psi = 0$ when the $B$ axis is parallel to the $x$-axis of the detector. The angle $\Psi$ is the rotational angle around the $C$ axis. For $\theta = 0$ and $\phi = 0$, $\Psi = 0$ corresponds to the $B$ axis oriented parallel to the y-axis of the detector with $A$ along the z-axis. For other $\theta$, $\phi$ values, the parallelepiped has to be first rotated $\theta$ degrees around $z$ and $\phi$ degrees around $y$, before doing a final rotation of $\Psi$ degrees around the resulting $C$ to obtain the final orientation of the parallelepiped. For example, for $\theta = 0$ and $\phi = 90$, we have that $\Psi = 0$ corresponds to $A$ along $x$ and $B$ along $y$, while for $\theta = 90$ and $\phi = 0$, $\Psi = 0$ corresponds to $A$ along $z$ and $B$ along $x$. .. _parallelepiped-orientation: .. figure:: img/parallelepiped_angle_definition.png Definition of the angles for oriented parallelepiped, shown with $A (abc[2] - abc[1]) length = np.where(selector, abc[0], abc[2]) # surface average radius (rough approximation) radius = np.sqrt(np.where(~selector, abc[0]*abc[1], abc[1]*abc[2]) / pi) ddd = 0.75 * radius * (2*radius*length + (length + radius)*(length + pi*radius)) return 0.5 * (ddd) ** (1. / 3.) # VR defaults to 1.0 def random(): import numpy as np length = 10**np.random.uniform(1, 4.7, size=3) pars = dict( length_a=length[0], length_b=length[1], length_c=length[2], ) return pars # parameters for demo demo = dict(scale=1, background=0, sld=6.3, sld_solvent=1.0, length_a=35, length_b=75, length_c=400, theta=45, phi=30, psi=15, length_a_pd=0.1, length_a_pd_n=10, length_b_pd=0.1, length_b_pd_n=1, length_c_pd=0.1, length_c_pd_n=1, theta_pd=10, theta_pd_n=1, phi_pd=10, phi_pd_n=1, psi_pd=10, psi_pd_n=10) # rkh 7/4/17 add random unit test for 2d, note make all params different, 2d values not tested against other codes or models qx, qy = 0.2 * cos(pi/6.), 0.2 * sin(pi/6.) tests = [[{}, 0.2, 0.17758004974], [{}, [0.2], [0.17758004974]], [{'theta':10.0, 'phi':20.0}, (qx, qy), 0.0089517140475], [{'theta':10.0, 'phi':20.0}, [(qx, qy)], [0.0089517140475]], ] del qx, qy # not necessary to delete, but cleaner sasmodels/sasmodels/models/peak_lorentz.py000066400000000000000000000035651317715334700214200ustar00rootroot00000000000000r""" This model describes a Lorentzian shaped peak on a flat background. Definition ---------- The scattering intensity $I(q)$ is calculated as .. math:: I(q) = \frac{scale}{\bigl(1+\bigl(\frac{q-q_0}{B}\bigr)^2\bigr)} + background with the peak having height of $I_0$ centered at $q_0$ and having a HWHM (half-width half-maximum) of B. For 2D data the scattering intensity is calculated in the same way as 1D, where the $q$ vector is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- None. """ from numpy import inf name = "peak_lorentz" title = "A Lorentzian peak on a flat background" description = """\ Class that evaluates a lorentzian shaped peak. F(q) = scale/(1+[(q-q0)/B]^2 ) + background The model has three parameters: scale = scale peak_pos = peak position peak_hwhm = half-width-half-maximum of peak background= incoherent background""" category = "shape-independent" # ["name", "units", default, [lower, upper], "type", "description"], parameters = [["peak_pos", "1/Ang", 0.05, [-inf, inf], "", "Peak postion in q"], ["peak_hwhm", "1/Ang", 0.005, [-inf, inf], "", "HWHM of peak"], ] def Iq(q, peak_pos, peak_hwhm): """ Return I(q) """ inten = (1/(1+((q-peak_pos)/peak_hwhm)**2)) return inten Iq.vectorized = True # Iq accepts an array of q values def random(): import numpy as np peak_pos = 10**np.random.uniform(-3, -1) peak_hwhm = peak_pos * 10**np.random.uniform(-3, 0) pars = dict( #background=0, scale=10**np.random.uniform(2, 6), peak_pos=peak_pos, peak_hwhm=peak_hwhm, ) return pars demo = dict(scale=100, background=1.0, peak_pos=0.05, peak_hwhm=0.005) tests = [[{'scale':100.0, 'background':1.0}, 0.001, 2.0305]] sasmodels/sasmodels/models/pearl_necklace.c000066400000000000000000000065011317715334700214360ustar00rootroot00000000000000double form_volume(double radius, double edge_sep, double thick_string, double fp_num_pearls); double Iq(double q, double radius, double edge_sep, double thick_string, double fp_num_pearls, double sld, double string_sld, double solvent_sld); #define INVALID(v) (v.thick_string >= v.radius || v.num_pearls <= 0) // From Igor library static double pearl_necklace_kernel(double q, double radius, double edge_sep, double thick_string, int num_pearls, double sld_pearl, double sld_string, double sld_solv) { // number of string segments const int num_strings = num_pearls - 1; //each masses: contrast * volume const double contrast_pearl = sld_pearl - sld_solv; const double contrast_string = sld_string - sld_solv; const double string_vol = edge_sep * M_PI_4 * thick_string * thick_string; const double pearl_vol = M_4PI_3 * radius * radius * radius; const double m_string = contrast_string * string_vol; const double m_pearl = contrast_pearl * pearl_vol; // center to center distance between the neighboring pearls const double A_s = edge_sep + 2.0 * radius; //sine functions of a pearl // Note: lim_(q->0) Si(q*a)/(q*b) = a/b // So therefore: // beta = q==0. ? 1.0 : (Si(q*(A_s-radius)) - Si(q*radius))/q_edge; // gamma = q==0. ? 1.0 : Si(q_edge)/q_edge; // But there is a 1/(1-sinc) term below which blows up so don't bother const double q_edge = q * edge_sep; const double beta = (sas_Si(q*(A_s-radius)) - sas_Si(q*radius)) / q_edge; const double gamma = sas_Si(q_edge) / q_edge; const double psi = sas_3j1x_x(q*radius); // Precomputed sinc terms const double si = sas_sinx_x(q*A_s); const double omsi = 1.0 - si; const double pow_si = pow(si, num_pearls); // form factor for num_pearls const double sss = 2.0*square(m_pearl*psi) * ( - si * (1.0 - pow_si) / (omsi*omsi) + num_pearls / omsi - 0.5 * num_pearls ); // form factor for num_strings (like thin rods) const double srr = m_string * m_string * ( - 2.0 * (1.0 - pow_si/si)*beta*beta / (omsi*omsi) + 2.0 * num_strings*beta*beta / omsi + num_strings * (2.0*gamma - square(sas_sinx_x(q_edge/2.0))) ); // form factor for correlations const double srs = 4.0 * m_string * m_pearl * beta * psi * ( - si * (1.0 - pow_si/si) / (omsi*omsi) + num_strings / omsi ); const double form = sss + srr + srs; return 1.0e-4 * form; } double form_volume(double radius, double edge_sep, double thick_string, double fp_num_pearls) { const int num_pearls = (int)(fp_num_pearls + 0.5); //Force integer number of pearls const int num_strings = num_pearls - 1; const double string_vol = edge_sep * M_PI_4 * thick_string * thick_string; const double pearl_vol = M_4PI_3 * radius * radius * radius; const double volume = num_strings*string_vol + num_pearls*pearl_vol; return volume; } double Iq(double q, double radius, double edge_sep, double thick_string, double fp_num_pearls, double sld, double string_sld, double solvent_sld) { const int num_pearls = (int)(fp_num_pearls + 0.5); //Force integer number of pearls const double form = pearl_necklace_kernel(q, radius, edge_sep, thick_string, num_pearls, sld, string_sld, solvent_sld); return form; } sasmodels/sasmodels/models/pearl_necklace.py000066400000000000000000000122671317715334700216520ustar00rootroot00000000000000r""" This model provides the form factor for a pearl necklace composed of two elements: *N* pearls (homogeneous spheres of radius *R*) freely jointed by *M* rods (like strings - with a total mass *Mw* = *M* \* *m*\ :sub:`r` + *N* \* *m*\ :sub:`s`, and the string segment length (or edge separation) *l* (= *A* - 2\ *R*)). *A* is the center-to-center pearl separation distance. .. figure:: img/pearl_necklace_geometry.jpg Pearl Necklace schematic Definition ---------- The output of the scattering intensity function for the pearl_necklace is given by (Schweins, 2004) .. math:: I(q)=\frac{ \text{scale} }{V} \cdot \frac{(S_{ss}(q)+S_{ff}(q)+S_{fs}(q))} {(M \cdot m_f + N \cdot m_s)^2} + \text{bkg} where .. math:: S_{ss}(q) &= sm_s^2\psi^2(q)[\frac{N}{1-sin(qA)/qA}-\frac{N}{2}- \frac{1-(sin(qA)/qA)^N}{(1-sin(qA)/qA)^2}\cdot\frac{sin(qA)}{qA}] \\ S_{ff}(q) &= sm_r^2[M\{2\Lambda(q)-(\frac{sin(ql/2)}{ql/2})\}+ \frac{2M\beta^2(q)}{1-sin(qA)/qA}-2\beta^2(q)\cdot \frac{1-(sin(qA)/qA)^M}{(1-sin(qA)/qA)^2}] \\ S_{fs}(q) &= m_r \beta (q) \cdot m_s \psi (q) \cdot 4[ \frac{N-1}{1-sin(qA)/qA}-\frac{1-(sin(qA)/qA)^{N-1}}{(1-sin(qA)/qA)^2} \cdot \frac{sin(qA)}{qA}] \\ \psi(q) &= 3 \cdot \frac{sin(qR)-(qR)\cdot cos(qR)}{(qR)^3} \\ \Lambda(q) &= \frac{\int_0^{ql}\frac{sin(t)}{t}dt}{ql} \\ \beta(q) &= \frac{\int_{qR}^{q(A-R)}\frac{sin(t)}{t}dt}{ql} where the mass *m*\ :sub:`i` is (SLD\ :sub:`i` - SLD\ :sub:`solvent`) \* (volume of the *N* pearls/rods). *V* is the total volume of the necklace. The 2D scattering intensity is the same as $P(q)$ above, regardless of the orientation of the *q* vector. The returned value is scaled to units of |cm^-1| and the parameters of the pearl_necklace model are the following NB: *num_pearls* must be an integer. References ---------- R Schweins and K Huber, *Particle Scattering Factor of Pearl Necklace Chains*, *Macromol. Symp.* 211 (2004) 25-42 2004 """ from numpy import inf, pi name = "pearl_necklace" title = "Colloidal spheres chained together with no preferential orientation" description = """ Calculate form factor for Pearl Necklace Model [Macromol. Symp. 2004, 211, 25-42] Parameters: background:background scale: scale factor sld: the SLD of the pearl spheres sld_string: the SLD of the strings sld_solvent: the SLD of the solvent num_pearls: number of the pearls radius: the radius of a pearl edge_sep: the length of string segment; surface to surface thick_string: thickness (ie, diameter) of the string """ category = "shape:cylinder" # ["name", "units", default, [lower, upper], "type","description"], parameters = [["radius", "Ang", 80.0, [0, inf], "volume", "Mean radius of the chained spheres"], ["edge_sep", "Ang", 350.0, [0, inf], "volume", "Mean separation of chained particles"], ["thick_string", "Ang", 2.5, [0, inf], "volume", "Thickness of the chain linkage"], ["num_pearls", "none", 3, [1, inf], "volume", "Number of pearls in the necklace (must be integer)"], ["sld", "1e-6/Ang^2", 1.0, [-inf, inf], "sld", "Scattering length density of the chained spheres"], ["sld_string", "1e-6/Ang^2", 1.0, [-inf, inf], "sld", "Scattering length density of the chain linkage"], ["sld_solvent", "1e-6/Ang^2", 6.3, [-inf, inf], "sld", "Scattering length density of the solvent"], ] source = ["lib/sas_Si.c", "lib/sas_3j1x_x.c", "pearl_necklace.c"] single = False # use double precision unless told otherwise def volume(radius, edge_sep, thick_string, num_pearls): """ Calculates the total particle volume of the necklace. Redundant with form_volume. """ num_pearls = int(num_pearls + 0.5) number_of_strings = num_pearls - 1.0 string_vol = edge_sep * pi * pow((thick_string / 2.0), 2.0) pearl_vol = 4.0 /3.0 * pi * pow(radius, 3.0) total_vol = number_of_strings * string_vol total_vol += num_pearls * pearl_vol return total_vol def ER(radius, edge_sep, thick_string, num_pearls): """ Calculation for effective radius. """ num_pearls = int(num_pearls + 0.5) tot_vol = volume(radius, edge_sep, thick_string, num_pearls) rad_out = (tot_vol/(4.0/3.0*pi)) ** (1./3.) return rad_out def random(): import numpy as np radius = 10**np.random.uniform(1, 3) # 1 - 1000 thick_string = 10**np.random.uniform(0, np.log10(radius)-1) # 1 - radius/10 edge_sep = 10**np.random.uniform(0, 3) # 1 - 1000 num_pearls = np.round(10**np.random.uniform(0.3, 3)) # 2 - 1000 pars = dict( radius=radius, edge_sep=edge_sep, thick_string=thick_string, num_pearls=num_pearls, ) return pars # parameters for demo demo = dict(scale=1, background=0, radius=80.0, edge_sep=350.0, num_pearls=3, sld=1, sld_solvent=6.3, sld_string=1, thick_string=2.5, radius_pd=.2, radius_pd_n=5, edge_sep_pd=25.0, edge_sep_pd_n=5, num_pearls_pd=0, num_pearls_pd_n=0, thick_string_pd=0.2, thick_string_pd_n=5, ) tests = [[{}, 0.001, 17380.245], [{}, 'ER', 115.39502]] sasmodels/sasmodels/models/poly_gauss_coil.py000066400000000000000000000100301317715334700220770ustar00rootroot00000000000000#poly_gauss_coil model #conversion of Poly_GaussCoil.py #converted by Steve King, Mar 2016 r""" This empirical model describes the scattering from *polydisperse* polymer chains in theta solvents or polymer melts, assuming a Schulz-Zimm type molecular weight distribution. To describe the scattering from *monodisperse* polymer chains, see the :ref:`mono-gauss-coil` model. Definition ---------- .. math:: I(q) = \text{scale} \cdot I_0 \cdot P(q) + \text{background} where .. math:: I_0 &= \phi_\text{poly} \cdot V \cdot (\rho_\text{poly}-\rho_\text{solv})^2 \\ P(q) &= 2 [(1 + UZ)^{-1/U} + Z - 1] / [(1 + U) Z^2] \\ Z &= [(q R_g)^2] / (1 + 2U) \\ U &= (Mw / Mn) - 1 = \text{polydispersity ratio} - 1 \\ V &= M / (N_A \delta) Here, $\phi_\text{poly}$, is the volume fraction of polymer, $V$ is the volume of a polymer coil, $M$ is the molecular weight of the polymer, $N_A$ is Avogadro's Number, $\delta$ is the bulk density of the polymer, $\rho_\text{poly}$ is the sld of the polymer, $\rho_\text{solv}$ is the sld of the solvent, and $R_g$ is the radius of gyration of the polymer coil. The 2D scattering intensity is calculated in the same way as the 1D, but where the $q$ vector is redefined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- O Glatter and O Kratky (editors), *Small Angle X-ray Scattering*, Academic Press, (1982) Page 404. J S Higgins, H C Benoit, *Polymers and Neutron Scattering*, Oxford Science Publications, (1996). S M King, *Small Angle Neutron Scattering* in *Modern Techniques for Polymer Characterisation*, Wiley, (1999). http://www.ncnr.nist.gov/staff/hammouda/distance_learning/chapter_28.pdf """ import numpy as np from numpy import inf, expm1, power name = "poly_gauss_coil" title = "Scattering from polydisperse polymer coils" description = """ Evaluates the scattering from polydisperse polymer chains. """ category = "shape-independent" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type", "description"], parameters = [ ["i_zero", "1/cm", 70.0, [0.0, inf], "", "Intensity at q=0"], ["rg", "Ang", 75.0, [0.0, inf], "", "Radius of gyration"], ["polydispersity", "None", 2.0, [1.0, inf], "", "Polymer Mw/Mn"], ] # pylint: enable=bad-whitespace, line-too-long # NB: Scale and Background are implicit parameters on every model def Iq(q, i_zero, rg, polydispersity): # pylint: disable = missing-docstring u = polydispersity - 1.0 z = q**2 * (rg**2 / (1.0 + 2.0*u)) # need to trap the case of the polydispersity being 1 (ie, monodisperse!) if polydispersity == 1.0: result = 2.0 * (expm1(-z) + z) index = q != 0. result[index] /= z[index]**2 result[~index] = 1.0 else: # Taylor series around z=0 of (2*(1+uz)^(-1/u) + z - 1) / (z^2(u+1)) p = [ #(-1 - 20*u - 155*u**2 - 580*u**3 - 1044*u**4 - 720*u**5) / 2520., #(+1 + 14*u + 71*u**2 + 154*u**3 + 120*u**4) / 360., #(-1 - 9*u - 26*u**2 - 24*u**3) / 60., (+1 + 5*u + 6*u**2) / 12., (-1 - 2*u) / 3., (+1), ] result = 2.0 * (power(1.0 + u*z, -1.0/u) + z - 1.0) / (1.0 + u) index = z > 1e-4 result[index] /= z[index]**2 result[~index] = np.polyval(p, z[~index]) return i_zero * result Iq.vectorized = True # Iq accepts an array of q values def random(): import numpy as np rg = 10**np.random.uniform(0, 4) #rg = 1e3 polydispersity = 10**np.random.uniform(0, 3) pars = dict( #scale=1, background=0, i_zero=1e7, # i_zero is a simple scale rg=rg, polydispersity=polydispersity, ) return pars demo = dict(scale=1.0, i_zero=70.0, rg=75.0, polydispersity=2.0, background=0.0) # these unit test values taken from SasView 3.1.2 tests = [ [{'scale': 1.0, 'i_zero': 70.0, 'rg': 75.0, 'polydispersity': 2.0, 'background': 0.0}, [0.0106939, 0.469418], [57.6405, 0.169016]], ] sasmodels/sasmodels/models/polymer_excl_volume.py000066400000000000000000000114621317715334700230070ustar00rootroot00000000000000r""" This model describes the scattering from polymer chains subject to excluded volume effects and has been used as a template for describing mass fractals. Definition ---------- The form factor was originally presented in the following integral form (Benoit, 1957) .. math:: P(Q)=2\int_0^{1}dx(1-x)exp\left[-\frac{Q^2a^2}{6}n^{2v}x^{2v}\right] where $\nu$ is the excluded volume parameter (which is related to the Porod exponent $m$ as $\nu=1/m$ ), $a$ is the statistical segment length of the polymer chain, and $n$ is the degree of polymerization. This integral was later put into an almost analytical form as follows (Hammouda, 1993) .. math:: P(Q)=\frac{1}{\nu U^{1/2\nu}}\gamma\left(\frac{1}{2\nu},U\right) - \frac{1}{\nu U^{1/\nu}}\gamma\left(\frac{1}{\nu},U\right) where $\gamma(x,U)$ is the incomplete gamma function .. math:: \gamma(x,U)=\int_0^{U}dt\ exp(-t)t^{x-1} and the variable $U$ is given in terms of the scattering vector $Q$ as .. math:: U=\frac{Q^2a^2n^{2\nu}}{6} = \frac{Q^2R_{g}^2(2\nu+1)(2\nu+2)}{6} The square of the radius-of-gyration is defined as .. math:: R_{g}^2 = \frac{a^2n^{2\nu}}{(2\nu+1)(2\nu+2)} Note that this model applies only in the mass fractal range (ie, $5/3<=m<=3$ ) and **does not apply** to surface fractals ( $3 intensity in [cm-1] i_micelle *= ndensity; return(i_micelle); } double Iq(double q, double ndensity, double v_core, double v_corona, double solvent_sld, double core_sld, double corona_sld, double radius_core, double rg, double d_penetration, double n_aggreg) { return micelle_spherical_kernel(q, ndensity, v_core, v_corona, solvent_sld, core_sld, corona_sld, radius_core, rg, d_penetration, n_aggreg); } sasmodels/sasmodels/models/polymer_micelle.py000066400000000000000000000124641317715334700221020ustar00rootroot00000000000000r""" This model provides the form factor, $P(q)$, for a micelle with a spherical core and Gaussian polymer chains attached to the surface, thus may be applied to block copolymer micelles. To work well the Gaussian chains must be much smaller than the core, which is often not the case. Please study the reference carefully. Definition ---------- The 1D scattering intensity for this model is calculated according to the equations given by Pedersen (Pedersen, 2000), summarised briefly here. The micelle core is imagined as $N\_aggreg$ polymer heads, each of volume $v\_core$, which then defines a micelle core of $radius\_core$, which is a separate parameter even though it could be directly determined. The Gaussian random coil tails, of gyration radius $rg$, are imagined uniformly distributed around the spherical core, centred at a distance $radius\_core + d\_penetration.rg$ from the micelle centre, where $d\_penetration$ is of order unity. A volume $v\_corona$ is defined for each coil. The model in detail seems to separately parametrise the terms for the shape of I(Q) and the relative intensity of each term, so use with caution and check parameters for consistency. The spherical core is monodisperse, so it's intensity and the cross terms may have sharp oscillations (use q resolution smearing if needs be to help remove them). .. math:: P(q) = N^2\beta^2_s\Phi(qR)^2+N\beta^2_cP_c(q)+2N^2\beta_s\beta_cS_{sc}s_c(q)+N(N-1)\beta_c^2S_{cc}(q) \\ \beta_s = v\_core(sld\_core - sld\_solvent) \\ \beta_c = v\_corona(sld\_corona - sld\_solvent) where $N = n\_aggreg$, and for the spherical core of radius $R$ .. math:: \Phi(qR)= \frac{\sin(qr) - qr\cos(qr)}{(qr)^3} whilst for the Gaussian coils .. math:: P_c(q) &= 2 [\exp(-Z) + Z - 1] / Z^2 \\ Z &= (q R_g)^2 The sphere to coil ( core to corona) and coil to coil (corona to corona) cross terms are approximated by: .. math:: S_{sc}(q)=\Phi(qR)\psi(Z)\frac{sin(q(R+d.R_g))}{q(R+d.R_g)} \\ S_{cc}(q)=\psi(Z)^2\left[\frac{sin(q(R+d.R_g))}{q(R+d.R_g)} \right ]^2 \\ \psi(Z)=\frac{[1-exp^{-Z}]}{Z} Validation ---------- $P(q)$ above is multiplied by $ndensity$, and a units conversion of 10^{-13}, so $scale$ is likely 1.0 if the scattering data is in absolute units. This model has not yet been independently validated. References ---------- J Pedersen, *J. Appl. Cryst.*, 33 (2000) 637-640 """ from numpy import inf, pi name = "polymer_micelle" title = "Polymer micelle model" description = """ This model provides the form factor, $P(q)$, for a micelle with a spherical core and Gaussian polymer chains attached to the surface, thus may be applied to block copolymer micelles. To work well the Gaussian chains must be much smaller than the core, which is often not the case. Please study the reference to Pedersen and full documentation carefully. """ category = "shape:sphere" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type","description"], parameters = [ ["ndensity", "1e15/cm^3", 8.94, [0.0, inf], "", "Number density of micelles"], ["v_core", "Ang^3", 62624.0, [0.0, inf], "", "Core volume "], ["v_corona", "Ang^3", 61940.0, [0.0, inf], "", "Corona volume"], ["sld_solvent", "1e-6/Ang^2", 6.4, [0.0, inf], "sld", "Solvent scattering length density"], ["sld_core", "1e-6/Ang^2", 0.34, [0.0, inf], "sld", "Core scattering length density"], ["sld_corona", "1e-6/Ang^2", 0.8, [0.0, inf], "sld", "Corona scattering length density"], ["radius_core", "Ang", 45.0, [0.0, inf], "", "Radius of core ( must be >> rg )"], ["rg", "Ang", 20.0, [0.0, inf], "", "Radius of gyration of chains in corona"], ["d_penetration", "", 1.0, [-inf, inf], "", "Factor to mimic non-penetration of Gaussian chains"], ["n_aggreg", "", 6.0, [-inf, inf], "", "Aggregation number of the micelle"], ] # pylint: enable=bad-whitespace, line-too-long single = False source = ["lib/sas_3j1x_x.c", "polymer_micelle.c"] def random(): import numpy as np radius_core = 10**np.random.uniform(1, 3) rg = radius_core * 10**np.random.uniform(-2, -0.3) d_penetration = np.random.randn()*0.05 + 1 n_aggreg = np.random.randint(3, 30) # volume of head groups is the core volume over the number of groups, # with a correction for packing fraction of the head groups. v_core = 4*pi/3*radius_core**3/n_aggreg * 0.68 # Rg^2 for gaussian coil is a^2n/6 => a^2 = 6 Rg^2/n # a=2r => r = Rg sqrt(3/2n) # v = 4/3 pi r^3 n => v = 4/3 pi Rg^3 (3/2n)^(3/2) n = pi Rg^3 sqrt(6/n) tail_segments = np.random.randint(6, 30) v_corona = pi * rg**3 * np.sqrt(6/tail_segments) V = 4*pi/3*(radius_core + rg)**3 pars = dict( background=0, scale=1e7/V, ndensity=8.94, v_core=v_core, v_corona=v_corona, radius_core=radius_core, rg=rg, d_penetration=d_penetration, n_aggreg=n_aggreg, ) return pars tests = [ [{}, 0.01, 15.3532], ] # RKH 20Mar2016 - need to check whether the core & corona volumes are per # monomer ??? and how aggregation number works! # renamed from micelle_spherical_core to polymer_micelle, # moved from shape-independent to spheres section. # Ought to be able to add polydisp to core? And add ability to x by S(Q) ? sasmodels/sasmodels/models/porod.py000066400000000000000000000026561317715334700200460ustar00rootroot00000000000000r""" This model fits the Porod function .. math:: I(q) = C/q^4 to the data directly without any need for linearisation (cf. Log I(q) vs Log q). Here $C = 2\pi (\Delta\rho)^2 S_v$ is the scale factor where $S_v$ is the specific surface area (ie, surface area / volume) of the sample, and $\Delta\rho$ is the contrast factor. For 2D data: The 2D scattering intensity is calculated in the same way as 1D, where the q vector is defined as .. math:: q = \sqrt{q_x^2+q_y^2} References ---------- G Porod. *Kolloid Zeit*. 124 (1951) 83. L A Feigin, D I Svergun, G W Taylor. *Structure Analysis by Small-Angle X-ray and Neutron Scattering*. Springer. (1987) """ from numpy import power, inf, errstate name = "porod" title = "Porod function" description = """\ I(q) = scale/q^4 + background """ category = "shape-independent" parameters = [] def Iq(q): """ @param q: Input q-value """ with errstate(divide='ignore'): return q**-4 Iq.vectorized = True # Iq accepts an array of q values def random(): import numpy as np sld, solvent = np.random.uniform(-0.5, 12, size=2) radius = 10**np.random.uniform(1, 4.7) Vf = 10**np.random.uniform(-3, -1) scale = 1e-4 * Vf * 2*np.pi*(sld-solvent)**2/(3*radius) pars = dict( scale=scale, ) return pars demo = dict(scale=1.5, background=0.5) tests = [ [{'scale': 0.00001, 'background':0.01}, 0.04, 3.916250], [{}, 0.0, inf], ] sasmodels/sasmodels/models/power_law.py000066400000000000000000000031631317715334700207140ustar00rootroot00000000000000#power_law model #conversion of PowerLawAbsModel.py #converted by Steve King, Dec 2015 r""" This model calculates a simple power law with a flat background. Definition ---------- .. math:: I(q) = \text{scale} \cdot q^{-\text{power}} + \text{background} Note the minus sign in front of the exponent. The exponent *power* should therefore be entered as a **positive** number for fitting. Also note that unlike many other models, *scale* in this model is NOT explicitly related to a volume fraction. Be careful if combining this model with other models. References ---------- None. """ from numpy import inf, errstate name = "power_law" title = "Simple power law with a flat background" description = """ Evaluates the function I(q) = scale * q^(-power) + background NB: enter power as a positive number! """ category = "shape-independent" # ["name", "units", default, [lower, upper], "type", "description"], parameters = [["power", "", 4.0, [-inf, inf], "", "Power law exponent"]] # NB: Scale and Background are implicit parameters on every model def Iq(q, power): # pylint: disable=missing-docstring with errstate(divide='ignore'): result = q**-power return result Iq.vectorized = True # Iq accepts an array of q values def random(): import numpy as np power = np.random.uniform(1, 6) pars = dict( scale=0.1**power*10**np.random.uniform(-4, 2), power=power, ) return pars demo = dict(scale=1.0, power=4.0, background=0.0) tests = [ [{'scale': 1.0, 'power': 4.0, 'background' : 0.0}, [0.0106939, 0.469418], [7.64644e+07, 20.5949]], ] sasmodels/sasmodels/models/pringle.c000066400000000000000000000060411317715334700201450ustar00rootroot00000000000000double form_volume(double radius, double thickness, double alpha, double beta); double Iq(double q, double radius, double thickness, double alpha, double beta, double sld, double sld_solvent); static void _integrate_bessel( double radius, double alpha, double beta, double q_sin_psi, double q_cos_psi, double n, double *Sn, double *Cn) { // translate gauss point z in [-1,1] to a point in [0, radius] const double zm = 0.5*radius; const double zb = 0.5*radius; // evaluate at Gauss points double sumS = 0.0; // initialize integral double sumC = 0.0; // initialize integral double r; for (int i=0; i < 76; i++) { r = Gauss76Z[i]*zm + zb; const double qrs = r*q_sin_psi; const double qrrc = r*r*q_cos_psi; double y = Gauss76Wt[i] * r * sas_JN(n, beta*qrrc) * sas_JN(2*n, qrs); double S, C; SINCOS(alpha*qrrc, S, C); sumS += y*S; sumC += y*C; } *Sn = zm*sumS / (radius*radius); *Cn = zm*sumC / (radius*radius); } static double _sum_bessel_orders( double radius, double alpha, double beta, double q_sin_psi, double q_cos_psi) { //calculate sum term from n = -3 to 3 //Note 1: // S_n(-x) = (-1)^S_n(x) // => S_n^2(-x) = S_n^2(x), // => sum_-k^k Sk = S_0^2 + 2*sum_1^kSk^2 //Note 2: // better precision to sum terms from smaller to larger // though it doesn't seem to make a difference in this case. double Sn, Cn, sum; sum = 0.0; for (int n=3; n>0; n--) { _integrate_bessel(radius, alpha, beta, q_sin_psi, q_cos_psi, n, &Sn, &Cn); sum += 2.0*(Sn*Sn + Cn*Cn); } _integrate_bessel(radius, alpha, beta, q_sin_psi, q_cos_psi, 0, &Sn, &Cn); sum += Sn*Sn+ Cn*Cn; return sum; } static double _integrate_psi( double q, double radius, double thickness, double alpha, double beta) { // translate gauss point z in [-1,1] to a point in [0, pi/2] const double zm = M_PI_4; const double zb = M_PI_4; double sum = 0.0; for (int i = 0; i < 76; i++) { double psi = Gauss76Z[i]*zm + zb; double sin_psi, cos_psi; SINCOS(psi, sin_psi, cos_psi); double bessel_term = _sum_bessel_orders(radius, alpha, beta, q*sin_psi, q*cos_psi); double sinc_term = square(sas_sinx_x(q * thickness * cos_psi / 2.0)); double pringle_kernel = 4.0 * sin_psi * bessel_term * sinc_term; sum += Gauss76Wt[i] * pringle_kernel; } return zm * sum; } double form_volume(double radius, double thickness, double alpha, double beta) { return M_PI*radius*radius*thickness; } double Iq( double q, double radius, double thickness, double alpha, double beta, double sld, double sld_solvent) { double form = _integrate_psi(q, radius, thickness, alpha, beta); double contrast = sld - sld_solvent; double volume = M_PI*radius*radius*thickness; return 1.0e-4*form * square(contrast * volume); } sasmodels/sasmodels/models/pringle.py000066400000000000000000000071651317715334700203630ustar00rootroot00000000000000r""" Definition ---------- The form factor for this bent disc is essentially that of a hyperbolic paraboloid and calculated as .. math:: P(q) = (\Delta \rho )^2 V \int^{\pi/2}_0 d\psi \sin{\psi} sinc^2 \left( \frac{qd\cos{\psi}}{2} \right) \left[ \left( S^2_0+C^2_0\right) + 2\sum_{n=1}^{\infty} \left( S^2_n+C^2_n\right) \right] where .. math:: C_n = \frac{1}{r^2}\int^{R}_{0} r dr\cos(qr^2\alpha \cos{\psi}) J_n\left( qr^2\beta \cos{\psi}\right) J_{2n}\left( qr \sin{\psi}\right) .. math:: S_n = \frac{1}{r^2}\int^{R}_{0} r dr\sin(qr^2\alpha \cos{\psi}) J_n\left( qr^2\beta \cos{\psi}\right) J_{2n}\left( qr \sin{\psi}\right) and $\Delta \rho \text{ is } \rho_{pringle}-\rho_{solvent}$, $V$ is the volume of the disc, $\psi$ is the angle between the normal to the disc and the q vector, $d$ and $R$ are the "pringle" thickness and radius respectively, $\alpha$ and $\beta$ are the two curvature parameters, and $J_n$ is the n\ :sup:`th` order Bessel function of the first kind. .. figure:: img/pringles_fig1.png Schematic of model shape (Graphic from Matt Henderson, matt@matthen.com) Reference --------- Karen Edler, Universtiy of Bath, Private Communication. 