lssa-0.1.4/0000755000000000000000000000000013743165726010662 5ustar0000000000000000lssa-0.1.4/COPYING0000644000000000000000000010451313743165726011721 0ustar0000000000000000 GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 Copyright (C) 2007 Free Software Foundation, Inc. Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The GNU General Public License is a free, copyleft license for software and other kinds of works. The licenses for most software and other practical works are designed to take away your freedom to share and change the works. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change all versions of a program--to make sure it remains free software for all its users. We, the Free Software Foundation, use the GNU General Public License for most of our software; it applies also to any other work released this way by its authors. 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But first, please read . lssa-0.1.4/DESCRIPTION0000644000000000000000000000122313743165726012366 0ustar0000000000000000Name: lssa Version: 0.1.4 Date: 2020-10-18 Author: Ben Lewis Maintainer: Ben Lewis , John Donoghue Title: Least squares spectral analysis Description: A package implementing tools to compute spectral decompositions of irregularly-spaced time series. Currently includes functions based off the Lomb-Scargle periodogram and Adolf Mathias' implementation for R and C (see URLs). Url: https://octave.sourceforge.io/lssa/ Url2: http://www.jstatsoft.org/v11/i02 Problems: fast implementations, wavelet functions are currently not functional. Depends: octave (>= 3.6.0) Autoload: no License: GPLv3+ lssa-0.1.4/INDEX0000644000000000000000000000060113743165726011451 0ustar0000000000000000lssa >> Least Squares Spectral Analysis Windowing cubicwgt Periodogram lombcoeff lombnormcoeff Accelerated time-series functions fastlscomplex Complex time-series functions lscomplex Real time-series functions lsreal Correlation lscorrcoeff Wavelet Transform lswaveletcoeff # lscomplexwavelet lsrealwavelet ## The wavelet functions are unavailable until I can get them working. lssa-0.1.4/Makefile0000644000000000000000000002175713743165726012336 0ustar0000000000000000## Copyright 2015-2016 CarnĂ« Draug ## Copyright 2015-2016 Oliver Heimlich ## Copyright 2017 Julien Bect ## Copyright 2017 Olaf Till ## Copyright 2018 John Donoghue ## ## Copying and distribution of this file, with or without modification, ## are permitted in any medium without royalty provided the copyright ## notice and this notice are preserved. This file is offered as-is, ## without any warranty. ## Some basic tools (can be overriden using environment variables) SED ?= sed TAR ?= tar GREP ?= grep CUT ?= cut TR ?= tr ## Note the use of ':=' (immediate set) and not just '=' (lazy set). ## http://stackoverflow.com/a/448939/1609556 package := $(shell $(GREP) "^Name: " DESCRIPTION | $(CUT) -f2 -d" " | \ $(TR) '[:upper:]' '[:lower:]') version := $(shell $(GREP) "^Version: " DESCRIPTION | $(CUT) -f2 -d" ") ## These are the paths that will be created for the releases. target_dir := target release_dir := $(target_dir)/$(package)-$(version) release_tarball := $(target_dir)/$(package)-$(version).tar.gz html_dir := $(target_dir)/$(package)-html html_tarball := $(target_dir)/$(package)-html.tar.gz ## Using $(realpath ...) avoids problems with symlinks due to bug ## #50994 in Octaves scripts/pkg/private/install.m. But at least the ## release directory above is needed in the relative form, for 'git ## archive --format=tar --prefix=$(release_dir). real_target_dir := $(realpath .)/$(target_dir) installation_dir := $(real_target_dir)/.installation package_list := $(installation_dir)/.octave_packages install_stamp := $(installation_dir)/.install_stamp ## These can be set by environment variables which allow to easily ## test with different Octave versions. ifndef OCTAVE OCTAVE := octave endif OCTAVE := $(OCTAVE) --no-gui --silent --norc MKOCTFILE ?= mkoctfile ## Command used to set permissions before creating tarballs FIX_PERMISSIONS ?= chmod -R a+rX,u+w,go-w,ug-s ## Detect which VCS is used vcs := $(if $(wildcard .hg),hg,$(if $(wildcard .git),git,unknown)) ifeq ($(vcs),hg) release_dir_dep := .hg/dirstate HG := hg HG_CMD = $(HG) --config alias.$(1)=$(1) --config defaults.$(1)= $(1) HG_ID := $(shell $(call HG_CMD,identify) --id | sed -e 's/+//' ) REPO_TIMESTAMP := $(firstword $(shell $(call HG_CMD,log) --rev $(HG_ID) --template '{date|hgdate}')) endif ifeq ($(vcs),git) release_dir_dep := .git/index GIT := git REPO_TIMESTAMP := $(firstword $(shell $(GIT) log -n1 --date=unix --format="%ad")) endif TAR_REPRODUCIBLE_OPTIONS := --sort=name --mtime="@$(REPO_TIMESTAMP)" --owner=0 --group=0 --numeric-owner TAR_OPTIONS := --format=ustar $(TAR_REPRODUCIBLE_OPTIONS) ## .PHONY indicates targets that are not filenames ## (https://www.gnu.org/software/make/manual/html_node/Phony-Targets.html) .PHONY: help ## make will display the command before runnning them. Use @command ## to not display it (makes specially sense for echo). help: @echo "Targets:" @echo " dist - Create $(release_tarball) for release." @echo " html - Create $(html_tarball) for release." @echo " release - Create both of the above and show md5sums." @echo " install - Install the package in $(installation_dir), where it is not visible in a normal Octave session." @echo " check - Execute package tests." @echo " doctest - Test the help texts with the doctest package." @echo " run - Run Octave with the package installed in $(installation_dir) in the path." @echo " clean - Remove everything made with this Makefile." ## ## Recipes for release tarballs (package + html) ## .PHONY: release dist html clean-tarballs clean-unpacked-release ## To make a release, build the distribution and html tarballs. release: dist html md5sum $(release_tarball) $(html_tarball) @echo "Upload @ https://sourceforge.net/p/octave/package-releases/new/" @echo " and note the changeset the release corresponds to" ## dist and html targets are only PHONY/alias targets to the release ## and html tarballs. dist: $(release_tarball) html: $(html_tarball) ## An implicit rule with a recipe to build the tarballs correctly. %.tar.gz: % $(TAR) -cf - $(TAR_OPTIONS) -C "$(target_dir)/" "$(notdir $<)" | gzip -9n > "$@" clean-tarballs: @echo "## Cleaning release tarballs (package + html)..." -$(RM) $(release_tarball) $(html_tarball) @echo ## Create the unpacked package. ## ## Notes: ## * having ".hg/dirstate" (or ".git/index") as a prerequesite means it is ## only rebuilt if we are at a different commit. ## * the variable RM usually defaults to "rm -f" ## * having this recipe separate from the one that makes the tarball ## makes it easy to have packages in alternative formats (such as zip) ## * note that if a commands needs to be run in a specific directory, ## the command to "cd" needs to be on the same line. Each line restores ## the original working directory. $(release_dir): $(release_dir_dep) -$(RM) -r "$@" ifeq (${vcs},hg) hg archive --exclude ".hg*" --type files "$@" endif ifeq (${vcs},git) git archive --format=tar --prefix="$@/" HEAD | $(TAR) -x $(RM) "$@/.gitignore" endif ## Don't fall back to run the supposed necessary contents of ## 'bootstrap' here. Users are better off if they provide ## 'bootstrap'. Administrators, checking build reproducibility, can ## put in the missing 'bootstrap' file if they feel they know its ## necessary contents. ifneq (,$(wildcard src/bootstrap)) cd "$@/src" && ./bootstrap && $(RM) -r "autom4te.cache" endif ## Uncomment this if your src/Makefile.in has these targets for ## pre-building something