2012. Derivation by Stefan Alexandru Rautu. **Author:** Andrew Jackson **on:** 2008 **Last Modified by:** Wojciech Wpotrzebowski **on:** March 20, 2016 **Last Reviewed by:** Andrew Jackson **on:** September 26, 2016 """ from numpy import inf, pi name = "pringle" title = "The Pringle model provides the form factor, $P(q)$, for a 'pringle' \ or 'saddle-shaped' disc that is bent in two directions." description = """\ """ category = "shape:cylinder" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type","description"], parameters = [ ["radius", "Ang", 60.0, [0, inf], "volume", "Pringle radius"], ["thickness", "Ang", 10.0, [0, inf], "volume", "Thickness of pringle"], ["alpha", "", 0.001, [-inf, inf], "volume", "Curvature parameter alpha"], ["beta", "", 0.02, [-inf, inf], "volume", "Curvature paramter beta"], ["sld", "1e-6/Ang^2", 1.0, [-inf, inf], "sld", "Pringle sld"], ["sld_solvent", "1e-6/Ang^2", 6.3, [-inf, inf], "sld", "Solvent sld"] ] # pylint: enable=bad-whitespace, line-too-long source = ["lib/polevl.c", "lib/sas_J0.c", "lib/sas_J1.c", \ "lib/sas_JN.c", "lib/gauss76.c", "pringle.c"] def ER(radius, thickness, alpha, beta): """ Return equivalent radius (ER) """ ddd = 0.75 * radius * (2 * radius * thickness + (thickness + radius) \ * (thickness + pi * radius)) return 0.5 * (ddd) ** (1. / 3.) def random(): import numpy as np alpha, beta = 10**np.random.uniform(-1, 1, size=2) radius = 10**np.random.uniform(1, 3) thickness = 10**np.random.uniform(0.7, 2) pars = dict( radius=radius, thickness=thickness, alpha=alpha, beta=beta, ) return pars tests = [ [{'scale' : 1.0, 'radius': 60.0, 'thickness': 10.0, 'alpha': 0.001, 'beta': 0.02, 'sld': 1.0, 'sld_solvent': 6.3, 'background': 0.001, }, 0.1, 9.87676], [{'scale' : 1.0, 'radius': 60.0, 'thickness': 10.0, 'alpha': 0.001, 'beta': 0.02, 'sld': 1.0, 'sld_solvent': 6.3, 'background': 0.001, }, 0.01, 290.56723], [{'scale' : 1.0, 'radius': 60.0, 'thickness': 10.0, 'alpha': 0.001, 'beta': 0.02, 'sld': 1.0, 'sld_solvent': 6.3, 'background': 0.001, }, 0.001, 317.40847], ] sasmodels/sasmodels/models/raspberry.c000066400000000000000000000051231317715334700205160ustar00rootroot00000000000000double form_volume(double radius_lg); double Iq(double q, double sld_lg, double sld_sm, double sld_solvent, double volfraction_lg, double volfraction_sm, double surf_fraction, double radius_lg, double radius_sm, double penetration); double form_volume(double radius_lg) { //Because of the complex structure, volume normalization must //happen in the Iq code below. Thus the form volume is set to 1.0 here double volume=1.0; return volume; } double Iq(double q, double sld_lg, double sld_sm, double sld_solvent, double volfraction_lg, double volfraction_sm, double surface_fraction, double radius_lg, double radius_sm, double penetration) { // Ref: J. coll. inter. sci. (2010) vol. 343 (1) pp. 36-41. double vfL, rL, sldL, vfS, rS, sldS, deltaS, delrhoL, delrhoS, sldSolv; double VL, VS, Np, f2, fSs; double psiL,psiS; double sfLS,sfSS; double slT; vfL = volfraction_lg; rL = radius_lg; sldL = sld_lg; vfS = volfraction_sm; fSs = surface_fraction; rS = radius_sm; sldS = sld_sm; deltaS = penetration; sldSolv = sld_solvent; delrhoL = fabs(sldL - sldSolv); delrhoS = fabs(sldS - sldSolv); VL = M_4PI_3*rL*rL*rL; VS = M_4PI_3*rS*rS*rS; //Number of small particles per large particle Np = vfS*fSs*VL/vfL/VS; //Total scattering length difference slT = delrhoL*VL + Np*delrhoS*VS; //Form factors for each particle psiL = sas_3j1x_x(q*rL); psiS = sas_3j1x_x(q*rS); //Cross term between large and small particles sfLS = psiL*psiS*sas_sinx_x(q*(rL+deltaS*rS)); //Cross term between small particles at the surface sfSS = psiS*psiS*sas_sinx_x(q*(rL+deltaS*rS))*sas_sinx_x(q*(rL+deltaS*rS)); //Large sphere form factor term f2 = delrhoL*delrhoL*VL*VL*psiL*psiL; //Small sphere form factor term f2 += Np*delrhoS*delrhoS*VS*VS*psiS*psiS; //Small particle - small particle cross term f2 += Np*(Np-1)*delrhoS*delrhoS*VS*VS*sfSS; //Large-small particle cross term f2 += 2*Np*delrhoL*delrhoS*VL*VS*sfLS; //Normalise by total scattering length difference if (f2 != 0.0){ f2 = f2/slT/slT; } //I(q) for large-small composite particles f2 = f2*(vfL*delrhoL*delrhoL*VL + vfS*fSs*Np*delrhoS*delrhoS*VS); //I(q) for free small particles f2+= vfS*(1.0-fSs)*delrhoS*delrhoS*VS*psiS*psiS; // normalize to single particle volume and convert to 1/cm f2 *= 1.0e8; // [=] 1/cm f2 *= 1.0e-12; // convert for (1/A^-6)^2 to (1/A)^2 return f2; } sasmodels/sasmodels/models/raspberry.py000066400000000000000000000163011317715334700207240ustar00rootroot00000000000000r""" Definition ---------- The figure below shows a schematic of a large droplet surrounded by several smaller particles forming a structure similar to that of Pickering emulsions. .. figure:: img/raspberry_geometry.jpg Schematic of the raspberry model In order to calculate the form factor of the entire complex, the self-correlation of the large droplet, the self-correlation of the particles, the correlation terms between different particles and the cross terms between large droplet and small particles all need to be calculated. Consider two infinitely thin shells of radii $R_1$ and $R_2$ separated by distance $r$. The general structure of the equation is then the form factor of the two shells multiplied by the phase factor that accounts for the separation of their centers. .. math:: S(q) = \frac{\sin(qR_1)}{qR_1}\frac{\sin(qR_2)}{qR_2}\frac{\sin(qr)}{qr} In this case, the large droplet and small particles are solid spheres rather than thin shells. Thus the two terms must be integrated over $R_L$ and $R_S$ respectively using the weighting function of a sphere. We then obtain the functions for the form of the two spheres: .. math:: \Psi_L = \int_0^{R_L}(4\pi R^2_L)\frac{\sin(qR_L)}{qR_L}dR_L = \frac{3[\sin(qR_L)-qR_L\cos(qR_L)]}{(qR_L)^2} .. math:: \Psi_S = \int_0^{R_S}(4\pi R^2_S)\frac{\sin(qR_S)}{qR_S}dR_S = \frac{3[\sin(qR_S)-qR_L\cos(qR_S)]}{(qR_S)^2} The cross term between the large droplet and small particles is given by: .. math:: S_{LS} = \Psi_L\Psi_S\frac{\sin(q(R_L+\delta R_S))}{q(R_L+\delta\ R_S)} and the self term between small particles is given by: .. math:: S_{SS} = \Psi_S^2\biggl[\frac{\sin(q(R_L+\delta R_S))}{q(R_L+\delta\ R_S)} \biggr]^2 The number of small particles per large droplet, $N_p$, is given by: .. math:: N_p = \frac{\phi_S\phi_\text{surface}V_L}{\phi_L V_S} where $\phi_S$ is the volume fraction of small particles in the sample, $\phi_\text{surface}$ is the fraction of the small particles that are adsorbed to the large droplets, $\phi_L$ is the volume fraction of large droplets in the sample, and $V_S$ and $V_L$ are the volumes of individual small particles and large droplets respectively. The form factor of the entire complex can now be calculated including the excess scattering length densities of the components $\Delta\rho_L$ and $\Delta\rho_S$, where $\Delta\rho_x = \left|\rho_x-\rho_\text{solvent}\right|$ : .. math:: P_{LS} = \frac{1}{M^2}\bigl[(\Delta\rho_L)^2V_L^2\Psi_L^2 +N_p(\Delta\rho_S)^2V_S^2\Psi_S^2 + N_p(1-N_p)(\Delta\rho_S)^2V_S^2S_{SS} + 2N_p\Delta\rho_L\Delta\rho_SV_LV_SS_{LS}\bigr] where M is the total scattering length of the whole complex : .. math:: M = \Delta\rho_LV_L + N_p\Delta\rho_SV_S In a real system, there will ususally be an excess of small particles such that some fraction remain unbound. Therefore the overall scattering intensity is given by: .. math:: I(Q) = I_{LS}(Q) + I_S(Q) = (\phi_L(\Delta\rho_L)^2V_L + \phi_S\phi_\text{surface}N_p(\Delta\rho_S)^2V_S)P_{LS} + \phi_S(1-\phi_\text{surface})(\Delta\rho_S)^2V_S\Psi_S^2 A useful parameter to extract is the fraction of the surface area of the large droplets that is covered by small particles. This can be calculated from the model parameters as: .. math:: \chi = \frac{4\phi_L\phi_\text{surface}(R_L+\delta R_S)}{\phi_LR_S} References ---------- K Larson-Smith, A Jackson, and D C Pozzo, *Small angle scattering model for Pickering emulsions and raspberry particles*, *Journal of Colloid and Interface Science*, 343(1) (2010) 36-41 **Author:** Andrew Jackson **on:** 2008 **Modified by:** Andrew Jackson **on:** March 20, 2016 **Reviewed by:** Andrew Jackson **on:** March 20, 2016 """ from numpy import inf name = "raspberry" title = "Calculates the form factor, *P(q)*, for a 'Raspberry-like' structure \ where there are smaller spheres at the surface of a larger sphere, such as the \ structure of a Pickering emulsion." description = """ RaspBerryModel: volfraction_lg = volume fraction large spheres radius_lg = radius large sphere (A) sld_lg = sld large sphere (A-2) volfraction_sm = volume fraction small spheres radius_sm = radius small sphere (A) surface_fraction = fraction of small spheres at surface sld_sm = sld small sphere penetration = small sphere penetration (A) sld_solvent = sld solvent background = background (cm-1) Ref: J. coll. inter. sci. (2010) vol. 343 (1) pp. 36-41.""" category = "shape:sphere" # [ "name", "units", default, [lower, upper], "type", "description"], parameters = [["sld_lg", "1e-6/Ang^2", -0.4, [-inf, inf], "sld", "large particle scattering length density"], ["sld_sm", "1e-6/Ang^2", 3.5, [-inf, inf], "sld", "small particle scattering length density"], ["sld_solvent", "1e-6/Ang^2", 6.36, [-inf, inf], "sld", "solvent scattering length density"], ["volfraction_lg", "", 0.05, [-inf, inf], "", "volume fraction of large spheres"], ["volfraction_sm", "", 0.005, [-inf, inf], "", "volume fraction of small spheres"], ["surface_fraction", "", 0.4, [-inf, inf], "", "fraction of small spheres at surface"], ["radius_lg", "Ang", 5000, [0, inf], "volume", "radius of large spheres"], ["radius_sm", "Ang", 100, [0, inf], "", "radius of small spheres"], ["penetration", "Ang", 0, [-1, 1], "", "fractional penetration depth of small spheres into large sphere"], ] source = ["lib/sas_3j1x_x.c", "raspberry.c"] def random(): import numpy as np # Limit volume fraction to 20% each volfraction_lg = 10**np.random.uniform(-3, -0.3) volfraction_sm = 10**np.random.uniform(-3, -0.3) # Prefer most particles attached (peak near 60%), but not all or none surface_fraction = np.random.beta(6, 4) radius_lg = 10**np.random.uniform(1.7, 4.7) # 500 - 50000 A radius_sm = 10**np.random.uniform(-3, -0.3)*radius_lg # 0.1% - 20% penetration = np.random.beta(1, 10) # up to 20% pen. for 90% of examples pars = dict( volfraction_lg=volfraction_lg, volfraction_sm=volfraction_sm, surface_fraction=surface_fraction, radius_lg=radius_lg, radius_sm=radius_sm, penetration=penetration, ) return pars # parameters for demo demo = dict(scale=1, background=0.001, sld_lg=-0.4, sld_sm=3.5, sld_solvent=6.36, volfraction_lg=0.05, volfraction_sm=0.005, surface_fraction=0.4, radius_lg=5000, radius_sm=100, penetration=0.0, radius_lg_pd=.2, radius_lg_pd_n=10) # TODO: update tests so the parameters correspond to SasView parameters # The model was re-parameterized so the results have changed. # NOTE: test results taken from values returned by SasView 3.1.2, with # 0.001 added for a non-zero default background. #tests = [[{}, 0.0412755102041, 0.286669115234], # [{}, 0.5, 0.00103818393658], # ] sasmodels/sasmodels/models/rectangular_prism.c000066400000000000000000000047031317715334700222310ustar00rootroot00000000000000double form_volume(double length_a, double b2a_ratio, double c2a_ratio); double Iq(double q, double sld, double solvent_sld, double length_a, double b2a_ratio, double c2a_ratio); double form_volume(double length_a, double b2a_ratio, double c2a_ratio) { return length_a * (length_a*b2a_ratio) * (length_a*c2a_ratio); } double Iq(double q, double sld, double solvent_sld, double length_a, double b2a_ratio, double c2a_ratio) { const double length_b = length_a * b2a_ratio; const double length_c = length_a * c2a_ratio; const double a_half = 0.5 * length_a; const double b_half = 0.5 * length_b; const double c_half = 0.5 * length_c; //Integration limits to use in Gaussian quadrature const double v1a = 0.0; const double v1b = M_PI_2; //theta integration limits const double v2a = 0.0; const double v2b = M_PI_2; //phi integration limits double outer_sum = 0.0; for(int i=0; i<76; i++) { const double theta = 0.5 * ( Gauss76Z[i]*(v1b-v1a) + v1a + v1b ); double sin_theta, cos_theta; SINCOS(theta, sin_theta, cos_theta); const double termC = sas_sinx_x(q * c_half * cos_theta); double inner_sum = 0.0; for(int j=0; j<76; j++) { double phi = 0.5 * ( Gauss76Z[j]*(v2b-v2a) + v2a + v2b ); double sin_phi, cos_phi; SINCOS(phi, sin_phi, cos_phi); // Amplitude AP from eqn. (12), rewritten to avoid round-off effects when arg=0 const double termA = sas_sinx_x(q * a_half * sin_theta * sin_phi); const double termB = sas_sinx_x(q * b_half * sin_theta * cos_phi); const double AP = termA * termB * termC; inner_sum += Gauss76Wt[j] * AP * AP; } inner_sum = 0.5 * (v2b-v2a) * inner_sum; outer_sum += Gauss76Wt[i] * inner_sum * sin_theta; } double answer = 0.5*(v1b-v1a)*outer_sum; // Normalize by Pi (Eqn. 16). // The term (ABC)^2 does not appear because it was introduced before on // the definitions of termA, termB, termC. // The factor 2 appears because the theta integral has been defined between // 0 and pi/2, instead of 0 to pi. answer /= M_PI_2; //Form factor P(q) // Multiply by contrast^2 and volume^2 const double volume = length_a * length_b * length_c; answer *= square((sld-solvent_sld)*volume); // Convert from [1e-12 A-1] to [cm-1] answer *= 1.0e-4; return answer; } sasmodels/sasmodels/models/rectangular_prism.py000066400000000000000000000121631317715334700224360ustar00rootroot00000000000000# rectangular_prism model # Note: model title and parameter table are inserted automatically r""" This model provides the form factor, $P(q)$, for a rectangular prism. Note that this model is almost totally equivalent to the existing :ref:`parallelepiped` model. The only difference is that the way the relevant parameters are defined here ($a$, $b/a$, $c/a$ instead of $a$, $b$, $c$) which allows use of polydispersity with this model while keeping the shape of the prism (e.g. setting $b/a = 1$ and $c/a = 1$ and applying polydispersity to *a* will generate a distribution of cubes of different sizes). Note also that, contrary to :ref:`parallelepiped`, it does not compute the 2D scattering. Definition ---------- The 1D scattering intensity for this model was calculated by Mittelbach and Porod (Mittelbach, 1961), but the implementation here is closer to the equations given by Nayuk and Huber (Nayuk, 2012). Note also that the angle definitions used in the code and the present documentation correspond to those used in (Nayuk, 2012) (see Fig. 1 of that reference), with $\theta$ corresponding to $\alpha$ in that paper, and not to the usual convention used for example in the :ref:`parallelepiped` model. As the present model does not compute the 2D scattering, this has no further consequences. In this model the scattering from a massive parallelepiped with an orientation with respect to the scattering vector given by $\theta$ and $\phi$ .. math:: A_P\,(q) = \frac{\sin \left( \tfrac{1}{2}qC \cos\theta \right) }{\tfrac{1}{2} qC \cos\theta} \,\times\, \frac{\sin \left( \tfrac{1}{2}qA \cos\theta \right) }{\tfrac{1}{2} qA \cos\theta} \,\times\ , \frac{\sin \left( \tfrac{1}{2}qB \cos\theta \right) }{\tfrac{1}{2} qB \cos\theta} where $A$, $B$ and $C$ are the sides of the parallelepiped and must fulfill $A \le B \le C$, $\theta$ is the angle between the $z$ axis and the longest axis of the parallelepiped $C$, and $\phi$ is the angle between the scattering vector (lying in the $xy$ plane) and the $y$ axis. The normalized form factor in 1D is obtained averaging over all possible orientations .. math:: P(q) = \frac{2}{\pi} \int_0^{\frac{\pi}{2}} \, \int_0^{\frac{\pi}{2}} A_P^2(q) \, \sin\theta \, d\theta \, d\phi And the 1D scattering intensity is calculated as .. math:: I(q) = \text{scale} \times V \times (\rho_\text{p} - \rho_\text{solvent})^2 \times P(q) where $V$ is the volume of the rectangular prism, $\rho_\text{p}$ is the scattering length of the parallelepiped, $\rho_\text{solvent}$ is the scattering length of the solvent, and (if the data are in absolute units) *scale* represents the volume fraction (which is unitless). **The 2D scattering intensity is not computed by this model.** Validation ---------- Validation of the code was conducted by comparing the output of the 1D model to the output of the existing :ref:`parallelepiped` model. References ---------- P Mittelbach and G Porod, *Acta Physica Austriaca*, 14 (1961) 185-211 R Nayuk and K Huber, *Z. Phys. Chem.*, 226 (2012) 837-854 """ from numpy import pi, inf, sqrt name = "rectangular_prism" title = "Rectangular parallelepiped with uniform scattering length density." description = """ I(q)= scale*V*(sld - sld_solvent)^2*P(q,theta,phi)+background P(q,theta,phi) = (2/pi) * double integral from 0 to pi/2 of ... AP^2(q)*sin(theta)*dtheta*dphi AP = S(q*C*cos(theta)/2) * S(q*A*sin(theta)*sin(phi)/2) * S(q*B*sin(theta)*cos(phi)/2) S(x) = sin(x)/x """ category = "shape:parallelepiped" # ["name", "units", default, [lower, upper], "type","description"], parameters = [["sld", "1e-6/Ang^2", 6.3, [-inf, inf], "sld", "Parallelepiped scattering length density"], ["sld_solvent", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Solvent scattering length density"], ["length_a", "Ang", 35, [0, inf], "volume", "Shorter side of the parallelepiped"], ["b2a_ratio", "", 1, [0, inf], "volume", "Ratio sides b/a"], ["c2a_ratio", "", 1, [0, inf], "volume", "Ratio sides c/a"], ] source = ["lib/gauss76.c", "rectangular_prism.c"] def ER(length_a, b2a_ratio, c2a_ratio): """ Return equivalent radius (ER) """ b_side = length_a * b2a_ratio c_side = length_a * c2a_ratio # surface average radius (rough approximation) surf_rad = sqrt(length_a * b_side / pi) ddd = 0.75 * surf_rad * (2 * surf_rad * c_side + (c_side + surf_rad) * (c_side + pi * surf_rad)) return 0.5 * (ddd) ** (1. / 3.) def random(): import numpy as np a, b, c = 10**np.random.uniform(1, 4.7, size=3) pars = dict( length_a=a, b2a_ratio=b/a, c2a_ratio=c/a, ) return pars # parameters for demo demo = dict(scale=1, background=0, sld=6.3, sld_solvent=1.0, length_a=35, b2a_ratio=1, c2a_ratio=1, length_a_pd=0.1, length_a_pd_n=10, b2a_ratio_pd=0.1, b2a_ratio_pd_n=1, c2a_ratio_pd=0.1, c2a_ratio_pd_n=1) tests = [[{}, 0.2, 0.375248406825], [{}, [0.2], [0.375248406825]], ] sasmodels/sasmodels/models/ref/000077500000000000000000000000001317715334700171145ustar00rootroot00000000000000sasmodels/sasmodels/models/ref/NIST_IGOR_SANS_Model_Docs_v4.10.pdf000066400000000000000000311457211317715334700247660ustar00rootroot00000000000000%PDF-1.3 % 4 0 obj << /Length 5 0 R /Filter /FlateDecode >> stream x\ےFr}WT#U[{Zk74[?`d7=$AZ|ԍ zBi^DV^Ofe7 e)8+ *<}٪g_:._~醪ķ{ `9}#OR\aޱfyģҤdM}rQ\"4OƷl$1Q ')L̥I7{\liv=M1}mݒtvdie'0G?wOHK"l22Ӫ rXav%v( s ,C(?t+%_"YoLfU6-Rw T#70߫yLLR.t"yxFw$6ۤnBOMфODKq H,(n) [Bi4|\Ay^f;="M,gzd D6ţ)F!&fw"7"OjOwKuxai oRyyB5 =d+p2sy!CJdb ޶W(=OkQݤeyNy*<F,aݑ-A#qg&U*]XѪ;ۭd)I?3!QIW(no0>>s2DD#ݶ%![i#n3 #@SIYjPy͐a i7强PEuR>U}pDu@LDY'U}'5BvY蝬{΁ڞe9P.!Nt9T8U ,(kIE]y5qa=,RH!߭vIӲi*m,ME}4C;Kt+8ֺf=g}3cuSX]znN!*:H+F~iHJJࡖnuAzneo5=)E^m_OܱuzW_NE7%4)N`ٵDJOTb~հ=W#ѭ3Z@AsZҕ 5|q4`bZ$R/|KJK⡇ALWW՗*C6x mWj_L`ӝ`=;]AO*v=C*z}i jwˮ=+ZOY. -H.ƨɭn 0f{)nP$+kN28w@dai 7 J=y\hY#UXZ3Rrn{ !~|H%`i/kZ>]VMd^wJdeAAd; 3F!C*V'v=TB2b 5',mFZ.쁦h<2 T$T,l:*m*J]w&,d H[<vE2B4<7JTsVLMY 7lP>Xݾ5R A) oe*ThZ_?fyCj5*S3`vZ];A| 0QܸV@Sl0jz6Yg[BlgEG O_&xJ%>w0{ڃ޵j32ؐAĚM-1>i;LjQ듾Ӱ/l}Q/3vOwͩ>pH%~vM՟JKY ]9>zF:KCgI{b<. $"_˿[iV|gvnUMAP>,ҝ+*ST{:8Ǘ=jp X+$V$|fKPFl@4K dRQڤtdNJ~c*;LzE!#~,kCs'Qn6.j* #֫\{W2ۯJP /A)/]*hgLd[VM:,Q7zWnY`# 9M63:]CdDFEi{NBnȾٻβ(|@C?ی63 ziaˢK+4_ym.>&OJ# zN"R` SөryNu羚$/A^ ]D&URmPaD^`wN(2׾ݯn;q/Sqqw 'Idgdl !E^p3gBcjxC=|=Ӗcs6ԇw;HE MMQmٱ2 4z NН5`-~g2cCqxTyYD0kY&G[)嘰:NF#4zk;&7 2aWIZ2DXˠ(В]go#\cD|-csC?,ȰV =[To5 3 yC"uvlA__B^urrj!Z`TǴ[#+UE {![oל}T VmAU0${잰sfյl|4xCu9mLI{P*7[Ц"(1q~3vD)\oGm[vg4^-fפ P G/C8s{Ԓ$+Z 1W/j}FjK/9 }; c쥣)Wt?dJ{cMˉ0䅣qsWzSUйB;X47/_oF"s8e"TV큎? `+W3 L9d1YbOL*6t@y^#)v$7^3~5^,Dr:g5N:.ӆKpAۜ_68€Yq=@"da[v8)R$x&,GKY@RZyfXG9Q9O'i }ًh\!vUh=Su[S0G;ǝEŠS7";1>A05Lsy)yH8I*|j|PWÊA{7 v5B^-@蜆{c4c,~+8?uk@iCxդ)mm@:y,>5qdrEN-010macIiҹΞfԵF:Q6|laSRj3oaRo.RezCkpx9y@AC4vXfcoÌ'3G5E-BB^~\ja{̧M_~'_™pyGTMCCe$p|`K*QJ.]57#D,67fU [i!@aNMb&X&D 6}d/hWMa2pԆWWznri,IÃ;?wiۣﭽM93>-׋BkA'#."ѫ+B鑒k`0fBrGn8ۣ&&9T=dT_/@ C"!:PEDHa K;8V}^W :hvpVt2~dXmSZA:k& *9D_Z endstream endobj 5 0 obj 5421 endobj 2 0 obj << /Type /Page /Parent 3 0 R /Resources 6 0 R /Contents 4 0 R /MediaBox [0 0 612 792] >> endobj 6 0 obj << /ProcSet [ /PDF /Text ] /ColorSpace << /Cs1 7 0 R >> /Font << /F1.0 8 0 R >> >> endobj 9 0 obj << /Length 10 0 R /N 3 /Alternate /DeviceRGB /Filter /FlateDecode >> stream xwTSϽ7" %z ;HQIP&vDF)VdTG"cE b PQDE݌k 5ޚYg}׺PtX4X\XffGD=HƳ.d,P&s"7C$ E6<~&S2)212 "įl+ɘ&Y4Pޚ%ᣌ\%g|eTI(L0_&l2E9r9hxgIbטifSb1+MxL 0oE%YmhYh~S=zU&ϞAYl/$ZUm@O ޜl^ ' lsk.+7oʿ9V;?#I3eE妧KD d9i,UQ h A1vjpԁzN6p\W p G@ K0ށiABZyCAP8C@&*CP=#t] 4}a ٰ;GDxJ>,_“@FXDBX$!k"EHqaYbVabJ0՘cVL6f3bձX'?v 6-V``[a;p~\2n5׌ &x*sb|! ߏƿ' Zk! $l$T4QOt"y\b)AI&NI$R$)TIj"]&=&!:dGrY@^O$ _%?P(&OJEBN9J@y@yCR nXZOD}J}/G3ɭk{%Oחw_.'_!JQ@SVF=IEbbbb5Q%O@%!BӥyҸM:e0G7ӓ e%e[(R0`3R46i^)*n*|"fLUo՝mO0j&jajj.ϧwϝ_4갺zj=U45nɚ4ǴhZ ZZ^0Tf%9->ݫ=cXgN].[7A\SwBOK/X/_Q>QG[ `Aaac#*Z;8cq>[&IIMST`ϴ kh&45ǢYYF֠9<|y+ =X_,,S-,Y)YXmĚk]c}džjcΦ浭-v};]N"&1=xtv(}'{'IߝY) Σ -rqr.d._xpUەZM׍vm=+KGǔ ^WWbj>:>>>v}/avO8 FV> 2 u/_$\BCv< 5 ]s.,4&yUx~xw-bEDCĻHGKwFGEGME{EEKX,YFZ ={$vrK .3\rϮ_Yq*©L_wד+]eD]cIIIOAu_䩔)3ѩiB%a+]3='/40CiU@ёL(sYfLH$%Y jgGeQn~5f5wugv5k֮\۹Nw]m mHFˍenQQ`hBBQ-[lllfjۗ"^bO%ܒY}WwvwXbY^Ю]WVa[q`id2JjGէ{׿m>PkAma꺿g_DHGGu;776ƱqoC{P38!9 ҝˁ^r۽Ug9];}}_~imp㭎}]/}.{^=}^?z8hc' O*?f`ϳgC/Oϩ+FFGGόzˌㅿ)ѫ~wgbk?Jި9mdwi獵ޫ?cǑOO?w| x&mf endstream endobj 10 0 obj 2612 endobj 7 0 obj [ /ICCBased 9 0 R ] endobj 12 0 obj << /Length 13 0 R /Filter /FlateDecode >> stream x\Ks8WHז|1d2ص{A56Hd__HA=S%! 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00000 n 0006546072 00000 n 0006546479 00000 n 0006546668 00000 n 0006566341 00000 n 0006566365 00000 n 0006566619 00000 n 0006567366 00000 n 0006567412 00000 n 0006567466 00000 n 0006567498 00000 n 0006567519 00000 n 0006567548 00000 n 0006567592 00000 n 0006567613 00000 n trailer << /Size 1889 /Root 1866 0 R /Info 1 0 R /ID [ ] >> startxref 6567831 %%EOF sasmodels/sasmodels/models/rpa.c000066400000000000000000000441341317715334700172740ustar00rootroot00000000000000double Iq(double q, double fp_case_num, double N[], double Phi[], double v[], double L[], double b[], double Kab, double Kac, double Kad, double Kbc, double Kbd, double Kcd ); double Iq(double q, double fp_case_num, double N[], // DEGREE OF POLYMERIZATION double Phi[], // VOL FRACTION double v[], // SPECIFIC VOLUME double L[], // SCATT. LENGTH double b[], // SEGMENT LENGTH double Kab, double Kac, double Kad, // CHI PARAM double Kbc, double Kbd, double Kcd ) { int icase = (int)(fp_case_num+0.5); double Nab,Nac,Nad,Nbc,Nbd,Ncd; double Phiab,Phiac,Phiad,Phibc,Phibd,Phicd; double vab,vac,vad,vbc,vbd,vcd; double m; double Xa,Xb,Xc,Xd; double Paa,S0aa,Pab,S0ab,Pac,S0ac,Pad,S0ad; double S0ba,Pbb,S0bb,Pbc,S0bc,Pbd,S0bd; double S0ca,S0cb,Pcc,S0cc,Pcd,S0cd; double S0da,S0db,S0dc; double Pdd,S0dd; double Kaa,Kbb,Kcc; double Kba,Kca,Kcb; double Kda,Kdb,Kdc,Kdd; double Zaa,Zab,Zac,Zba,Zbb,Zbc,Zca,Zcb,Zcc; double DenT,T11,T12,T13,T21,T22,T23,T31,T32,T33; double Y1,Y2,Y3,X11,X12,X13,X21,X22,X23,X31,X32,X33; double ZZ,DenQ1,DenQ2,DenQ3,DenQ,Q11,Q12,Q13,Q21,Q22,Q23,Q31,Q32,Q33; double N11,N12,N13,N21,N22,N23,N31,N32,N33; double M11,M12,M13,M21,M22,M23,M31,M32,M33; double S11,S12,S13,S14,S21,S22,S23,S24; double S31,S32,S33,S34,S41,S42,S43,S44; double Lad,Lbd,Lcd,Nav,Intg; // Set values for non existent parameters (eg. no A or B in case 0 and 1 etc) //icase was shifted to N-1 from the original code if (icase <= 1){ Phi[0] = Phi[1] = 0.0000001; N[0] = N[1] = 1000.0; L[0] = L[1] = 1.e-12; v[0] = v[1] = 100.0; b[0] = b[1] = 5.0; Kab = Kac = Kad = Kbc = Kbd = -0.0004; } else if ((icase > 1) && (icase <= 4)){ Phi[0] = 0.0000001; N[0] = 1000.0; L[0] = 1.e-12; v[0] = 100.0; b[0] = 5.0; Kab = Kac = Kad = -0.0004; } // Set volume fraction of component D based on constraint that sum of vol frac =1 Phi[3]=1.0-Phi[0]-Phi[1]-Phi[2]; //set up values for cross terms in case of block copolymers (1,3,4,6,7,8,9) Nab=sqrt(N[0]*N[1]); Nac=sqrt(N[0]*N[2]); Nad=sqrt(N[0]*N[3]); Nbc=sqrt(N[1]*N[2]); Nbd=sqrt(N[1]*N[3]); Ncd=sqrt(N[2]*N[3]); vab=sqrt(v[0]*v[1]); vac=sqrt(v[0]*v[2]); vad=sqrt(v[0]*v[3]); vbc=sqrt(v[1]*v[2]); vbd=sqrt(v[1]*v[3]); vcd=sqrt(v[2]*v[3]); Phiab=sqrt(Phi[0]*Phi[1]); Phiac=sqrt(Phi[0]*Phi[2]); Phiad=sqrt(Phi[0]*Phi[3]); Phibc=sqrt(Phi[1]*Phi[2]); Phibd=sqrt(Phi[1]*Phi[3]); Phicd=sqrt(Phi[2]*Phi[3]); // Calculate Q^2 * Rg^2 for each homopolymer assuming random walk Xa=q*q*b[0]*b[0]*N[0]/6.0; Xb=q*q*b[1]*b[1]*N[1]/6.0; Xc=q*q*b[2]*b[2]*N[2]/6.0; Xd=q*q*b[3]*b[3]*N[3]/6.0; //calculate all partial structure factors Pij and normalize n^2 Paa=2.0*(exp(-Xa)-1.0+Xa)/(Xa*Xa); // free A chain form factor S0aa=N[0]*Phi[0]*v[0]*Paa; // Phi * Vp * P(Q)= I(Q0)/delRho^2 Pab=((1.0-exp(-Xa))/Xa)*((1.0-exp(-Xb))/Xb); //AB diblock (anchored Paa * anchored Pbb) partial form factor S0ab=(Phiab*vab*Nab)*Pab; Pac=((1.0-exp(-Xa))/Xa)*exp(-Xb)*((1.0-exp(-Xc))/Xc); //ABC triblock AC partial form factor S0ac=(Phiac*vac*Nac)*Pac; Pad=((1.0-exp(-Xa))/Xa)*exp(-Xb-Xc)*((1.0-exp(-Xd))/Xd); //ABCD four block S0ad=(Phiad*vad*Nad)*Pad; S0ba=S0ab; Pbb=2.0*(exp(-Xb)-1.0+Xb)/(Xb*Xb); // free B chain S0bb=N[1]*Phi[1]*v[1]*Pbb; Pbc=((1.0-exp(-Xb))/Xb)*((1.0-exp(-Xc))/Xc); // BC diblock S0bc=(Phibc*vbc*Nbc)*Pbc; Pbd=((1.0-exp(-Xb))/Xb)*exp(-Xc)*((1.0-exp(-Xd))/Xd); // BCD triblock S0bd=(Phibd*vbd*Nbd)*Pbd; S0ca=S0ac; S0cb=S0bc; Pcc=2.0*(exp(-Xc)-1.0+Xc)/(Xc*Xc); // Free C chain S0cc=N[2]*Phi[2]*v[2]*Pcc; Pcd=((1.0-exp(-Xc))/Xc)*((1.0-exp(-Xd))/Xd); // CD diblock S0cd=(Phicd*vcd*Ncd)*Pcd; S0da=S0ad; S0db=S0bd; S0dc=S0cd; Pdd=2.0*(exp(-Xd)-1.0+Xd)/(Xd*Xd); // free D chain S0dd=N[3]*Phi[3]*v[3]*Pdd; // Reset all unused partial structure factors to 0 (depends on case) //icase was shifted to N-1 from the original code switch(icase){ case 0: S0aa=0.000001; S0ab=0.000002; S0ac=0.000003; S0ad=0.000004; S0bb=0.000005; S0bc=0.000006; S0bd=0.000007; S0cd=0.000008; break; case 1: S0aa=0.000001; S0ab=0.000002; S0ac=0.000003; S0ad=0.000004; S0bb=0.000005; S0bc=0.000006; S0bd=0.000007; break; case 2: S0aa=0.000001; S0ab=0.000002; S0ac=0.000003; S0ad=0.000004; S0bc=0.000005; S0bd=0.000006; S0cd=0.000007; break; case 3: S0aa=0.000001; S0ab=0.000002; S0ac=0.000003; S0ad=0.000004; S0bc=0.000005; S0bd=0.000006; break; case 4: S0aa=0.000001; S0ab=0.000002; S0ac=0.000003; S0ad=0.000004; break; case 5: S0ab=0.000001; S0ac=0.000002; S0ad=0.000003; S0bc=0.000004; S0bd=0.000005; S0cd=0.000006; break; case 6: S0ab=0.000001; S0ac=0.000002; S0ad=0.000003; S0bc=0.000004; S0bd=0.000005; break; case 7: S0ab=0.000001; S0ac=0.000002; S0ad=0.000003; break; case 8: S0ac=0.000001; S0ad=0.000002; S0bc=0.000003; S0bd=0.000004; break; default : //case 9: break; } S0ba=S0ab; S0ca=S0ac; S0cb=S0bc; S0da=S0ad; S0db=S0bd; S0dc=S0cd; // self chi parameter is 0 ... of course Kaa=0.0; Kbb=0.0; Kcc=0.0; Kdd=0.0; Kba=Kab; Kca=Kac; Kcb=Kbc; Kda=Kad; Kdb=Kbd; Kdc=Kcd; Zaa=Kaa-Kad-Kad; Zab=Kab-Kad-Kbd; Zac=Kac-Kad-Kcd; Zba=Kba-Kbd-Kad; Zbb=Kbb-Kbd-Kbd; Zbc=Kbc-Kbd-Kcd; Zca=Kca-Kcd-Kad; Zcb=Kcb-Kcd-Kbd; Zcc=Kcc-Kcd-Kcd; DenT=(-(S0ac*S0bb*S0ca) + S0ab*S0bc*S0ca + S0ac*S0ba*S0cb - S0aa*S0bc*S0cb - S0ab*S0ba*S0cc + S0aa*S0bb*S0cc); T11= (-(S0bc*S0cb) + S0bb*S0cc)/DenT; T12= (S0ac*S0cb - S0ab*S0cc)/DenT; T13= (-(S0ac*S0bb) + S0ab*S0bc)/DenT; T21= (S0bc*S0ca - S0ba*S0cc)/DenT; T22= (-(S0ac*S0ca) + S0aa*S0cc)/DenT; T23= (S0ac*S0ba - S0aa*S0bc)/DenT; T31= (-(S0bb*S0ca) + S0ba*S0cb)/DenT; T32= (S0ab*S0ca - S0aa*S0cb)/DenT; T33= (-(S0ab*S0ba) + S0aa*S0bb)/DenT; Y1=T11*S0ad+T12*S0bd+T13*S0cd+1.0; Y2=T21*S0ad+T22*S0bd+T23*S0cd+1.0; Y3=T31*S0ad+T32*S0bd+T33*S0cd+1.0; X11=Y1*Y1; X12=Y1*Y2; X13=Y1*Y3; X21=Y2*Y1; X22=Y2*Y2; X23=Y2*Y3; X31=Y3*Y1; X32=Y3*Y2; X33=Y3*Y3; ZZ=S0ad*(T11*S0ad+T12*S0bd+T13*S0cd)+S0bd*(T21*S0ad+T22*S0bd+T23*S0cd)+S0cd*(T31*S0ad+T32*S0bd+T33*S0cd); // D is considered the matrix or background component so enters here m=1.0/(S0dd-ZZ); N11=m*X11+Zaa; N12=m*X12+Zab; N13=m*X13+Zac; N21=m*X21+Zba; N22=m*X22+Zbb; N23=m*X23+Zbc; N31=m*X31+Zca; N32=m*X32+Zcb; N33=m*X33+Zcc; M11= N11*S0aa + N12*S0ab + N13*S0ac; M12= N11*S0ab + N12*S0bb + N13*S0bc; M13= N11*S0ac + N12*S0bc + N13*S0cc; M21= N21*S0aa + N22*S0ab + N23*S0ac; M22= N21*S0ab + N22*S0bb + N23*S0bc; M23= N21*S0ac + N22*S0bc + N23*S0cc; M31= N31*S0aa + N32*S0ab + N33*S0ac; M32= N31*S0ab + N32*S0bb + N33*S0bc; M33= N31*S0ac + N32*S0bc + N33*S0cc; DenQ1=1.0+M11-M12*M21+M22+M11*M22-M13*M31-M13*M22*M31; DenQ2= M12*M23*M31+M13*M21*M32-M23*M32-M11*M23*M32+M33+M11*M33; DenQ3= -M12*M21*M33+M22*M33+M11*M22*M33; DenQ=DenQ1+DenQ2+DenQ3; Q11= (1.0 + M22-M23*M32 + M33 + M22*M33)/DenQ; Q12= (-M12 + M13*M32 - M12*M33)/DenQ; Q13= (-M13 - M13*M22 + M12*M23)/DenQ; Q21= (-M21 + M23*M31 - M21*M33)/DenQ; Q22= (1.0 + M11 - M13*M31 + M33 + M11*M33)/DenQ; Q23= (M13*M21 - M23 - M11*M23)/DenQ; Q31= (-M31 - M22*M31 + M21*M32)/DenQ; Q32= (M12*M31 - M32 - M11*M32)/DenQ; Q33= (1.0 + M11 - M12*M21 + M22 + M11*M22)/DenQ; S11= Q11*S0aa + Q21*S0ab + Q31*S0ac; S12= Q12*S0aa + Q22*S0ab + Q32*S0ac; S13= Q13*S0aa + Q23*S0ab + Q33*S0ac; S14=-S11-S12-S13; S21= Q11*S0ba + Q21*S0bb + Q31*S0bc; S22= Q12*S0ba + Q22*S0bb + Q32*S0bc; S23= Q13*S0ba + Q23*S0bb + Q33*S0bc; S24=-S21-S22-S23; S31= Q11*S0ca + Q21*S0cb + Q31*S0cc; S32= Q12*S0ca + Q22*S0cb + Q32*S0cc; S33= Q13*S0ca + Q23*S0cb + Q33*S0cc; S34=-S31-S32-S33; S41=S14; S42=S24; S43=S34; S44=S11+S22+S33+2.0*S12+2.0*S13+2.0*S23; //calculate contrast where L[i] is the scattering length of i and D is the matrix //Note that should multiply by Nav to get units of SLD which will become // Nav*2 in the next line (SLD^2) but then normalization in that line would //need to divide by Nav leaving only Nav or sqrt(Nav) before squaring. Nav=6.022045e+23; Lad=(L[0]/v[0]-L[3]/v[3])*sqrt(Nav); Lbd=(L[1]/v[1]-L[3]/v[3])*sqrt(Nav); Lcd=(L[2]/v[2]-L[3]/v[3])*sqrt(Nav); Intg=Lad*Lad*S11+Lbd*Lbd*S22+Lcd*Lcd*S33+2.0*Lad*Lbd*S12+2.0*Lbd*Lcd*S23+2.0*Lad*Lcd*S13; //rescale for units of Lij^2 (fm^2 to cm^2) Intg *= 1.0e-26; return Intg; /* Attempts at a new implementation --- supressed for now #if 1 // Sasview defaults if (icase <= 1) { N[0]=N[1]=1000.0; Phi[0]=Phi[1]=0.0000001; Kab=Kac=Kad=Kbc=Kbd=-0.0004; L[0]=L[1]=1.0e-12; v[0]=v[1]=100.0; b[0]=b[1]=5.0; } else if (icase <= 4) { Phi[0]=0.0000001; Kab=Kac=Kad=-0.0004; L[0]=1.0e-12; v[0]=100.0; b[0]=5.0; } #else if (icase <= 1) { N[0]=N[1]=0.0; Phi[0]=Phi[1]=0.0; Kab=Kac=Kad=Kbc=Kbd=0.0; L[0]=L[1]=L[3]; v[0]=v[1]=v[3]; b[0]=b[1]=0.0; } else if (icase <= 4) { N[0] = 0.0; Phi[0]=0.0; Kab=Kac=Kad=0.0; L[0]=L[3]; v[0]=v[3]; b[0]=0.0; } #endif const double Xa = q*q*b[0]*b[0]*N[0]/6.0; const double Xb = q*q*b[1]*b[1]*N[1]/6.0; const double Xc = q*q*b[2]*b[2]*N[2]/6.0; const double Xd = q*q*b[3]*b[3]*N[3]/6.0; // limit as Xa goes to 0 is 1 const double Pa = Xa==0 ? 1.0 : -expm1(-Xa)/Xa; const double Pb = Xb==0 ? 1.0 : -expm1(-Xb)/Xb; const double Pc = Xc==0 ? 1.0 : -expm1(-Xc)/Xc; const double Pd = Xd==0 ? 1.0 : -expm1(-Xd)/Xd; // limit as Xa goes to 0 is 1 const double Paa = Xa==0 ? 1.0 : 2.0*(1.0-Pa)/Xa; const double Pbb = Xb==0 ? 1.0 : 2.0*(1.0-Pb)/Xb; const double Pcc = Xc==0 ? 1.0 : 2.0*(1.0-Pc)/Xc; const double Pdd = Xd==0 ? 1.0 : 2.0*(1.0-Pd)/Xd; // Note: S0ij only defined for copolymers; otherwise set to zero // 0: C/D binary mixture // 1: C-D diblock copolymer // 2: B/C/D ternery mixture // 3: B/C-D binary mixture,1 homopolymer, 1 diblock copolymer // 4: B-C-D triblock copolymer // 5: A/B/C/D quaternary mixture // 6: A/B/C-D ternery mixture, 2 homopolymer, 1 diblock copolymer // 7: A/B-C-D binary mixture, 1 homopolymer, 1 triblock copolymer // 8: A-B/C-D binary mixture, 2 diblock copolymer // 9: A-B-C-D tetra-block copolymer #if 0 const double S0aa = icase<5 ? 1.0 : N[0]*Phi[0]*v[0]*Paa; const double S0bb = icase<2 ? 1.0 : N[1]*Phi[1]*v[1]*Pbb; const double S0cc = N[2]*Phi[2]*v[2]*Pcc; const double S0dd = N[3]*Phi[3]*v[3]*Pdd; const double S0ab = icase<8 ? 0.0 : sqrt(N[0]*v[0]*Phi[0]*N[1]*v[1]*Phi[1])*Pa*Pb; const double S0ac = icase<9 ? 0.0 : sqrt(N[0]*v[0]*Phi[0]*N[2]*v[2]*Phi[2])*Pa*Pc*exp(-Xb); const double S0ad = icase<9 ? 0.0 : sqrt(N[0]*v[0]*Phi[0]*N[3]*v[3]*Phi[3])*Pa*Pd*exp(-Xb-Xc); const double S0bc = (icase!=4 && icase!=7 && icase!= 9) ? 0.0 : sqrt(N[1]*v[1]*Phi[1]*N[2]*v[2]*Phi[2])*Pb*Pc; const double S0bd = (icase!=4 && icase!=7 && icase!= 9) ? 0.0 : sqrt(N[1]*v[1]*Phi[1]*N[3]*v[3]*Phi[3])*Pb*Pd*exp(-Xc); const double S0cd = (icase==0 || icase==2 || icase==5) ? 0.0 : sqrt(N[2]*v[2]*Phi[2]*N[3]*v[3]*Phi[3])*Pc*Pd; #else // sasview equivalent //printf("Xc=%g, S0cc=%g*%g*%g*%g\n",Xc,N[2],Phi[2],v[2],Pcc); double S0aa = N[0]*Phi[0]*v[0]*Paa; double S0bb = N[1]*Phi[1]*v[1]*Pbb; double S0cc = N[2]*Phi[2]*v[2]*Pcc; double S0dd = N[3]*Phi[3]*v[3]*Pdd; double S0ab = sqrt(N[0]*v[0]*Phi[0]*N[1]*v[1]*Phi[1])*Pa*Pb; double S0ac = sqrt(N[0]*v[0]*Phi[0]*N[2]*v[2]*Phi[2])*Pa*Pc*exp(-Xb); double S0ad = sqrt(N[0]*v[0]*Phi[0]*N[3]*v[3]*Phi[3])*Pa*Pd*exp(-Xb-Xc); double S0bc = sqrt(N[1]*v[1]*Phi[1]*N[2]*v[2]*Phi[2])*Pb*Pc; double S0bd = sqrt(N[1]*v[1]*Phi[1]*N[3]*v[3]*Phi[3])*Pb*Pd*exp(-Xc); double S0cd = sqrt(N[2]*v[2]*Phi[2]*N[3]*v[3]*Phi[3])*Pc*Pd; switch(icase){ case 0: S0aa=0.000001; S0ab=0.000002; S0ac=0.000003; S0ad=0.000004; S0bb=0.000005; S0bc=0.000006; S0bd=0.000007; S0cd=0.000008; break; case 1: S0aa=0.000001; S0ab=0.000002; S0ac=0.000003; S0ad=0.000004; S0bb=0.000005; S0bc=0.000006; S0bd=0.000007; break; case 2: S0aa=0.000001; S0ab=0.000002; S0ac=0.000003; S0ad=0.000004; S0bc=0.000005; S0bd=0.000006; S0cd=0.000007; break; case 3: S0aa=0.000001; S0ab=0.000002; S0ac=0.000003; S0ad=0.000004; S0bc=0.000005; S0bd=0.000006; break; case 4: S0aa=0.000001; S0ab=0.000002; S0ac=0.000003; S0ad=0.000004; break; case 5: S0ab=0.000001; S0ac=0.000002; S0ad=0.000003; S0bc=0.000004; S0bd=0.000005; S0cd=0.000006; break; case 6: S0ab=0.000001; S0ac=0.000002; S0ad=0.000003; S0bc=0.000004; S0bd=0.000005; break; case 7: S0ab=0.000001; S0ac=0.000002; S0ad=0.000003; break; case 8: S0ac=0.000001; S0ad=0.000002; S0bc=0.000003; S0bd=0.000004; break; default : //case 9: break; } #endif // eq 12a: \kappa_{ij}^F = \chi_{ij}^F - \chi_{i0}^F - \chi_{j0}^F const double Kaa = 0.0; const double Kbb = 0.0; const double Kcc = 0.0; //const double Kdd = 0.0; const double Zaa = Kaa - Kad - Kad; const double Zab = Kab - Kad - Kbd; const double Zac = Kac - Kad - Kcd; const double Zbb = Kbb - Kbd - Kbd; const double Zbc = Kbc - Kbd - Kcd; const double Zcc = Kcc - Kcd - Kcd; //printf("Za: %10.5g %10.5g %10.5g\n", Zaa, Zab, Zac); //printf("Zb: %10.5g %10.5g %10.5g\n", Zab, Zbb, Zbc); //printf("Zc: %10.5g %10.5g %10.5g\n", Zac, Zbc, Zcc); // T = inv(S0) const double DenT = (- S0ac*S0bb*S0ac + S0ab*S0bc*S0ac + S0ac*S0ab*S0bc - S0aa*S0bc*S0bc - S0ab*S0ab*S0cc + S0aa*S0bb*S0cc); const double T11 = (-S0bc*S0bc + S0bb*S0cc)/DenT; const double T12 = ( S0ac*S0bc - S0ab*S0cc)/DenT; const double T13 = (-S0ac*S0bb + S0ab*S0bc)/DenT; const double T22 = (-S0ac*S0ac + S0aa*S0cc)/DenT; const double T23 = ( S0ac*S0ab - S0aa*S0bc)/DenT; const double T33 = (-S0ab*S0ab + S0aa*S0bb)/DenT; //printf("T1: %10.5g %10.5g %10.5g\n", T11, T12, T13); //printf("T2: %10.5g %10.5g %10.5g\n", T12, T22, T23); //printf("T3: %10.5g %10.5g %10.5g\n", T13, T23, T33); // eq 18e: m = 1/(S0_{dd} - s0^T inv(S0) s0) const double ZZ = S0ad*(T11*S0ad + T12*S0bd + T13*S0cd) + S0bd*(T12*S0ad + T22*S0bd + T23*S0cd) + S0cd*(T13*S0ad + T23*S0bd + T33*S0cd); const double m=1.0/(S0dd-ZZ); // eq 18d: Y = inv(S0)s0 + e const double Y1 = T11*S0ad + T12*S0bd + T13*S0cd + 1.0; const double Y2 = T12*S0ad + T22*S0bd + T23*S0cd + 1.0; const double Y3 = T13*S0ad + T23*S0bd + T33*S0cd + 1.0; // N = mYY^T + \kappa^F const double N11 = m*Y1*Y1 + Zaa; const double N12 = m*Y1*Y2 + Zab; const double N13 = m*Y1*Y3 + Zac; const double N22 = m*Y2*Y2 + Zbb; const double N23 = m*Y2*Y3 + Zbc; const double N33 = m*Y3*Y3 + Zcc; //printf("N1: %10.5g %10.5g %10.5g\n", N11, N12, N13); //printf("N2: %10.5g %10.5g %10.5g\n", N12, N22, N23); //printf("N3: %10.5g %10.5g %10.5g\n", N13, N23, N33); //printf("S0a: %10.5g %10.5g %10.5g\n", S0aa, S0ab, S0ac); //printf("S0b: %10.5g %10.5g %10.5g\n", S0ab, S0bb, S0bc); //printf("S0c: %10.5g %10.5g %10.5g\n", S0ac, S0bc, S0cc); // M = I + S0 N const double Maa = N11*S0aa + N12*S0ab + N13*S0ac + 1.0; const double Mab = N11*S0ab + N12*S0bb + N13*S0bc; const double Mac = N11*S0ac + N12*S0bc + N13*S0cc; const double Mba = N12*S0aa + N22*S0ab + N23*S0ac; const double Mbb = N12*S0ab + N22*S0bb + N23*S0bc + 1.0; const double Mbc = N12*S0ac + N22*S0bc + N23*S0cc; const double Mca = N13*S0aa + N23*S0ab + N33*S0ac; const double Mcb = N13*S0ab + N23*S0bb + N33*S0bc; const double Mcc = N13*S0ac + N23*S0bc + N33*S0cc + 1.0; //printf("M1: %10.5g %10.5g %10.5g\n", Maa, Mab, Mac); //printf("M2: %10.5g %10.5g %10.5g\n", Mba, Mbb, Mbc); //printf("M3: %10.5g %10.5g %10.5g\n", Mca, Mcb, Mcc); // Q = inv(M) = inv(I + S0 N) const double DenQ = (+ Maa*Mbb*Mcc - Maa*Mbc*Mcb - Mab*Mba*Mcc + Mab*Mbc*Mca + Mac*Mba*Mcb - Mac*Mbb*Mca); const double Q11 = ( Mbb*Mcc - Mbc*Mcb)/DenQ; const double Q12 = (-Mab*Mcc + Mac*Mcb)/DenQ; const double Q13 = ( Mab*Mbc - Mac*Mbb)/DenQ; //const double Q21 = (-Mba*Mcc + Mbc*Mca)/DenQ; const double Q22 = ( Maa*Mcc - Mac*Mca)/DenQ; const double Q23 = (-Maa*Mbc + Mac*Mba)/DenQ; //const double Q31 = ( Mba*Mcb - Mbb*Mca)/DenQ; //const double Q32 = (-Maa*Mcb + Mab*Mca)/DenQ; const double Q33 = ( Maa*Mbb - Mab*Mba)/DenQ; //printf("Q1: %10.5g %10.5g %10.5g\n", Q11, Q12, Q13); //printf("Q2: %10.5g %10.5g %10.5g\n", Q21, Q22, Q23); //printf("Q3: %10.5g %10.5g %10.5g\n", Q31, Q32, Q33); // eq 18c: inv(S) = inv(S0) + mYY^T + \kappa^F // eq A1 in the appendix // To solve for S, use: // S = inv(inv(S^0) + N) inv(S^0) S^0 // = inv(S^0 inv(S^0) + N) S^0 // = inv(I + S^0 N) S^0 // = Q S^0 const double S11 = Q11*S0aa + Q12*S0ab + Q13*S0ac; const double S12 = Q12*S0aa + Q22*S0ab + Q23*S0ac; const double S13 = Q13*S0aa + Q23*S0ab + Q33*S0ac; const double S22 = Q12*S0ab + Q22*S0bb + Q23*S0bc; const double S23 = Q13*S0ab + Q23*S0bb + Q33*S0bc; const double S33 = Q13*S0ac + Q23*S0bc + Q33*S0cc; // If the full S is needed...it isn't since Ldd = (rho_d - rho_d) = 0 below //const double S14=-S11-S12-S13; //const double S24=-S12-S22-S23; //const double S34=-S13-S23-S33; //const double S44=S11+S22+S33 + 2.0*(S12+S13+S23); // eq 12 of Akcasu, 1990: I(q) = L^T S L // Note: eliminate cases without A and B polymers by setting Lij to 0 // Note: 1e-13 to convert from fm to cm for scattering length const double sqrt_Nav=sqrt(6.022045e+23) * 1.0e-13; const double Lad = icase<5 ? 0.0 : (L[0]/v[0] - L[3]/v[3])*sqrt_Nav; const double Lbd = icase<2 ? 0.0 : (L[1]/v[1] - L[3]/v[3])*sqrt_Nav; const double Lcd = (L[2]/v[2] - L[3]/v[3])*sqrt_Nav; const double result=Lad*Lad*S11 + Lbd*Lbd*S22 + Lcd*Lcd*S33 + 2.0*(Lad*Lbd*S12 + Lbd*Lcd*S23 + Lad*Lcd*S13); return result; */ } sasmodels/sasmodels/models/rpa.py000066400000000000000000000124031317715334700174740ustar00rootroot00000000000000r""" Definition ---------- Calculates the macroscopic scattering intensity for a multi-component homogeneous mixture of polymers using the Random Phase Approximation. This general formalism contains 10 specific cases Case 0: C/D binary mixture of homopolymers Case 1: C-D diblock copolymer Case 2: B/C/D ternary mixture of homopolymers Case 3: C/C-D mixture of a homopolymer B and a diblock copolymer C-D Case 4: B-C-D triblock copolymer Case 5: A/B/C/D quaternary mixture of homopolymers Case 6: A/B/C-D mixture of two homopolymers A/B and a diblock C-D Case 7: A/B-C-D mixture of a homopolymer A and a triblock B-C-D Case 8: A-B/C-D mixture of two diblock copolymers A-B and C-D Case 9: A-B-C-D tetra-block copolymer .. note:: These case numbers are different from those in the NIST SANS package! The models are based on the papers by Akcasu *et al.* and by Hammouda assuming the polymer follows Gaussian statistics such that $R_g^2 = n b^2/6$ where $b$ is the statistical segment length and $n$ is the number of statistical segment lengths. A nice tutorial on how these are constructed and implemented can be found in chapters 28 and 39 of Boualem Hammouda's 'SANS Toolbox'. In brief the macroscopic cross sections are derived from the general forms for homopolymer scattering and the multiblock cross-terms while the inter polymer cross terms are described in the usual way by the $\chi$ parameter. USAGE NOTES: * Only one case can be used at any one time. * The RPA (mean field) formalism only applies only when the multicomponent polymer mixture is in the homogeneous mixed-phase region. * **Component D is assumed to be the "background" component (ie, all contrasts are calculated with respect to component D).** So the scattering contrast for a C/D blend = [SLD(component C) - SLD(component D)]\ :sup:`2`. * Depending on which case is being used, the number of fitting parameters can vary. .. Note:: * In general the degrees of polymerization, the volume fractions, the molar volumes, and the neutron scattering lengths for each component are obtained from other methods and held fixed while The *scale* parameter should be held equal to unity. * The variables are normally the segment lengths ($b_a$, $b_b$, etc.) and $\chi$ parameters ($K_{ab}$, $K_{ac}$, etc). References ---------- A Z Akcasu, R Klein and B Hammouda, *Macromolecules*, 26 (1993) 4136. B. Hammouda, *Advances in Polymer Science* 106 (1993) 87. B. Hammouda, *SANS Toolbox* https://www.ncnr.nist.gov/staff/hammouda/the_sans_toolbox.pdf. Authorship and Verification ---------------------------- * **Author:** Boualem Hammouda - NIST IGOR/DANSE **Date:** pre 2010 * **Converted to sasmodels by:** Paul Kienzle **Date:** July 18, 2016 * **Last Modified by:** Paul Butler **Date:** March 12, 2017 * **Last Reviewed by:** Paul Butler **Date:** March 12, 2017 """ from numpy import inf name = "rpa" title = "Random Phase Approximation" description = """ This formalism applies to multicomponent polymer mixtures in the homogeneous (mixed) phase region only. Case 0: C/D binary mixture of homopolymers Case 1: C-D diblock copolymer Case 2: B/C/D ternary mixture of homopolymers Case 3: B/C-D mixture of homopolymer b and diblock copolymer C-D Case 4: B-C-D triblock copolymer Case 5: A/B/C/D quaternary mixture of homopolymers Case 6: A/B/C-D mixture of two homopolymers A/B and a diblock C-D Case 7: A/B-C-D mixture of a homopolymer A and a triblock B-C-D Case 8: A-B/C-D mixture of two diblock copolymers A-B and C-D Case 9: A-B-C-D four-block copolymer See details in the model function help """ category = "shape-independent" CASES = [ "C+D binary mixture", "C:D diblock copolymer", "B+C+D ternary mixture", "B+C:D binary mixture", "B:C:D triblock copolymer", "A+B+C+D quaternary mixture", "A+B+C:D ternary mixture", "A+B:C:D binary mixture", "A:B+C:D binary mixture", "A:B:C:D quadblock copolymer", ] # ["name", "units", default, [lower, upper], "type","description"], parameters = [ ["case_num", "", 1, [CASES], "", "Component organization"], ["N[4]", "", 1000.0, [1, inf], "", "Degree of polymerization"], ["Phi[4]", "", 0.25, [0, 1], "", "volume fraction"], ["v[4]", "mL/mol", 100.0, [0, inf], "", "molar volume"], ["L[4]", "fm", 10.0, [-inf, inf], "", "scattering length"], ["b[4]", "Ang", 5.0, [0, inf], "", "segment length"], ["K12", "", -0.0004, [-inf, inf], "", "A:B interaction parameter"], ["K13", "", -0.0004, [-inf, inf], "", "A:C interaction parameter"], ["K14", "", -0.0004, [-inf, inf], "", "A:D interaction parameter"], ["K23", "", -0.0004, [-inf, inf], "", "B:C interaction parameter"], ["K24", "", -0.0004, [-inf, inf], "", "B:D interaction parameter"], ["K34", "", -0.0004, [-inf, inf], "", "C:D interaction parameter"], ] source = ["rpa.c"] single = False control = "case_num" HIDE_ALL = set("Phi4".split()) HIDE_A = set("N1 Phi1 v1 L1 b1 K12 K13 K14".split()).union(HIDE_ALL) HIDE_AB = set("N2 Phi2 v2 L2 b2 K23 K24".split()).union(HIDE_A) def hidden(case_num): """ Return a list of parameters to hide depending on the multiplicity parameter. """ case_num = int(case_num+0.5) if case_num < 2: return HIDE_AB elif case_num < 5: return HIDE_A else: return HIDE_ALL sasmodels/sasmodels/models/sc_paracrystal.c000066400000000000000000000067301317715334700215240ustar00rootroot00000000000000double form_volume(double radius); double Iq(double q, double dnn, double d_factor, double radius, double sphere_sld, double solvent_sld); double Iqxy(double qx, double qy, double dnn, double d_factor, double radius, double sphere_sld, double solvent_sld, double theta, double phi, double psi); double form_volume(double radius) { return sphere_volume(radius); } static double sc_eval(double theta, double phi, double temp3, double temp4, double temp5) { double cnt, snt; SINCOS(theta, cnt, snt); double cnp, snp; SINCOS(phi, cnp, snp); double temp6 = snt; double temp7 = -1.0*temp3*snt*cnp; double temp8 = temp3*snt*snp; double temp9 = temp3*cnt; double result = temp6/((1.0-temp4*cos((temp7))+temp5)* (1.0-temp4*cos((temp8))+temp5)* (1.0-temp4*cos((temp9))+temp5)); return (result); } static double sc_integrand(double dnn, double d_factor, double qq, double xx, double yy) { //Function to calculate integrand values for simple cubic structure double da = d_factor*dnn; double temp1 = qq*qq*da*da; double temp2 = cube(-expm1(-temp1)); double temp3 = qq*dnn; double temp4 = 2.0*exp(-0.5*temp1); double temp5 = exp(-1.0*temp1); double integrand = temp2*sc_eval(yy,xx,temp3,temp4,temp5)/M_PI_2; return(integrand); } double Iq(double q, double dnn, double d_factor, double radius, double sphere_sld, double solvent_sld) { const double va = 0.0; const double vb = M_PI_2; //orientation average, outer integral double summ=0.0; double answer=0.0; for(int i=0;i<150;i++) { //setup inner integral over the ellipsoidal cross-section double summj=0.0; double zi = ( Gauss150Z[i]*(vb-va) + va + vb )/2.0; for(int j=0;j<150;j++) { //150 gauss points for the inner integral double zij = ( Gauss150Z[j]*(vb-va) + va + vb )/2.0; double tmp = Gauss150Wt[j] * sc_integrand(dnn,d_factor,q,zi,zij); summj += tmp; } //now calculate the value of the inner integral answer = (vb-va)/2.0*summj; //now calculate outer integral double tmp = Gauss150Wt[i] * answer; summ += tmp; } //final scaling is done at the end of the function, after the NT_FP64 case answer = (vb-va)/2.0*summ; //Volume fraction calculated from lattice symmetry and sphere radius // NB: 4/3 pi r^3 / dnn^3 = 4/3 pi(r/dnn)^3 const double latticeScale = sphere_volume(radius/dnn); answer *= sphere_form(q, radius, sphere_sld, solvent_sld)*latticeScale; return answer; } double Iqxy(double qx, double qy, double dnn, double d_factor, double radius, double sphere_sld, double solvent_sld, double theta, double phi, double psi) { double q, zhat, yhat, xhat; ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); const double qd = q*dnn; const double arg = 0.5*square(qd*d_factor); const double tanh_qd = tanh(arg); const double cosh_qd = cosh(arg); const double Zq = tanh_qd/(1. - cos(qd*zhat)/cosh_qd) * tanh_qd/(1. - cos(qd*yhat)/cosh_qd) * tanh_qd/(1. - cos(qd*xhat)/cosh_qd); const double Fq = sphere_form(q, radius, sphere_sld, solvent_sld)*Zq; //the occupied volume of the lattice const double lattice_scale = sphere_volume(radius/dnn); return lattice_scale * Fq; } sasmodels/sasmodels/models/sc_paracrystal.py000066400000000000000000000135751317715334700217370ustar00rootroot00000000000000r""" Calculates the scattering from a **simple cubic lattice** with paracrystalline distortion. Thermal vibrations are considered to be negligible, and the size of the paracrystal is infinitely large. Paracrystalline distortion is assumed to be isotropic and characterized by a Gaussian distribution. Definition ---------- The scattering intensity $I(q)$ is calculated as .. math:: I(q) = \text{scale}\frac{V_\text{lattice}P(q)Z(q)}{V_p} + \text{background} where scale is the volume fraction of spheres, $V_p$ is the volume of the primary particle, $V_\text{lattice}$ is a volume correction for the crystal structure, $P(q)$ is the form factor of the sphere (normalized), and $Z(q)$ is the paracrystalline structure factor for a simple cubic structure. Equation (16) of the 1987 reference is used to calculate $Z(q)$, using equations (13)-(15) from the 1987 paper for Z1, Z2, and Z3. The lattice correction (the occupied volume of the lattice) for a simple cubic structure of particles of radius *R* and nearest neighbor separation *D* is .. math:: V_\text{lattice}=\frac{4\pi}{3}\frac{R^3}{D^3} The distortion factor (one standard deviation) of the paracrystal is included in the calculation of $Z(q)$ .. math:: \Delta a = gD where *g* is a fractional distortion based on the nearest neighbor distance. The simple cubic lattice is .. figure:: img/sc_crystal_geometry.jpg For a crystal, diffraction peaks appear at reduced q-values given by .. math:: \frac{qD}{2\pi} = \sqrt{h^2+k^2+l^2} where for a simple cubic lattice any h, k, l are allowed and none are forbidden. Thus the peak positions correspond to (just the first 5) .. math:: :nowrap: \begin{align*} q/q_0 \quad & \quad 1 & \sqrt{2} \quad & \quad \sqrt{3} \quad & \sqrt{4} \quad & \quad \sqrt{5}\quad \\ Indices \quad & (100) & \quad (110) \quad & \quad (111) & (200) \quad & \quad (210) \end{align*} .. note:: The calculation of *Z(q)* is a double numerical integral that must be carried out with a high density of points to properly capture the sharp peaks of the paracrystalline scattering. So be warned that the calculation is SLOW. Go get some coffee. Fitting of any experimental data must be resolution smeared for any meaningful fit. This makes a triple integral. Very, very slow. Go get lunch! The 2D (Anisotropic model) is based on the reference below where *I(q)* is approximated for 1d scattering. Thus the scattering pattern for 2D may not be accurate. Note that we are not responsible for any incorrectness of the 2D model computation. .. figure:: img/parallelepiped_angle_definition.png Orientation of the crystal with respect to the scattering plane, when $\theta = \phi = 0$ the $c$ axis is along the beam direction (the $z$ axis). Reference --------- Hideki Matsuoka et. al. *Physical Review B,* 36 (1987) 1754-1765 (Original Paper) Hideki Matsuoka et. al. *Physical Review B,* 41 (1990) 3854 -3856 (Corrections to FCC and BCC lattice structure calculation) """ from numpy import inf name = "sc_paracrystal" title = "Simple cubic lattice with paracrystalline distortion" description = """ P(q)=(scale/Vp)*V_lattice*P(q)*Z(q)+bkg where scale is the volume fraction of sphere, Vp = volume of the primary particle, V_lattice = volume correction for for the crystal structure, P(q)= form factor of the sphere (normalized), Z(q)= paracrystalline structure factor for a simple cubic structure. [Simple Cubic ParaCrystal Model] Parameters; scale: volume fraction of spheres bkg:background, R: radius of sphere dnn: Nearest neighbor distance d_factor: Paracrystal distortion factor radius: radius of the spheres sldSph: SLD of the sphere sldSolv: SLD of the solvent """ category = "shape:paracrystal" single = False # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type","description"], parameters = [["dnn", "Ang", 220.0, [0.0, inf], "", "Nearest neighbor distance"], ["d_factor", "", 0.06, [-inf, inf], "", "Paracrystal distortion factor"], ["radius", "Ang", 40.0, [0.0, inf], "volume", "Radius of sphere"], ["sld", "1e-6/Ang^2", 3.0, [0.0, inf], "sld", "Sphere scattering length density"], ["sld_solvent", "1e-6/Ang^2", 6.3, [0.0, inf], "sld", "Solvent scattering length density"], ["theta", "degrees", 0, [-360, 360], "orientation", "c axis to beam angle"], ["phi", "degrees", 0, [-360, 360], "orientation", "rotation about beam"], ["psi", "degrees", 0, [-360, 360], "orientation", "rotation about c axis"] ] # pylint: enable=bad-whitespace, line-too-long source = ["lib/sas_3j1x_x.c", "lib/sphere_form.c", "lib/gauss150.c", "sc_paracrystal.c"] def random(): import numpy as np # copied from bcc_paracrystal radius = 10**np.random.uniform(1.3, 4) d_factor = 10**np.random.uniform(-2, -0.7) # sigma_d in 0.01-0.7 dnn_fraction = np.random.beta(a=10, b=1) dnn = radius*4/np.sqrt(4)/dnn_fraction pars = dict( #sld=1, sld_solvent=0, scale=1, background=1e-32, dnn=dnn, d_factor=d_factor, radius=radius, ) return pars tests = [ # Accuracy tests based on content in test/utest_extra_models.py, 2d tests added April 10, 2017 [{}, 0.001, 10.3048], [{}, 0.215268, 0.00814889], [{}, 0.414467, 0.001313289], [{'theta': 10.0, 'phi': 20, 'psi': 30.0}, (0.045, -0.035), 18.0397138402], [{'theta': 10.0, 'phi': 20, 'psi': 30.0}, (0.023, 0.045), 0.0177333171285], ] sasmodels/sasmodels/models/sphere.py000066400000000000000000000057241317715334700202100ustar00rootroot00000000000000r""" For information about polarised and magnetic scattering, see the :ref:`magnetism` documentation. Definition ---------- The 1D scattering intensity is calculated in the following way (Guinier, 1955) .. math:: I(q) = \frac{\text{scale}}{V} \cdot \left[ 3V(\Delta\rho) \cdot \frac{\sin(qr) - qr\cos(qr))}{(qr)^3} \right]^2 + \text{background} where *scale* is a volume fraction, $V$ is the volume of the scatterer, $r$ is the radius of the sphere and *background* is the background level. *sld* and *sld_solvent* are the scattering length densities (SLDs) of the scatterer and the solvent respectively, whose difference is $\Delta\rho$. Note that if your data is in absolute scale, the *scale* should represent the volume fraction (which is unitless) if you have a good fit. If not, it should represent the volume fraction times a factor (by which your data might need to be rescaled). The 2D scattering intensity is the same as above, regardless of the orientation of $\vec q$. Validation ---------- Validation of our code was done by comparing the output of the 1D model to the output of the software provided by the NIST (Kline, 2006). References ---------- A Guinier and G. Fournet, *Small-Angle Scattering of X-Rays*, John Wiley and Sons, New York, (1955) *2013/09/09 and 2014/01/06 - Description reviewed by S King and P Parker.* """ from numpy import inf name = "sphere" title = "Spheres with uniform scattering length density" description = """\ P(q)=(scale/V)*[3V(sld-sld_solvent)*(sin(qr)-qr cos(qr)) /(qr)^3]^2 + background r: radius of sphere V: The volume of the scatter sld: the SLD of the sphere sld_solvent: the SLD of the solvent """ category = "shape:sphere" # ["name", "units", default, [lower, upper], "type","description"], parameters = [["sld", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Layer scattering length density"], ["sld_solvent", "1e-6/Ang^2", 6, [-inf, inf], "sld", "Solvent scattering length density"], ["radius", "Ang", 50, [0, inf], "volume", "Sphere radius"], ] source = ["lib/sas_3j1x_x.c", "lib/sphere_form.c"] # No volume normalization despite having a volume parameter # This should perhaps be volume normalized? form_volume = """ return sphere_volume(radius); """ Iq = """ return sphere_form(q, radius, sld, sld_solvent); """ def ER(radius): """ Return equivalent radius (ER) """ return radius # VR defaults to 1.0 def random(): import numpy as np radius = 10**np.random.uniform(1.3, 4) pars = dict( radius=radius, ) return pars tests = [ [{}, 0.2, 0.726362], [{"scale": 1., "background": 0., "sld": 6., "sld_solvent": 1., "radius": 120., "radius_pd": 0.2, "radius_pd_n":45}, 0.2, 0.228843], [{"radius": 120., "radius_pd": 0.2, "radius_pd_n":45}, "ER", 120.], [{"radius": 120., "radius_pd": 0.2, "radius_pd_n":45}, "VR", 1.], ] sasmodels/sasmodels/models/spherical_sld.c000066400000000000000000000062321317715334700213230ustar00rootroot00000000000000static double form_volume( double fp_n_shells, double thickness[], double interface[]) { int n_shells= (int)(fp_n_shells + 0.5); double r = 0.0; for (int i=0; i < n_shells; i++) { r += thickness[i] + interface[i]; } return M_4PI_3*cube(r); } static double blend(int shape, double nu, double z) { if (shape==0) { const double num = sas_erf(nu * M_SQRT1_2 * (2.0*z - 1.0)); const double denom = 2.0 * sas_erf(nu * M_SQRT1_2); return num/denom + 0.5; } else if (shape==1) { return pow(z, nu); } else if (shape==2) { return 1.0 - pow(1.0 - z, nu); } else if (shape==3) { return expm1(-nu*z)/expm1(-nu); } else if (shape==4) { return expm1(nu*z)/expm1(nu); } else { return NAN; } } static double f_linear(double q, double r, double contrast, double slope) { const double qr = q * r; const double qrsq = qr * qr; const double bes = sas_3j1x_x(qr); double sinqr, cosqr; SINCOS(qr, sinqr, cosqr); const double fun = 3.0*r*(2.0*qr*sinqr - (qrsq-2.0)*cosqr)/(qrsq*qrsq); const double vol = M_4PI_3 * cube(r); return vol*(bes*contrast + fun*slope); } static double Iq( double q, double fp_n_shells, double sld_solvent, double sld[], double thickness[], double interface[], double shape[], double nu[], double fp_n_steps) { // iteration for # of shells + core + solvent int n_shells = (int)(fp_n_shells + 0.5); int n_steps = (int)(fp_n_steps + 0.5); double f=0.0; double r=0.0; for (int shell=0; shell r^3=0 => f=0, so works for core as well. f -= M_4PI_3 * cube(r) * sld_l * sas_3j1x_x(q*r); r += thickness[shell]; f += M_4PI_3 * cube(r) * sld_l * sas_3j1x_x(q*r); // iterate over sub_shells in the interface const double dr = interface[shell]/n_steps; const double delta = (shell==n_shells-1 ? sld_solvent : sld[shell+1]) - sld_l; const double nu_shell = fmax(fabs(nu[shell]), 1.e-14); const int shape_shell = (int)(shape[shell]); // if there is no interface the equations don't work if (dr == 0.) continue; double sld_in = sld_l; for (int step=1; step <= n_steps; step++) { // find sld_i at the outer boundary of sub-shell step //const double z = (double)step/(double)n_steps; const double z = (double)step/(double)n_steps; const double fraction = blend(shape_shell, nu_shell, z); const double sld_out = fraction*delta + sld_l; // calculate slope const double slope = (sld_out - sld_in)/dr; const double contrast = sld_in - slope*r; // iteration for the left and right boundary of the shells f -= f_linear(q, r, contrast, slope); r += dr; f += f_linear(q, r, contrast, slope); sld_in = sld_out; } } // add in solvent effect f -= M_4PI_3 * cube(r) * sld_solvent * sas_3j1x_x(q*r); const double f2 = f * f * 1.0e-4; return f2; } sasmodels/sasmodels/models/spherical_sld.py000066400000000000000000000234321317715334700215320ustar00rootroot00000000000000r""" Similarly to the onion, this model provides the form factor, $P(q)$, for a multi-shell sphere, where the interface between the each neighboring shells can be described by the error function, power-law, or exponential functions. The scattering intensity is computed by building a continuous custom SLD profile along the radius of the particle. The SLD profile is composed of a number of uniform shells with interfacial shells between them. .. figure:: img/spherical_sld_profile.png Example SLD profile Unlike the model (using an analytical integration), the interfacial shells here are sub-divided and numerically integrated assuming each sub-shell is described by a line function, with *n_steps* sub-shells per interface. The form factor is normalized by the total volume of the sphere. Interface shapes are as follows:: 0: erf($\nu z$) 1: Rpow($z^\nu$) 2: Lpow($z^\nu$) 3: Rexp($-\nu z$) 4: Lexp($-\nu z$) Definition ---------- The form factor $P(q)$ in 1D is calculated by: .. math:: P(q) = \frac{f^2}{V_\text{particle}} \text{ where } f = f_\text{core} + \sum_{\text{inter}_i=0}^N f_{\text{inter}_i} + \sum_{\text{flat}_i=0}^N f_{\text{flat}_i} +f_\text{solvent} For a spherically symmetric particle with a particle density $\rho_x(r)$ the sld function can be defined as: .. math:: f_x = 4 \pi \int_{0}^{\infty} \rho_x(r) \frac{\sin(qr)} {qr^2} r^2 dr so that individual terms can be calculated as follows: .. math:: f_\text{core} &= 4 \pi \int_{0}^{r_\text{core}} \rho_\text{core} \frac{\sin(qr)} {qr} r^2 dr = 3 \rho_\text{core} V(r_\text{core}) \Big[ \frac{\sin(qr_\text{core}) - qr_\text{core} \cos(qr_\text{core})} {qr_\text{core}^3} \Big] \\ f_{\text{inter}_i} &= 4 \pi \int_{\Delta t_{ \text{inter}_i } } \rho_{ \text{inter}_i } \frac{\sin(qr)} {qr} r^2 dr \\ f_{\text{shell}_i} &= 4 \pi \int_{\Delta t_{ \text{inter}_i } } \rho_{ \text{flat}_i } \frac{\sin(qr)} {qr} r^2 dr = 3 \rho_{ \text{flat}_i } V ( r_{ \text{inter}_i } + \Delta t_{ \text{inter}_i } ) \Big[ \frac{\sin(qr_{\text{inter}_i} + \Delta t_{ \text{inter}_i } ) - q (r_{\text{inter}_i} + \Delta t_{ \text{inter}_i }) \cos(q( r_{\text{inter}_i} + \Delta t_{ \text{inter}_i } ) ) } {q ( r_{\text{inter}_i} + \Delta t_{ \text{inter}_i } )^3 } \Big] -3 \rho_{ \text{flat}_i } V(r_{ \text{inter}_i }) \Big[ \frac{\sin(qr_{\text{inter}_i}) - qr_{\text{flat}_i} \cos(qr_{\text{inter}_i}) } {qr_{\text{inter}_i}^3} \Big] \\ f_\text{solvent} &= 4 \pi \int_{r_N}^{\infty} \rho_\text{solvent} \frac{\sin(qr)} {qr} r^2 dr = 3 \rho_\text{solvent} V(r_N) \Big[ \frac{\sin(qr_N) - qr_N \cos(qr_N)} {qr_N^3} \Big] Here we assumed that the SLDs of the core and solvent are constant in $r$. The SLD at the interface between shells, $\rho_{\text {inter}_i}$ is calculated with a function chosen by an user, where the functions are Exp: .. math:: \rho_{{inter}_i} (r) &= \begin{cases} B \exp\Big( \frac {\pm A(r - r_{\text{flat}_i})} {\Delta t_{ \text{inter}_i }} \Big) +C & \mbox{for } A \neq 0 \\ B \Big( \frac {(r - r_{\text{flat}_i})} {\Delta t_{ \text{inter}_i }} \Big) +C & \mbox{for } A = 0 \\ \end{cases} Power-Law .. math:: \rho_{{inter}_i} (r) &= \begin{cases} \pm B \Big( \frac {(r - r_{\text{flat}_i} )} {\Delta t_{ \text{inter}_i }} \Big) ^A +C & \mbox{for } A \neq 0 \\ \rho_{\text{flat}_{i+1}} & \mbox{for } A = 0 \\ \end{cases} Erf: .. math:: \rho_{{inter}_i} (r) = \begin{cases} B \text{erf} \Big( \frac { A(r - r_{\text{flat}_i})} {\sqrt{2} \Delta t_{ \text{inter}_i }} \Big) +C & \mbox{for } A \neq 0 \\ B \Big( \frac {(r - r_{\text{flat}_i} )} {\Delta t_{ \text{inter}_i }} \Big) +C & \mbox{for } A = 0 \\ \end{cases} The functions are normalized so that they vary between 0 and 1, and they are constrained such that the SLD is continuous at the boundaries of the interface as well as each sub-shell. Thus B and C are determined. Once $\rho_{\text{inter}_i}$ is found at the boundary of the sub-shell of the interface, we can find its contribution to the form factor $P(q)$ .. math:: f_{\text{inter}_i} &= 4 \pi \int_{\Delta t_{ \text{inter}_i } } \rho_{ \text{inter}_i } \frac{\sin(qr)} {qr} r^2 dr = 4 \pi \sum_{j=1}^{n_\text{steps}} \int_{r_j}^{r_{j+1}} \rho_{ \text{inter}_i } (r_j) \frac{\sin(qr)} {qr} r^2 dr \\ \approx 4 \pi \sum_{j=1}^{n_\text{steps}} \Big[ 3 ( \rho_{ \text{inter}_i } ( r_{j+1} ) - \rho_{ \text{inter}_i } ( r_{j} ) V (r_j) \Big[ \frac {r_j^2 \beta_\text{out}^2 \sin(\beta_\text{out}) - (\beta_\text{out}^2-2) \cos(\beta_\text{out}) } {\beta_\text{out}^4 } \Big] \\ {} - 3 ( \rho_{ \text{inter}_i } ( r_{j+1} ) - \rho_{ \text{inter}_i } ( r_{j} ) V ( r_{j-1} ) \Big[ \frac {r_{j-1}^2 \sin(\beta_\text{in}) - (\beta_\text{in}^2-2) \cos(\beta_\text{in}) } {\beta_\text{in}^4 } \Big] \\ {} + 3 \rho_{ \text{inter}_i } ( r_{j+1} ) V ( r_j ) \Big[ \frac {\sin(\beta_\text{out}) - \cos(\beta_\text{out}) } {\beta_\text{out}^4 } \Big] - 3 \rho_{ \text{inter}_i } ( r_{j} ) V ( r_j ) \Big[ \frac {\sin(\beta_\text{in}) - \cos(\beta_\text{in}) } {\beta_\text{in}^4 } \Big] \Big] where .. math:: :nowrap: \begin{align*} V(a) &= \frac {4\pi}{3}a^3 && \\ a_\text{in} \sim \frac{r_j}{r_{j+1} -r_j} \text{, } & a_\text{out} \sim \frac{r_{j+1}}{r_{j+1} -r_j} \\ \beta_\text{in} &= qr_j \text{, } & \beta_\text{out} &= qr_{j+1} \end{align*} We assume $\rho_{\text{inter}_j} (r)$ is approximately linear within the sub-shell $j$. Finally the form factor can be calculated by .. math:: P(q) = \frac{[f]^2} {V_\text{particle}} \mbox{ where } V_\text{particle} = V(r_{\text{shell}_N}) For 2D data the