for the release (e.g. documentation). # cd "$@/src" && ./configure && $(MAKE) prebuild && \ # $(MAKE) distclean && $(RM) Makefile ## ${FIX_PERMISSIONS} "$@" run_in_place = $(OCTAVE) --eval ' pkg ("local_list", "$(package_list)"); ' \ --eval ' pkg ("load", "$(package)"); ' # html_options = --eval 'options = get_html_options ("octave-forge");' ## Uncomment this for package documentation. ##html_options = --eval 'options = get_html_options ("octave-forge");' \ ## --eval 'options.package_doc = "$(package).texi";' html_options = --eval 'options = get_html_options ("octave-forge");' $(html_dir): $(install_stamp) $(RM) -r "$@"; $(run_in_place) \ --eval ' pkg load generate_html; ' \ $(html_options) \ --eval ' generate_package_html ("$(package)", "$@", options); '; $(FIX_PERMISSIONS) "$@"; clean-unpacked-release: @echo "## Cleaning unpacked release tarballs (package + html)..." -$(RM) -r $(release_dir) $(html_dir) @echo ## ## Recipes for installing the package. ## .PHONY: install clean-install octave_install_commands = \ ' llist_path = pkg ("local_list"); \ mkdir ("$(installation_dir)"); \ load (llist_path); \ local_packages(cellfun (@ (x) strcmp ("$(package)", x.name), local_packages)) = []; \ save ("$(package_list)", "local_packages"); \ pkg ("local_list", "$(package_list)"); \ pkg ("prefix", "$(installation_dir)", "$(installation_dir)"); \ pkg ("install", "-local", "-verbose", "$(release_tarball)"); ' ## Install unconditionally. Maybe useful for testing installation with ## different versions of Octave. install: $(release_tarball) @echo "Installing package under $(installation_dir) ..." $(OCTAVE) --eval $(octave_install_commands) touch $(install_stamp) ## Install only if installation (under target/...) is not current. $(install_stamp): $(release_tarball) @echo "Installing package under $(installation_dir) ..." $(OCTAVE) --eval $(octave_install_commands) touch $(install_stamp) clean-install: @echo "## Cleaning installation under $(installation_dir) ..." -$(RM) -r $(installation_dir) @echo ## ## Recipes for testing purposes ## .PHONY: run doctest check ## Start an Octave session with the package directories on the path for ## interactice test of development sources. run: $(install_stamp) $(run_in_place) --persist ## Test example blocks in the documentation. Needs doctest package ## https://octave.sourceforge.io/doctest/index.html doctest: $(install_stamp) $(run_in_place) --eval 'pkg load doctest;' \ --eval "targets = pkg('list', '$(package)'){1}.dir;" \ --eval "doctest (targets);" ## Test package. octave_test_commands = \ ' pkgs = pkg("list", "$(package)"); \ dirs = {pkgs{1}.dir}; \ __run_test_suite__ (dirs, {}); ' ## the following works, too, but provides no overall summary output as ## __run_test_suite__ does: ## ## else cellfun (@runtests, horzcat (cellfun (@ (dir) ostrsplit (([~, dirs] = system (sprintf ("find %s -type d", dir))), "\n\r", true), dirs, "UniformOutput", false){:})); endif ' check: $(install_stamp) $(run_in_place) --eval $(octave_test_commands) clean-check: @echo "## Removing fntests.log..." -$(RM) $(target_dir)/fntests.log @echo ## ## CLEAN ## .PHONY: clean clean: clean-tarballs clean-unpacked-release clean-install clean-check @echo "## Removing target directory (if empty)..." -rmdir $(target_dir) @echo @echo "## Cleaning done" @echo lssa-0.1.4/NEWS0000644000000000000000000000361513743165726011366 0ustar0000000000000000Summary of changes in lssa 0.1.4: ** Code updates to support install in Octave 6.0 Summary of changes in lssa 0.1.3: ** Mark fastlscomplex BIT as a known failure (Bug #53963) ** Update package with maintainer makefile ** Code updates to support install in Octave 4.4 Summary of changes in lssa 0.1.2: ** All functions now have input checks in place to return useful errors as opposed to division by zero, etc. Documentation has also been improved. Summary of status of the intial lssa release, 0.1.1: Current status: ** lscomplex and lsreal both produce accurate results; they can be slow for very large datasets. ** fastlscomplex is accurate for the first octave of results; there is still an error I need to pin down in the merging for additional octaves. fastlsreal is disabled at the moment as I move to an implementation based on the new fastlscomplex. ** lscorrcoeff works, although I'm still attempting to understand the initial author's reasoning. Its generated results are relevant to any given data set, but it does not appear to be normalized to any great extent. ** There are two wavelet functions under development, but they are not included in this release as they are currently not functional. For all your wavelet needs, the specific transformation used is available in the lswaveletcoeff function, and will generate a single cosine/sine magnitude pair (as a complex number) for a complex-valued series (this function may be joined by a companion for real-valued series) and can be looped to simulate a full wavelet transform. ** For all the working functions, tests have been written and formatted to Octave coding standards. These tests should pass on any given architecture (there was some question about that previously) and often provide examples of how the function operates. For a few functions, there are demo scripts. lssa-0.1.4/ONEWS0000644000000000000000000000266213743165726011506 0ustar0000000000000000Welcome to the first release of lssa, 0.1.1 Current status: ** lscomplex and lsreal both produce accurate results; they can be slow for very large datasets. ** fastlscomplex is accurate for the first octave of results; there is still an error I need to pin down in the merging for additional octaves. fastlsreal is disabled at the moment as I move to an implementation based on the new fastlscomplex. ** lscorrcoeff works, although I'm still attempting to understand the initial author's reasoning. Its generated results are relevant to any given data set, but it does not appear to be normalized to any great extent. ** There are two wavelet functions under development, but they are not included in this release as they are currently not functional. For all your wavelet needs, the specific transformation used is available in the lswaveletcoeff function, and will generate a single cosine/sine magnitude pair (as a complex number) for a complex-valued series (this function may be joined by a companion for real-valued series) and can be looped to simulate a full wavelet transform. ** For all the working functions, tests have been written and formatted to Octave coding standards. These tests should pass on any given architecture (there was some question about that previously) and often provide examples of how the function operates. For a few functions, there are demo scripts. lssa-0.1.4/data/0000755000000000000000000000000013743165726011573 5ustar0000000000000000lssa-0.1.4/data/ch4.csv0000644000000000000000000002534613743165726013000 0ustar0000000000000000149.2,5683,2347,668 173.1,6828,3634,636 177.4,7043,3833,595 228.7,9528,6225,588 236.4,9901,6614,574 266,11334,8113,616 303.8,13526,10189,667 321.2,14538,11013,621 325,14775,11143,511 331.7,15215,11329,477 342.1,15922,11719,501 356,16974,12626,662 365.6,17755,13412,610 366.2,17803,13457,642 381.7,19089,14241,445 426.3,22829,16417,395 443.5,24315,17695,363 458.3,25557,18950,349 471,26595,20004,379 491.3,28356,21636,348 506.4,29630,22977,406 507.4,29716,23059,339 510.2,29967,23392,371 513.6,30250,23714,377 517.6,30591,24146,403 519.7,30761,24327,403 522.5,30998,24643,340 522.6,31011,24654,360 522.7,31020,24662,381 525.6,31266,24875,358 528.2,31487,25073,392 532.2,31828,25423,377 532.4,31845,25440,381 532.4,31845,25440,379 535,32058,25684,360 540,32465,25999,363 541.5,32583,26099,382 541.5,32583,26099,386 545.2,32887,26336,387 547,33042,26471,412 549.4,33240,26672,426 552,33461,26884,418 554.2,33646,27064,448 556.5,33833,27342,464 560.2,34136,27702,435 562.5,34318,27951,416 563.1,34371,28016,403 565.2,34530,28195,382 569.2,34832,28551,396 571.4,34985,28743,425 574.3,35210,28943,435 577.8,35464,29130,436 581.8,35766,29410,421 582.8,35839,29493,416 583.3,35876,29542,429 589.2,36346,30175,481 591.7,36558,30385,489 593.8,36729,30591,482 599.1,37157,31088,394 602.6,37444,31479,429 609.7,38013,32176,469 612,38203,32384,505 615.5,38491,32715,548 617.7,38678,32952,532 619.5,38826,33161,520 622.2,39039,33474,530 625.1,39268,33823,509 627.6,39464,34108,500 627.6,39464,34108,483 629.2,39593,34285,484 633.4,39917,34644,418 635.1,40060,34784,403 639.5,40424,35038,459 641.3,40573,35163,414 644.6,40841,35387,375 648,41112,35573,423 649.2,41209,35645,443 653.8,41551,35883,431 664.1,42305,36641,484 682,43702,38109,520 683,43785,38201,493 694.6,44764,39388,424 699.5,45181,39828,448 706.1,45770,40626,537 712.9,46360,41358,522 724.8,47360,42131,441 748.3,49296,43546,419 765.3,50634,44788,402 788.2,52446,47024,466 812,54457,49398,504 834.8,56300,51174,480 860.6,58258,52870,514 885.3,60288,55564,528 911.4,62633,57737,442 937.3,65016,59604,411 962.4,67405,61582,414 986.3,69627,63694,415 1011.3,71767,65701,434 1037.5,74017,68495,424 1062.2,76023,71014,458 1087.2,78042,72849,430 1112.6,80064,75367,462 1137.7,81921,76875,402 1162.1,83615,78995,438 1186.5,85262,81122,497 1209.7,86826,82843,545 1237.2,88808,84929,594 1261.2,90609,86323,529 1289.2,92632,88051,425 1309.2,94039,89363,417 1338.2,96047,91691,454 1363.7,97841,93660,443 1387.2,99498,95349,406 1413,101234,96900,407 1442.8,103125,99067,476 1451.4,103726,99833,480 1463.3,104574,100842,521 1476.1,105492,101829,493 1505,107599,103372,559 1526.2,109395,105204,591 1532,109872,105675,564 1542.1,110674,106203,437 1557.4,111923,107007,451 1582.8,113952,108994,468 1614.8,116215,111442,448 1627.7,117059,112559,443 1630.3,117221,112793,463 1637.7,117677,113479,505 1638.8,117747,113574,483 1643.4,118037,114031,497 1649,118376,114508,511 1654.5,118705,115060,485 1658.6,118958,115401,503 1664.5,119314,115768,520 1667.6,119504,116037,550 1669.5,119620,116200,531 1671.3,119728,116353,548 1674.2,119907,116605,575 1680,120259,117052,541 1684.5,120528,117342,555 1686.2,120623,117446,572 1688.4,120749,117589,590 1694,121079,117964,560 1694.6,121116,118010,573 1697.7,121296,118205,575 1704.7,121710,118631,563 1708.8,121941,118853,559 1714.2,122245,119164,589 1716,122345,119273,573 1719.4,122538,119499,584 1722.6,122718,119704,591 1731.2,123222,120320,603 1735.2,123443,120571,601 1736.8,123535,120652,578 1739,123658,120765,606 1744.3,123953,121090,592 1751.5,124348,121561,598 1754.3,124505,121752,594 1759.4,124787,122020,618 1765.5,125136,122367,592 1768.5,125298,122528,594 1770,125380,122606,600 1775.7,125692,122968,598 1780,125933,123279,604 1783.1,126109,123445,601 1786.8,126316,123677,622 1789.2,126447,123815,602 1789.4,126458,123826,630 1794.2,126710,124077,618 1797.8,126893,124244,619 1804.5,127236,124597,610 1814.8,127750,125176,649 1818.4,127930,125354,645 1819.6,127992,125424,623 1820.4,128032,125468,677 1824.6,128239,125679,672 1831,128549,126093,633 1832.3,128614,126200,644 1834.2,128712,126343,644 1834.7,128738,126380,636 1838.5,128932,126652,632 1844.8,129266,127008,638 1848.4,129450,127214,655 1852.3,129669,127440,666 1853.9,129752,127526,683 1857.4,129937,127716,653 1860.6,130111,127890,687 1863.8,130286,128080,708 1869.4,130605,128364,710 1870.2,130653,128399,699 1874.4,130904,128576,700 1875.5,130973,128632,704 1878.8,131178,128812,676 1883.3,131459,129062,552 1884.2,131519,129125,565 1888.6,131813,129348,540 1893.4,132149,129675,560 1897.9,132470,129898,524 1903.6,132880,130172,542 1910.9,133444,130549,492 1921.5,134310,131146,477 1922.3,134383,131195,491 1932.1,135318,131795,453 1954.6,137611,133340,431 1969.9,139296,134211,399 1980.2,140452,135003,352 1987.4,141257,135683,357 1994.7,142075,136367,374 1998,142440,136659,377 2005.9,143326,137393,348 2009.4,143720,137686,339 2016.4,144496,138408,318 2030.9,146122,140072,319 2042.5,147403,141422,345 2063.7,149756,143980,355 2088.6,152467,146784,356 2102.4,154026,148566,400 2109,154786,149406,418 2116,155625,150303,410 2119,155987,150633,376 2127.2,156981,151441,395 2137.1,158157,152562,445 2143,158819,153173,414 2153.4,159908,154129,382 2164,161077,155299,377 2167.2,161450,155706,406 2177.3,162574,157299,403 2180.4,162912,157806,381 2196.4,164820,159791,376 2225,168391,162996,405 2247,170922,165278,420 2273,174105,169266,478 2302,177644,172596,456 2312.3,179000,174189,402 2325,180546,175440,468 2348,183525,178550,503 2363,185640,180779,522 2373,187067,181718,464 2386,188892,183355,470 2399,190587,185063,510 2414,192382,187199,445 2425,193816,189335,440 2437,195298,191057,414 2475,199904,195625,460 2501,202717,199292,558 2525,205458,202212,612 2543,207803,204283,482 2552,208947,205148,425 2554.9,209310,205439,421 2557.7,209648,205715,413 2560.9,210056,206122,436 2564.9,210526,206675,466 2567.5,210840,207033,463 2570.4,211178,207418,455 2574.2,211628,207991,496 2575.5,211784,208183,475 2579.9,212295,208796,476 2581.9,212531,209078,485 2584.7,212846,209414,515 2588.5,213282,209975,473 2590.4,213503,210237,498 2595.1,214036,210830,567 2596.7,214219,211005,503 2600.4,214642,211481,509 2603.7,215011,211929,586 2606.6,215343,212281,551 2609.7,215685,212662,554 2612.5,216019,213010,545 2615.5,216377,213385,569 2621.7,217099,214153,581 2629,217944,214996,558 2633.5,218492,215504,568 2636.7,218908,215879,586 2639.5,219276,216310,544 2643.7,219835,216923,557 2646.4,220230,217253,541 2649.4,220678,217577,483 2656.2,221718,218342,440 2659.5,222273,218767,436 2666.7,223548,219680,476 2669.4,224060,220047,473 2674.6,224993,220760,498 2676.9,225380,220997,480 2682.6,226339,221612,482 2691,227885,222958,494 2693.6,228349,223446,532 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3244.9,385814,382627,0.35 3250.9,389631,385590,0.65 3259.9,395516,391478,0.52 3268.9,400502,397554,0.55 3274.9,403775,401044,0.38 3277.9,405354,402666,0.24 3284.9,408947,406607,0.02 3290.9,411959,409860,-0.08 3296.9,415188,412938,0.02 3299.9,416824,414603,-0.06 lssa-0.1.4/inst/0000755000000000000000000000000013743165726011637 5ustar0000000000000000lssa-0.1.4/inst/cubicwgt.m0000644000000000000000000000371713743165726013634 0ustar0000000000000000## Copyright (C) 2012 Benjamin Lewis ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{a} =} cubicwgt (@var{series}) ## ## Returns the input series, windowed by a polynomial similar to a Hanning ## window. To window an arbitrary section of the series, subtract or add an ## offset to it to adjust the centre of the window; for an offset of k, the call ## would be cubicwgt (@var{s} - k). Similarly, the radius of the window is 1; ## if an arbitrary radius r is desired, dividing the series by the radius after ## centering is the best way to adjust to fit the window: cubicwgt ((@var{s} - ## k) / r). ## ## The windowing function itself is: ## w = 1 + ( x ^ 2 * ( 2 x - 3 ) ), x in [-1,1], else w = 0. ## ## @end deftypefn function a = cubicwgt (s) if (nargin != 1) print_usage (); endif ## s is the value/vector/matrix to be windowed a = abs (s); a = ifelse ((a < 1), 1 + ((a .^ 2) .* (2 .* a - 3)), 0); endfunction %!shared h, m, k %! h = 2; %! m = 0.01; %! k = [0, 3, 1.5, -1, -0.5, -0.25, 0.75]; %!assert (cubicwgt (h), 0 ); %!assert (cubicwgt (m), 1 + m ^ 2 * (2 * m - 3)); %!assert (cubicwgt (k), [1.00000, 0.00000, 0.00000, 0.00000, ... %! 