scattering intensity is calculated in the same way as 1D, where the $q$ vector is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} .. note:: The outer most radius is used as the effective radius for $S(Q)$ when $P(Q) * S(Q)$ is applied. References ---------- L A Feigin and D I Svergun, Structure Analysis by Small-Angle X-Ray and Neutron Scattering, Plenum Press, New York, (1987) """ import numpy as np from numpy import inf, expm1, sqrt from scipy.special import erf name = "spherical_sld" title = "Sperical SLD intensity calculation" description = """ I(q) = background = Incoherent background [1/cm] """ category = "shape:sphere" SHAPES = ["erf(|nu|*z)", "Rpow(z^|nu|)", "Lpow(z^|nu|)", "Rexp(-|nu|z)", "Lexp(-|nu|z)"] # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type", "description"], parameters = [["n_shells", "", 1, [1, 10], "volume", "number of shells"], ["sld_solvent", "1e-6/Ang^2", 1.0, [-inf, inf], "sld", "solvent sld"], ["sld[n_shells]", "1e-6/Ang^2", 4.06, [-inf, inf], "sld", "sld of the shell"], ["thickness[n_shells]", "Ang", 100.0, [0, inf], "volume", "thickness shell"], ["interface[n_shells]", "Ang", 50.0, [0, inf], "volume", "thickness of the interface"], ["shape[n_shells]", "", 0, [SHAPES], "", "interface shape"], ["nu[n_shells]", "", 2.5, [0, inf], "", "interface shape exponent"], ["n_steps", "", 35, [0, inf], "", "number of steps in each interface (must be an odd integer)"], ] # pylint: enable=bad-whitespace, line-too-long source = ["lib/polevl.c", "lib/sas_erf.c", "lib/sas_3j1x_x.c", "spherical_sld.c"] single = False # TODO: fix low q behaviour profile_axes = ['Radius (A)', 'SLD (1e-6/A^2)'] SHAPE_FUNCTIONS = [ lambda z, nu: erf(nu/sqrt(2)*(2*z-1))/(2*erf(nu/sqrt(2))) + 0.5, # erf lambda z, nu: z**nu, # Rpow lambda z, nu: 1 - (1-z)**nu, # Lpow lambda z, nu: expm1(-nu*z)/expm1(-nu), # Rexp lambda z, nu: expm1(nu*z)/expm1(nu), # Lexp ] def profile(n_shells, sld_solvent, sld, thickness, interface, shape, nu, n_steps): """ Returns shape profile with x=radius, y=SLD. """ n_shells = int(n_shells + 0.5) n_steps = int(n_steps + 0.5) z = [] rho = [] z_next = 0 # two sld points for core z.append(z_next) rho.append(sld[0]) for i in range(0, n_shells): z_next += thickness[i] z.append(z_next) rho.append(sld[i]) dz = interface[i]/n_steps sld_l = sld[i] sld_r = sld[i+1] if i < n_shells-1 else sld_solvent fun = SHAPE_FUNCTIONS[int(np.clip(shape[i], 0, len(SHAPE_FUNCTIONS)-1))] for step in range(1, n_steps+1): portion = fun(float(step)/n_steps, max(abs(nu[i]), 1e-14)) z_next += dz z.append(z_next) rho.append((sld_r - sld_l)*portion + sld_l) z.append(z_next*1.2) rho.append(sld_solvent) # return sld profile (r, beta) return np.asarray(z), np.asarray(rho) def ER(n_shells, thickness, interface): """Effective radius""" n_shells = int(n_shells + 0.5) total = (np.sum(thickness[:n_shells], axis=1) + np.sum(interface[:n_shells], axis=1)) return total demo = { "n_shells": 5, "n_steps": 35.0, "sld_solvent": 1.0, "sld": [2.07, 4.0, 3.5, 4.0, 3.5], "thickness": [50.0, 100.0, 100.0, 100.0, 100.0], "interface": [50.0]*5, "shape": [0]*5, "nu": [2.5]*5, } tests = [ # Results checked against sasview 3.1 [{"n_shells": 5, "n_steps": 35, "sld_solvent": 1.0, "sld": [2.07, 4.0, 3.5, 4.0, 3.5], "thickness": [50.0, 100.0, 100.0, 100.0, 100.0], "interface": [50]*5, "shape": [0]*5, "nu": [2.5]*5, }, 0.001, 750697.238], ] sasmodels/sasmodels/models/spinodal.py000066400000000000000000000045611317715334700205310ustar00rootroot00000000000000r""" Definition ---------- This model calculates the SAS signal of a phase separating solution under spinodal decomposition. The scattering intensity $I(q)$ is calculated as .. math:: I(q) = I_{max}\frac{(1+\gamma/2)x^2}{\gamma/2+x^{2+\gamma}}+B where $x=q/q_0$ and $B$ is a flat background. The characteristic structure length scales with the correlation peak at $q_0$. The exponent $\gamma$ is equal to $d+1$ with d the dimensionality of the off-critical concentration mixtures. A transition to $\gamma=2d$ is seen near the percolation threshold into the critical concentration regime. References ---------- H. Furukawa. Dynamics-scaling theory for phase-separating unmixing mixtures: Growth rates of droplets and scaling properties of autocorrelation functions. Physica A 123,497 (1984). Authorship and Verification ---------------------------- * **Author:** Dirk Honecker **Date:** Oct 7, 2016 * **Last Modified by:** * **Last Reviewed by:** """ from numpy import inf, errstate name = "spinodal" title = "Spinodal decomposition model" description = """\ I(q) = scale ((1+gamma/2)x^2)/(gamma/2+x^(2+gamma))+background List of default parameters: scale = scaling gamma = exponent x = q/q_0 q_0 = correlation peak position [1/A] background = Incoherent background""" category = "shape-independent" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type", "description"], parameters = [["gamma", "", 3.0, [-inf, inf], "", "Exponent"], ["q_0", "1/Ang", 0.1, [-inf, inf], "", "Correlation peak position"] ] # pylint: enable=bad-whitespace, line-too-long def Iq(q, gamma=3.0, q_0=0.1): """ :param q: Input q-value :param gamma: Exponent :param q_0: Correlation peak position :return: Calculated intensity """ with errstate(divide='ignore'): x = q/q_0 inten = ((1 + gamma / 2) * x ** 2) / (gamma / 2 + x ** (2 + gamma)) return inten Iq.vectorized = True # Iq accepts an array of q values def random(): import numpy as np pars = dict( scale=10**np.random.uniform(1, 3), gamma=np.random.uniform(0, 6), q_0=10**np.random.uniform(-3, -1), ) return pars demo = dict(scale=1, background=0, gamma=1, q_0=0.1) sasmodels/sasmodels/models/squarewell.py000066400000000000000000000112701317715334700210770ustar00rootroot00000000000000# Note: model title and parameter table are inserted automatically r""" This calculates the interparticle structure factor for a square well fluid spherical particles. The mean spherical approximation (MSA) closure was used for this calculation, and is not the most appropriate closure for an attractive interparticle potential. This solution has been compared to Monte Carlo simulations for a square well fluid, showing this calculation to be limited in applicability to well depths $\epsilon < 1.5$ kT and volume fractions $\phi < 0.08$. Positive well depths correspond to an attractive potential well. Negative well depths correspond to a potential "shoulder", which may or may not be physically reasonable. The stickyhardsphere model may be a better choice in some circumstances. Computed values may behave badly at extremely small $qR$. The well width $(\lambda)$ is defined as multiples of the particle diameter $(2 R)$. The interaction potential is: .. image:: img/squarewell.png .. math:: U(r) = \begin{cases} \infty & r < 2R \\ -\epsilon & 2R \leq r < 2R\lambda \\ 0 & r \geq 2R\lambda \end{cases} where $r$ is the distance from the center of the sphere of a radius $R$. In sasview the effective radius may be calculated from the parameters used in the form factor $P(q)$ that this $S(q)$ is combined with. For 2D data: The 2D scattering intensity is calculated in the same way as 1D, where the $q$ vector is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- R V Sharma, K C Sharma, *Physica*, 89A (1977) 213. """ from numpy import inf name = "squarewell" title = "Square well structure factor, with MSA closure" description = """\ [Square well structure factor, with MSA closure] Interparticle structure factor S(Q)for a hard sphere fluid with a narrow attractive well. Fits are prone to deliver non-physical parameters, use with care and read the references in the full manual. In sasview the effective radius will be calculated from the parameters used in P(Q). """ category = "structure-factor" structure_factor = True single = False #single = False # ["name", "units", default, [lower, upper], "type","description"], parameters = [ # [ "name", "units", default, [lower, upper], "type", # "description" ], ["radius_effective", "Ang", 50.0, [0, inf], "volume", "effective radius of hard sphere"], ["volfraction", "", 0.04, [0, 0.08], "", "volume fraction of spheres"], ["welldepth", "kT", 1.5, [0.0, 1.5], "", "depth of well, epsilon"], ["wellwidth", "diameters", 1.2, [1.0, inf], "", "width of well in diameters (=2R) units, must be > 1"], ] # No volume normalization despite having a volume parameter # This should perhaps be volume normalized? form_volume = """ return 1.0; """ Iq = """ // single precision is very poor at extreme small Q, would need a Taylor series double req,phis,edibkb,lambda,struc; double sigma,eta,eta2,eta3,eta4,etam1,etam14,alpha,beta,gamm; double x,sk,sk2,sk3,sk4,t1,t2,t3,t4,ck; double S,C,SL,CL; x= q; req = radius_effective; phis = volfraction; edibkb = welldepth; lambda = wellwidth; sigma = req*2.; eta = phis; eta2 = eta*eta; eta3 = eta*eta2; eta4 = eta*eta3; etam1 = 1. - eta; etam14 = etam1*etam1*etam1*etam1; // temp borrow sk for an intermediate calc sk = 1.0 +2.0*eta; sk *= sk; alpha = ( sk + eta3*( eta-4.0 ) )/etam14; beta = -(eta/3.0) * ( 18. + 20.*eta - 12.*eta2 + eta4 )/etam14; gamm = 0.5*eta*( sk + eta3*(eta-4.) )/etam14; // calculate the structure factor sk = x*sigma; sk2 = sk*sk; sk3 = sk*sk2; sk4 = sk3*sk; SINCOS(sk,S,C); SINCOS(lambda*sk,SL,CL); t1 = alpha * sk3 * ( S - sk * C ); t2 = beta * sk2 * 2.0*( sk*S - (0.5*sk2 - 1.)*C - 1.0 ); t3 = gamm*( ( 4.0*sk3 - 24.*sk ) * S - ( sk4 - 12.0*sk2 + 24.0 )*C + 24.0 ); t4 = -edibkb*sk3*(SL +sk*(C - lambda*CL) - S ); ck = -24.0*eta*( t1 + t2 + t3 + t4 )/sk3/sk3; struc = 1./(1.-ck); return(struc); """ # ER defaults to 0.0 # VR defaults to 1.0 def random(): import numpy as np pars = dict( scale=1, background=0, radius_effective=10**np.random.uniform(1, 4.7), volfraction=np.random.uniform(0.00001, 0.08), welldepth=np.random.uniform(0, 1.5), wellwidth=np.random.uniform(1, 1.2), ) return pars demo = dict(radius_effective=50, volfraction=0.04, welldepth=1.5, wellwidth=1.2, radius_effective_pd=0, radius_effective_pd_n=0) # tests = [ [{'scale': 1.0, 'background': 0.0, 'radius_effective': 50.0, 'volfraction': 0.04,'welldepth': 1.5, 'wellwidth': 1.2, 'radius_effective_pd': 0}, [0.001], [0.97665742]], ] # ADDED by: converting from sasview RKH ON: 16Mar2016 sasmodels/sasmodels/models/stacked_disks.c000066400000000000000000000120711317715334700213200ustar00rootroot00000000000000static double stacked_disks_kernel( double q, double halfheight, double thick_layer, double radius, int n_stacking, double sigma_dnn, double core_sld, double layer_sld, double solvent_sld, double sin_alpha, double cos_alpha, double d) { // q is the q-value for the calculation (1/A) // radius is the core radius of the cylinder (A) // *_sld are the respective SLD's // halfheight is the *Half* CORE-LENGTH of the cylinder = L (A) // zi is the dummy variable for the integration (x in Feigin's notation) const double besarg1 = q*radius*sin_alpha; //const double besarg2 = q*radius*sin_alpha; const double sinarg1 = q*halfheight*cos_alpha; const double sinarg2 = q*(halfheight+thick_layer)*cos_alpha; const double be1 = sas_2J1x_x(besarg1); //const double be2 = sas_2J1x_x(besarg2); const double be2 = be1; const double si1 = sas_sinx_x(sinarg1); const double si2 = sas_sinx_x(sinarg2); const double dr1 = core_sld - solvent_sld; const double dr2 = layer_sld - solvent_sld; const double area = M_PI*radius*radius; const double totald = 2.0*(thick_layer + halfheight); const double t1 = area * (2.0*halfheight) * dr1 * si1 * be1; const double t2 = area * dr2 * (totald*si2 - 2.0*halfheight*si1) * be2; double pq = square(t1 + t2); // loop for the structure factor S(q) double qd_cos_alpha = q*d*cos_alpha; //d*cos_alpha is the projection of d onto q (in other words the component //of d that is parallel to q. double debye_arg = -0.5*square(qd_cos_alpha*sigma_dnn); double sq=0.0; for (int kk=1; kkq^2, where is the ensemble average radius of gyration squared of the entire polymer - f is the number of arms on the star - the radius of gyration of an arm is given b Rg_arm^2 = R_g^2 * f/(3f-2) """ category = "shape-independent" single = False # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type","description"], parameters = [["rg_squared", "Ang^2", 100.0, [0.0, inf], "", "Ensemble radius of gyration SQUARED of the full polymer"], ["arms", "", 3, [1.0, 6.0], "", "Number of arms in the model"], ] # pylint: enable=bad-whitespace, line-too-long source = ["star_polymer.c"] def random(): import numpy as np pars = dict( #background=0, scale=10**np.random.uniform(1, 4), rg_squared=10**np.random.uniform(1, 8), arms=np.random.uniform(1, 6), ) return pars tests = [[{'rg_squared': 2.0, 'arms': 3.3, }, 0.5, 0.851646091108], [{'rg_squared': 1.0, 'arms': 2.0, 'background': 1.8, }, 1.0, 2.53575888234], ] # 23Mar2016 RKH edited docs, would this better use rg not rg^2 ? Numerical noise at extremely small q.rg sasmodels/sasmodels/models/stickyhardsphere.py000066400000000000000000000143701317715334700222730ustar00rootroot00000000000000# Note: model title and parameter table are inserted automatically r""" This calculates the interparticle structure factor for a hard sphere fluid with a narrow attractive well. A perturbative solution of the Percus-Yevick closure is used. The strength of the attractive well is described in terms of "stickiness" as defined below. The perturb (perturbation parameter), $\epsilon$, should be held between 0.01 and 0.1. It is best to hold the perturbation parameter fixed and let the "stickiness" vary to adjust the interaction strength. The stickiness, $\tau$, is defined in the equation below and is a function of both the perturbation parameter and the interaction strength. $\tau$ and $\epsilon$ are defined in terms of the hard sphere diameter $(\sigma = 2 R)$, the width of the square well, $\Delta$ (same units as $R$\ ), and the depth of the well, $U_o$, in units of $kT$. From the definition, it is clear that smaller $\tau$ means stronger attraction. .. math:: \tau &= \frac{1}{12\epsilon} \exp(u_o / kT) \\ \epsilon &= \Delta / (\sigma + \Delta) where the interaction potential is .. math:: U(r) = \begin{cases} \infty & r < \sigma \\ -U_o & \sigma \leq r \leq \sigma + \Delta \\ 0 & r > \sigma + \Delta \end{cases} The Percus-Yevick (PY) closure was used for this calculation, and is an adequate closure for an attractive interparticle potential. This solution has been compared to Monte Carlo simulations for a square well fluid, with good agreement. The true particle volume fraction, $\phi$, is not equal to $h$, which appears in most of the reference. The two are related in equation (24) of the reference. The reference also describes the relationship between this perturbation solution and the original sticky hard sphere (or adhesive sphere) model by Baxter. **NB**: The calculation can go haywire for certain combinations of the input parameters, producing unphysical solutions - in this case errors are reported to the command window and the $S(q)$ is set to -1 (so it will disappear on a log-log plot). Use tight bounds to keep the parameters to values that you know are physical (test them) and keep nudging them until the optimization does not hit the constraints. In sasview the effective radius may be calculated from the parameters used in the form factor $P(q)$ that this $S(q)$ is combined with. For 2D data the scattering intensity is calculated in the same way as 1D, where the $q$ vector is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- S V G Menon, C Manohar, and K S Rao, *J. Chem. Phys.*, 95(12) (1991) 9186-9190 """ # TODO: refactor so that we pull in the old sansmodels.c_extensions from numpy import inf name = "stickyhardsphere" title = "Sticky hard sphere structure factor, with Percus-Yevick closure" description = """\ [Sticky hard sphere structure factor, with Percus-Yevick closure] Interparticle structure factor S(Q)for a hard sphere fluid with a narrow attractive well. Fits are prone to deliver non-physical parameters, use with care and read the references in the full manual. In sasview the effective radius will be calculated from the parameters used in P(Q). """ category = "structure-factor" structure_factor = True single = False # ["name", "units", default, [lower, upper], "type","description"], parameters = [ # [ "name", "units", default, [lower, upper], "type", # "description" ], ["radius_effective", "Ang", 50.0, [0, inf], "volume", "effective radius of hard sphere"], ["volfraction", "", 0.2, [0, 0.74], "", "volume fraction of hard spheres"], ["perturb", "", 0.05, [0.01, 0.1], "", "perturbation parameter, epsilon"], ["stickiness", "", 0.20, [-inf, inf], "", "stickiness, tau"], ] def random(): import numpy as np pars = dict( scale=1, background=0, radius_effective=10**np.random.uniform(1, 4.7), volfraction=np.random.uniform(0.00001, 0.74), perturb=10**np.random.uniform(-2, -1), stickiness=np.random.uniform(0, 1), ) return pars # No volume normalization despite having a volume parameter # This should perhaps be volume normalized? form_volume = """ return 1.0; """ Iq = """ double onemineps,eta; double sig,aa,etam1,etam1sq,qa,qb,qc,radic; double lam,lam2,test,mu,alpha,beta; double kk,k2,k3,ds,dc,aq1,aq2,aq3,aq,bq1,bq2,bq3,bq,sq; onemineps = 1.0-perturb; eta = volfraction/onemineps/onemineps/onemineps; sig = 2.0 * radius_effective; aa = sig/onemineps; etam1 = 1.0 - eta; etam1sq=etam1*etam1; //C //C SOLVE QUADRATIC FOR LAMBDA //C qa = eta/6.0; qb = stickiness + eta/etam1; qc = (1.0 + eta/2.0)/etam1sq; radic = qb*qb - 2.0*qa*qc; if(radic<0) { //if(x>0.01 && x<0.015) // Print "Lambda unphysical - both roots imaginary" //endif return(-1.0); } //C KEEP THE SMALLER ROOT, THE LARGER ONE IS UNPHYSICAL radic = sqrt(radic); lam = (qb-radic)/qa; lam2 = (qb+radic)/qa; if(lam2test) { //if(x>0.01 && x<0.015) // Print "Lambda unphysical mu>test" //endif return(-1.0); } alpha = (1.0 + 2.0*eta - mu)/etam1sq; beta = (mu - 3.0*eta)/(2.0*etam1sq); //C //C CALCULATE THE STRUCTURE FACTOR //C kk = q*aa; k2 = kk*kk; k3 = kk*k2; SINCOS(kk,ds,dc); //ds = sin(kk); //dc = cos(kk); aq1 = ((ds - kk*dc)*alpha)/k3; aq2 = (beta*(1.0-dc))/k2; aq3 = (lam*ds)/(12.0*kk); aq = 1.0 + 12.0*eta*(aq1+aq2-aq3); // bq1 = alpha*(0.5/kk - ds/k2 + (1.0 - dc)/k3); bq2 = beta*(1.0/kk - ds/k2); bq3 = (lam/12.0)*((1.0 - dc)/kk); bq = 12.0*eta*(bq1+bq2-bq3); // sq = 1.0/(aq*aq +bq*bq); return(sq); """ # ER defaults to 0.0 # VR defaults to 1.0 demo = dict(radius_effective=200, volfraction=0.2, perturb=0.05, stickiness=0.2, radius_effective_pd=0.1, radius_effective_pd_n=40) # tests = [ [{'scale': 1.0, 'background': 0.0, 'radius_effective': 50.0, 'perturb': 0.05, 'stickiness': 0.2, 'volfraction': 0.1, 'radius_effective_pd': 0}, [0.001, 0.003], [1.09718, 1.087830]], ] sasmodels/sasmodels/models/surface_fractal.c000066400000000000000000000027551317715334700216410ustar00rootroot00000000000000// Don't need invalid test since fractal_dim_surf is not polydisperse // #define INVALID(v) (v.fractal_dim_surf <= 1.0 || v.fractal_dim_surf >= 3.0) double form_volume(double radius); double Iq(double q, double radius, double fractal_dim_surf, double cutoff_length); static double _surface_fractal_kernel(double q, double radius, double fractal_dim_surf, double cutoff_length) { // calculate P(q) const double pq = square(sas_3j1x_x(q*radius)); // calculate S(q) // Note: lim q->0 S(q) = -gamma(mmo) cutoff_length^mmo (mmo cutoff_length) // however, the surface fractal formula is invalid outside the range const double mmo = 5.0 - fractal_dim_surf; const double sq = sas_gamma(mmo) * pow(cutoff_length, mmo) * pow(1.0 + square(q*cutoff_length), -0.5*mmo) * sin(-mmo * atan(q*cutoff_length)) / q; // Empirically determined that the results are valid within this range. // Above 1/r, the form starts to oscillate; below //const double result = (q > 5./(3-fractal_dim_surf)/cutoff_length) && q < 1./radius // ? pq * sq : 0.); double result = pq * sq; // exclude negative results return result > 0. ? result : 0.; } double form_volume(double radius) { return M_4PI_3*cube(radius); } double Iq(double q, double radius, double fractal_dim_surf, double cutoff_length ) { return _surface_fractal_kernel(q, radius, fractal_dim_surf, cutoff_length); } sasmodels/sasmodels/models/surface_fractal.py000066400000000000000000000072321317715334700220420ustar00rootroot00000000000000r""" This model calculates the scattering from fractal-like aggregates based on the Mildner reference. Definition ---------- The scattering intensity $I(q)$ is calculated as .. math:: :nowrap: \begin{align*} I(q) &= \text{scale} \times P(q)S(q) + \text{background} \\ P(q) &= F(qR)^2 \\ F(x) &= \frac{3\left[\sin(x)-x\cos(x)\right]}{x^3} \\ S(q) &= \Gamma(5-D_S)\xi^{\,5-D_S}\left[1+(q\xi)^2 \right]^{-(5-D_S)/2} \sin\left[-(5-D_S) \tan^{-1}(q\xi) \right] q^{-1} \\ \text{scale} &= \text{scale factor}\, N V^1(\rho_\text{particle} - \rho_\text{solvent})^2 \\ V &= \frac{4}{3}\pi R^3 \end{align*} where $R$ is the radius of the building block, $D_S$ is the **surface** fractal dimension, $\xi$ is the cut-off length, $\rho_\text{solvent}$ is the scattering length density of the solvent and $\rho_\text{particle}$ is the scattering length density of particles. .. note:: The surface fractal dimension is only valid if $1 0$, $c_1 < 0$, and $c_2 >0$. For 2D data, scattering intensity is calculated in the same way as 1D, where the $q$ vector is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- M Teubner, R Strey, *J. Chem. Phys.*, 87 (1987) 3195 K V Schubert, R Strey, S R Kline and E W Kaler, *J. Chem. Phys.*, 101 (1994) 5343 H Endo, M Mihailescu, M. Monkenbusch, J Allgaier, G Gompper, D Richter, B Jakobs, T Sottmann, R Strey, and I Grillo, *J. Chem. Phys.*, 115 (2001), 580 """ from __future__ import division import numpy as np from numpy import inf, pi name = "teubner_strey" title = "Teubner-Strey model of microemulsions" description = """\ Calculates scattering according to the Teubner-Strey model """ category = "shape-independent" # ["name", "units", default, [lower, upper], "type","description"], parameters = [ ["volfraction_a", "", 0.5, [0, 1.0], "", "Volume fraction of phase a"], ["sld_a", "1e-6/Ang^2", 0.3, [-inf, inf], "", "SLD of phase a"], ["sld_b", "1e-6/Ang^2", 6.3, [-inf, inf], "", "SLD of phase b"], ["d", "Ang", 100.0, [0, inf], "", "Domain size (periodicity)"], ["xi", "Ang", 30.0, [0, inf], "", "Correlation length"], ] def Iq(q, volfraction_a, sld_a, sld_b, d, xi): """SAS form""" drho = sld_a - sld_b k = 2.0*pi*xi/d a2 = (1.0 + k**2)**2 c1 = 2.0*xi**2 * (1.0 - k**2) c2 = xi**4 prefactor = 8.0*pi * volfraction_a*(1.0 - volfraction_a) * drho**2 * c2/xi return 1.0e-4*prefactor / np.polyval([c2, c1, a2], q**2) Iq.vectorized = True # Iq accepts an array of q values def random(): import numpy as np d = 10**np.random.uniform(1, 4) xi = 10**np.random.uniform(-0.3, 2)*d pars = dict( #background=0, scale=100, volfraction_a=10**np.random.uniform(-3, 0), sld_a=np.random.uniform(-0.5, 12), sld_b=np.random.uniform(-0.5, 12), d=d, xi=xi, ) return pars demo = dict(scale=1, background=0, volfraction_a=0.5, sld_a=0.3, sld_b=6.3, d=100.0, xi=30.0) tests = [[{}, 0.06, 41.5918888453]] sasmodels/sasmodels/models/triaxial_ellipsoid.c000066400000000000000000000054231317715334700223710ustar00rootroot00000000000000double form_volume(double radius_equat_minor, double radius_equat_major, double radius_polar); double Iq(double q, double sld, double sld_solvent, double radius_equat_minor, double radius_equat_major, double radius_polar); double Iqxy(double qx, double qy, double sld, double sld_solvent, double radius_equat_minor, double radius_equat_major, double radius_polar, double theta, double phi, double psi); //#define INVALID(v) (v.radius_equat_minor > v.radius_equat_major || v.radius_equat_major > v.radius_polar) double form_volume(double radius_equat_minor, double radius_equat_major, double radius_polar) { return M_4PI_3*radius_equat_minor*radius_equat_major*radius_polar; } double Iq(double q, double sld, double sld_solvent, double radius_equat_minor, double radius_equat_major, double radius_polar) { const double pa = square(radius_equat_minor/radius_equat_major) - 1.0; const double pc = square(radius_polar/radius_equat_major) - 1.0; // translate a point in [-1,1] to a point in [0, pi/2] const double zm = M_PI_4; const double zb = M_PI_4; double outer = 0.0; for (int i=0;i<76;i++) { //const double u = Gauss76Z[i]*(upper-lower)/2 + (upper + lower)/2; const double phi = Gauss76Z[i]*zm + zb; const double pa_sinsq_phi = pa*square(sin(phi)); double inner = 0.0; const double um = 0.5; const double ub = 0.5; for (int j=0;j<76;j++) { // translate a point in [-1,1] to a point in [0, 1] const double usq = square(Gauss76Z[j]*um + ub); const double r = radius_equat_major*sqrt(pa_sinsq_phi*(1.0-usq) + 1.0 + pc*usq); const double fq = sas_3j1x_x(q*r); inner += Gauss76Wt[j] * fq * fq; } outer += Gauss76Wt[i] * inner; // correcting for dx later } // translate integration ranges from [-1,1] to [lower,upper] and normalize by 4 pi const double fqsq = outer/4.0; // = outer*um*zm*8.0/(4.0*M_PI); const double s = (sld - sld_solvent) * form_volume(radius_equat_minor, radius_equat_major, radius_polar); return 1.0e-4 * s * s * fqsq; } double Iqxy(double qx, double qy, double sld, double sld_solvent, double radius_equat_minor, double radius_equat_major, double radius_polar, double theta, double phi, double psi) { double q, xhat, yhat, zhat; ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); const double r = sqrt(square(radius_equat_minor*xhat) + square(radius_equat_major*yhat) + square(radius_polar*zhat)); const double fq = sas_3j1x_x(q*r); const double s = (sld - sld_solvent) * form_volume(radius_equat_minor, radius_equat_major, radius_polar); return 1.0e-4 * square(s * fq); } sasmodels/sasmodels/models/triaxial_ellipsoid.py000066400000000000000000000165461317715334700226070ustar00rootroot00000000000000# triaxial ellipsoid model # Note: model title and parameter table are inserted automatically r""" Definition ---------- .. figure:: img/triaxial_ellipsoid_geometry.jpg Ellipsoid with $R_a$ as *radius_equat_minor*, $R_b$ as *radius_equat_major* and $R_c$ as *radius_polar*. Given an ellipsoid .. math:: \frac{X^2}{R_a^2} + \frac{Y^2}{R_b^2} + \frac{Z^2}{R_c^2} = 1 the scattering for randomly oriented particles is defined by the average over all orientations $\Omega$ of: .. math:: P(q) = \text{scale}(\Delta\rho)^2\frac{V}{4 \pi}\int_\Omega\Phi^2(qr)\,d\Omega + \text{background} where .. math:: \Phi(qr) &= 3 j_1(qr)/qr = 3 (\sin qr - qr \cos qr)/(qr)^3 \\ r^2 &= R_a^2e^2 + R_b^2f^2 + R_c^2g^2 \\ V &= \tfrac{4}{3} \pi R_a R_b R_c The $e$, $f$ and $g$ terms are the projections of the orientation vector on $X$, $Y$ and $Z$ respectively. Keeping the orientation fixed at the canonical axes, we can integrate over the incident direction using polar angle $-\pi/2 \le \gamma \le \pi/2$ and equatorial angle $0 \le \phi \le 2\pi$ (as defined in ref [1]), .. math:: \langle\Phi^2\rangle = \int_0^{2\pi} \int_{-\pi/2}^{\pi/2} \Phi^2(qr) \cos \gamma\,d\gamma d\phi with $e = \cos\gamma \sin\phi$, $f = \cos\gamma \cos\phi$ and $g = \sin\gamma$. A little algebra yields .. math:: r^2 = b^2(p_a \sin^2 \phi \cos^2 \gamma + 1 + p_c \sin^2 \gamma) for .. math:: p_a = \frac{a^2}{b^2} - 1 \text{ and } p_c = \frac{c^2}{b^2} - 1 Due to symmetry, the ranges can be restricted to a single quadrant $0 \le \gamma \le \pi/2$ and $0 \le \phi \le \pi/2$, scaling the resulting integral by 8. The computation is done using the substitution $u = \sin\gamma$, $du = \cos\gamma\,d\gamma$, giving .. math:: \langle\Phi^2\rangle &= 8 \int_0^{\pi/2} \int_0^1 \Phi^2(qr) du d\phi \\ r^2 &= b^2(p_a \sin^2(\phi)(1 - u^2) + 1 + p_c u^2) Though for convenience we describe the three radii of the ellipsoid as equatorial and polar, they may be given in $any$ size order. To avoid multiple solutions, especially with Monte-Carlo fit methods, it may be advisable to restrict their ranges. For typical small angle diffraction situations there may be a number of closely similar "best fits", so some trial and error, or fixing of some radii at expected values, may help. To provide easy access to the orientation of the triaxial ellipsoid, we define the axis of the cylinder using the angles $\theta$, $\phi$ and $\psi$. These angles are defined analogously to the elliptical_cylinder below, note that angle $\phi$ is now NOT the same as in the equations above. .. figure:: img/elliptical_cylinder_angle_definition.png Definition of angles for oriented triaxial ellipsoid, where radii are for illustration here $a < b << c$ and angle $\Psi$ is a rotation around the axis of the particle. For oriented ellipsoids the *theta*, *phi* and *psi* orientation parameters will appear when fitting 2D data, see the :ref:`elliptical-cylinder` model for further information. .. _triaxial-ellipsoid-angles: .. figure:: img/triaxial_ellipsoid_angle_projection.png Some examples for an oriented triaxial ellipsoid. The radius-of-gyration for this system is $R_g^2 = (R_a R_b R_c)^2/5$. The contrast $\Delta\rho$ is defined as SLD(ellipsoid) - SLD(solvent). In the parameters, $R_a$ is the minor equatorial radius, $R_b$ is the major equatorial radius, and $R_c$ is the polar radius of the ellipsoid. NB: The 2nd virial coefficient of the triaxial solid ellipsoid is calculated after sorting the three radii to give the most appropriate prolate or oblate form, from the new polar radius $R_p = R_c$ and effective equatorial radius, $R_e = \sqrt{R_a R_b}$, to then be used as the effective radius for $S(q)$ when $P(q) \cdot S(q)$ is applied. Validation ---------- Validation of our code was done by comparing the output of the 1D calculation to the angular average of the output of 2D calculation over all possible angles. References ---------- [1] Finnigan, J.A., Jacobs, D.J., 1971. *Light scattering by ellipsoidal particles in solution*, J. Phys. D: Appl. Phys. 4, 72-77. doi:10.1088/0022-3727/4/1/310 Authorship and Verification ---------------------------- * **Author:** NIST IGOR/DANSE **Date:** pre 2010 * **Last Modified by:** Paul Kienzle (improved calculation) **Date:** April 4, 2017 * **Last Reviewed by:** Paul Kienzle & Richard Heenan **Date:** April 4, 2017 """ from numpy import inf, sin, cos, pi name = "triaxial_ellipsoid" title = "Ellipsoid of uniform scattering length density with three independent axes." description = """ Triaxial ellipsoid - see main documentation. """ category = "shape:ellipsoid" # ["name", "units", default, [lower, upper], "type","description"], parameters = [["sld", "1e-6/Ang^2", 4, [-inf, inf], "sld", "Ellipsoid scattering length density"], ["sld_solvent", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Solvent scattering length density"], ["radius_equat_minor", "Ang", 20, [0, inf], "volume", "Minor equatorial radius, Ra"], ["radius_equat_major", "Ang", 400, [0, inf], "volume", "Major equatorial radius, Rb"], ["radius_polar", "Ang", 10, [0, inf], "volume", "Polar radius, Rc"], ["theta", "degrees", 60, [-360, 360], "orientation", "polar axis to beam angle"], ["phi", "degrees", 60, [-360, 360], "orientation", "rotation about beam"], ["psi", "degrees", 60, [-360, 360], "orientation", "rotation about polar axis"], ] source = ["lib/sas_3j1x_x.c", "lib/gauss76.c", "triaxial_ellipsoid.c"] def ER(radius_equat_minor, radius_equat_major, radius_polar): """ Returns the effective radius used in the S*P calculation """ import numpy as np from .ellipsoid import ER as ellipsoid_ER # now that radii can be in any size order, radii need sorting a,b,c # where a~b and c is either much smaller or much larger radii = np.vstack((radius_equat_major, radius_equat_minor, radius_polar)) radii = np.sort(radii, axis=0) selector = (radii[1] - radii[0]) > (radii[2] - radii[1]) polar = np.where(selector, radii[0], radii[2]) equatorial = np.sqrt(np.where(~selector, radii[0]*radii[1], radii[1]*radii[2])) return ellipsoid_ER(polar, equatorial) def random(): import numpy as np a, b, c = 10**np.random.uniform(1, 4.7, size=3) pars = dict( radius_equat_minor=a, radius_equat_major=b, radius_polar=c, ) return pars demo = dict(scale=1, background=0, sld=6, sld_solvent=1, theta=30, phi=15, psi=5, radius_equat_minor=25, radius_equat_major=36, radius_polar=50, radius_equat_minor_pd=0, radius_equat_minor_pd_n=1, radius_equat_major_pd=0, radius_equat_major_pd_n=1, radius_polar_pd=.2, radius_polar_pd_n=30, theta_pd=15, theta_pd_n=45, phi_pd=15, phi_pd_n=1, psi_pd=15, psi_pd_n=1) q = 0.1 # april 6 2017, rkh add unit tests # NOT compared with any other calc method, assume correct! # check 2d test after pull #890 qx = q*cos(pi/6.0) qy = q*sin(pi/6.0) tests = [[{}, 0.05, 24.8839548033], [{'theta':80., 'phi':10.}, (qx, qy), 166.712060266 ], ] del qx, qy # not necessary to delete, but cleaner sasmodels/sasmodels/models/two_lorentzian.py000066400000000000000000000132071317715334700217730ustar00rootroot00000000000000r""" Definition ---------- The scattering intensity $I(q)$ is calculated as .. math:: I(q) = \frac{A}{1 +(Q\xi_1)^n} + \frac{C}{1 +(Q\xi_2)^m} + \text{B} where $A$ = Lorentzian scale factor #1, $C$ = Lorentzian scale #2, $\xi_1$ and $\xi_2$ are the corresponding correlation lengths, and $n$ and $m$ are the respective power law exponents (set $n = m = 2$ for Ornstein-Zernicke behaviour). For 2D data the scattering intensity is calculated in the same way as 1D, where the $q$ vector is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- None. **Author:** NIST IGOR/DANSE **on:** pre 2010 **Last Modified by:** Piotr rozyczko **on:** January 29, 2016 **Last Reviewed by:** Paul Butler **on:** March 21, 2016 """ from numpy import inf, power name = "two_lorentzian" title = "This model calculates an empirical functional form for SAS data \ characterized by two Lorentzian-type functions." description = """I(q) = scale_1/(1.0 + pow((q*length_1),exponent_1)) + scale_2/(1.0 + pow((q*length_2),exponent_2) )+ background scale_1 = Lorentzian term scaling #1 length_1 = Lorentzian screening length #1 [A] exponent_1 = Lorentzian exponent #1 scale_2 = Lorentzian term scaling #2 length_2 = Lorentzian screening length #2 [A] exponent_2 = Lorentzian exponent #2 background = Incoherent background """ category = "shape-independent" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type", "description"], parameters = [["lorentz_scale_1", "", 10.0, [-inf, inf], "", "First power law scale factor"], ["lorentz_length_1", "Ang", 100.0, [-inf, inf], "", "First Lorentzian screening length"], ["lorentz_exp_1", "", 3.0, [-inf, inf], "", "First exponent of power law"], ["lorentz_scale_2", "", 1.0, [-inf, inf], "", "Second scale factor for broad Lorentzian peak"], ["lorentz_length_2", "Ang", 10.0, [-inf, inf], "", "Second Lorentzian screening length"], ["lorentz_exp_2", "", 2.0, [-inf, inf], "", "Second exponent of power law"], ] # pylint: enable=bad-whitespace, line-too-long def Iq(q, lorentz_scale_1=10.0, lorentz_length_1=100.0, lorentz_exp_1=3.0, lorentz_scale_2=1.0, lorentz_length_2=10.0, lorentz_exp_2=2.0): """ :param q: Input q-value (float or [float, float]) :param lorentz_scale_1: Second scale factor for broad Lorentzian peak :param lorentz_length_1: First Lorentzian screening length :param lorentz_exp_1: Exponent of the second Lorentz function :param lorentz_scale_2: Second scale factor for broad Lorentzian peak :param lorentz_length_2: Second Lorentzian screening length :param lorentz_exp_2: Exponent of the second Lorentz function :return: Calculated intensity """ # pylint: disable=bad-whitespace intensity = lorentz_scale_1/(1.0 + power(q*lorentz_length_1, lorentz_exp_1)) intensity += lorentz_scale_2/(1.0 + power(q*lorentz_length_2, lorentz_exp_2)) # pylint: enable=bad-whitespace return intensity Iq.vectorized = True # Iq accepts an array of q values def random(): import numpy as np scale = 10**np.random.uniform(0, 4, 2) length = 10**np.random.uniform(1, 4, 2) expon = np.random.uniform(1, 6, 2) pars = dict( #background=0, scale=1, # scale provided in model lorentz_scale_1=scale[0], lorentz_length_1=length[0], lorentz_exp_1=expon[0], lorentz_scale_2=scale[1], lorentz_length_2=length[1], lorentz_exp_2=expon[1], ) return pars demo = dict(scale=1, background=0.1, lorentz_scale_1=10, lorentz_length_1=100.0, lorentz_exp_1=3.0, lorentz_scale_2=1, lorentz_length_2=10, lorentz_exp_2=2.0) tests = [ # Accuracy tests based on content in test/utest_extra_models.py [{'lorentz_scale_1': 10.0, 'lorentz_length_1': 100.0, 'lorentz_exp_1': 3.0, 'lorentz_scale_2': 1.0, 'lorentz_length_2': 10.0, 'lorentz_exp_2': 2.0, 'background': 0.1, }, 0.001, 11.08991], [{'lorentz_scale_1': 10.0, 'lorentz_length_1': 100.0, 'lorentz_exp_1': 3.0, 'lorentz_scale_2': 1.0, 'lorentz_length_2': 10.0, 'lorentz_exp_2': 2.0, 'background': 0.1, }, 0.150141, 0.410245], [{'lorentz_scale_1': 10.0, 'lorentz_length_1': 100.0, 'lorentz_exp_1': 3.0, 'lorentz_scale_2': 1.0, 'lorentz_length_2': 10.0, 'lorentz_exp_2': 2.0, 'background': 0.1, }, 0.442528, 0.148699], # Additional tests with larger range of parameters [{'lorentz_scale_1': 10.0, 'lorentz_length_1': 100.0, 'lorentz_exp_1': 3.0, 'lorentz_scale_2': 1.0, 'lorentz_length_2': 10.0, 'lorentz_exp_2': 2.0, }, 0.000332070182643, 10.9996228107], [{'lorentz_scale_1': 0.0, 'lorentz_length_1': 0.0, 'lorentz_exp_1': 0.0, 'lorentz_scale_2': 0.0, 'lorentz_length_2': 0.0, 'lorentz_exp_2': 0.0, 'background': 100.0 }, 5.0, 100.0], [{'lorentz_scale_1': 200.0, 'lorentz_length_1': 10.0, 'lorentz_exp_1': 0.1, 'lorentz_scale_2': 0.1, 'lorentz_length_2': 5.0, 'lorentz_exp_2': 2.0 }, 20000., 45.5659201896], ] sasmodels/sasmodels/models/two_power_law.py000066400000000000000000000105221317715334700216020ustar00rootroot00000000000000r""" Definition ---------- The scattering intensity $I(q)$ is calculated as .. math:: I(q) = \begin{cases} A q^{-m1} + \text{background} & q <= q_c \\ C q^{-m2} + \text{background} & q > q_c \end{cases} where $q_c$ = the location of the crossover from one slope to the other, $A$ = the scaling coefficent that sets the overall intensity of the lower Q power law region, $m1$ = power law exponent at low Q, and $m2$ = power law exponent at high Q. The scaling of the second power law region (coefficent C) is then automatically scaled to match the first by following formula: .. math:: C = \frac{A q_c^{m2}}{q_c^{m1}} .. note:: Be sure to enter the power law exponents as positive values! For 2D data the scattering intensity is calculated in the same way as 1D, where the $q$ vector is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- None. **Author:** NIST IGOR/DANSE **on:** pre 2010 **Last Modified by:** Wojciech Wpotrzebowski **on:** February 18, 2016 **Last Reviewed by:** Paul Butler **on:** March 21, 2016 """ from numpy import inf, power, empty, errstate name = "two_power_law" title = "This model calculates an empirical functional form for SAS data \ characterized by two power laws." description = """ I(q) = coef_A*pow(qval,-1.0*power1) + background for q<=q_c =C*pow(qval,-1.0*power2) + background for q>q_c where C=coef_A*pow(q_c,-1.0*power1)/pow(q_c,-1.0*power2). coef_A = scaling coefficent q_c = crossover location [1/A] power_1 (=m1) = power law exponent at low Q power_2 (=m2) = power law exponent at high Q background = Incoherent background [1/cm] """ category = "shape-independent" # pylint: disable=bad-whitespace, line-too-long # ["name", "units", default, [lower, upper], "type", "description"], parameters = [ ["coefficent_1", "", 1.0, [-inf, inf], "", "coefficent A in low Q region"], ["crossover", "1/Ang", 0.04,[0, inf], "", "crossover location"], ["power_1", "", 1.0, [0, inf], "", "power law exponent at low Q"], ["power_2", "", 4.0, [0, inf], "", "power law exponent at high Q"], ] # pylint: enable=bad-whitespace, line-too-long def Iq(q, coefficent_1=1.0, crossover=0.04, power_1=1.0, power_2=4.0, ): """ :param q: Input q-value (float or [float, float]) :param coefficent_1: Scaling coefficent at low Q :param crossover: Crossover location :param power_1: Exponent of power law function at low Q :param power_2: Exponent of power law function at high Q :return: Calculated intensity """ result= empty(q.shape, 'd') index = (q <= crossover) with errstate(divide='ignore'): coefficent_2 = coefficent_1 * power(crossover, power_2 - power_1) result[index] = coefficent_1 * power(q[index], -power_1) result[~index] = coefficent_2 * power(q[~index], -power_2) return result Iq.vectorized = True # Iq accepts an array of q values def random(): import numpy as np coefficient_1 = 1 crossover = 10**np.random.uniform(-3, -1) power_1 = np.random.uniform(1, 6) power_2 = np.random.uniform(1, 6) pars = dict( scale=1, #background=0, coefficient_1=coefficient_1, crossover=crossover, power_1=power_1, power_2=power_2, ) return pars demo = dict(scale=1, background=0.0, coefficent_1=1.0, crossover=0.04, power_1=1.0, power_2=4.0) tests = [ # Accuracy tests based on content in test/utest_extra_models.py [{'coefficent_1': 1.0, 'crossover': 0.04, 'power_1': 1.0, 'power_2': 4.0, 'background': 0.0, }, 0.001, 1000], [{'coefficent_1': 1.0, 'crossover': 0.04, 'power_1': 1.0, 'power_2': 4.0, 'background': 0.0, }, 0.150141, 0.125945], [{'coefficent_1': 1.0, 'crossover': 0.04, 'power_1': 1.0, 'power_2': 4.0, 'background': 0.0, }, 0.442528, 0.00166884], [{'coefficent_1': 1.0, 'crossover': 0.04, 'power_1': 1.0, 'power_2': 4.0, 'background': 0.0, }, (0.442528, 0.00166884), 0.00166884], ] sasmodels/sasmodels/models/unified_power_Rg.py000066400000000000000000000106101317715334700221770ustar00rootroot00000000000000r""" Definition ---------- This model employs the empirical multiple level unified Exponential/Power-law fit method developed by Beaucage. Four functions are included so that 1, 2, 3, or 4 levels can be used. In addition a 0 level has been added which simply calculates .. math:: I(q) = \text{scale} / q + \text{background} The Beaucage method is able to reasonably approximate the scattering from many different types of particles, including fractal clusters, random coils (Debye equation), ellipsoidal particles, etc. The model works best for mass fractal systems characterized by Porod exponents between 5/3 and 3. It should not be used for surface fractal systems. Hammouda (2010) has pointed out a deficiency in the way this model handles the transitioning between the Guinier and Porod regimes and which can create artefacts that appear as kinks in the fitted model function. Also see the Guinier_Porod model. The empirical fit function is: .. math:: I(q) = \text{background} + \sum_{i=1}^N \Bigl[ G_i \exp\Bigl(-\frac{q^2R_{gi}^2}{3}\Bigr) + B_i \exp\Bigl(-\frac{q^2R_{g(i+1)}^2}{3}\Bigr) \Bigl(\frac{1}{q_i^*}\Bigr)^{P_i} \Bigr] where .. math:: q_i^* = q \left[\operatorname{erf} \left(\frac{q R_{gi}}{\sqrt{6}}\right) \right]^{-3} For each level, the four parameters $G_i$, $R_{gi}$, $B_i$ and $P_i$ must be chosen. Beaucage has an additional factor $k$ in the definition of $q_i^*$ which is ignored here. For example, to approximate the scattering from random coils (Debye equation), set $R_{gi}$ as the Guinier radius, $P_i = 2$, and $B_i = 2 G_i / R_{gi}$ See the references for further information on choosing the parameters. For 2D data: The 2D scattering intensity is calculated in the same way as 1D, where the $q$ vector is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} References ---------- G Beaucage, *J. Appl. Cryst.*, 28 (1995) 717-728 G Beaucage, *J. Appl. Cryst.*, 29 (1996) 134-146 B Hammouda, *Analysis of the Beaucage model, J. Appl. Cryst.*, (2010), 43, 1474-1478 """ from __future__ import division import numpy as np from numpy import inf, exp, sqrt, errstate from scipy.special import erf category = "shape-independent" name = "unified_power_Rg" title = "Unified Power Rg" description = """ The Beaucage model employs the empirical multiple level unified Exponential/Power-law fit method developed by G. Beaucage. Four functions are included so that 1, 2, 3, or 4 levels can be used. """ # pylint: disable=bad-whitespace, line-too-long parameters = [ ["level", "", 1, [1, 6], "", "Level number"], ["rg[level]", "Ang", 15.8, [0, inf], "", "Radius of gyration"], ["power[level]", "", 4, [-inf, inf], "", "Power"], ["B[level]", "1/cm", 4.5e-6, [-inf, inf], "", ""], ["G[level]", "1/cm", 400, [0, inf], "", ""], ] # pylint: enable=bad-whitespace, line-too-long def Iq(q, level, rg, power, B, G): level = int(level + 0.5) if level == 0: with errstate(divide='ignore'): return 1./q with errstate(divide='ignore', invalid='ignore'): result = np.zeros(q.shape, 'd') for i in range(level): exp_now = exp(-(q*rg[i])**2/3.) pow_now = (erf(q*rg[i]/sqrt(6.))**3/q)**power[i] if i < level-1: exp_next = exp(-(q*rg[i+1])**2/3.) else: exp_next = 1 result += G[i]*exp_now + B[i]*exp_next*pow_now result[q == 0] = np.sum(G[:level]) return result Iq.vectorized = True def random(): import numpy as np from scipy.special import gamma level = np.minimum(np.random.poisson(0.5) + 1, 6) n = level power = np.random.uniform(1.6, 3, n) rg = 10**np.random.uniform(1, 5, n) G = np.random.uniform(0.1, 10, n)**2 * 10**np.random.uniform(0.3, 3, n) B = G * power / rg**power * gamma(power/2) scale = 10**np.random.uniform(1, 4) pars = dict( #background=0, scale=scale, level=level, ) pars.update(("power%d"%(k+1), v) for k, v in enumerate(power)) pars.update(("rg%d"%(k+1), v) for k, v in enumerate(rg)) pars.update(("B%d"%(k+1), v) for k, v in enumerate(B)) pars.update(("G%d"%(k+1), v) for k, v in enumerate(G)) return pars demo = dict( level=2, rg=[15.8, 21], power=[4, 2], B=[4.5e-6, 0.0006], G=[400, 3], scale=1., background=0., ) sasmodels/sasmodels/models/vesicle.c000066400000000000000000000021271317715334700201400ustar00rootroot00000000000000double form_volume(double radius, double thickness); double Iq(double q, double sld, double sld_solvent, double volfraction, double radius, double thickness); double form_volume(double radius, double thickness) { //note that for the vesicle model, the volume is ONLY the shell volume return M_4PI_3*(cube(radius+thickness) - cube(radius)); } double Iq(double q, double sld, double sld_solvent, double volfraction, double radius, double thickness) /* scattering from a unilamellar vesicle. same functional form as the core-shell sphere, but more intuitive for a vesicle */ { double vol,contrast,f,f2; // core first, then add in shell contrast = sld_solvent-sld; vol = M_4PI_3*cube(radius); f = vol * sas_3j1x_x(q*radius) * contrast; //now the shell. No volume normalization as this is done by the caller contrast = sld-sld_solvent; vol = M_4PI_3*cube(radius+thickness); f += vol * sas_3j1x_x(q*(radius+thickness)) * contrast; //rescale to [cm-1]. f2 = volfraction * f*f*1.0e-4; return f2; } sasmodels/sasmodels/models/vesicle.py000066400000000000000000000123751317715334700203540ustar00rootroot00000000000000r""" Definition ---------- The 1D scattering intensity is calculated in the following way (Guinier, 1955) .. math:: P(q) = \frac{\phi}{V_\text{shell}} \left[ \frac{3V_{\text{core}}({\rho_{\text{solvent}} - \rho_{\text{shell}})j_1(qR_{\text{core}})}}{qR_{\text{core}}} + \frac{3V_{\text{tot}}(\rho_{\text{shell}} - \rho_{\text{solvent}}) j_1(qR_{\text{tot}})}{qR_{\text{tot}}} \right]^2 + \text{background} where $\phi$ is the volume fraction of shell material, $V_{shell}$ is the volume of the shell, $V_{\text{cor}}$ is the volume of the core, $V_{\text{tot}}$ is the total volume, $R_{\text{core}}$ is the radius of the core, $R_{\text{tot}}$ is the outer radius of the shell, $\rho_{\text{solvent}}$ is the scattering length density of the solvent (which is the same as for the core in this case), $\rho_{\text{scale}}$ is the scattering length density of the shell, background is a flat background level (due for example to incoherent scattering in the case of neutrons), and $j_1$ is the spherical bessel function $j_1 = (\sin(x) - x \cos(x))/ x^2$. The functional form is identical to a "typical" core-shell structure, except that the scattering is normalized by the volume that is contributing to the scattering, namely the volume of the shell alone, the scattering length density of the core is fixed the same as that of the solvent, the scale factor when the data are on an absolute scale is equivalent to the volume fraction of material in the shell rather than the entire core+shell sphere, and the parameterization is done in terms of the core radius = $R_{\text{core}}$ and the shell thickness = $R_{\text{tot}} - R_{\text{core}}$. .. figure:: img/vesicle_geometry.jpg Vesicle geometry. The 2D scattering intensity is the same as *P(q)* above, regardless of the orientation of the *q* vector which is defined as .. math:: q = \sqrt{q_x^2 + q_y^2} NB: The outer most radius (= *radius* + *thickness*) is used as the effective radius for *S(Q)* when *P(Q)* \* *S(Q)* is applied. References ---------- A Guinier and G. Fournet, *Small-Angle Scattering of X-Rays*, John Wiley and Sons, New York, (1955) **Author:** NIST IGOR/DANSE **on:** pre 2010 **Last Modified by:** Paul Butler **on:** March 20, 2016 **Last Reviewed by:** Paul Butler **on:** March 20, 2016 """ from numpy import pi, inf name = "vesicle" title = "This model provides the form factor, *P(q)*, for an unilamellar \ vesicle. This is model is effectively identical to the hollow sphere \ reparameterized to be more intuitive for a vesicle and normalizing the \ form factor by the volume of the shell." description = """ Model parameters: radius : the core radius of the vesicle thickness: the shell thickness sld: the shell SLD sld_solvent: the solvent (and core) SLD background: incoherent background volfraction: shell volume fraction scale : scale factor = 1 if on absolute scale""" category = "shape:sphere" # [ "name", "units", default, [lower, upper], "type", "description"], parameters = [["sld", "1e-6/Ang^2", 0.5, [-inf, inf], "sld", "vesicle shell scattering length density"], ["sld_solvent", "1e-6/Ang^2", 6.36, [-inf, inf], "sld", "solvent scattering length density"], ["volfraction", "", 0.05, [0, 1.0], "", "volume fraction of shell"], ["radius", "Ang", 100, [0, inf], "volume", "vesicle core radius"], ["thickness", "Ang", 30, [0, inf], "volume", "vesicle shell thickness"], ] source = ["lib/sas_3j1x_x.c", "vesicle.c"] def ER(radius, thickness): ''' returns the effective radius used in the S*P calculation :param radius: core radius :param thickness: shell thickness ''' return radius + thickness def VR(radius, thickness): ''' returns the volumes of the shell and of the whole sphere including the core plus shell - is used to normalize when including polydispersity. :param radius: core radius :param thickness: shell thickness :return whole: volume of core and shell :return whole-core: volume of the shell ''' whole = 4./3. * pi * (radius + thickness)**3 core = 4./3. * pi * radius**3 return whole, whole - core def random(): import numpy as np total_radius = 10**np.random.uniform(1.3, 5) radius = total_radius * np.random.uniform(0, 1) thickness = total_radius - radius volfraction = 10**np.random.uniform(-3, -1) pars = dict( #background=0, scale=1, # volfraction is part of the model, so scale=1 radius=radius, thickness=thickness, volfraction=volfraction, ) return pars # parameters for demo demo = dict(sld=0.5, sld_solvent=6.36, volfraction=0.05, radius=100, thickness=30, radius_pd=.2, radius_pd_n=10, thickness_pd=.2, thickness_pd_n=10) # NOTE: test results taken from values returned by SasView 3.1.2, with # 0.001 added for a non-zero default background. tests = [[{}, 0.0005, 859.916526646], [{}, 0.100600200401, 1.77063682331], [{}, 0.5, 0.00355351388906], [{}, 'ER', 130.], [{}, 'VR', 0.54483386436], ] sasmodels/sasmodels/product.py000066400000000000000000000317201317715334700171120ustar00rootroot00000000000000""" Product model ------------- The product model multiplies the structure factor by the form factor, modulated by the effective radius of the form. The resulting model has a attributes of both the model description (with parameters, etc.) and the module evaluator (with call, release, etc.). To use it, first load form factor P and structure factor S, then create *make_product_info(P, S)*. """ from __future__ import print_function, division from copy import copy import numpy as np # type: ignore from .modelinfo import Parameter, ParameterTable, ModelInfo from .kernel import KernelModel, Kernel from .details import make_details, dispersion_mesh try: from typing import Tuple except ImportError: pass # TODO: make estimates available to constraints #ESTIMATED_PARAMETERS = [ # ["est_radius_effective", "A", 0.0, [0, np.inf], "", "Estimated effective radius"], # ["est_volume_ratio", "", 1.0, [0, np.inf], "", "Estimated volume ratio"], #] ER_ID = "radius_effective" VF_ID = "volfraction" # TODO: core_shell_sphere model has suppressed the volume ratio calculation # revert it after making VR and ER available at run time as constraints. def make_product_info(p_info, s_info): # type: (ModelInfo, ModelInfo) -> ModelInfo """ Create info block for product model. """ # Make sure effective radius is the first parameter and # make sure volume fraction is the second parameter of the # structure factor calculator. Structure factors should not # have any magnetic parameters if not len(s_info.parameters.kernel_parameters) >= 2: raise TypeError("S needs {} and {} as its first parameters".format(ER_ID, VF_ID)) if not s_info.parameters.kernel_parameters[0].id == ER_ID: raise TypeError("S needs {} as first parameter".format(ER_ID)) if not s_info.parameters.kernel_parameters[1].id == VF_ID: raise TypeError("S needs {} as second parameter".format(VF_ID)) if not s_info.parameters.magnetism_index == []: raise TypeError("S should not have SLD parameters") p_id, p_name, p_pars = p_info.id, p_info.name, p_info.parameters s_id, s_name, s_pars = s_info.id, s_info.name, s_info.parameters # Create list of parameters for the combined model. Skip the first # parameter of S, which we verified above is effective radius. If there # are any names in P that overlap with those in S, modify the name in S # to distinguish it. p_set = set(p.id for p in p_pars.kernel_parameters) s_list = [(_tag_parameter(par) if par.id in p_set else par) for par in s_pars.kernel_parameters[1:]] # Check if still a collision after renaming. This could happen if for # example S has volfrac and P has both volfrac and volfrac_S. if any(p.id in p_set for p in s_list): raise TypeError("name collision: P has P.name and P.name_S while S has S.name") translate_name = dict((old.id, new.id) for old, new in zip(s_pars.kernel_parameters[1:], s_list)) combined_pars = p_pars.kernel_parameters + s_list parameters = ParameterTable(combined_pars) parameters.max_pd = p_pars.max_pd + s_pars.max_pd def random(): combined_pars = p_info.random() s_names = set(par.id for par in s_pars.kernel_parameters[1:]) s = s_info.random() combined_pars.update((translate_name[k], v) for k, v in s_info.random().items() if k in s_names) return combined_pars model_info = ModelInfo() model_info.id = '@'.join((p_id, s_id)) model_info.name = '@'.join((p_name, s_name)) model_info.filename = None model_info.title = 'Product of %s and %s'%(p_name, s_name) model_info.description = model_info.title model_info.docs = model_info.title model_info.category = "custom" model_info.parameters = parameters model_info.random = random #model_info.single = p_info.single and s_info.single model_info.structure_factor = False model_info.variant_info = None #model_info.tests = [] #model_info.source = [] # Iq, Iqxy, form_volume, ER, VR and sesans # Remember the component info blocks so we can build the model model_info.composition = ('product', [p_info, s_info]) model_info.control = p_info.control model_info.hidden = p_info.hidden if getattr(p_info, 'profile', None) is not None: profile_pars = set(p.id for p in p_info.parameters.kernel_parameters) def profile(**kwargs): # extract the profile args kwargs = dict((k, v) for k, v in kwargs.items() if k in profile_pars) return p_info.profile(**kwargs) else: profile = None model_info.profile = profile model_info.profile_axes = p_info.profile_axes # TODO: delegate random to p_info, s_info #model_info.random = lambda: {} ## Show the parameter table #from .compare import get_pars, parlist #print("==== %s ====="%model_info.name) #values = get_pars(model_info) #print(parlist(model_info, values, is2d=True)) return model_info def _tag_parameter(par): """ Tag the parameter name with _S to indicate that the parameter comes from the structure factor parameter set. This is only necessary if the form factor model includes a parameter of the same name as a parameter in the structure factor. """ par = copy(par) # Protect against a vector parameter in S by appending the vector length # to the renamed parameter. Note: haven't tested this since no existing # structure factor models contain vector parameters. vector_length = par.name[len(par.id):] par.id = par.id + "_S" par.name = par.id + vector_length return par class ProductModel(KernelModel): def __init__(self, model_info, P, S): # type: (ModelInfo, KernelModel, KernelModel) -> None #: Combined info plock for the product model self.info = model_info #: Form factor modelling individual particles. self.P = P #: Structure factor modelling interaction between particles. self.S = S #: Model precision. This is not really relevant, since it is the #: individual P and S models that control the effective dtype, #: converting the q-vectors to the correct type when the kernels #: for each are created. Ideally this should be set to the more #: precise type to avoid loss of precision, but precision in q is #: not critical (single is good enough for our purposes), so it just #: uses the precision of the form factor. self.dtype = P.dtype # type: np.dtype def make_kernel(self, q_vectors): # type: (List[np.ndarray]) -> Kernel # Note: may be sending the q_vectors to the GPU twice even though they # are only needed once. It would mess up modularity quite a bit to # handle this optimally, especially since there are many cases where # separate q vectors are needed (e.g., form in python and structure # in opencl; or both in opencl, but one in single precision and the # other in double precision). p_kernel = self.P.make_kernel(q_vectors) s_kernel = self.S.make_kernel(q_vectors) return ProductKernel(self.info, p_kernel, s_kernel) def release(self): # type: (None) -> None """ Free resources associated with the model. """ self.P.release() self.S.release() class ProductKernel(Kernel): def __init__(self, model_info, p_kernel, s_kernel): # type: (ModelInfo, Kernel, Kernel) -> None self.info = model_info self.p_kernel = p_kernel self.s_kernel = s_kernel self.dtype = p_kernel.dtype self.results = [] # type: List[np.ndarray] def __call__(self, call_details, values, cutoff, magnetic): # type: (CallDetails, np.ndarray, float, bool) -> np.ndarray p_info, s_info = self.info.composition[1] # if there are magnetic parameters, they will only be on the # form factor P, not the structure factor S. nmagnetic = len(self.info.parameters.magnetism_index) if nmagnetic: spin_index = self.info.parameters.npars + 2 magnetism = values[spin_index: spin_index+3+3*nmagnetic] else: magnetism = [] nvalues = self.info.parameters.nvalues nweights = call_details.num_weights weights = values[nvalues:nvalues + 2*nweights] # Construct the calling parameters for P. p_npars = p_info.parameters.npars p_length = call_details.length[:p_npars] p_offset = call_details.offset[:p_npars] p_details = make_details(p_info, p_length, p_offset, nweights) # Set p scale to the volume fraction in s, which is the first of the # 'S' parameters in the parameter list, or 2+np in 0-origin. volfrac = values[2+p_npars] p_values = [[volfrac, 0.0], values[2:2+p_npars], magnetism, weights] spacer = (32 - sum(len(v) for v in p_values)%32)%32 p_values.append([0.]*spacer) p_values = np.hstack(p_values).astype(self.p_kernel.dtype) # Call ER and VR for P since these are needed for S. p_er, p_vr = calc_er_vr(p_info, p_details, p_values) s_vr = (volfrac/p_vr if p_vr != 0. else volfrac) #print("volfrac:%g p_er:%g p_vr:%g s_vr:%g"%(volfrac,p_er,p_vr,s_vr)) # Construct the calling parameters for S. # The effective radius is not in the combined parameter list, so # the number of 'S' parameters is one less than expected. The # computed effective radius needs to be added into the weights # vector, especially since it is a polydisperse parameter in the # stand-alone structure factor models. We will added it at the # end so the remaining offsets don't need to change. s_npars = s_info.parameters.npars-1 s_length = call_details.length[p_npars:p_npars+s_npars] s_offset = call_details.offset[p_npars:p_npars+s_npars] s_length = np.hstack((1, s_length)) s_offset = np.hstack((nweights, s_offset)) s_details = make_details(s_info, s_length, s_offset, nweights+1) v, w = weights[:nweights], weights[nweights:] s_values = [ # scale=1, background=0, radius_effective=p_er, volfraction=s_vr [1., 0., p_er, s_vr], # structure factor parameters start after scale, background and # all the form factor parameters. Skip the volfraction parameter # as well, since it is computed elsewhere, and go to the end of the # parameter list. values[2+p_npars+1:2+p_npars+s_npars], # no magnetism parameters to include for S # add er into the (value, weights) pairs v, [p_er], w, [1.0] ] spacer = (32 - sum(len(v) for v in s_values)%32)%32 s_values.append([0.]