0.50000, 0.84375, 0.15625], 1e-6); %! ## Tests cubicwgt on two scalars and two vectors; cubicwgt will work %! ## on any array input. lssa-0.1.4/inst/lombcoeff.m0000644000000000000000000000407413743165726013756 0ustar0000000000000000## Copyright (C) 2012 Benjamin Lewis ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{c} =} lombcoeff (@var{time}, @var{mag}, @var{freq}) ## ## Return the Lomb Periodogram value at one frequency for a time series. ## ## @seealso{lombnormcoeff} ## @end deftypefn function coeff = lombcoeff (T, X, o) if (nargin != 3) print_usage (); elseif (! all (size (T) == size (X))) error ("lombcoeff: Time series vectors of uneven size"); elseif (! isscalar (o)) error ("lombcoeff: Supplied frequency is not a scalar"); elseif (o == 0) error ("lombcoeff: Supplied frequency is not a frequency"); endif oT = o .* T; theta = atan2 (sum (sin (2 * oT)), sum (cos (2 * oT))) ./ (2 * o); coeff = (sum (X .* cos (oT - theta)) ^2 / sum (cos (oT - theta) .^2) + sum (X .* sin (oT - theta)) ^2 / sum (sin (oT - theta) .^2)); endfunction %!shared t, x, o, maxfreq %! maxfreq = 4 / (2 * pi); %! t = linspace (0, 8); %! x = (2 .* sin (maxfreq .* t) + %! 3 .* sin ((3/4) * maxfreq .* t) - %! 0.5 .* sin ((1/4) * maxfreq .* t) - %! 0.2 .* cos (maxfreq .* t) + %! cos ((1/4) * maxfreq .* t)); %! o = [maxfreq , (3/4 * maxfreq) , (1/4 * maxfreq)]; %!assert (lombcoeff (t, x, maxfreq), 1076.77574184435, 5e-10); %!assert (lombcoeff (t, x, 3/4*maxfreq), 1226.53572492183, 5e-10); %!assert (lombcoeff (t, x, 1/4*maxfreq), 1341.63962181896, 5e-10); lssa-0.1.4/inst/lombnormcoeff.m0000644000000000000000000000431013743165726014643 0ustar0000000000000000## Copyright (c) 2012 Benjamin Lewis ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{c} =} lombnormcoeff (@var{time}, @var{mag}, @var{freq}) ## ## Return the normalized Lomb Periodogram value at one frequency for a time ## series. ## ## @seealso{lombcoeff} ## ## @end deftypefn function coeff = lombnormcoeff (T, X, omega) if (nargin != 3) print_usage (); elseif (! all (size (T) == size (X))) error ("lombnormcoeff: Time series vectors of uneven size"); elseif (! isscalar (omega)) error ("lombnormcoeff: Supplied frequency is not a scalar"); elseif (omega == 0) error ("lombnormcoeff: Supplied frequency is not a frequency"); endif xmean = mean (X); theta = atan2 (sum (sin (2 .* omega .*T)), sum (cos (2 .* omega .* T))) / (2*omega); coeff = ((sum ((X-xmean) .* cos (omega .* T - theta)) .^ 2 / sum (cos (omega .* T - theta) .^ 2) + sum ((X-xmean) .* sin (omega .* T - theta)) .^ 2 / sum (sin (omega .* T - theta) .^ 2 )) / (2 * var(X))); endfunction %!shared t, x, o, maxfreq %! maxfreq = 4 / (2 * pi); %! t = linspace (0, 8); %! x = (2 .* sin (maxfreq .* t) + %! 3 .* sin ((3/4) * maxfreq .* t) - %! 0.5 .* sin((1/4) * maxfreq .* t) - %! 0.2 .* cos (maxfreq .* t) + %! cos ((1/4) * maxfreq .*t)); %! o = [maxfreq , (3/4 * maxfreq) , (1/4 * maxfreq)]; %!assert (lombnormcoeff (t,x,o(1)), 44.7068607258824, 5e-10); %!assert (lombnormcoeff (t,x,o(2)), 35.7769955188467, 5e-10); %!assert (lombnormcoeff (t,x,o(3)), 20.7577786183241, 5e-10); lssa-0.1.4/inst/lscomplex.m0000644000000000000000000000655613743165726014037 0ustar0000000000000000## Copyright (C) 2012 Benjamin Lewis ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{t} =} lscomplex (@var{time}, @var{mag}, @var{maxfreq}, @var{numcoeff}, @var{numoctaves}) ## ## Return a series of least-squares transforms of a complex-valued time series. ## Each transform is minimized independently at each frequency. @var{numcoeff} ## frequencies are tested for each of @var{numoctaves} octaves, starting from ## @var{maxfreq}. ## ## Each result (a + bi) at a given frequency, o, defines the real and imaginary ## coefficients for a sum of cosine and sine functions: a cos(ot) + b i ## sin(ot). The specific frequency can be determined by its index in @var{t}, ## @var{ind}, as @var{maxfreq} * 2 ^ (- (@var{ind} - 1) / @var{numcoeff}). ## ## @seealso{lsreal} ## @end deftypefn function transform = lscomplex (t, x, omegamax, ncoeff, noctave) if (nargin != 5) print_usage (); elseif (! isvector (t)) error ("lscomplex: Time values are not a vector"); elseif (! isvector (x)) error ("lscomplex: Magnitude values are not a vector"); elseif (! all (size (t) == size (x))) error ("lscomplex: Size of time vector, magnitude vector unequal"); elseif (! isscalar (omegamax)) error ("lscomplex: More than one value for maximum frequency specified"); elseif (! isscalar (ncoeff)) error ("lscomplex: More than one number of frequencies per octave specified"); elseif (! isscalar (noctave)) error ("lscomplex: More than one number of octaves to traverse specified"); elseif (omegamax == 0) error ("lscomplex: Specified maximum frequency is not a frequency"); elseif (noctave == 0) error ("lscomplex: No octaves of results requested"); elseif (ncoeff == 0) error ("lscomplex: No frequencies per octave requested"); elseif (ncoeff != floor (ncoeff)) error ("lscomplex: Specified number of frequencies per octave is not integral"); elseif (noctave != floor (noctave)) error ("lscomplex: Specified number of octaves of results is not integral"); endif n = numel (t); iter = 0 : (ncoeff * noctave - 1); omul = (2 .^ (- iter / ncoeff)); ot = t(:) * (omul * omegamax); transform = sum ((cos (ot) - (sin (ot) .* i)) .* x(:), 1) / n; endfunction %!test %! maxfreq = 4 / ( 2 * pi ); %! t = [0:0.008:8]; %! x = ( 2 .* sin (maxfreq .* t) + %! 3 .* sin ( (3 / 4) * maxfreq .* t)- %! 0.5 .* sin ((1/4) * maxfreq .* t) - %! 0.2 .* cos (maxfreq .* t) + %! cos ((1/4) * maxfreq .* t)); %! assert (lscomplex (t, x, maxfreq, 2, 2), %! [(-0.400924546169395 - 2.371555305867469i), ... %! (1.218065147708429 - 2.256125004156890i), ... %! (1.935428592212907 - 1.539488163739336i), ... %! (2.136692292751917 - 0.980532175174563i)], 5e-10); lssa-0.1.4/inst/lscomplexwavelet.m0000644000000000000000000001077013743165726015420 0ustar0000000000000000## Copyright (C) 2012 Ben Lewis ## ## This software is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## ## @deftypefn {Function File} {@var{t} =} lscomplexwavelet (@var{time}, ##@var{mag}, @var{maxfreq}, @var{numcoeff}, @var{numoctave}, @var{min_time}, ##@var{max_time}, @var{step_time}, @var{sigma} ## ## ## @end deftypefn function transform = lscomplexwavelet( T, X, omegamax, ncoeff, noctave, tmin, tmax, tstep, sigma = 0.05) ## This function applies a wavelet version of the lscomplex transform; the ## transform is applied for each of multiple windows centred on different time ## values, depending on how many windows are required, since the number of ## windows required for each frequency decreases as the size of the windows ## increases. A higher frequency requires a smaller window to accurately ## capture its details, while a low frequency requires a larger window to ## accomodate its commensurately slower rate of change. For each window, the ## time series is weighted against the cubicwgt function, whose shape is near ## coincident with the Hanning window; unlike the Hanning window, however, the ## cubicwgt window does not involve trigonometric functions—thus it is faster ## to apply to large sets. (Well, testing on my system suggests that for very ## large data sets it actually slows down as it needs to allocate more ## memory. In this instance, a loop may be more effective than a vectorized ## function; more study is needed.) After the window is found, the transform ## is taken at the given frequency, wherein each term is also multiplied by ## the value of the window at its position in the time