*spacer) s_values = np.hstack(s_values).astype(self.s_kernel.dtype) # Call the kernels p_result = self.p_kernel(p_details, p_values, cutoff, magnetic) s_result = self.s_kernel(s_details, s_values, cutoff, False) #print("p_npars",p_npars,s_npars,p_er,s_vr,values[2+p_npars+1:2+p_npars+s_npars]) #call_details.show(values) #print("values", values) #p_details.show(p_values) #print("=>", p_result) #s_details.show(s_values) #print("=>", s_result) # remember the parts for plotting later self.results = [p_result, s_result] #import pylab as plt #plt.subplot(211); plt.loglog(self.p_kernel.q_input.q, p_result, '-') #plt.subplot(212); plt.loglog(self.s_kernel.q_input.q, s_result, '-') #plt.figure() return values[0]*(p_result*s_result) + values[1] def release(self): # type: () -> None self.p_kernel.release() self.s_kernel.release() def calc_er_vr(model_info, call_details, values): # type: (ModelInfo, ParameterSet) -> Tuple[float, float] if model_info.ER is None and model_info.VR is None: return 1.0, 1.0 nvalues = model_info.parameters.nvalues value = values[nvalues:nvalues + call_details.num_weights] weight = values[nvalues + call_details.num_weights: nvalues + 2*call_details.num_weights] npars = model_info.parameters.npars pairs = [(value[offset:offset+length], weight[offset:offset+length]) for p, offset, length in zip(model_info.parameters.call_parameters[2:2+npars], call_details.offset, call_details.length) if p.type == 'volume'] value, weight = dispersion_mesh(model_info, pairs) if model_info.ER is not None: individual_radii = model_info.ER(*value) radius_effective = np.sum(weight*individual_radii) / np.sum(weight) else: radius_effective = 1.0 if model_info.VR is not None: whole, part = model_info.VR(*value) volume_ratio = np.sum(weight*part)/np.sum(weight*whole) else: volume_ratio = 1.0 return radius_effective, volume_ratio sasmodels/sasmodels/resolution.py000066400000000000000000001172631317715334700176440ustar00rootroot00000000000000""" Define the resolution functions for the data. This defines classes for 1D and 2D resolution calculations. """ from __future__ import division from scipy.special import erf # type: ignore from numpy import sqrt, log, log10, exp, pi # type: ignore import numpy as np # type: ignore __all__ = ["Resolution", "Perfect1D", "Pinhole1D", "Slit1D", "apply_resolution_matrix", "pinhole_resolution", "slit_resolution", "pinhole_extend_q", "slit_extend_q", "bin_edges", "interpolate", "linear_extrapolation", "geometric_extrapolation", ] MINIMUM_RESOLUTION = 1e-8 MINIMUM_ABSOLUTE_Q = 0.02 # relative to the minimum q in the data class Resolution(object): """ Abstract base class defining a 1D resolution function. *q* is the set of q values at which the data is measured. *q_calc* is the set of q values at which the theory needs to be evaluated. This may extend and interpolate the q values. *apply* is the method to call with I(q_calc) to compute the resolution smeared theory I(q). """ q = None # type: np.ndarray q_calc = None # type: np.ndarray def apply(self, theory): """ Smear *theory* by the resolution function, returning *Iq*. """ raise NotImplementedError("Subclass does not define the apply function") class Perfect1D(Resolution): """ Resolution function to use when there is no actual resolution smearing to be applied. It has the same interface as the other resolution functions, but returns the identity function. """ def __init__(self, q): self.q_calc = self.q = q def apply(self, theory): return theory class Pinhole1D(Resolution): r""" Pinhole aperture with q-dependent gaussian resolution. *q* points at which the data is measured. *q_width* gaussian 1-sigma resolution at each data point. *q_calc* is the list of points to calculate, or None if this should be estimated from the *q* and *q_width*. """ def __init__(self, q, q_width, q_calc=None, nsigma=3): #*min_step* is the minimum point spacing to use when computing the #underlying model. It should be on the order of #$\tfrac{1}{10}\tfrac{2\pi}{d_\text{max}}$ to make sure that fringes #are computed with sufficient density to avoid aliasing effects. # Protect against calls with q_width=0. The extend_q function will # not extend the q if q_width is 0, but q_width must be non-zero when # constructing the weight matrix to avoid division by zero errors. # In practice this should never be needed, since resolution should # default to Perfect1D if the pinhole geometry is not defined. self.q, self.q_width = q, q_width self.q_calc = (pinhole_extend_q(q, q_width, nsigma=nsigma) if q_calc is None else np.sort(q_calc)) # Protect against models which are not defined for very low q. Limit # the smallest q value evaluated (in absolute) to 0.02*min cutoff = MINIMUM_ABSOLUTE_Q*np.min(self.q) self.q_calc = self.q_calc[abs(self.q_calc) >= cutoff] # Build weight matrix from calculated q values self.weight_matrix = pinhole_resolution(self.q_calc, self.q, np.maximum(q_width, MINIMUM_RESOLUTION)) self.q_calc = abs(self.q_calc) def apply(self, theory): return apply_resolution_matrix(self.weight_matrix, theory) class Slit1D(Resolution): """ Slit aperture with resolution function. *q* points at which the data is measured. *dqx* slit width in qx *dqy* slit height in qy *q_calc* is the list of points to calculate, or None if this should be estimated from the *q* and *q_width*. The *weight_matrix* is computed by :func:`slit1d_resolution` """ def __init__(self, q, qx_width, qy_width=0., q_calc=None): # Remember what width/dqy was used even though we won't need them # after the weight matrix is constructed self.qx_width, self.qy_width = qx_width, qy_width # Allow independent resolution on each point even though it is not # needed in practice. if np.isscalar(qx_width): qx_width = np.ones(len(q))*qx_width else: qx_width = np.asarray(qx_width) if np.isscalar(qy_width): qy_width = np.ones(len(q))*qy_width else: qy_width = np.asarray(qy_width) self.q = q.flatten() self.q_calc = slit_extend_q(q, qx_width, qy_width) \ if q_calc is None else np.sort(q_calc) # Protect against models which are not defined for very low q. Limit # the smallest q value evaluated (in absolute) to 0.02*min cutoff = MINIMUM_ABSOLUTE_Q*np.min(self.q) self.q_calc = self.q_calc[abs(self.q_calc) >= cutoff] # Build weight matrix from calculated q values self.weight_matrix = \ slit_resolution(self.q_calc, self.q, qx_width, qy_width) self.q_calc = abs(self.q_calc) def apply(self, theory): return apply_resolution_matrix(self.weight_matrix, theory) def apply_resolution_matrix(weight_matrix, theory): """ Apply the resolution weight matrix to the computed theory function. """ #print("apply shapes", theory.shape, weight_matrix.shape) Iq = np.dot(theory[None, :], weight_matrix) #print("result shape",Iq.shape) return Iq.flatten() def pinhole_resolution(q_calc, q, q_width): """ Compute the convolution matrix *W* for pinhole resolution 1-D data. Each row *W[i]* determines the normalized weight that the corresponding points *q_calc* contribute to the resolution smeared point *q[i]*. Given *W*, the resolution smearing can be computed using *dot(W,q)*. *q_calc* must be increasing. *q_width* must be greater than zero. """ # The current algorithm is a midpoint rectangle rule. In the test case, # neither trapezoid nor Simpson's rule improved the accuracy. edges = bin_edges(q_calc) #edges[edges < 0.0] = 0.0 # clip edges below zero cdf = erf((edges[:, None] - q[None, :]) / (sqrt(2.0)*q_width)[None, :]) weights = cdf[1:] - cdf[:-1] weights /= np.sum(weights, axis=0)[None, :] return weights def slit_resolution(q_calc, q, width, height, n_height=30): r""" Build a weight matrix to compute *I_s(q)* from *I(q_calc)*, given $q_\perp$ = *width* and $q_\parallel$ = *height*. *n_height* is is the number of steps to use in the integration over $q_\parallel$ when both $q_\perp$ and $q_\parallel$ are non-zero. Each $q$ can have an independent width and height value even though current instruments use the same slit setting for all measured points. If slit height is large relative to width, use: .. math:: I_s(q_i) = \frac{1}{\Delta q_\perp} \int_0^{\Delta q_\perp} I\left(\sqrt{q_i^2 + q_\perp^2}\right) \,dq_\perp If slit width is large relative to height, use: .. math:: I_s(q_i) = \frac{1}{2 \Delta q_\parallel} \int_{-\Delta q_\parallel}^{\Delta q_\parallel} I\left(|q_i + q_\parallel|\right) \,dq_\parallel For a mixture of slit width and height use: .. math:: I_s(q_i) = \frac{1}{2 \Delta q_\parallel \Delta q_\perp} \int_{-\Delta q_\parallel}^{\Delta q_\parallel} \int_0^{\Delta q_\perp} I\left(\sqrt{(q_i + q_\parallel)^2 + q_\perp^2}\right) \,dq_\perp dq_\parallel **Definition** We are using the mid-point integration rule to assign weights to each element of a weight matrix $W$ so that .. math:: I_s(q) = W\,I(q_\text{calc}) If *q_calc* is at the mid-point, we can infer the bin edges from the pairwise averages of *q_calc*, adding the missing edges before *q_calc[0]* and after *q_calc[-1]*. For $q_\parallel = 0$, the smeared value can be computed numerically using the $u$ substitution .. math:: u_j = \sqrt{q_j^2 - q^2} This gives .. math:: I_s(q) \approx \sum_j I(u_j) \Delta u_j where $I(u_j)$ is the value at the mid-point, and $\Delta u_j$ is the difference between consecutive edges which have been first converted to $u$. Only $u_j \in [0, \Delta q_\perp]$ are used, which corresponds to $q_j \in \left[q, \sqrt{q^2 + \Delta q_\perp}\right]$, so .. math:: W_{ij} = \frac{1}{\Delta q_\perp} \Delta u_j = \frac{1}{\Delta q_\perp} \left( \sqrt{q_{j+1}^2 - q_i^2} - \sqrt{q_j^2 - q_i^2} \right) \ \text{if}\ q_j \in \left[q_i, \sqrt{q_i^2 + q_\perp^2}\right] where $I_s(q_i)$ is the theory function being computed and $q_j$ are the mid-points between the calculated values in *q_calc*. We tweak the edges of the initial and final intervals so that they lie on integration limits. (To be precise, the transformed midpoint $u(q_j)$ is not necessarily the midpoint of the edges $u((q_{j-1}+q_j)/2)$ and $u((q_j + q_{j+1})/2)$, but it is at least in the interval, so the approximation is going to be a little better than the left or right Riemann sum, and should be good enough for our purposes.) For $q_\perp = 0$, the $u$ substitution is simpler: .. math:: u_j = \left|q_j - q\right| so .. math:: W_{ij} = \frac{1}{2 \Delta q_\parallel} \Delta u_j = \frac{1}{2 \Delta q_\parallel} (q_{j+1} - q_j) \ \text{if}\ q_j \in \left[q-\Delta q_\parallel, q+\Delta q_\parallel\right] However, we need to support cases were $u_j < 0$, which means using $2 (q_{j+1} - q_j)$ when $q_j \in \left[0, q_\parallel-q_i\right]$. This is not an issue for $q_i > q_\parallel$. For both $q_\perp > 0$ and $q_\parallel > 0$ we perform a 2 dimensional integration with .. math:: u_{jk} = \sqrt{q_j^2 - (q + (k\Delta q_\parallel/L))^2} \ \text{for}\ k = -L \ldots L for $L$ = *n_height*. This gives .. math:: W_{ij} = \frac{1}{2 \Delta q_\perp q_\parallel} \sum_{k=-L}^L \Delta u_{jk} \left(\frac{\Delta q_\parallel}{2 L + 1}\right) """ #np.set_printoptions(precision=6, linewidth=10000) # The current algorithm is a midpoint rectangle rule. q_edges = bin_edges(q_calc) # Note: requires q > 0 #q_edges[q_edges < 0.0] = 0.0 # clip edges below zero weights = np.zeros((len(q), len(q_calc)), 'd') #print(q_calc) for i, (qi, w, h) in enumerate(zip(q, width, height)): if w == 0. and h == 0.: # Perfect resolution, so return the theory value directly. # Note: assumes that q is a subset of q_calc. If qi need not be # in q_calc, then we can do a weighted interpolation by looking # up qi in q_calc, then weighting the result by the relative # distance to the neighbouring points. weights[i, :] = (q_calc == qi) elif h == 0: weights[i, :] = _q_perp_weights(q_edges, qi, w) elif w == 0: in_x = 1.0 * ((q_calc >= qi-h) & (q_calc <= qi+h)) abs_x = 1.0*(q_calc < abs(qi - h)) if qi < h else 0. #print(qi - h, qi + h) #print(in_x + abs_x) weights[i, :] = (in_x + abs_x) * np.diff(q_edges) / (2*h) else: for k in range(-n_height, n_height+1): weights[i, :] += _q_perp_weights(q_edges, qi+k*h/n_height, w) weights[i, :] /= 2*n_height + 1 return weights.T def _q_perp_weights(q_edges, qi, w): # Convert bin edges from q to u u_limit = np.sqrt(qi**2 + w**2) u_edges = q_edges**2 - qi**2 u_edges[q_edges < abs(qi)] = 0. u_edges[q_edges > u_limit] = u_limit**2 - qi**2 weights = np.diff(np.sqrt(u_edges))/w #print("i, qi",i,qi,qi+width) #print(q_calc) #print(weights) return weights def pinhole_extend_q(q, q_width, nsigma=3): """ Given *q* and *q_width*, find a set of sampling points *q_calc* so that each point $I(q)$ has sufficient support from the underlying function. """ q_min, q_max = np.min(q - nsigma*q_width), np.max(q + nsigma*q_width) return linear_extrapolation(q, q_min, q_max) def slit_extend_q(q, width, height): """ Given *q*, *width* and *height*, find a set of sampling points *q_calc* so that each point I(q) has sufficient support from the underlying function. """ q_min, q_max = np.min(q-height), np.max(np.sqrt((q+height)**2 + width**2)) return geometric_extrapolation(q, q_min, q_max) def bin_edges(x): """ Determine bin edges from bin centers, assuming that edges are centered between the bins. Note: this uses the arithmetic mean, which may not be appropriate for log-scaled data. """ if len(x) < 2 or (np.diff(x) < 0).any(): raise ValueError("Expected bins to be an increasing set") edges = np.hstack([ x[0] - 0.5*(x[1] - x[0]), # first point minus half first interval 0.5*(x[1:] + x[:-1]), # mid points of all central intervals x[-1] + 0.5*(x[-1] - x[-2]), # last point plus half last interval ]) return edges def interpolate(q, max_step): """ Returns *q_calc* with points spaced at most max_step apart. """ step = np.diff(q) index = step > max_step if np.any(index): inserts = [] for q_i, step_i in zip(q[:-1][index], step[index]): n = np.ceil(step_i/max_step) inserts.extend(q_i + np.arange(1, n)*(step_i/n)) # Extend a couple of fringes beyond the end of the data inserts.extend(q[-1] + np.arange(1, 8)*max_step) q_calc = np.sort(np.hstack((q, inserts))) else: q_calc = q return q_calc def linear_extrapolation(q, q_min, q_max): """ Extrapolate *q* out to [*q_min*, *q_max*] using the step size in *q* as a guide. Extrapolation below uses about the same size as the first interval. Extrapolation above uses about the same size as the final interval. Note that extrapolated values may be negative. """ q = np.sort(q) if q_min + 2*MINIMUM_RESOLUTION < q[0]: n_low = np.ceil((q[0]-q_min) / (q[1]-q[0])) if q[1] > q[0] else 15 q_low = np.linspace(q_min, q[0], n_low+1)[:-1] else: q_low = [] if q_max - 2*MINIMUM_RESOLUTION > q[-1]: n_high = np.ceil((q_max-q[-1]) / (q[-1]-q[-2])) if q[-1] > q[-2] else 15 q_high = np.linspace(q[-1], q_max, n_high+1)[1:] else: q_high = [] return np.concatenate([q_low, q, q_high]) def geometric_extrapolation(q, q_min, q_max, points_per_decade=None): r""" Extrapolate *q* to [*q_min*, *q_max*] using geometric steps, with the average geometric step size in *q* as the step size. if *q_min* is zero or less then *q[0]/10* is used instead. *points_per_decade* sets the ratio between consecutive steps such that there will be $n$ points used for every factor of 10 increase in *q*. If *points_per_decade* is not given, it will be estimated as follows. Starting at $q_1$ and stepping geometrically by $\Delta q$ to $q_n$ in $n$ points gives a geometric average of: .. math:: \log \Delta q = (\log q_n - \log q_1) / (n - 1) From this we can compute the number of steps required to extend $q$ from $q_n$ to $q_\text{max}$ by $\Delta q$ as: .. math:: n_\text{extend} = (\log q_\text{max} - \log q_n) / \log \Delta q Substituting: .. math:: n_\text{extend} = (n-1) (\log q_\text{max} - \log q_n) / (\log q_n - \log q_1) """ q = np.sort(q) if points_per_decade is None: log_delta_q = (len(q) - 1) / (log(q[-1]) - log(q[0])) else: log_delta_q = log(10.) / points_per_decade if q_min < q[0]: if q_min < 0: q_min = q[0]*MINIMUM_ABSOLUTE_Q n_low = log_delta_q * (log(q[0])-log(q_min)) q_low = np.logspace(log10(q_min), log10(q[0]), np.ceil(n_low)+1)[:-1] else: q_low = [] if q_max > q[-1]: n_high = log_delta_q * (log(q_max)-log(q[-1])) q_high = np.logspace(log10(q[-1]), log10(q_max), np.ceil(n_high)+1)[1:] else: q_high = [] return np.concatenate([q_low, q, q_high]) ############################################################################ # unit tests ############################################################################ import unittest def eval_form(q, form, pars): """ Return the SAS model evaluated at *q*. *form* is the SAS model returned from :fun:`core.load_model`. *pars* are the parameter values to use when evaluating. """ from sasmodels import direct_model kernel = form.make_kernel([q]) theory = direct_model.call_kernel(kernel, pars) kernel.release() return theory def gaussian(q, q0, dq): """ Return the Gaussian resolution function. *q0* is the center, *dq* is the width and *q* are the points to evaluate. """ return exp(-0.5*((q-q0)/dq)**2)/(sqrt(2*pi)*dq) def romberg_slit_1d(q, width, height, form, pars): """ Romberg integration for slit resolution. This is an adaptive integration technique. It is called with settings that make it slow to evaluate but give it good accuracy. """ from scipy.integrate import romberg # type: ignore par_set = set([p.name for p in form.info.parameters.call_parameters]) if any(k not in par_set for k in pars.keys()): extra = set(pars.keys()) - par_set raise ValueError("bad parameters: [%s] not in [%s]" % (", ".join(sorted(extra)), ", ".join(sorted(pars.keys())))) if np.isscalar(width): width = [width]*len(q) if np.isscalar(height): height = [height]*len(q) _int_w = lambda w, qi: eval_form(sqrt(qi**2 + w**2), form, pars) _int_h = lambda h, qi: eval_form(abs(qi+h), form, pars) # If both width and height are defined, then it is too slow to use dblquad. # Instead use trapz on a fixed grid, interpolated into the I(Q) for # the extended Q range. #_int_wh = lambda w, h, qi: eval_form(sqrt((qi+h)**2 + w**2), form, pars) q_calc = slit_extend_q(q, np.asarray(width), np.asarray(height)) Iq = eval_form(q_calc, form, pars) result = np.empty(len(q)) for i, (qi, w, h) in enumerate(zip(q, width, height)): if h == 0.: total = romberg(_int_w, 0, w, args=(qi,), divmax=100, vec_func=True, tol=0, rtol=1e-8) result[i] = total/w elif w == 0.: total = romberg(_int_h, -h, h, args=(qi,), divmax=100, vec_func=True, tol=0, rtol=1e-8) result[i] = total/(2*h) else: w_grid = np.linspace(0, w, 21)[None, :] h_grid = np.linspace(-h, h, 23)[:, None] u_sub = sqrt((qi+h_grid)**2 + w_grid**2) f_at_u = np.interp(u_sub, q_calc, Iq) #print(np.trapz(Iu, w_grid, axis=1)) total = np.trapz(np.trapz(f_at_u, w_grid, axis=1), h_grid[:, 0]) result[i] = total / (2*h*w) # from scipy.integrate import dblquad # r, err = dblquad(_int_wh, -h, h, lambda h: 0., lambda h: w, # args=(qi,)) # result[i] = r/(w*2*h) # r should be [float, ...], but it is [array([float]), array([float]),...] return result def romberg_pinhole_1d(q, q_width, form, pars, nsigma=5): """ Romberg integration for pinhole resolution. This is an adaptive integration technique. It is called with settings that make it slow to evaluate but give it good accuracy. """ from scipy.integrate import romberg # type: ignore par_set = set([p.name for p in form.info.parameters.call_parameters]) if any(k not in par_set for k in pars.keys()): extra = set(pars.keys()) - par_set raise ValueError("bad parameters: [%s] not in [%s]" % (", ".join(sorted(extra)), ", ".join(sorted(pars.keys())))) func = lambda q, q0, dq: eval_form(q, form, pars)*gaussian(q, q0, dq) total = [romberg(func, max(qi-nsigma*dqi, 1e-10*q[0]), qi+nsigma*dqi, args=(qi, dqi), divmax=100, vec_func=True, tol=0, rtol=1e-8) for qi, dqi in zip(q, q_width)] return np.asarray(total).flatten() class ResolutionTest(unittest.TestCase): """ Test the resolution calculations. """ def setUp(self): self.x = 0.001*np.arange(1, 11) self.y = self.Iq(self.x) def Iq(self, q): "Linear function for resolution unit test" return 12.0 - 1000.0*q def test_perfect(self): """ Perfect resolution and no smearing. """ resolution = Perfect1D(self.x) theory = self.Iq(resolution.q_calc) output = resolution.apply(theory) np.testing.assert_equal(output, self.y) def test_slit_zero(self): """ Slit smearing with perfect resolution. """ resolution = Slit1D(self.x, qx_width=0, qy_width=0, q_calc=self.x) theory = self.Iq(resolution.q_calc) output = resolution.apply(theory) np.testing.assert_equal(output, self.y) @unittest.skip("not yet supported") def test_slit_high(self): """ Slit smearing with height 0.005 """ resolution = Slit1D(self.x, qx_width=0, qy_width=0.005, q_calc=self.x) theory = self.Iq(resolution.q_calc) output = resolution.apply(theory) answer = [ 9.0618, 8.6402, 8.1187, 7.1392, 6.1528, 5.5555, 4.5584, 3.5606, 2.5623, 2.0000, ] np.testing.assert_allclose(output, answer, atol=1e-4) @unittest.skip("not yet supported") def test_slit_both_high(self): """ Slit smearing with width < 100*height. """ q = np.logspace(-4, -1, 10) resolution = Slit1D(q, qx_width=0.2, qy_width=np.inf) theory = 1000*self.Iq(resolution.q_calc**4) output = resolution.apply(theory) answer = [ 8.85785, 8.43012, 7.92687, 6.94566, 6.03660, 5.40363, 4.40655, 3.40880, 2.41058, 2.00000, ] np.testing.assert_allclose(output, answer, atol=1e-4) @unittest.skip("not yet supported") def test_slit_wide(self): """ Slit smearing with width 0.0002 """ resolution = Slit1D(self.x, qx_width=0.0002, qy_width=0, q_calc=self.x) theory = self.Iq(resolution.q_calc) output = resolution.apply(theory) answer = [ 11.0, 10.0, 9.0, 8.0, 7.0, 6.0, 5.0, 4.0, 3.0, 2.0, ] np.testing.assert_allclose(output, answer, atol=1e-4) @unittest.skip("not yet supported") def test_slit_both_wide(self): """ Slit smearing with width > 100*height. """ resolution = Slit1D(self.x, qx_width=0.0002, qy_width=0.000001, q_calc=self.x) theory = self.Iq(resolution.q_calc) output = resolution.apply(theory) answer = [ 11.0, 10.0, 9.0, 8.0, 7.0, 6.0, 5.0, 4.0, 3.0, 2.0, ] np.testing.assert_allclose(output, answer, atol=1e-4) def test_pinhole_zero(self): """ Pinhole smearing with perfect resolution """ resolution = Pinhole1D(self.x, 0.0*self.x) theory = self.Iq(resolution.q_calc) output = resolution.apply(theory) np.testing.assert_equal(output, self.y) def test_pinhole(self): """ Pinhole smearing with dQ = 0.001 [Note: not dQ/Q = 0.001] """ resolution = Pinhole1D(self.x, 0.001*np.ones_like(self.x), q_calc=self.x) theory = 12.0-1000.0*resolution.q_calc output = resolution.apply(theory) answer = [ 10.44785079, 9.84991299, 8.98101708, 7.99906585, 6.99998311, 6.00001689, 5.00093415, 4.01898292, 3.15008701, 2.55214921, ] np.testing.assert_allclose(output, answer, atol=1e-8) class IgorComparisonTest(unittest.TestCase): """ Test resolution calculations against those returned by Igor. """ def setUp(self): self.pars = TEST_PARS_PINHOLE_SPHERE from sasmodels import core self.model = core.load_model("sphere", dtype='double') def _eval_sphere(self, pars, resolution): from sasmodels import direct_model kernel = self.model.make_kernel([resolution.q_calc]) theory = direct_model.call_kernel(kernel, pars) result = resolution.apply(theory) kernel.release() return result def _compare(self, q, output, answer, tolerance): #err = (output - answer)/answer #idx = abs(err) >= tolerance #problem = zip(q[idx], output[idx], answer[idx], err[idx]) #print("\n".join(str(v) for v in problem)) np.testing.assert_allclose(output, answer, rtol=tolerance) def test_perfect(self): """ Compare sphere model with NIST Igor SANS, no resolution smearing. """ pars = TEST_PARS_SLIT_SPHERE data_string = TEST_DATA_SLIT_SPHERE data = np.loadtxt(data_string.split('\n')).T q, _, answer, _ = data resolution = Perfect1D(q) output = self._eval_sphere(pars, resolution) self._compare(q, output, answer, 1e-6) def test_pinhole(self): """ Compare pinhole resolution smearing with NIST Igor SANS """ pars = TEST_PARS_PINHOLE_SPHERE data_string = TEST_DATA_PINHOLE_SPHERE data = np.loadtxt(data_string.split('\n')).T q, q_width, answer = data resolution = Pinhole1D(q, q_width) output = self._eval_sphere(pars, resolution) # TODO: relative error should be lower self._compare(q, output, answer, 3e-4) def test_pinhole_romberg(self): """ Compare pinhole resolution smearing with romberg integration result. """ pars = TEST_PARS_PINHOLE_SPHERE data_string = TEST_DATA_PINHOLE_SPHERE pars['radius'] *= 5 data = np.loadtxt(data_string.split('\n')).T q, q_width, answer = data answer = romberg_pinhole_1d(q, q_width, self.model, pars) ## Getting 0.1% requires 5 sigma and 200 points per fringe #q_calc = interpolate(pinhole_extend_q(q, q_width, nsigma=5), # 2*np.pi/pars['radius']/200) #tol = 0.001 ## The default 3 sigma and no extra points gets 1% q_calc = None # type: np.ndarray tol = 0.01 resolution = Pinhole1D(q, q_width, q_calc=q_calc) output = self._eval_sphere(pars, resolution) if 0: # debug plot import matplotlib.pyplot as plt # type: ignore resolution = Perfect1D(q) source = self._eval_sphere(pars, resolution) plt.loglog(q, source, '.') plt.loglog(q, answer, '-', hold=True) plt.loglog(q, output, '-', hold=True) plt.show() self._compare(q, output, answer, tol) def test_slit(self): """ Compare slit resolution smearing with NIST Igor SANS """ pars = TEST_PARS_SLIT_SPHERE data_string = TEST_DATA_SLIT_SPHERE data = np.loadtxt(data_string.split('\n')).T q, delta_qv, _, answer = data resolution = Slit1D(q, qx_width=delta_qv, qy_width=0) output = self._eval_sphere(pars, resolution) # TODO: eliminate Igor test since it is too inaccurate to be useful. # This means we can eliminate the test data as well, and instead # use a generated q vector. self._compare(q, output, answer, 0.5) def test_slit_romberg(self): """ Compare slit resolution smearing with romberg integration result. """ pars = TEST_PARS_SLIT_SPHERE data_string = TEST_DATA_SLIT_SPHERE data = np.loadtxt(data_string.split('\n')).T q, delta_qv, _, answer = data answer = romberg_slit_1d(q, delta_qv, 0., self.model, pars) q_calc = slit_extend_q(interpolate(q, 2*np.pi/pars['radius']/20), delta_qv[0], 0.) resolution = Slit1D(q, qx_width=delta_qv, qy_width=0, q_calc=q_calc) output = self._eval_sphere(pars, resolution) # TODO: relative error should be lower self._compare(q, output, answer, 0.025) def test_ellipsoid(self): """ Compare romberg integration for ellipsoid model. """ from .core import load_model pars = { 'scale':0.05, 'radius_polar':500, 'radius_equatorial':15000, 'sld':6, 'sld_solvent': 1, } form = load_model('ellipsoid', dtype='double') q = np.logspace(log10(4e-5), log10(2.5e-2), 68) width, height = 0.117, 0. resolution = Slit1D(q, qx_width=width, qy_width=height) answer = romberg_slit_1d(q, width, height, form, pars) output = resolution.apply(eval_form(resolution.q_calc, form, pars)) # TODO: 10% is too much error; use better algorithm #print(np.max(abs(answer-output)/answer)) self._compare(q, output, answer, 0.1) #TODO: can sas q spacing be too sparse for the resolution calculation? @unittest.skip("suppress sparse data test; not supported by current code") def test_pinhole_sparse(self): """ Compare pinhole resolution smearing with NIST Igor SANS on sparse data """ pars = TEST_PARS_PINHOLE_SPHERE data_string = TEST_DATA_PINHOLE_SPHERE data = np.loadtxt(data_string.split('\n')).T q, q_width, answer = data[:, ::20] # Take every nth point resolution = Pinhole1D(q, q_width) output = self._eval_sphere(pars, resolution) self._compare(q, output, answer, 1e-6) # pinhole sphere parameters TEST_PARS_PINHOLE_SPHERE = { 'scale': 1.0, 'background': 0.01, 'radius': 60.0, 'sld': 1, 'sld_solvent': 6.3, } # Q, dQ, I(Q) calculated by NIST Igor SANS package TEST_DATA_PINHOLE_SPHERE = """\ 0.001278 0.0002847 2538.41176383 0.001562 0.0002905 2536.91820405 0.001846 0.0002956 2535.13182479 0.002130 0.0003017 2533.06217813 0.002414 0.0003087 2530.70378586 0.002698 0.0003165 2528.05024192 0.002982 0.0003249 2525.10408349 0.003266 0.0003340 2521.86667499 0.003550 0.0003437 2518.33907750 0.003834 0.0003539 2514.52246995 0.004118 0.0003646 2510.41798319 0.004402 0.0003757 2506.02690988 0.004686 0.0003872 2501.35067884 0.004970 0.0003990 2496.38678318 0.005253 0.0004112 2491.16237596 0.005537 0.0004237 2485.63911673 0.005821 0.0004365 2479.83657083 0.006105 0.0004495 2473.75676948 0.006389 0.0004628 2467.40145990 0.006673 0.0004762 2460.77293372 0.006957 0.0004899 2453.86724627 0.007241 0.0005037 2446.69623838 0.007525 0.0005177 2439.25775219 0.007809 0.0005318 2431.55421398 0.008093 0.0005461 2423.58785521 0.008377 0.0005605 2415.36158137 0.008661 0.0005750 2406.87009473 0.008945 0.0005896 2398.12841186 0.009229 0.0006044 2389.13360806 0.009513 0.0006192 2379.88958042 0.009797 0.0006341 2370.39776774 0.010080 0.0006491 2360.69528793 0.010360 0.0006641 2350.85169027 0.010650 0.0006793 2340.42023633 0.010930 0.0006945 2330.11206013 0.011220 0.0007097 2319.20109972 0.011500 0.0007251 2308.43503981 0.011780 0.0007404 2297.44820179 0.012070 0.0007558 2285.83853677 0.012350 0.0007713 2274.41290746 0.012640 0.0007868 2262.36219581 0.012920 0.0008024 2250.51169731 0.013200 0.0008180 2238.45596231 0.013490 0.0008336 2225.76495666 0.013770 0.0008493 2213.29618391 0.014060 0.0008650 2200.19110751 0.014340 0.0008807 2187.34050325 0.014620 0.0008965 2174.30529864 0.014910 0.0009123 2160.61632548 0.015190 0.0009281 2147.21038112 0.015470 0.0009440 2133.62023580 0.015760 0.0009598 2119.37907426 0.016040 0.0009757 2105.45234903 0.016330 0.0009916 2090.86319102 0.016610 0.0010080 2076.60576032 0.016890 0.0010240 2062.19214565 0.017180 0.0010390 2047.10550219 0.017460 0.0010550 2032.38715621 0.017740 0.0010710 2017.52560123 0.018030 0.0010880 2001.99124318 0.018310 0.0011040 1986.84662060 0.018600 0.0011200 1971.03389745 0.018880 0.0011360 1955.61395119 0.019160 0.0011520 1940.08291563 0.019450 0.0011680 1923.87672225 0.019730 0.0011840 1908.10656374 0.020020 0.0012000 1891.66297192 0.020300 0.0012160 1875.66789021 0.020580 0.0012320 1859.56357196 0.020870 0.0012490 1842.79468290 0.021150 0.0012650 1826.50064489 0.021430 0.0012810 1810.11533702 0.021720 0.0012970 1793.06840882 0.022000 0.0013130 1776.51153580 0.022280 0.0013290 1759.87201249 0.022570 0.0013460 1742.57354412 0.022850 0.0013620 1725.79397319 0.023140 0.0013780 1708.35831550 0.023420 0.0013940 1691.45256069 0.023700 0.0014110 1674.48561783 0.023990 0.0014270 1656.86525366 0.024270 0.0014430 1639.79847285 0.024550 0.0014590 1622.68887088 0.024840 0.0014760 1604.96421100 0.025120 0.0014920 1587.85768129 0.025410 0.0015080 1569.99297335 0.025690 0.0015240 1552.84580279 0.025970 0.0015410 1535.54074115 0.026260 0.0015570 1517.75249337 0.026540 0.0015730 1500.40115023 0.026820 0.0015900 1483.03632237 0.027110 0.0016060 1465.05942429 0.027390 0.0016220 1447.67682181 0.027670 0.0016390 1430.46495191 0.027960 0.0016550 1412.49232282 0.028240 0.0016710 1395.13182318 0.028520 0.0016880 1377.93439837 0.028810 0.0017040 1359.99528971 0.029090 0.0017200 1342.67274512 0.029370 0.0017370 1325.55375609 """ # Slit sphere parameters TEST_PARS_SLIT_SPHERE = { 'scale': 0.01, 'background': 0.01, 'radius': 60000, 'sld': 1, 'sld_solvent': 4, } # Q dQ I(Q) I_smeared(Q) TEST_DATA_SLIT_SPHERE = """\ 2.26097e-05 0.117 5.5781372896e+09 1.4626077708e+06 2.53847e-05 0.117 5.0363141458e+09 1.3117318023e+06 2.81597e-05 0.117 4.4850108103e+09 1.1594863713e+06 3.09347e-05 0.117 3.9364658459e+09 1.0094881630e+06 3.37097e-05 0.117 3.4019975074e+09 8.6518941303e+05 3.92597e-05 0.117 2.4139519814e+09 6.0232158311e+05 4.48097e-05 0.117 1.5816877820e+09 3.8739994090e+05 5.03597e-05 0.117 9.3715407224e+08 2.2745304775e+05 5.59097e-05 0.117 4.8387917428e+08 1.2101295768e+05 6.14597e-05 0.117 2.0193586928e+08 6.0055107771e+04 6.70097e-05 0.117 5.5886110911e+07 3.2749521065e+04 7.25597e-05 0.117 3.7782348010e+06 2.6350963616e+04 7.81097e-05 0.117 5.3407817904e+06 2.9624963314e+04 8.36597e-05 0.117 2.7975485523e+07 3.4403962254e+04 8.92097e-05 0.117 4.9845448282e+07 3.6130017903e+04 9.47597e-05 0.117 6.0092588905e+07 3.3495107849e+04 1.00310e-04 0.117 5.6823430831e+07 2.7475726279e+04 1.05860e-04 0.117 4.3857024036e+07 2.0144282226e+04 1.11410e-04 0.117 2.7277144760e+07 1.3647403260e+04 1.22510e-04 0.117 3.3119334113e+06 6.6519711526e+03 1.33610e-04 0.117 1.4412859402e+06 6.9726212813e+03 1.44710e-04 0.117 8.5620162463e+06 8.1441335775e+03 1.55810e-04 0.117 9.6957429033e+06 6.4559996521e+03 1.66910e-04 0.117 4.3818341914e+06 3.6252154156e+03 1.78010e-04 0.117 2.7448997387e+05 2.4006505342e+03 1.89110e-04 0.117 8.0472009936e+05 2.8187789089e+03 2.00210e-04 0.117 2.8149552834e+06 3.0915662855e+03 2.11310e-04 0.117 2.7510907861e+06 2.3722530293e+03 2.22410e-04 0.117 1.0053133293e+06 1.4473468311e+03 2.33510e-04 0.117 5.8428305052e+03 1.2048540556e+03 2.44610e-04 0.117 5.1699305004e+05 1.4625670042e+03 2.55710e-04 0.117 1.2120227268e+06 1.5010705973e+03 2.66810e-04 0.117 9.7896842846e+05 1.1336343426e+03 2.77910e-04 0.117 2.5507264791e+05 8.1848818080e+02 3.05660e-04 0.117 5.2403101181e+05 7.4913374357e+02 3.33410e-04 0.117 5.8699343809e+04 4.4669964560e+02 3.61160e-04 0.117 3.0844327150e+05 4.6774007542e+02 3.88910e-04 0.117 8.3360142970e+03 2.7169550220e+02 4.16660e-04 0.117 1.8630080583e+05 3.0710983679e+02 4.44410e-04 0.117 3.1616804732e-01 1.7959006831e+02 4.72160e-04 0.117 1.1299016314e+05 2.0763952339e+02 4.99910e-04 0.117 2.9952522747e+03 1.2536542765e+02 5.27660e-04 0.117 6.7625695649e+04 1.4013969777e+02 5.55410e-04 0.117 7.6927460089e+03 8.2145593180e+01 6.10910e-04 0.117 1.1229057779e+04 8.4519745643e+01 6.66410e-04 0.117 1.3035567943e+04 8.1554625609e+01 7.21910e-04 0.117 1.3309931343e+04 7.4437319172e+01 7.77410e-04 0.117 1.2462626212e+04 6.4697088261e+01 8.32910e-04 0.117 1.0912927143e+04 5.3773301044e+01 8.88410e-04 0.117 9.0172597469e+03 4.2843375753e+01 9.43910e-04 0.117 7.0496495917e+03 3.2771032724e+01 9.99410e-04 0.117 5.2030483682e+03 2.4113557144e+01 1.05491e-03 0.117 3.5988976711e+03 1.7160773658e+01 1.11041e-03 0.117 2.2996060652e+03 1.2016626459e+01 1.22141e-03 0.117 6.4766590598e+02 6.0373017740e+00 1.33241e-03 0.117 4.1963483264e+01 4.5215452974e+00 1.44341e-03 0.117 6.3370708246e+01 5.1054681903e+00 1.55441e-03 0.117 3.0736750577e+02 5.9176165298e+00 1.66541e-03 0.117 5.0327682399e+02 5.9815000189e+00 1.77641e-03 0.117 5.4084331454e+02 5.1634639625e+00 1.88741e-03 0.117 4.3488671756e+02 3.8535158148e+00 1.99841e-03 0.117 2.6322287860e+02 2.5824997753e+00 2.10941e-03 0.117 1.0793633150e+02 1.7315517194e+00 2.22041e-03 0.117 1.8474448850e+01 1.4077213604e+00 2.33141e-03 0.117 1.5864062279e+00 1.4771560682e+00 2.44241e-03 0.117 3.2267213848e+01 1.6916253448e+00 2.55341e-03 0.117 7.4289116207e+01 1.8274751193e+00 2.66441e-03 0.117 9.9000521929e+01 1.7706812289e+00 """ def main(): """ Run tests given is sys.argv. Returns 0 if success or 1 if any tests fail. """ import sys import xmlrunner # type: ignore suite = unittest.TestSuite() suite.addTest(unittest.defaultTestLoader.loadTestsFromModule(sys.modules[__name__])) runner = xmlrunner.XMLTestRunner(output='logs') result = runner.run(suite) return 1 if result.failures or result.errors else 0 ############################################################################ # usage demo ############################################################################ def _eval_demo_1d(resolution, title): import sys from sasmodels import core from sasmodels import direct_model name = sys.argv[1] if len(sys.argv) > 1 else 'cylinder' if name == 'cylinder': pars = {'length':210, 'radius':500, 'background': 0} elif name == 'teubner_strey': pars = {'a2':0.003, 'c1':-1e4, 'c2':1e10, 'background':0.312643} elif name == 'sphere' or name == 'spherepy': pars = TEST_PARS_SLIT_SPHERE elif name == 'ellipsoid': pars = { 'scale':0.05, 'background': 0, 'r_polar':500, 'r_equatorial':15000, 'sld':6, 'sld_solvent': 1, } else: pars = {} model_info = core.load_model_info(name) model = core.build_model(model_info) kernel = model.make_kernel([resolution.q_calc]) theory = direct_model.call_kernel(kernel, pars) Iq = resolution.apply(theory) if isinstance(resolution, Slit1D): width, height = resolution.dqx, resolution.dqy Iq_romb = romberg_slit_1d(resolution.q, width, height, model, pars) else: dq = resolution.q_width Iq_romb = romberg_pinhole_1d(resolution.q, dq, model, pars) import matplotlib.pyplot as plt # type: ignore plt.loglog(resolution.q_calc, theory, label='unsmeared') plt.loglog(resolution.q, Iq, label='smeared', hold=True) plt.loglog(resolution.q, Iq_romb, label='romberg smeared', hold=True) plt.legend() plt.title(title) plt.xlabel("Q (1/Ang)") plt.ylabel("I(Q) (1/cm)") def demo_pinhole_1d(): """ Show example of pinhole smearing. """ q = np.logspace(-4, np.log10(0.2), 400) q_width = 0.1*q resolution = Pinhole1D(q, q_width) _eval_demo_1d(resolution, title="10% dQ/Q Pinhole Resolution") def demo_slit_1d(): """ Show example of slit smearing. """ q = np.logspace(-4, np.log10(0.2), 100) w = h = 0. #w = 0.000000277790 w = 0.0277790 #h = 0.00277790 #h = 0.0277790 resolution = Slit1D(q, w, h) _eval_demo_1d(resolution, title="(%g,%g) Slit Resolution"%(w, h)) def demo(): """ Run the resolution demos. """ import matplotlib.pyplot as plt # type: ignore plt.subplot(121) demo_pinhole_1d() #plt.yscale('linear') plt.subplot(122) demo_slit_1d() #plt.yscale('linear') plt.show() if __name__ == "__main__": #demo() main() sasmodels/sasmodels/resolution2d.py000066400000000000000000000223411317715334700200620ustar00rootroot00000000000000""" #This software was developed by the University of Tennessee as part of the #Distributed Data Analysis of Neutron Scattering Experiments (DANSE) #project funded by the US National Science Foundation. #See the license text in license.txt """ from __future__ import division import numpy as np # type: ignore from numpy import pi, cos, sin, sqrt # type: ignore from . import resolution from .resolution import Resolution ## Singular point SIGMA_ZERO = 1.0e-010 ## Limit of how many sigmas to be covered for the Gaussian smearing # default: 2.5 to cover 98.7% of Gaussian NSIGMA = 3.0 ## Defaults NR = {'xhigh':10, 'high':5, 'med':5, 'low':3} NPHI = {'xhigh':20, 'high':12, 'med':6, 'low':4} ## Defaults N_SLIT_PERP = {'xhigh':1000, 'high':500, 'med':200, 'low':50} N_SLIT_PERP_DOC = ", ".join("%s=%d"%(name, value) for value, name in sorted((2*v+1, k) for k, v in N_SLIT_PERP.items())) class Pinhole2D(Resolution): """ Gaussian Q smearing class for SAS 2d data """ def __init__(self, data=None, index=None, nsigma=NSIGMA, accuracy='Low', coords='polar'): """ Assumption: equally spaced bins in dq_r, dq_phi space. :param data: 2d data used to set the smearing parameters :param index: 1d array with len(data) to define the range of the calculation: elements are given as True or False :param nr: number of bins in dq_r-axis :param nphi: number of bins in dq_phi-axis :param coord: coordinates [string], 'polar' or 'cartesian' """ ## Accuracy: Higher stands for more sampling points in both directions ## of r and phi. ## number of bins in r axis for over-sampling self.nr = NR[accuracy.lower()] ## number of bins in phi axis for over-sampling self.nphi = NPHI[accuracy.lower()] ## maximum nsigmas self.nsigma = nsigma self.coords = coords self._init_data(data, index) def _init_data(self, data, index): """ Get qx_data, qy_data, dqx_data,dqy_data, and calculate phi_data=arctan(qx_data/qy_data) """ # TODO: maybe don't need to hold copy of qx,qy,dqx,dqy,data,index # just need q_calc and weights self.data = data self.index = index if index is not None else slice(None) self.qx_data = data.qx_data[self.index] self.qy_data = data.qy_data[self.index] self.q_data = data.q_data[self.index] dqx = getattr(data, 'dqx_data', None) dqy = getattr(data, 'dqy_data', None) if dqx is not None and dqy is not None: # Here dqx and dqy mean dq_parr and dq_perp self.dqx_data = dqx[self.index] self.dqy_data = dqy[self.index] ## Remove singular points if exists self.dqx_data[self.dqx_data < SIGMA_ZERO] = SIGMA_ZERO self.dqy_data[self.dqy_data < SIGMA_ZERO] = SIGMA_ZERO qx_calc, qy_calc, weights = self._calc_res() self.q_calc = [qx_calc, qy_calc] self.q_calc_weights = weights else: # No resolution information self.dqx_data = self.dqy_data = None self.q_calc = [self.qx_data, self.qy_data] self.q_calc_weights = None #self.phi_data = np.arctan(self.qx_data / self.qy_data) def _calc_res(self): """ Over sampling of r_nbins times phi_nbins, calculate Gaussian weights, then find smeared intensity """ nr, nphi = self.nr, self.nphi # Total number of bins = # of bins nbins = nr * nphi # Number of bins in the dqr direction (polar coordinate of dqx and dqy) bin_size = self.nsigma / nr # in dq_r-direction times # of bins in dq_phi-direction # data length in the range of self.index nq = len(self.qx_data) # Mean values of dqr at each bins # starting from the half of bin size r = bin_size / 2.0 + np.arange(nr) * bin_size # mean values of qphi at each bines phi = np.arange(nphi) dphi = phi * 2.0 * pi / nphi dphi = dphi.repeat(nr) ## Transform to polar coordinate, # and set dphi at each data points ; 1d array dphi = dphi.repeat(nq) q_phi = self.qy_data / self.qx_data # Starting angle is different between polar # and cartesian coordinates. #if self.coords != 'polar': # dphi += np.arctan( q_phi * self.dqx_data/ \ # self.dqy_data).repeat(nbins).reshape(nq,\ # nbins).transpose().flatten() # The angle (phi) of the original q point q_phi = np.arctan(q_phi).repeat(nbins)\ .reshape([nq, nbins]).transpose().flatten() ## Find Gaussian weight for each dq bins: The weight depends only # on r-direction (The integration may not need) weight_res = (np.exp(-0.5 * (r - bin_size / 2.0)**2) - np.exp(-0.5 * (r + bin_size / 2.0)**2)) # No needs of normalization here. #weight_res /= np.sum(weight_res) weight_res = weight_res.repeat(nphi).reshape(nr, nphi) weight_res = weight_res.transpose().flatten() ## Set dr for all dq bins for averaging dr = r.repeat(nphi).reshape(nr, nphi).transpose().flatten() ## Set dqr for all data points dqx = np.outer(dr, self.dqx_data).flatten() dqy = np.outer(dr, self.dqy_data).flatten() qx = self.qx_data.repeat(nbins)\ .reshape(nq, nbins).transpose().flatten() qy = self.qy_data.repeat(nbins)\ .reshape(nq, nbins).transpose().flatten() # The polar needs rotation by -q_phi if self.coords == 'polar': q_r = sqrt(qx**2 + qy**2) qx_res = ((dqx*cos(dphi) + q_r) * cos(-q_phi) + dqy*sin(dphi) * sin(-q_phi)) qy_res = (-(dqx*cos(dphi) + q_r) * sin(-q_phi) + dqy*sin(dphi) * cos(-q_phi)) else: qx_res = qx + dqx*cos(dphi) qy_res = qy + dqy*sin(dphi) return qx_res, qy_res, weight_res def apply(self, theory): if self.q_calc_weights is not None: # TODO: interpolate rather than recomputing all the different qx,qy # Resolution needs to be applied nq, nbins = len(self.qx_data), self.nr * self.nphi ## Reshape into 2d array to use np weighted averaging theory = np.reshape(theory, (nbins, nq)) ## Averaging with Gaussian weighting: normalization included. value = np.average(theory, axis=0, weights=self.q_calc_weights) ## Return the smeared values in the range of self.index return value else: return theory class Slit2D(Resolution): """ Slit aperture with resolution function on an oriented sample. *q* points at which the data is measured. *qx_width* slit width in qx *qy_width* slit height in qy; current implementation requires a fixed qy_width for all q points. *q_calc* is the list of q points to calculate, or None if this should be estimated from the *q* and *qx_width*. *accuracy* determines the number of *qy* points to compute for each *q*. The values are stored in sasmodels.resolution2d.N_SLIT_PERP. The default values are: %s """ __doc__ = __doc__%N_SLIT_PERP_DOC def __init__(self, q, qx_width, qy_width=0., q_calc=None, accuracy='low'): # Remember what q and width was used even though we won't need them # after the weight matrix is constructed self.q, self.qx_width, self.qy_width = q, qx_width, qy_width # Allow independent resolution on each qx point even though it is not # needed in practice. Set qy_width to the maximum qy width. if np.isscalar(qx_width): qx_width = np.ones(len(q))*qx_width else: qx_width = np.asarray(qx_width) if not np.isscalar(qy_width): qy_width = np.max(qy_width) # Build grid of qx, qy points if q_calc is not None: qx_calc = np.sort(q_calc) else: qx_calc = resolution.pinhole_extend_q(q, qx_width, nsigma=3) qy_min, qy_max = np.log10(np.min(q)), np.log10(qy_width) qy_calc = np.logspace(qy_min, qy_max, N_SLIT_PERP[accuracy]) qy_calc = np.hstack((-qy_calc[::-1], 0, qy_calc)) self.q_calc = [v.flatten() for v in np.meshgrid(qx_calc, qy_calc)] self.qx_calc, self.qy_calc = qx_calc, qy_calc self.nx, self.ny = len(qx_calc), len(qy_calc) self.dy = 2*qy_width/self.ny # Build weight matrix for resolution integration if np.any(qx_width > 0): self.weights = resolution.pinhole_resolution(qx_calc, q, np.maximum(qx_width, resolution.MINIMUM_RESOLUTION)) elif len(qx_calc) == len(q) and np.all(qx_calc == q): self.weights = None else: raise ValueError("Slit2D fails with q_calc != q") def apply(self, theory): Iq = np.trapz(theory.reshape(self.ny, self.nx), axis=0, x=self.qy_calc) if self.weights is not None: Iq = resolution.apply_resolution_matrix(self.weights, Iq) return Iq sasmodels/sasmodels/rst2html.py000066400000000000000000000173621317715334700172170ustar00rootroot00000000000000r""" Convert a restructured text document to html. Inline math markup can uses the *math* directive, or it can use latex style *\$expression\$*. Math can be rendered using simple html and unicode, or with mathjax. """ import re from contextlib import contextmanager # CRUFT: locale.getlocale() fails on some versions of OS X # See https://bugs.python.org/issue18378 import locale if hasattr(locale, '_parse_localename'): try: locale._parse_localename('UTF-8') except ValueError: _old_parse_localename = locale._parse_localename def _parse_localename(localename): code = locale.normalize(localename) if code == 'UTF-8': return None, code else: return _old_parse_localename(localename) locale._parse_localename = _parse_localename from docutils.core import publish_parts from docutils.writers.html4css1 import HTMLTranslator from docutils.nodes import SkipNode def rst2html(rst, part="whole", math_output="mathjax"): r""" Convert restructured text into simple html. Valid *math_output* formats for formulas include: - html - mathml - mathjax See ``_ for details. The following *part* choices are available: - whole: the entire html document - html_body: document division with title and contents and footer - body: contents only There are other parts, but they don't make sense alone: subtitle, version, encoding, html_prolog, header, meta, html_title, title, stylesheet, html_subtitle, html_body, body, head, body_suffix, fragment, docinfo, html_head, head_prefix, body_prefix, footer, body_pre_docinfo, whole """ # Ick! mathjax doesn't work properly with math-output, and the # others don't work properly with math_output! if math_output == "mathjax": settings = {"math_output": math_output} else: settings = {"math-output": math_output} # TODO: support stylesheets #html_root = "/full/path/to/_static/" #sheets = [html_root+s for s in ["basic.css","classic.css"]] #settings["embed_styesheet"] = True #settings["stylesheet_path"] = sheets # math2html and mathml do not support \frac12 rst = replace_compact_fraction(rst) # mathml, html do not support \tfrac if math_output in ("mathml", "html"): rst = rst.replace(r'\tfrac', r'\frac') rst = replace_dollar(rst) with suppress_html_errors(): parts = publish_parts(source=rst, writer_name='html', settings_overrides=settings) return parts[part] @contextmanager def suppress_html_errors(): r""" Context manager for keeping error reports out of the generated HTML. Within the context, system message nodes in the docutils parse tree will be ignored. After the context, the usual behaviour will be restored. """ visit_system_message = HTMLTranslator.visit_system_message HTMLTranslator.visit_system_message = _skip_node yield None HTMLTranslator.visit_system_message = visit_system_message def _skip_node(self, node): raise SkipNode _compact_fraction = re.compile(r"(\\[cdt]?frac)([0-9])([0-9])") def replace_compact_fraction(content): r""" Convert \frac12 to \frac{1}{2} for broken latex parsers """ return _compact_fraction.sub(r"\1{\2}{\3}", content) _dollar = re.compile(r"(?:^|(?<=\s|[(]))[$]([^\n]*?)(? SasviewModelType """ Find a model by name. If the model name ends in py, try loading it from custom models, otherwise look for it in the list of builtin models. """ # TODO: used by sum/product model to load an existing model # TODO: doesn't handle custom models properly if modelname.endswith('.py'): return load_custom_model(modelname) elif modelname in MODELS: return MODELS[modelname] else: raise ValueError("unknown model %r"%modelname) # TODO: figure out how to say that the return type is a subclass def load_standard_models(): # type: () -> List[SasviewModelType] """ Load and return the list of predefined models. If there is an error loading a model, then a traceback is logged and the model is not returned. """ for name in core.list_models(): try: MODELS[name] = _make_standard_model(name) except Exception: logger.error(traceback.format_exc()) if SUPPORT_OLD_STYLE_PLUGINS: _register_old_models() return list(MODELS.values()) def load_custom_model(path): # type: (str) -> SasviewModelType """ Load a custom model given the model path. """ model = MODEL_BY_PATH.get(path, None) if model is not None and model.timestamp == getmtime(path): #logger.info("Model already loaded %s", path) return model #logger.info("Loading model %s", path) kernel_module = custom.load_custom_kernel_module(path) if hasattr(kernel_module, 'Model'): model = kernel_module.Model # Old style models do not set the name in the class attributes, so # set it here; this name will be overridden when the object is created # with an instance variable that has the same value. if model.name == "": model.name = splitext(basename(path))[0] if not hasattr(model, 'filename'): model.filename = abspath(kernel_module.__file__).replace('.pyc', '.py') if not hasattr(model, 'id'): model.id = splitext(basename(model.filename))[0] else: model_info = modelinfo.make_model_info(kernel_module) model = make_model_from_info(model_info) model.timestamp = getmtime(path) # If a model name already exists and we are loading a different model, # use the model file name as the model name. if model.name in MODELS and not model.filename == MODELS[model.name].filename: _previous_name = model.name model.name = model.id # If the new model name is still in the model list (for instance, # if we put a cylinder.py in our plug-in directory), then append # an identifier. if model.name in MODELS and not model.filename == MODELS[model.name].filename: model.name = model.id + '_user' logger.info("Model %s already exists: using %s [%s]", _previous_name, model.name, model.filename) MODELS[model.name] = model MODEL_BY_PATH[path] = model return model def make_model_from_info(model_info): # type: (ModelInfo) -> SasviewModelType """ Convert *model_info* into a SasView model wrapper. """ def __init__(self, multiplicity=None): SasviewModel.__init__(self, multiplicity=multiplicity) attrs = _generate_model_attributes(model_info) attrs['__init__'] = __init__ attrs['filename'] = model_info.filename ConstructedModel = type(model_info.name, (SasviewModel,), attrs) # type: SasviewModelType return ConstructedModel def _make_standard_model(name): # type: (str) -> SasviewModelType """ Load the sasview model defined by *name*. *name* can be a standard model name or a path to a custom model. Returns a class that can be used directly as a sasview model. """ kernel_module = generate.load_kernel_module(name) model_info = modelinfo.make_model_info(kernel_module) return make_model_from_info(model_info) def _register_old_models(): # type: () -> None """ Place the new models into sasview under the old names. Monkey patch sas.sascalc.fit as sas.models so that sas.models.pluginmodel is available to the plugin modules. """ import sys import sas # needed in order to set sas.models import sas.sascalc.fit sys.modules['sas.models'] = sas.sascalc.fit sas.models = sas.sascalc.fit import sas.models from sasmodels.conversion_table import CONVERSION_TABLE for new_name, conversion in CONVERSION_TABLE.get((3, 1, 2), {}).items(): # CoreShellEllipsoidModel => core_shell_ellipsoid:1 new_name = new_name.split(':')[0] old_name = conversion[0] if len(conversion) < 3 else conversion[2] module_attrs = {old_name: find_model(new_name)} ConstructedModule = type(old_name, (), module_attrs) old_path = 'sas.models.' + old_name setattr(sas.models, old_path, ConstructedModule) sys.modules[old_path] = ConstructedModule def MultiplicationModel(form_factor, structure_factor): # type: ("SasviewModel", "SasviewModel") -> "SasviewModel" model_info = product.make_product_info(form_factor._model_info, structure_factor._model_info) ConstructedModel = make_model_from_info(model_info) return ConstructedModel(form_factor.multiplicity) def _generate_model_attributes(model_info): # type: (ModelInfo) -> Dict[str, Any] """ Generate the class attributes for the model. This should include all the information necessary to query the model details so that you do not need to instantiate a model to query it. All the attributes should be immutable to avoid accidents. """ # TODO: allow model to override axis labels input/output name/unit # Process multiplicity non_fittable = [] # type: List[str] xlabel = model_info.profile_axes[0] if model_info.profile is not None else "" variants = MultiplicityInfo(0, "", [], xlabel) for p in model_info.parameters.kernel_parameters: if p.name == model_info.control: non_fittable.append(p.name) variants = MultiplicityInfo( len(p.choices) if p.choices else int(p.limits[1]), p.name, p.choices, xlabel ) break # Only a single drop-down list parameter available fun_list = [] for p in model_info.parameters.kernel_parameters: if p.choices: fun_list = p.choices if p.length > 1: non_fittable.extend(p.id+str(k) for k in range(1, p.length+1)) break # Organize parameter sets orientation_params = [] magnetic_params = [] fixed = [] for p in model_info.parameters.user_parameters({}, is2d=True): if p.type == 'orientation': orientation_params.append(p.name) orientation_params.append(p.name+".width") fixed.append(p.name+".width") elif p.type == 'magnetic': orientation_params.append(p.name) magnetic_params.append(p.name) fixed.append(p.name+".width") # Build class dictionary attrs = {} # type: Dict[str, Any] attrs['_model_info'] = model_info attrs['name'] = model_info.name attrs['id'] = model_info.id attrs['description'] = model_info.description attrs['category'] = model_info.category attrs['is_structure_factor'] = model_info.structure_factor attrs['is_form_factor'] = model_info.ER is not None attrs['is_multiplicity_model'] = variants[0] > 1 attrs['multiplicity_info'] = variants attrs['orientation_params'] = tuple(orientation_params) attrs['magnetic_params'] = tuple(magnetic_params) attrs['fixed'] = tuple(fixed) attrs['non_fittable'] = tuple(non_fittable) attrs['fun_list'] = tuple(fun_list) return attrs class SasviewModel(object): """ Sasview wrapper for opencl/ctypes model. """ # Model parameters for the specific model are set in the class constructor # via the _generate_model_attributes function, which subclasses # SasviewModel. They are included here for typing and documentation # purposes. _model = None # type: KernelModel _model_info = None # type: ModelInfo #: load/save name for the model id = None # type: str #: display name for the model name = None # type: str #: short model description description = None # type: str #: default model category category = None # type: str #: names of the orientation parameters in the order they appear orientation_params = None # type: List[str] #: names of the magnetic parameters in the order they appear magnetic_params = None # type: List[str] #: names of the fittable parameters fixed = None # type: List[str] # TODO: the attribute fixed is ill-named # Axis labels input_name = "Q" input_unit = "A^{-1}" output_name = "Intensity" output_unit = "cm^{-1}" #: default cutoff for polydispersity cutoff = 1e-5 # Note: Use non-mutable values for class attributes to avoid errors #: parameters that are not fitted non_fittable = () # type: Sequence[str] #: True if model should appear as a structure factor is_structure_factor = False #: True if model should appear as a form factor is_form_factor = False #: True if model has multiplicity is_multiplicity_model = False #: Multiplicity information multiplicity_info = None # type: MultiplicityInfoType # Per-instance variables #: parameter {name: value} mapping params = None # type: Dict[str, float] #: values for dispersion width, npts, nsigmas and type dispersion = None # type: Dict[str, Any] #: units and limits for each parameter details = None # type: Dict[str, Sequence[Any]] # # actual type is Dict[str, List[str, float, float]] #: multiplicity value, or None if no multiplicity on the model multiplicity = None # type: Optional[int] #: memory for polydispersity array if using ArrayDispersion (used by sasview). _persistency_dict = None # type: Dict[str, Tuple[np.ndarray, np.ndarray]] def __init__(self, multiplicity=None): # type: (Optional[int]) -> None # TODO: _persistency_dict to persistency_dict throughout sasview # TODO: refactor multiplicity to encompass variants # TODO: dispersion should be a class # TODO: refactor multiplicity info # TODO: separate profile view from multiplicity # The button label, x and y axis labels and scale need to be under # the control of the model, not the fit page. Maximum flexibility, # the fit page would supply the canvas and the profile could plot # how it wants, but this assumes matplotlib. Next level is that # we provide some sort of data description including title, labels # and lines to plot. # Get the list of hidden parameters given the multiplicity # Don't include multiplicity in the list of parameters self.multiplicity = multiplicity if multiplicity is not None: hidden = self._model_info.get_hidden_parameters(multiplicity) hidden |= set([self.multiplicity_info.control]) else: hidden = set() if self._model_info.structure_factor: hidden.add('scale') hidden.add('background') self._model_info.parameters.defaults['background'] = 0. self._persistency_dict = {} self.params = collections.OrderedDict() self.dispersion = collections.OrderedDict() self.details = {} for p in self._model_info.parameters.user_parameters({}, is2d=True): if p.name in hidden: continue self.params[p.name] = p.default self.details[p.id] = [p.units, p.limits[0], p.limits[1]] if p.polydisperse: self.details[p.id+".width"] = [ "", 0.0, 1.0 if p.relative_pd else np.inf ] self.dispersion[p.name] = { 'width': 0, 'npts': 35, 'nsigmas': 3, 'type': 'gaussian', } def __get_state__(self): # type: () -> Dict[str, Any] state = self.__dict__.copy() state.pop('_model') # May need to reload model info on set state since it has pointers # to python implementations of Iq, etc. #state.pop('_model_info') return state def __set_state__(self, state): # type: (Dict[str, Any]) -> None self.__dict__ = state self._model = None def __str__(self): # type: () -> str """ :return: string representation """ return self.name def is_fittable(self, par_name): # type: (str) -> bool """ Check if a given parameter is fittable or not :param par_name: the parameter name to check """ return par_name in self.fixed #For the future #return self.params[str(par_name)].is_fittable() def getProfile(self): # type: () -> (np.ndarray, np.ndarray) """ Get SLD profile : return: (z, beta) where z is a list of depth of the transition points beta is a list of the corresponding SLD values """ args = {} # type: Dict[str, Any] for p in self._model_info.parameters.kernel_parameters: if p.id == self.multiplicity_info.control: value = float(self.multiplicity) elif p.length == 1: value = self.params.get(p.id, np.NaN) else: value = np.array([self.params.get(p.id+str(k), np.NaN) for k in range(1, p.length+1)]) args[p.id] = value x, y = self._model_info.profile(**args) return x, 1e-6*y def setParam(self, name, value): # type: (str, float) -> None """ Set the value of a model parameter :param name: name of the parameter :param value: value of the parameter """ # Look for dispersion parameters toks = name.split('.') if len(toks) == 2: for item in self.dispersion.keys(): if item == toks[0]: for par in self.dispersion[item]: if par == toks[1]: self.dispersion[item][par] = value return else: # Look for standard parameter for item in self.params.keys(): if item == name: self.params[item] = value return raise ValueError("Model does not contain parameter %s" % name) def getParam(self, name): # type: (str) -> float """ Set the value of a model parameter :param name: name of the parameter """ # Look for dispersion parameters toks = name.split('.') if len(toks) == 2: for item in self.dispersion.keys(): if item == toks[0]: for par in self.dispersion[item]: if par == toks[1]: return self.dispersion[item][par] else: # Look for standard parameter for item in self.params.keys(): if item == name: return self.params[item] raise ValueError("Model does not contain parameter %s" % name) def getParamList(self): # type: () -> Sequence[str] """ Return a list of all available parameters for the model """ param_list = list(self.params.keys()) # WARNING: Extending the list with the dispersion parameters param_list.extend(self.getDispParamList()) return param_list def getDispParamList(self): # type: () -> Sequence[str] """ Return a list of polydispersity parameters for the model """ # TODO: fix test so that parameter order doesn't matter ret = ['%s.