series. This reduces ## the size of the time series under consideration and improves the local ## accuracy of the transform to the frequency in question. ## ## My problem with the code as it stands is, it doesn't have a good way of ## determining the window size. Sigma is currently up to the user, and sigma ## determines the window width (but that might be best.) Moreover, the method ## of windowing involved (from the source code provided with the paper, ## Mathias, A. et. al. "Algorithms for Spectral Analysis of Irregularly ## Sampled Time Series". Journal of Statistical Software, vol. 11 issue 2, May ## 2004.) does not seem to always cover all values in the data set, and makes ## me suspicious of its ability to accurately transform a data set. ## transform = cell(noctave*ncoeff,1); for octave_iter = 1:noctave ## In fastnu.c, winrad is set as Ï€/(sigma*omegaoct); I suppose this is ## ... feasible, although it will need to be noted that if sigma is set too ## large, the windows will exclude data. I can work with that. ## ## An additional consideration is that for coeff_iter = 1:ncoeff ## in this, win_t is the centre of the window in question ## Although that will vary depending on the window. This is just an ## implementation for the first window. current_iteration = (octave_iter-1)*ncoeff+coeff_iter; window_radius = pi / ( sigma * omegamax * ( 2 ^ ( current_iteration - 1 ) ) ); window_count = 2 * ceil ( ( tmax - tmin ) / window_radius ) - 1; omega = current_frequency = omegamax * 2 ^ ( - octave_iter*coeff_iter / ncoeff ); transform{current_iteration}=zeros(1,window_count); ## win_t is the centre of the current window. win_t = tmin + window_radius; for iter_window = 1:window_count ## Computes the transform as stated in the paper for each given frequency. zeta = sum ( cubicwgt ( sigma .* omega .* ( T - win_t ) ) .* exp ( -i .* omega .* ( T - win_t ) ) .* X ) / sum ( cubicwgt ( sigma .* omega .* ( T - win_t ) ) .* exp ( -i .* omega .* ( T - win_t ) ) ); transform{current_iteration}(iter_window) = zeta; window_min += window_radius ; endfor endfor endfor endfunction lssa-0.1.4/inst/lscorrcoeff.m0000644000000000000000000001213713743165726014330 0ustar0000000000000000## Copyright (C) 2012 Benjamin Lewis ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{c} =} lscorrcoeff (@var{time1}, @var{mag1}, @var{time2}, @var{mag2}, @var{time}, @var{freq}) ## @deftypefnx {Function File} {@var{c} =} lscorrcoeff (@var{time1}, @var{mag1}, @var{time2}, @var{mag2}, @var{time}, @var{freq}, @var{window} = @var{cubicwgt}) ## @deftypefnx {Function File} {@var{c} =} lscorrcoeff (@var{time1}, @var{mag1}, @var{time2}, @var{mag2}, @var{time}, @var{freq}, @var{window} = @var{cubicwgt}, @var{winradius} = 1) ## ## Return the coefficient of the wavelet correlation of two complex time ## series. The correlation is only effective at a given time and frequency. ## The windowing function applied by default is cubicwgt, this can be changed by ## passing a different function handle to @var{window}, while the radius applied ## is set by @var{winradius}. Note that this will be most effective when both ## series have had their mean value (if it is not zero) subtracted (and stored ## separately); this reduces the constant-offset error further, and allows the ## functions to be compared on their periodic features rather than their ## constant features. ## ## @seealso{lswaveletcoeff, lscomplexwavelet, lsrealwavelet} ## ## @end deftypefn function coeff = lscorrcoeff (x1, y1, x2, y2, t, o, wgt = @cubicwgt, wgtrad = 1) ## Input checking is absolutely necessary. if (!((nargin >= 6) && (nargin <= 8))) print_usage (); ## Test to be sure x1, y1, x2, y2 are all vectors, and that t and o are ## scalars. elseif (! isvector (x1)) error ("lscorrcoeff: First time series time values are not a vector"); elseif (! isvector (y1)) error ("lscorrcoeff: First time series magnitude values are not a vector"); elseif (! isvector (x2)) error ("lscorrcoeff: Second time series time values are not a vector"); elseif (! isvector (y2)) error ("lscorrcoeff: Second time series magnitude values are not a vector"); elseif (! isscalar (t)) error ("lscorrcoeff: Window centre is not a scalar"); elseif (! isscalar (o)) error ("lscorrcoeff: Specified frequency is not a scalar"); elseif (! isscalar (wgtrad)) error ("lscorrcoeff: Window radius is not a scalar"); elseif (! all (size (x1) == size (y1))) error ("lscorrcoeff: First time series vectors not of matching size"); elseif (! all (size (x2) == size (y2))) error ("lscorrcoeff: Second time series vectors not of matching size"); endif ## How to determine if a weight function has been assigned or not? (Possible ## to get name of function?) so = 0.05 * o; ## The first solution that comes to mind is admittedly slightly ## ugly and has a data footprint of O(2n) but it is vectorised. mask = (abs (x1 - t) * so) < wgtrad; rx1 = x1(mask); ## FIXME : Needs to have a noisy error if length(y1) != length(x1) -- add this! ry1 = y1(mask); mask = (abs (x2 - t) * so ) < wgtrad; rx2 = x2(mask); ry2 = y2(mask); windowed_element_count = length (rx1); if (windowed_element_count == 0) error("lscorrcoeff: No time-series elements contained in window"); endif s = sum (wgt ((rx1 - t) .* so)) * sum (wgt ((rx2 - t ) .* so )); if (s != 0) coeff = sum (wgt ((rx1 - t) .* so) .* exp (i * o .* rx1) .* ry1) * ... sum (wgt ((rx2 - t) .* so) .* exp (i * o .* rx2) .* conj (ry2)) / s; else coeff = 0; endif endfunction %!shared t, p, x, y, z, o, maxfreq %! maxfreq = 4 / (2 * pi); %! t = linspace (0, 8); %! x = (2 .* sin (maxfreq .* t) + %! 3 .* sin ((3/4) * maxfreq .* t) - %! 0.5 .* sin ((1/4) * maxfreq .* t) - %! 0.2 .* cos (maxfreq .* t) + %! cos ((1/4) * maxfreq .* t)); %! y = - x; %! p = linspace (0, 8, 500); %! z = (2 .* sin (maxfreq .* p) + %! 3 .* sin ((3/4) * maxfreq .* p) - %! 0.5 .* sin ((1/4) * maxfreq .* p) - %! 0.2 .* cos (maxfreq .* p) + %! cos ((1/4) * maxfreq .* p)); %! o = [maxfreq , (3/4 * maxfreq) , (1/4 * maxfreq)]; %!assert (lscorrcoeff (t, x, t, x, 0.5, maxfreq), %! -5.54390340863576 - 1.82439880893383i, 5e-10); %!assert (lscorrcoeff (t, x, t, y, 0.5, maxfreq), %! 5.54390340863576 + 1.82439880893383i, 5e-10); %!assert (lscorrcoeff (t, x, p, z, 0.5, maxfreq), %! -5.55636741054624 - 1.82803733863170i, 5e-10); ## Demo with sin, cos as Nir suggested. %!demo %! ## This generates the correlation coefficient at time 0.5 and circular freq. 0.9 %! x = 1:10; %! y = sin (x); %! z = cos (x); %! a = lscorrcoeff (x, y, x, z, 0.5, 0.9) lssa-0.1.4/inst/lsreal.m0000644000000000000000000001017013743165726013276 0ustar0000000000000000## Copyright (C) 2012 Benjamin Lewis ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{t} =} lsreal (@var{time}, @var{mag}, @var{maxfreq}, @var{numcoeff}, @var{numoctaves}) ## ## Return a series of least-squares transforms of a real-valued time series. ## Each transform is minimized independently for each frequency. The method ## used is a Lomb-Scargle transform of the real-valued (@var{time}, @var{mag}) ## series, starting from frequency @var{maxfreq} and descending @var{numoctaves} ## octaves with @var{numcoeff} coefficients per octave. ## ## The result of the transform for each frequency is the coefficient of a sum of ## sine and cosine functions modified by that frequency, in the form of a ## complex number—where the cosine coefficient is encoded in the real term, and ## the sine coefficient is encoded in the imaginary term. Each frequency is fit ## independently from the others, and to minimize very low frequency error, ## consider storing the mean of a dataset with a constant or near-constant ## offset separately, and subtracting it from the dataset. ## ## @seealso{lscomplex} ## @end deftypefn function transform = lsreal (t, x, omegamax, ncoeff, noctave) ## Sanity checks to make sure that the user can get meaningful errors. if (nargin != 5) print_usage (); elseif (! isvector (t)) error ("lsreal: Time values are not a vector"); elseif (! isvector (x)) error ("lsreal: Magnitude values are not a vector"); elseif (! all (size (t) == size (x))) error ("lsreal: Size of time vector, magnitude vector unequal"); elseif (! isscalar (omegamax)) error ("lsreal: More than one value for maximum frequency specified"); elseif (! isscalar (ncoeff)) error ("lsreal: More than one number of frequencies per octave specified"); elseif (! isscalar (noctave)) error ("lsreal: More than one number of octaves to traverse specified"); elseif (omegamax == 0) error ("lsreal: Specified maximum frequency is not a frequency"); elseif (noctave == 0) error ("lsreal: No octaves of results requested"); elseif (ncoeff == 0) error ("lsreal: No frequencies per octave requested"); elseif (ncoeff != floor (ncoeff)) error ("lsreal: Specified number of frequencies per octave is not integral"); elseif (noctave != floor (noctave)) error ("lsreal: Specified number of octaves of results is not integral"); endif n = numel (t); iter = 0 : (ncoeff * noctave - 1); omul = (2 .^ (- iter / ncoeff)); ## For a given frequency, the iota term is taken at twice the frequency of the ## zeta term. ot = t(:) * (omul * omegamax); oit = t(:) * (omul * omegamax * 2); zeta = sum ((cos (ot) - (sin (ot) .* i)) .* x(:), 1) / n; iota = sum ((cos (oit) - (sin (oit) .* i)), 1) / n; transform = 2 .* (conj (zeta) - conj (iota) .* zeta) ./ (1 - abs (iota) .^ 2); endfunction %!test %! maxfreq = 4 / ( 2 * pi ); %! t = linspace(0,8); %! x = ( 2 .* sin ( maxfreq .* t ) + %! 3 .* sin ( (3/4) * maxfreq .* t ) - %! 0.5 .* sin ( (1/4) * maxfreq .* t ) - %! 0.2 .* cos ( maxfreq .* t ) + %! cos ( (1/4) * maxfreq .* t ) ); %! # In the assert here, I've got an error bound large enough to catch %! # individual system errors which would present no real issue. %! assert (lsreal (t,x,maxfreq,2,2), %! [(-1.68275915310663 + 4.70126183846743i), ... %! (1.93821553170889 + 4.95660209883437i), ... %! (4.38145452686697 + 2.14403733658600i), ... %! (5.27425332281147 - 0.73933440226597i)], %! 5e-10) lssa-0.1.4/inst/lsrealwavelet.m0000644000000000000000000000772113743165726014676 0ustar0000000000000000## Copyright (C) 2012 Benjamin Lewis ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ##-*- texinfo -*- ## @deftypefn {Function File} {t =} lsrealwavelet( @var{time}, @var{mag}, ## @var{maxfreq}, @var{coefficients}, @var{octaves}, @var{time_min}, ## @var{time_max}, @var{min_window_count} ) ## ## Computes a windowed transform of the supplied (@var{time}, @var{mag}) series ## of real-valued magnitudes, applying progressively wider windows as the ## frequencies tested decline from the maximum frequency. ## ## Currently non-functional. ## ## @seealso{lscomplexwavelet, lswaveletcoeff, lscorrcoeff} ## ## @end deftypefn function transform = lsrealwavelet(T, X, maxfreq, ncoeff, noctave, t_min, t_max, minimum_window_number ) omegamult = 2 ^ ( - 1/ ncoeff ) omegamult_inv = 1 / omegamult minimum_window_width = ( t_max - t_min ) / minimum_window_number; minimum_window_radius = minimum_window_width / 2; sigma = maxfreq * 2 ^ ( noctave ) / minimum_window_radius; ## sigma needs to be such that | t _ k - t | = minimum_window_radius implies ## that sigma * maxfrequency * 2 ^ ( - noctave ) * minimum_window_radius = 1 ## for a specific other frequency, sigma * frequency * window_radius = 1 means ## window_radius = 1 / ( frequency * sigma ) o = maxfreq; # zeta _ ( t , omega ) = sum(w(sigma omega (t_k - t )e^(-i omega (t_k - t))xi_k) # / sum( w(sigma omega ( t_k - t ) ) ); # # w ( t ) = { 1 - 3 | t | ^ 2 + 2 | t | ^ 3 , t in [ - 1 , 1 ] ; 0 for others } # Now, I *think* that this transform is supposed to be applied by taking # t as the centre of each window, while sigma should scale the time # values inside the window to the window. I think. transform = cell(noctave*ncoeff,1); for iter = 1:(noctave*ncoeff) ## in this, win_t is the centre of the window in question window_min = t_min; ## Although that will vary depending on the window. This is just an ## implementation for the first window. current_frequency = maxfreq * 2 ^ ( - iter / ncoeff ); current_radius = 1 / ( current_frequency * sigma ); current_window_number = ceil( ( t_max - t_min ) / current_radius); transform{iter} = zeros(1,current_window_number); win_t = window_min + current_radius; for iter_window = 1:current_window_number ## the beautiful part of this code is that if parts end up falling outside the ## vector, it won't matter (although it's wasted computations.) ## I may add a trap to avoid too many wasted cycles. windowed_t = ((abs (T-win_t) < current_radius) .* T); ## this will of course involve an additional large memory allocation, at least in the short term, ## but it's faster to do the operation once on the time series, then multiply it by the data series. iota0 = sum ( cubicwgt (windowed_t ./ current_radius ) ); zeta = sum( cubicwgt ((windowed_t - win_t) ./ current_radius) .* exp( - i * o .* windowed_t ) .* X ) / iota0; iota = sum( cubicwgt ((windowed_t - win_t) ./ current_radius) .* exp( - i * 2 * o .* windowed_t) .* X ) / sum ( cubicwgt( windowed_t .* 2 * o ) ); transform{iter}(iter_window) = 2 * ( conj(zeta) * iota0 + zeta * conj(iota) ) / ( ( length ( find (windowed_t)) + iota0 ) ^ 2 - real(iota) ^ 2 - imag(iota) ^ 2 ); window_min += 2 * current_radius; ## I remain hesitant about this value, since it is entirely possible necessary precision will be lost. Should I try to reduce that? endfor o *= omegamult; endfor endfunction lssa-0.1.4/inst/lswaveletcoeff.m0000644000000000000000000000731513743165726015034 0ustar0000000000000000## Copyright (C) 2012 Benjamin Lewis ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{c} =} lswaveletcoeff (@var{t}, @var{x}, @var{time}, @var{freq}) ## @deftypefnx {Function File} {@var{c} =} lswaveletcoeff (@var{t}, @var{x}, @var{time}, @var{freq}, @var{window}=cubicwgt) ## @deftypefnx {Function File} {@var{c} =} lswaveletcoeff (@var{t}, @var{x}, @var{time}, @var{freq}, @var{window}=cubicwgt, @var{winradius}=1) ## ## Return the wavelet transform of a complex time series in a given window. The ## transform takes a complex time series (@var{t}, @var{x}) at time @var{time} ## and frequency @var{freq}, then applies a windowing function to it; the ## default is cubicwgt, however by providing a function handle for the optional ## variable @var{window}, the user may select their own function; to determine ## the radius of the interval around the @var{time} selected, set ## @var{winradius} to some value other than 1. ## ## This transform operates identically to the transform at the heart of ## lscomplexwavelet, however for one window only. ## ## @seealso{lscorrcoeff, lscomplexwavelet, lsrealwavelet} ## ## @end deftypefn function coeff = lswaveletcoeff (x, y, t, o, wgt = @cubicwgt, wgtrad = 1) if (! (nargin >= 4) && (nargin <= 6)) print_usage (); elseif (! isvector (x)) error ("lswaveletcoeff: Time values are not a vector"); elseif (! isvector (y)) error ("lswaveletcoeff: Magnitude values are not a vector"); elseif (! all (size (x) == size (y))) error ("lswaveletcoeff: Time series vectors of uneven size"); elseif (! isscalar (t)) error ("lswaveletcoeff: Window centre specified is not scalar"); elseif (! isscalar (o)) error ("lswaveletcoeff: Frequency specified is not scalar"); elseif (! isscalar (wgtrad)) error ("lswaveletcoeff: Window radius specified is not scalar"); endif so = 0.05 .