%s' % (p_name, ext) for p_name in self.dispersion.keys() for ext in ('npts', 'nsigmas', 'width')] #print(ret) return ret def clone(self): # type: () -> "SasviewModel" """ Return a identical copy of self """ return deepcopy(self) def run(self, x=0.0): # type: (Union[float, (float, float), List[float]]) -> float """ Evaluate the model :param x: input q, or [q,phi] :return: scattering function P(q) **DEPRECATED**: use calculate_Iq instead """ if isinstance(x, (list, tuple)): # pylint: disable=unpacking-non-sequence q, phi = x return self.calculate_Iq([q*math.cos(phi)], [q*math.sin(phi)])[0] else: return self.calculate_Iq([x])[0] def runXY(self, x=0.0): # type: (Union[float, (float, float), List[float]]) -> float """ Evaluate the model in cartesian coordinates :param x: input q, or [qx, qy] :return: scattering function P(q) **DEPRECATED**: use calculate_Iq instead """ if isinstance(x, (list, tuple)): return self.calculate_Iq([x[0]], [x[1]])[0] else: return self.calculate_Iq([x])[0] def evalDistribution(self, qdist): # type: (Union[np.ndarray, Tuple[np.ndarray, np.ndarray], List[np.ndarray]]) -> np.ndarray r""" Evaluate a distribution of q-values. :param qdist: array of q or a list of arrays [qx,qy] * For 1D, a numpy array is expected as input :: evalDistribution(q) where *q* is a numpy array. * For 2D, a list of *[qx,qy]* is expected with 1D arrays as input :: qx = [ qx[0], qx[1], qx[2], ....] qy = [ qy[0], qy[1], qy[2], ....] If the model is 1D only, then .. math:: q = \sqrt{q_x^2+q_y^2} """ if isinstance(qdist, (list, tuple)): # Check whether we have a list of ndarrays [qx,qy] qx, qy = qdist if not self._model_info.parameters.has_2d: return self.calculate_Iq(np.sqrt(qx ** 2 + qy ** 2)) else: return self.calculate_Iq(qx, qy) elif isinstance(qdist, np.ndarray): # We have a simple 1D distribution of q-values return self.calculate_Iq(qdist) else: raise TypeError("evalDistribution expects q or [qx, qy], not %r" % type(qdist)) def calc_composition_models(self, qx): """ returns parts of the composition model or None if not a composition model. """ # TODO: have calculate_Iq return the intermediates. # # The current interface causes calculate_Iq() to be called twice, # once to get the combined result and again to get the intermediate # results. This is necessary for now. # Long term, the solution is to change the interface to calculate_Iq # so that it returns a results object containing all the bits: # the A, B, C, ... of the composition model (and any subcomponents?) # the P and S of the product model, # the combined model before resolution smearing, # the sasmodel before sesans conversion, # the oriented 2D model used to fit oriented usans data, # the final I(q), # ... # # Have the model calculator add all of these blindly to the data # tree, and update the graphs which contain them. The fitter # needs to be updated to use the I(q) value only, ignoring the rest. # # The simple fix of returning the existing intermediate results # will not work for a couple of reasons: (1) another thread may # sneak in to compute its own results before calc_composition_models # is called, and (2) calculate_Iq is currently called three times: # once with q, once with q values before qmin and once with q values # after q max. Both of these should be addressed before # replacing this code. composition = self._model_info.composition if composition and composition[0] == 'product': # only P*S for now with calculation_lock: self._calculate_Iq(qx) return self._intermediate_results else: return None def calculate_Iq(self, qx, qy=None): # type: (Sequence[float], Optional[Sequence[float]]) -> np.ndarray """ Calculate Iq for one set of q with the current parameters. If the model is 1D, use *q*. If 2D, use *qx*, *qy*. This should NOT be used for fitting since it copies the *q* vectors to the card for each evaluation. """ ## uncomment the following when trying to debug the uncoordinated calls ## to calculate_Iq #if calculation_lock.locked(): # logger.info("calculation waiting for another thread to complete") # logger.info("\n".join(traceback.format_stack())) with calculation_lock: return self._calculate_Iq(qx, qy) def _calculate_Iq(self, qx, qy=None): #core.HAVE_OPENCL = False if self._model is None: self._model = core.build_model(self._model_info) if qy is not None: q_vectors = [np.asarray(qx), np.asarray(qy)] else: q_vectors = [np.asarray(qx)] calculator = self._model.make_kernel(q_vectors) parameters = self._model_info.parameters pairs = [self._get_weights(p) for p in parameters.call_parameters] #weights.plot_weights(self._model_info, pairs) call_details, values, is_magnetic = make_kernel_args(calculator, pairs) #call_details.show() #print("pairs", pairs) #print("params", self.params) #print("values", values) #print("is_mag", is_magnetic) result = calculator(call_details, values, cutoff=self.cutoff, magnetic=is_magnetic) self._intermediate_results = getattr(calculator, 'results', None) calculator.release() self._model.release() return result def calculate_ER(self): # type: () -> float """ Calculate the effective radius for P(q)*S(q) :return: the value of the effective radius """ if self._model_info.ER is None: return 1.0 else: value, weight = self._dispersion_mesh() fv = self._model_info.ER(*value) #print(values[0].shape, weights.shape, fv.shape) return np.sum(weight * fv) / np.sum(weight) def calculate_VR(self): # type: () -> float """ Calculate the volf ratio for P(q)*S(q) :return: the value of the volf ratio """ if self._model_info.VR is None: return 1.0 else: value, weight = self._dispersion_mesh() whole, part = self._model_info.VR(*value) return np.sum(weight * part) / np.sum(weight * whole) def set_dispersion(self, parameter, dispersion): # type: (str, weights.Dispersion) -> Dict[str, Any] """ Set the dispersion object for a model parameter :param parameter: name of the parameter [string] :param dispersion: dispersion object of type Dispersion """ if parameter in self.params: # TODO: Store the disperser object directly in the model. # The current method of relying on the sasview GUI to # remember them is kind of funky. # Note: can't seem to get disperser parameters from sasview # (1) Could create a sasview model that has not yet been # converted, assign the disperser to one of its polydisperse # parameters, then retrieve the disperser parameters from the # sasview model. # (2) Could write a disperser parameter retriever in sasview. # (3) Could modify sasview to use sasmodels.weights dispersers. # For now, rely on the fact that the sasview only ever uses # new dispersers in the set_dispersion call and create a new # one instead of trying to assign parameters. self.dispersion[parameter] = dispersion.get_pars() else: raise ValueError("%r is not a dispersity or orientation parameter") def _dispersion_mesh(self): # type: () -> List[Tuple[np.ndarray, np.ndarray]] """ Create a mesh grid of dispersion parameters and weights. Returns [p1,p2,...],w where pj is a vector of values for parameter j and w is a vector containing the products for weights for each parameter set in the vector. """ pars = [self._get_weights(p) for p in self._model_info.parameters.call_parameters if p.type == 'volume'] return dispersion_mesh(self._model_info, pars) def _get_weights(self, par): # type: (Parameter) -> Tuple[np.ndarray, np.ndarray] """ Return dispersion weights for parameter """ if par.name not in self.params: if par.name == self.multiplicity_info.control: return [self.multiplicity], [1.0] else: # For hidden parameters use the default value. value = self._model_info.parameters.defaults.get(par.name, np.NaN) return [value], [1.0] elif par.polydisperse: dis = self.dispersion[par.name] if dis['type'] == 'array': value, weight = dis['values'], dis['weights'] else: value, weight = weights.get_weights( dis['type'], dis['npts'], dis['width'], dis['nsigmas'], self.params[par.name], par.limits, par.relative_pd) return value, weight / np.sum(weight) else: return [self.params[par.name]], [1.0] def test_cylinder(): # type: () -> float """ Test that the cylinder model runs, returning the value at [0.1,0.1]. """ Cylinder = _make_standard_model('cylinder') cylinder = Cylinder() return cylinder.evalDistribution([0.1, 0.1]) def test_structure_factor(): # type: () -> float """ Test that 2-D hardsphere model runs and doesn't produce NaN. """ Model = _make_standard_model('hardsphere') model = Model() value = model.evalDistribution([0.1, 0.1]) if np.isnan(value): raise ValueError("hardsphere returns null") def test_rpa(): # type: () -> float """ Test that the 2-D RPA model runs """ RPA = _make_standard_model('rpa') rpa = RPA(3) return rpa.evalDistribution([0.1, 0.1]) def test_empty_distribution(): # type: () -> None """ Make sure that sasmodels returns NaN when there are no polydispersity points """ Cylinder = _make_standard_model('cylinder') cylinder = Cylinder() cylinder.setParam('radius', -1.0) cylinder.setParam('background', 0.) Iq = cylinder.evalDistribution(np.asarray([0.1])) assert np.isnan(Iq[0]), "empty distribution fails" def test_model_list(): # type: () -> None """ Make sure that all models build as sasview models """ from .exception import annotate_exception for name in core.list_models(): try: _make_standard_model(name) except: annotate_exception("when loading "+name) raise def test_old_name(): # type: () -> None """ Load and run cylinder model from sas.models.CylinderModel """ if not SUPPORT_OLD_STYLE_PLUGINS: return try: # if sasview is not on the path then don't try to test it import sas except ImportError: return load_standard_models() from sas.models.CylinderModel import CylinderModel CylinderModel().evalDistribution([0.1, 0.1]) if __name__ == "__main__": print("cylinder(0.1,0.1)=%g"%test_cylinder()) #test_empty_distribution() sasmodels/sasmodels/sesans.py000066400000000000000000000054151317715334700167300ustar00rootroot00000000000000""" Conversion of scattering cross section from SANS (I(q), or rather, ds/dO) in absolute units (cm-1)into SESANS correlation function G using a Hankel transformation, then converting the SESANS correlation function into polarisation from the SESANS experiment Everything is in units of metres except specified otherwise (NOT TRUE!!!) Everything is in conventional units (nm for spin echo length) Wim Bouwman (w.g.bouwman@tudelft.nl), June 2013 """ from __future__ import division import numpy as np # type: ignore from numpy import pi, exp # type: ignore from scipy.special import j0 class SesansTransform(object): """ Spin-Echo SANS transform calculator. Similar to a resolution function, the SesansTransform object takes I(q) for the set of *q_calc* values and produces a transformed dataset *SElength* (A) is the set of spin-echo lengths in the measured data. *zaccept* (1/A) is the maximum acceptance of scattering vector in the spin echo encoding dimension (for ToF: Q of min(R) and max(lam)). *Rmax* (A) is the maximum size sensitivity; larger radius requires more computation time. """ #: SElength from the data in the original data units; not used by transform #: but the GUI uses it, so make sure that it is present. q = None # type: np.ndarray #: q values to calculate when computing transform q_calc = None # type: np.ndarray # transform arrays _H = None # type: np.ndarray _H0 = None # type: np.ndarray def __init__(self, z, SElength, lam, zaccept, Rmax): # type: (np.ndarray, float, float) -> None #import logging; logging.info("creating SESANS transform") self.q = z self._set_hankel(SElength, lam, zaccept, Rmax) def apply(self, Iq): # tye: (np.ndarray) -> np.ndarray G0 = np.dot(self._H0, Iq) G = np.dot(self._H.T, Iq) P = G - G0 return P def _set_hankel(self, SElength, lam, zaccept, Rmax): # type: (np.ndarray, float, float) -> None # Force float32 arrays, otherwise run into memory problems on some machines SElength = np.asarray(SElength, dtype='float32') #Rmax = #value in text box somewhere in FitPage? q_max = 2*pi / (SElength[1] - SElength[0]) q_min = 0.1 * 2*pi / (np.size(SElength) * SElength[-1]) q = np.arange(q_min, q_max, q_min, dtype='float32') dq = q_min H0 = np.float32(dq/(2*pi)) * q repq = np.tile(q, (SElength.size, 1)).T repSE = np.tile(SElength, (q.size, 1)) H = np.float32(dq/(2*pi)) * j0(repSE*repq) * repq replam = np.tile(lam, (q.size, 1)) reptheta = np.arcsin(repq*replam/2*np.pi) mask = reptheta > zaccept H[mask] = 0 self.q_calc = q self._H, self._H0 = H, H0 sasmodels/sasmodels/weights.py000066400000000000000000000176061317715334700171130ustar00rootroot00000000000000""" SAS distributions for polydispersity. """ # TODO: include dispersion docs with the disperser models from __future__ import division, print_function from math import sqrt # type: ignore from collections import OrderedDict import numpy as np # type: ignore from scipy.special import gammaln # type: ignore # TODO: include dispersion docs with the disperser models class Dispersion(object): """ Base dispersion object. Subclasses should define *_weights(center, sigma, lb, ub)* which returns the x points and their corresponding weights. """ type = "base disperser" default = dict(npts=35, width=0, nsigmas=3) def __init__(self, npts=None, width=None, nsigmas=None): self.npts = self.default['npts'] if npts is None else npts self.width = self.default['width'] if width is None else width self.nsigmas = self.default['nsigmas'] if nsigmas is None else nsigmas def get_pars(self): """ Return the parameters to the disperser as a dictionary. """ pars = {'type': self.type} pars.update(self.__dict__) return pars # pylint: disable=no-self-use def set_weights(self, values, weights): """ Set the weights on the disperser if it is :class:`ArrayDispersion`. """ raise RuntimeError("set_weights is only available for ArrayDispersion") def get_weights(self, center, lb, ub, relative): """ Return the weights for the distribution. *center* is the center of the distribution *lb*, *ub* are the min and max allowed values *relative* is True if the distribution width is proportional to the center value instead of absolute. For polydispersity use relative. For orientation parameters use absolute. """ sigma = self.width * center if relative else self.width if sigma == 0 or self.npts < 2: if lb <= center <= ub: return np.array([center], 'd'), np.array([1.], 'd') else: return np.array([], 'd'), np.array([], 'd') x, px = self._weights(center, sigma, lb, ub) return x, px def _weights(self, center, sigma, lb, ub): """actual work of computing the weights""" raise NotImplementedError def _linspace(self, center, sigma, lb, ub): """helper function to provide linear spaced weight points within range""" npts, nsigmas = self.npts, self.nsigmas x = center + np.linspace(-nsigmas*sigma, +nsigmas*sigma, npts) x = x[(x >= lb) & (x <= ub)] return x class GaussianDispersion(Dispersion): r""" Gaussian dispersion, with 1-\ $\sigma$ width. .. math:: w = \exp\left(-\tfrac12 (x - c)^2/\sigma^2\right) """ type = "gaussian" default = dict(npts=35, width=0, nsigmas=3) def _weights(self, center, sigma, lb, ub): # TODO: sample high probability regions more densely # i.e., step uniformly in cumulative density rather than x value # so weight = 1/Npts for all weights, but values are unevenly spaced x = self._linspace(center, sigma, lb, ub) px = np.exp((x-center)**2 / (-2.0 * sigma * sigma)) return x, px class RectangleDispersion(Dispersion): r""" Uniform dispersion, with width $\sqrt{3}\sigma$. .. math:: w = 1 """ type = "rectangle" default = dict(npts=35, width=0, nsigmas=1.70325) def _weights(self, center, sigma, lb, ub): x = self._linspace(center, sigma, lb, ub) x = x[np.fabs(x-center) <= np.fabs(sigma)*sqrt(3.0)] return x, np.ones_like(x) class LogNormalDispersion(Dispersion): r""" log Gaussian dispersion, with 1-\ $\sigma$ width. .. math:: w = \frac{\exp\left(-\tfrac12 (\ln x - c)^2/\sigma^2\right)}{x\sigma} """ type = "lognormal" default = dict(npts=80, width=0, nsigmas=8) def _weights(self, center, sigma, lb, ub): x = self._linspace(center, sigma, max(lb, 1e-8), max(ub, 1e-8)) # sigma in the lognormal function is in ln(R) space, thus needs converting sig = np.fabs(sigma/center) px = np.exp(-0.5*((np.log(x)-np.log(center))/sig)**2)/(x*sig) return x, px class SchulzDispersion(Dispersion): r""" Schultz dispersion, with 1-\ $\sigma$ width. .. math:: w = \frac{z^z\,R^{z-1}}{e^{Rz}\,c \Gamma(z)} where $c$ is the center of the distribution, $R = x/c$ and $z=(c/\sigma)^2$. This is evaluated using logarithms as .. math:: w = \exp\left(z \ln z + (z-1)\ln R - Rz - \ln c - \ln \Gamma(z) \right) """ type = "schulz" default = dict(npts=80, width=0, nsigmas=8) def _weights(self, center, sigma, lb, ub): x = self._linspace(center, sigma, max(lb, 1e-8), max(ub, 1e-8)) R = x/center z = (center/sigma)**2 arg = z*np.log(z) + (z-1)*np.log(R) - R*z - np.log(center) - gammaln(z) px = np.exp(arg) return x, px class ArrayDispersion(Dispersion): r""" Empirical dispersion curve. Use :meth:`set_weights` to set $w = f(x)$. """ type = "array" default = dict(npts=35, width=0, nsigmas=1) def __init__(self, npts=None, width=None, nsigmas=None): Dispersion.__init__(self, npts, width, nsigmas) self.values = np.array([0.], 'd') self.weights = np.array([1.], 'd') def set_weights(self, values, weights): """ Set the weights for the given x values. """ self.values = np.ascontiguousarray(values, 'd') self.weights = np.ascontiguousarray(weights, 'd') self.npts = len(values) def _weights(self, center, sigma, lb, ub): # TODO: rebin the array dispersion using npts # TODO: use a distribution that can be recentered and scaled x = self.values #x = center + self.values*sigma idx = (x >= lb) & (x <= ub) x = x[idx] px = self.weights[idx] return x, px # dispersion name -> disperser lookup table. # Maintain order since this is used by sasview GUI to order the options in # the dispersion type combobox. MODELS = OrderedDict((d.type, d) for d in ( RectangleDispersion, ArrayDispersion, LogNormalDispersion, GaussianDispersion, SchulzDispersion, )) def get_weights(disperser, n, width, nsigmas, value, limits, relative): """ Return the set of values and weights for a polydisperse parameter. *disperser* is the name of the disperser. *n* is the number of points in the weight vector. *width* is the width of the disperser distribution. *nsigmas* is the number of sigmas to span for the dispersion convolution. *value* is the value of the parameter in the model. *limits* is [lb, ub], the lower and upper bound on the possible values. *relative* is true if *width* is defined in proportion to the value of the parameter, and false if it is an absolute width. Returns *(value, weight)*, where *value* and *weight* are vectors. """ if disperser == "array": raise NotImplementedError("Don't handle arrays through get_weights; use values and weights directly") cls = MODELS[disperser] obj = cls(n, width, nsigmas) v, w = obj.get_weights(value, limits[0], limits[1], relative) return v, w def plot_weights(model_info, pairs): # type: (ModelInfo, List[Tuple[np.ndarray, np.ndarray]]) -> None """ Plot the weights returned by :func:`get_weights`. *model_info* is :param model_info: :param pairs: :return: """ import pylab if any(len(values)>1 for values, weights in pairs): labels = [p.name for p in model_info.parameters.call_parameters] pylab.interactive(True) pylab.figure() for (v,w), s in zip(pairs, labels): if len(v) > 1: #print("weights for", s, v, w) pylab.plot(v, w, '-o', label=s) pylab.grid(True) pylab.legend() #pylab.show() sasmodels/sesansdemo.py000066400000000000000000000061331317715334700156010ustar00rootroot00000000000000# Example of conversion of scattering cross section from SANS in absolute # units into SESANS using a Hankel transformation # everything is in units of metres except specified otherwise # Wim Bouwman (w.g.bouwman@tudelft.nl), June 2013 from __future__ import division from pylab import * from scipy.special import jv as besselj # q-range parameters q = arange(0.0003, 1.0, 0.0003); # [nm^-1] range wide enough for Hankel transform dq=(q[1]-q[0])*1e9; # [m^-1] step size in q, needed for integration nq=len(q); Lambda=2e-10; # [m] wavelength # sample parameters phi=0.1; # volume fraction R=100; # [nm] radius particles DeltaRho=6e14; # [m^-2] V=4/3*pi*R**3 * 1e-27; # [m^3] th=0.002; # [m] thickness sample #2 PHASE SYSTEM st= 1.5*Lambda**2*DeltaRho**2*th*phi*(1-phi)*R*1e-9 # scattering power in sesans formalism # Form factor solid sphere qr=q*R; P=(3.*(sin(qr)-qr*cos(qr)) / qr**3)**2; # Structure factor dilute S=1.; #2 PHASE SYSTEM # scattered intensity [m^-1] in absolute units according to SANS I=phi*(1-phi)*V*(DeltaRho**2)*P*S; clf() subplot(211) # plot the SANS calculation plot(q,I,'k') loglog(q,I) xlim([0.01, 1]) ylim([1, 1e9]) xlabel(r'$Q [nm^{-1}]$') ylabel(r'$d\Sigma/d\Omega [m^{-1}]$') # Hankel transform to nice range for plot nz=61; zz=linspace(0,240,nz); # [nm], should be less than reciprocal from q G=zeros(nz); for i in range(len(zz)): integr=besselj(0,q*zz[i])*I*q; G[i]=sum(integr); G=G*dq*1e9*2*pi; # integr step, conver q into [m**-1] and 2 pi circle integr # plot(zz,G); stt= th*Lambda**2/4/pi/pi*G[0] # scattering power according to SANS formalism PP=exp(th*Lambda**2/4/pi/pi*(G-G[0])); subplot(212) plot(zz,PP,'k',label="Hankel transform") # Hankel transform 1D xlabel('spin-echo length [nm]') ylabel('polarisation normalised') hold(True) # Cosine transformation of 2D scattering patern if False: qy,qz = meshgrid(q,q) qr=R*sqrt(qy**2 + qz**2); # reuse variable names Hankel transform, but now 2D P=(3.*(sin(qr)-qr*cos(qr)) / qr**3)**2; # Structure factor dilute S=1.; # scattered intensity [m^-1] in absolute units according to SANS I=phi*V*(DeltaRho**2)*P*S; GG=zeros(nz); for i in range(len(zz)): integr=cos(qz*zz[i])*I; GG[i]=sum(sum(integr)); GG=4*GG* dq**2; # take integration step into account take 4 quadrants # plot(zz,GG); sstt= th*Lambda**2/4/pi/pi*GG[0] # scattering power according to SANS formalism PPP=exp(th*Lambda**2/4/pi/pi*(GG-GG[0])); plot(zz,PPP,label="cosine transform") # cosine transform 2D # For comparison calculation in SESANS formalism, which overlaps perfectly def gsphere(z,r): """ Calculate SESANS-correlation function for a solid sphere. Wim Bouwman after formulae Timofei Kruglov J.Appl.Cryst. 2003 article """ d = z/r g = zeros_like(z) g[d==0] = 1. low = ((d > 0) & (d < 2)) dlow = d[low] dlow2 = dlow**2 print dlow.shape, dlow2.shape g[low] = sqrt(1-dlow2/4.)*(1+dlow2/8.) + dlow2/2.*(1-dlow2/16.)*log(dlow/(2.+sqrt(4.-dlow2))) return g if True: plot(zz,exp(st*(gsphere(zz,R)-1)),'r', label="analytical") legend() show() sasmodels/setup.py000066400000000000000000000035451317715334700146040ustar00rootroot00000000000000try: from setuptools import setup except ImportError: from distutils.core import setup def find_version(package): """Read package version string from __init__.py""" import os with open(os.path.join(package, '__init__.py')) as fid: for line in fid.readlines(): if line.startswith('__version__'): line = line[:line.find('#')] # strip comment, if any version = line.split('=', 2)[1].strip() if version[0] != version[-1] or version[0] not in "\"'": break return version[1:-1] raise RuntimeError("Could not read version from %s/__init__.py"%package) setup( name='sasmodels', version=find_version('sasmodels'), description="sasmodels package", long_description=open('README.rst').read(), author="SasView Collaboration", author_email="management@sasview.org", url="http://www.sasview.org", keywords="small-angle x-ray and neutron scattering analysis", download_url="https://github.com/SasView/sasmodels", classifiers=[ 'Development Status :: 4 - Beta', 'Environment :: Console', 'Intended Audience :: Science/Research', 'License :: Public Domain', 'Operating System :: OS Independent', 'Programming Language :: Python', 'Programming Language :: C', 'Topic :: Scientific/Engineering', 'Topic :: Scientific/Engineering :: Chemistry', 'Topic :: Scientific/Engineering :: Physics', ], packages=[ 'sasmodels', 'sasmodels.models', 'sasmodels.custom' ], package_data={ 'sasmodels.models': ['*.c', 'lib/*.c'], 'sasmodels': ['*.c', '*.cl'], }, install_requires = [ ], extras_require = { 'OpenCL': ["pyopencl"], 'Bumps': ["bumps"], 'TinyCC': ["tinycc"], }, ) sasmodels/setup_py2exe.py000077500000000000000000000275631317715334700161110ustar00rootroot00000000000000#!/usr/bin/env python # Copyright (C) 2006-2010, University of Maryland # # Permission is hereby granted, free of charge, to any person obtaining a copy # of this software and associated documentation files (the "Software"), to deal # in the Software without restriction, including without limitation the rights # to use, copy, modify, merge, publish, distribute, sublicense, and/ or sell # copies of the Software, and to permit persons to whom the Software is # furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included in # all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR # IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE # AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER # LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, # OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN # THE SOFTWARE. # Author: James Krycka """ This script uses py2exe to create dist\bumps.exe and dist\bumps_gui.exe for running the Bumps application in either CLI or GUI mode. These executables start the application and import the rest of the application code stored in library.zip. The python interpreter and other required python packages and dlls are also placed in the zip file. Additional resource files that are needed when Bumps is run are copied to the dist directory tree. On completion, the contents of the dist directory tree can be used by the Inno Setup Compiler (via a separate script) to build a Windows installer/uninstaller for deployment of the Bumps application. For testing purposes, bumps.exe or bumps_gui.exe can be run from the dist directory. """ import os import sys #sys.dont_write_bytecode = True # Force build before continuing os.system('"%s" setup.py build' % sys.executable) # Remove the current directory from the python path here = os.path.abspath(os.path.dirname(__file__)) sys.path = [p for p in sys.path if os.path.abspath(p) != here] import glob from distutils.core import setup from distutils.util import get_platform # Augment the setup interface with the py2exe command and make sure the py2exe # option is passed to setup. import py2exe if len(sys.argv) == 1: sys.argv.append('py2exe') # Put the build lib on the start of the path. # For packages with binary extensions, need platform. If it is a pure # script library, use an empty platform string. platform = '.%s-%s' % (get_platform(), sys.version[:3]) #platform = '' build_lib = os.path.abspath('build/lib' + platform) sys.path.insert(0, build_lib) # print "\n".join(sys.path) import wx import matplotlib matplotlib.use('WXAgg') import periodictable # Retrieve the application version string. import bumps version = bumps.__version__ from bumps.gui.resources import resources as gui_resources # A manifest is required to be included in a py2exe image (or accessible as a # file in the image directory) when wxPython is included so that the Windows XP # theme is used when rendering wx widgets. The manifest must be matched to the # version of Python that is being used. # # Create a manifest for use with Python 2.5 on Windows XP or Vista. It is # adapted from the Python manifest file (C:\Python25\pythonw.exe.manifest). manifest_for_python25 = """ %(prog)s """ # Create a manifest for use with Python 2.6 or 2.7 on Windows XP or Vista. manifest_for_python26 = """ %(prog)s """ # Select the appropriate manifest to use. if sys.version_info >= (3, 0) or sys.version_info < (2, 5): print("*** This script only works with Python 2.5, 2.6, or 2.7.") sys.exit() elif sys.version_info >= (2, 6): manifest = manifest_for_python26 elif sys.version_info >= (2, 5): manifest = manifest_for_python25 # Create a list of all files to include along side the executable being built # in the dist directory tree. Each element of the data_files list is a tuple # consisting of a path (relative to dist\) and a list of files in that path. data_files = [] # Add resource files that need to reside in the same directory as the image. data_files.append(('.', [os.path.join('.', 'LICENSE.txt')])) data_files.append(('.', [os.path.join('.', 'README.txt')])) data_files.append(('.', [os.path.join('.', 'bin', 'bumps_launch.bat')])) # Add application specific data files from the bumps\bumps-data folder. data_files += gui_resources.data_files() # Add data files from the matplotlib\mpl-data folder and its subfolders. # For matploblib prior to version 0.99 see the examples at the end of the file. data_files += matplotlib.get_py2exe_datafiles() # Add data files from the periodictable\xsf folder. data_files += periodictable.data_files() # Add example directories and their files. An empty directory is ignored. # Note that Inno Setup will determine where these files will be placed such as # C:\My Documents\... instead of the installation folder. for path in glob.glob(os.path.join('examples', '*')): if os.path.isdir(path): for file in glob.glob(os.path.join(path, '*.*')): data_files.append((path, [file])) else: data_files.append(('examples', [path])) for path in glob.glob(os.path.join('doc', 'examples', '*')): if os.path.isdir(path): for file in glob.glob(os.path.join(path, '*.*')): data_files.append((path, [file])) else: data_files.append(('doc', [path])) # Add PDF documentation to the dist staging directory. pdf = os.path.join('doc', 'Bumps.pdf') if os.path.isfile(pdf): data_files.append(('doc', [pdf])) else: print("*** %s not found - building frozen image without it ***" % pdf) # Add the Microsoft Visual C++ 2008 redistributable kit if we are building with # Python 2.6 or 2.7. This kit will be installed on the target system as part # of the installation process for the frozen image. Note that the Python 2.5 # interpreter requires msvcr71.dll which is included in the Python25 package, # however, Python 2.6 and 2.7 require the msvcr90.dll but they do not bundle it # with the Python26 or Python27 package. Thus, for Python 2.6 and later, the # appropriate dll must be present on the target system at runtime. if sys.version_info >= (2, 6): pypath = os.path.dirname(sys.executable) data_files.append(('.', [os.path.join(pypath, 'vcredist_x86.exe')])) # Specify required packages to bundle in the executable image. packages = ['numpy', 'scipy', 'matplotlib', 'pytz', 'pyparsing', 'periodictable', 'bumps', 'sasmodels', 'pyopencl', ] # Specify files to include in the executable image. includes = [] # Specify files to exclude from the executable image. # - We can safely exclude Tk/Tcl and Qt modules because our app uses wxPython. # - We do not use ssl services so they are omitted. # - We can safely exclude the TkAgg matplotlib backend because our app uses # "matplotlib.use('WXAgg')" to override the default matplotlib configuration. # - On the web it is widely recommended to exclude certain lib*.dll modules # but this does not seem necessary any more (but adding them does not hurt). # - Python25 requires mscvr71.dll, however, Win XP includes this file. # - Since we do not support Win 9x systems, w9xpopen.dll is not needed. # - For some reason cygwin1.dll gets included by default, but it is not needed. excludes = ['Tkinter', 'PyQt4', '_ssl', '_tkagg', 'numpy.distutils.test'] dll_excludes = ['libgdk_pixbuf-2.0-0.dll', 'libgobject-2.0-0.dll', 'libgdk-win32-2.0-0.dll', 'tcl84.dll', 'tk84.dll', 'QtGui4.dll', 'QtCore4.dll', 'msvcr71.dll', 'msvcp90.dll', 'w9xpopen.exe', 'cygwin1.dll'] class Target(object): """This class stores metadata about the distribution in a dictionary.""" def __init__(self, **kw): self.__dict__.update(kw) self.version = version clientCLI = Target( name='Bumps', description='Bumps CLI application', # module to run on application start script=os.path.join('bin', 'bumps_cli.py'), dest_base='bumps', # file name part of the exe file to create # also need to specify in data_files icon_resources=[ (1, os.path.join('bumps', 'gui', 'resources', 'bumps.ico'))], bitmap_resources=[], other_resources=[(24, 1, manifest % dict(prog='Bumps'))]) clientGUI = Target( name='Bumps', description='Bumps GUI application', # module to run on application start script=os.path.join('bin', 'bumps_gui.py'), dest_base='bumps_gui', # file name part of the exe file to create # also need to specify in data_files icon_resources=[ (1, os.path.join('bumps', 'gui', 'resources', 'bumps.ico'))], bitmap_resources=[], other_resources=[(24, 1, manifest % dict(prog='Bumps'))]) # Now we do the work to create a standalone distribution using py2exe. # # When the application is run in console mode, a console window will be created # to receive any logging or error messages and the application will then create # a separate GUI application window. # # When the application is run in windows mode, it will create a GUI application # window and no console window will be provided. Output to stderr will be # written to .log. setup( console=[clientCLI], windows=[clientGUI], options={'py2exe': { 'packages': packages, 'includes': includes, 'excludes': excludes, 'dll_excludes': dll_excludes, 'compressed': 1, # standard compression 'optimize': 0, # no byte-code optimization 'dist_dir': "dist", # where to put py2exe results 'xref': False, # display cross reference (as html doc) 'bundle_files': 1, # bundle python25.dll in library.zip } }, # Since we are building two exe's, do not put the shared library in each # of them. Instead create a single, separate library.zip file. # zipfile=None, # bundle library.zip in exe data_files=data_files # list of files to copy to dist directory )

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