* o; if ((ndims (x) == 2) && ! (rows (x) == 1)) x = reshape (x, 1, length (x)); y = reshape (y, 1, length (y)); endif mask = (abs (x - t) * so < wgtrad); rx = x(mask); ry = y(mask); ## Going by the R code, this can use the same mask. s = sum (wgt ((x - t) .* so)); coeff = ifelse (s != 0, sum (wgt ((rx - t) .* so) .* exp (i .* o .* (rx - t)) .* ry) ./ s, 0); endfunction %!shared t, p, x, y, maxfreq %! maxfreq = 4 / (2 * pi); %! t = linspace (0, 8); %! x = (2 .* sin (maxfreq .* t) + %! 3 .* sin ((3/4) * maxfreq .* t) - %! 0.5 .* sin ((1/4) * maxfreq .* t) - %! 0.2 .* cos (maxfreq .* t) + %! cos ((1/4) * maxfreq .* t)); %! y = - x; %! p = linspace (0, 8, 500); %!assert (lswaveletcoeff (t, x, 0.5, maxfreq), %! 0.383340407638780 + 2.385251997545446i, 5e-10); %!assert (lswaveletcoeff (t, y, 3.3, 3/4 * maxfreq), %! -2.35465091096084 + 1.01892561714824i, 5e-10); %!demo %! ## Generates the wavelet transform coefficient for time 0.5 and circ. freq. 0.9, for row & column vectors. %! x = 1:10; %! y = sin (x); %! xt = x'; %! yt = y'; %! a = lswaveletcoeff (x, y, 0.5, 0.9) %! b = lswaveletcoeff (xt, yt, 0.5, 0.9) lssa-0.1.4/samples/0000755000000000000000000000000013743165726012326 5ustar0000000000000000lssa-0.1.4/samples/SampleDataSet.m0000644000000000000000000000201413743165726015170 0ustar0000000000000000## Copyright (C) 2012 Benjamin Lewis ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## No function structure to this, I just want to use it to store the ## sums of sines and cosines I'll use for testing. xvec = linspace(0,8,1000); maxfreq = 4 / ( 2 * pi ); yvec = ( 2.*sin(maxfreq.*xvec) + 3.*sin((3/4)*maxfreq.*xvec) - 0.5 .* sin((1/4)*maxfreq.*xvec) - 0.2 .* cos(maxfreq .* xvec) + cos((1/4)*maxfreq.*xvec)); lssa-0.1.4/samples/SampleScriptWithVostokData0000644000000000000000000001661413743165726017523 0ustar0000000000000000## Copyright (C) 2012 Benjamin Lewis ## Licensed under the GNU GPL v2 ## This is just a sample script to introduce the purpose and usage of ## the Lomb-Scargle Least Squares method with experimental data, here ## using the Vostok ice core data collected and measured by J.R. Petit ## et. al. and published in Nature; also available from the NOAA's ## Paleoclimatology pages here: ## . co2 = csvread("./data/co2.csv")(2:end,2:end); ch4 = csvread("./data/ch4.csv")(2:end,2:end); o18 = csvread("./data/o18.csv")(2:end,2:end); deut = csvread("./data/deut.csv")(2:end,2:end); dust = csvread("./data/dust.csv")(2:end,2:end); ## The limited ranges are to deal with artifacts from the extraction of ## the R data, notably that it leaves an extra column on the front of 0s ## and the first row is text that Octave refuses to process. ## Columns in co2 are Depth, Ice Age, Gas Age, and CO2 Concentration. ## Columns in ch4 are Depth, Ice Age, Gas Age, and CH4 Concentration. ## Columns in o18 are Depth, Ice Age, Gas Age, and Atmospheric O18. ## Columns in dust are Depth, Ice Age, Dust Concentration. ## Columns in deut are Depth, Ice Age, D concentration, and DeltaTS. co2_fig = figure("visible","off","name","CO2"); ch4_fig = figure("visible","off","name","CH4"); o18_fig = figure("visible","off","name","O18"); deut_fig = figure("visible","off","name","Deuterium"); dust_fig = figure("visible","off","name","Dust"); ## Generates figures and attaches handles to them for easy access. ## Now we need some data to display; I'll run a few functions. ls_complex_co2_ice_age = lscomplex(co2(:,2),co2(:,4),1,100,20); ls_complex_co2_gas_age = lscomplex(co2(:,3),co2(:,4),1,100,20); ls_real_co2_ice_age = lsreal(co2(:,2),co2(:,4),1,100,20); ls_real_co2_gas_age = lsreal(co2(:,3),co2(:,4),1,100,20); ls_complex_ch4_ice_age = lscomplex(ch4(:,2),ch4(:,4),1,100,20); ls_complex_ch4_gas_age = lscomplex(ch4(:,3),ch4(:,4),1,100,20); ls_real_ch4_ice_age = lsreal(ch4(:,2),ch4(:,4),1,100,20); ls_real_ch4_gas_age = lsreal(ch4(:,3),ch4(:,4),1,100,20); ls_complex_o18_ice_age = lscomplex(o18(:,2),o18(:,4),1,100,20); ls_complex_o18_gas_age = lscomplex(o18(:,3),o18(:,4),1,100,20); ls_real_o18_ice_age = lsreal(o18(:,2),o18(:,4),1,100,20); ls_real_o18_gas_age = lsreal(o18(:,3),o18(:,4),1,100,20); ls_complex_deut = lscomplex(deut(:,2),deut(:,3),1,100,20); ls_real_deut = lsreal(deut(:,2),deut(:,3),1,100,20); ls_complex_dust = lscomplex(dust(:,2),dust(:,3),1,100,20); ls_real_dust = lsreal(dust(:,2),dust(:,3),1,100,20); x_data_axis_vector = [ -430000, 0 ]; ## Useful because all of the data extends over 430 000 years up to the ## present. ## Setting up the CO2 plots: figure(co2_fig); subplot(4,2,1); axis(x_data_axis_vector); plot(-(co2(:,2)),co2(:,4)); title("Gas levels over ice age"); subplot(4,2,2); axis(x_data_axis_vector); plot(-(co2(:,3),co2(:,4)); title("Gas levels over gas age"); subplot(4,2,3); plot(real(ls_complex_co2_ice_age)); hold on; plot(imag(ls_complex_co2_ice_age),'r'); title("Complex L-S transform of Gas/ice age data"); legend("Real part","Imaginary part"); subplot(4,2,4); plot(real(ls_complex_co2_gas_age)); hold on; plot(imag(ls_complex_co2_gas_age),'r'); title("Complex L-S transform of Gas/gas age data"); legend("Real part","Imaginary part"); subplot(4,2,5); plot(real(ls_real_co2_ice_age)); hold on; plot(imag(ls_real_co2_ice_age),'r'); title("Real L-S transform of Gas/ice age data"); legend("Real part","Imaginary part"); subplot(4,2,6); plot(real(ls_real_co2_gas_age)); hold on; plot(imag(ls_real_co2_gas_age)); title("Real L-S transform of Gas/gas age data"); legend("Real part","Imaginary part"); ## At this point, we have transforms of both datasets, real and complex, ## and just need to figure out what cool thing to do with the remaining slot. ## Setting up the CH4 plots figure(ch4_fig); subplot(4,2,1); axis(x_data_axis_vector); plot(-(ch4(:,2)),ch4(:,4)); title("Gas levels over ice age"); subplot(4,2,2); axis(x_data_axis_vector); plot(-(ch4(:,3),ch4(:,4)); title("Gas levels over gas age"); subplot(4,2,3); plot(real(ls_complex_ch4_ice_age)); hold on; plot(imag(ls_complex_ch4_ice_age),'r'); title("Complex L-S transform of Gas/ice age data"); legend("Real part","Imaginary part"); subplot(4,2,4); plot(real(ls_complex_ch4_gas_age)); hold on; plot(imag(ls_complex_ch4_gas_age),'r'); title("Complex L-S transform of Gas/gas age data"); legend("Real part","Imaginary part"); subplot(4,2,5); plot(real(ls_real_ch4_ice_age)); hold on; plot(imag(ls_real_ch4_ice_age),'r'); title("Real L-S transform of Gas/ice age data"); legend("Real part","Imaginary part"); subplot(4,2,6); plot(real(ls_real_ch4_gas_age)); hold on; plot(imag(ls_real_ch4_gas_age)); title("Real L-S transform of Gas/gas age data"); legend("Real part","Imaginary part"); ## Setting up the O18 plots: figure(o18_fig); subplot(4,2,1); axis(x_data_axis_vector); plot(-(o18(:,2)),o18(:,4)); title("Gas levels over ice age"); subplot(4,2,2); axis(x_data_axis_vector); plot(-(o18(:,3),o18(:,4)); title("Gas levels over gas age"); subplot(4,2,3); plot(real(ls_complex_o18_ice_age)); hold on; plot(imag(ls_complex_o18_ice_age),'r'); title("Complex L-S transform of Gas/ice age data"); legend("Real part","Imaginary part"); subplot(4,2,4); plot(real(ls_complex_o18_gas_age)); hold on; plot(imag(ls_complex_o18_gas_age),'r'); title("Complex L-S transform of Gas/gas age data"); legend("Real part","Imaginary part"); subplot(4,2,5); plot(real(ls_real_o18_ice_age)); hold on; plot(imag(ls_real_o18_ice_age),'r'); title("Real L-S transform of Gas/ice age data"); legend("Real part","Imaginary part"); subplot(4,2,6); plot(real(ls_real_o18_gas_age)); hold on; plot(imag(ls_real_o18_gas_age)); title("Real L-S transform of Gas/gas age data"); legend("Real part","Imaginary part"); ## Setting up Dust plots: figure(dust_fig); subplot(4,1,1); axis(x_data_axis_vector); plot(-(dust(:,2)),dust(:,3)); title("Dust levels over ice age"); subplot(4,1,2); plot(real(ls_complex_dust_ice_age)); hold on; plot(imag(ls_complex_dust_ice_age),'r'); title("Complex L-S transform of Dust/ice age data"); legend("Real part","Imaginary part"); subplot(4,1,3); plot(real(ls_real_dust_ice_age)); hold on; plot(imag(ls_real_dust_ice_age),'r'); title("Real L-S transform of Dust/ice age data"); legend("Real part","Imaginary part"); ## Setting up Deuterium plots: figure(deut_fig); subplot(4,1,1); axis(x_data_axis_vector); plot(-(deut(:,2)),deut(:,3)); title("Deuterium levels over ice age"); subplot(4,1,2); plot(real(ls_complex_deut_ice_age)); hold on; plot(imag(ls_complex_deut_ice_age),'r'); title("Complex L-S transform of Deuterium/ice age data"); legend("Real part","Imaginary part"); subplot(4,1,3); plot(real(ls_real_deut_ice_age)); hold on; plot(imag(ls_real_deut_ice_age),'r'); title("Real L-S transform of Deuterium/ice age data"); legend("Real part","Imaginary part"); co2_ch4_comparison_figure = figure("visible","off","name","CO2/CH4 comparison"); subplot(4,1,1); axes(x_data_axis_vector); plot(-(co2(:,2)),co2(:,4)); hold on; plot(-(ch4(:,2)),ch4(:,4),'g'); title("CO2 and CH4 data"); legend("CO2","CH4"); subplot(4,1,2); plot(abs(ls_complex_co2_ice_age)); hold on; plot(abs(ls_complex_ch4_gas_age),'g'); title("Abs. values of CO2 and CH4 L-S complex transforms"); legend("CO2,CH4"); ## to implement: ## - displays of all the data and flaws in trying to model with just ## using L-S data ## - correlations of every data set with every other data set ## - Comparing ls* results to periodogram resultslssa-0.1.4/src/0000755000000000000000000000000013743165726011451 5ustar0000000000000000lssa-0.1.4/src/Makefile0000644000000000000000000000134713743165726013116 0ustar0000000000000000MKOCTFILE ?= mkoctfile GREP ?= grep CC_SOURCES := $(wildcard *.cc) CC_TST_SOURCES := $(shell $(GREP) --files-with-matches '^%!' $(CC_SOURCES)) TST_SOURCES := $(patsubst %.cc,../inst/test/%.cc-tst,$(CC_TST_SOURCES)) all: fastlscomplex.oct $(TST_SOURCES) fastlscomplex.oct: fastlscomplex.cc $(MKOCTFILE) fastlscomplex.cc # fastlsreal compilation is disabled for the time being #fastlsreal.oct: fastlsreal.cc # $(MKOCTFILE) fastlsreal.cc ../inst/test: @mkdir -p "$@" $(TST_SOURCES): ../inst/test/%.cc-tst: %.cc | ../inst/test @echo "Extracting tests from $< ..." @$(RM) -f "$@" "$@-t" @( echo "## Generated from $<"; \ $(GREP) '^%!' "$<") > "$@" # helper function just in case clean: rm -f *.o *.oct *~ octave-core $(TST_SOURCES) lssa-0.1.4/src/fastlscomplex.cc0000644000000000000000000005063713743165726014657 0ustar0000000000000000/* Copyright (C) 2012 Benjamin Lewis * Copyright (C) 2016-2020 John Donoghue * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 3 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License along * with this program; if not, write to the Free Software Foundation, Inc., * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */ #include #include #include #include #include #include #include bool flscomplex (const RowVector & tvec, const ComplexRowVector & xvec, double maxfreq, int coefficients, int octaves, ComplexRowVector & result); DEFUN_DLD(fastlscomplex,args,nargout, "-*- texinfo -*-\n\ @deftypefn {Function File} { C = } fastlscomplex \ (@var{time},@var{magnitude},@var{maxfreq},@var{ncoeff},@var{noctave})\n \ \n\ Return a series of least-squares transforms of a complex time series via a divide and\n\ conquer algorithm. Each transform is minimized independently at each frequency,\n\ starting from @var{maxfreq} and descending over @var{ncoeff} frequencies for\n\ each of @var{noctave} octaves.\n\ \n\ For each result, the complex result for a given frequency o defines the real and\n\ imaginary sinusoids which have the least distance to the data set: for a + bi,\n\ the matching sinusoids are a cos (ot) + b i sin (ot).\n\ \n\ @seealso{lscomplex, fastlsreal}\n\ \n\ @end deftypefn") { octave_value_list retval; if (args.length() != 5) print_usage(); else if (!args(0).is_matrix_type() || args(0).rows() != 1) { error ("fastlscomplex: expected times to be a row vector"); return retval; } else if (!args(1).is_matrix_type() || args(1).rows() != 1) { error ("fastlscomplex: expected magnitude to be a row vector"); return retval; } else { RowVector tvals = args(0).row_vector_value (); ComplexRowVector xvals = args(1).complex_row_vector_value (); double omegamax = args(2).double_value (); int noctaves = args(3).int_value (); int ncoeff = args(4).int_value (); if (tvals.numel () != xvals.numel ()) { if (tvals.numel () > xvals.numel ()) { error ("fastlscomplex: More time values than magnitude values"); return retval; } else { error ("fastlscomplex: More magnitude values than time values"); return retval; } } if (ncoeff == 0) { error ("fastlscomplex: No coefficients to compute"); return retval; } if (noctaves == 0) { error ("fastlscomplex: No octaves to compute over"); return retval; } if (omegamax == 0) { error ("fastlscomplex: No difference between minimal and maximal frequency"); return retval; } ComplexRowVector results; if (flscomplex (tvals, xvals, omegamax, noctaves, ncoeff, results)) retval(0) = octave_value (results); else { error ("fastlscomplex: error in the underlying flscomplex function"); } } return retval; } bool flscomplex (const RowVector & tvec, const ComplexRowVector & xvec, double maxfreq, int octaves, int coefficients, ComplexRowVector & results) { struct Precomputation_Record { Precomputation_Record *next; std::complex power_series[12]; // I'm using 12 as a matter of compatibility, only. bool stored_data; }; const std::complex *xvec_ptr = xvec.data (); const double *tvec_ptr = tvec.data (); results.resize (coefficients * octaves); const std::complex *results_ptr = results.fortran_vec (); double tau, delta_tau, tau_0, tau_h, n_inv, mu, te, omega_oct, omega_multiplier, octavemax, omega_working, loop_tau_0, loop_delta_tau, on_1, n_1, o; double length = tvec_ptr[tvec.numel () - 1] - tvec_ptr[0]; int octave_iter, coeff_iter; std::complex zeta, zz, z_accumulator, exp_term, exp_multiplier, alpha, h, *tpra, *temp_ptr_alpha, temp_alpha[12], *tprb, *temp_ptr_beta, temp_beta[12], temp_array[12], *p, x; octave_idx_type n = tvec.numel (); for (int array_iter = 0; array_iter < 12; array_iter++) temp_array[array_iter] = std::complex (0 , 0); int factorial_array[12]; factorial_array[0] = 1; for (int i = 1; i < 12; i++) factorial_array[i] = factorial_array[i-1] * i; n_1 = n_inv = 1.0 / n; mu = (0.5 * M_PI) / length; // Per the article; this is in place to improve numerical accuracy if desired. /* Viz. the paper, in which Dtau = c / omega_max, and c is stated as pi/2 for floating point processors, * In the case of this computation, I'll go by the recommendation. */ delta_tau = (0.5 * M_PI) / maxfreq; tau_0 = tvec_ptr[0] + delta_tau; tau_h = tau_0; te = tau_h + delta_tau; octave_idx_type k = 0; // Iterator for accessing xvec, tvec. Precomputation_Record * precomp_records_head, *record_current, *record_tail, *record_ref, *record_next; record_current = precomp_records_head = new Precomputation_Record; for (te = tvec_ptr[k] + (2 * delta_tau) ; ;) { x = xvec_ptr[k]; { double t = mu *(tvec_ptr[k] - tau_h), tt; p = record_current->power_series; // p = 0 *p++ = x; // p = 1 tt = -t; h = x * tt; *p++ = std::complex (-h.imag (), h.real ()); // p = 2 tt *= t*(1.0/2.0); *p++ = x*tt; // p = 3 tt *= t*(-1.0/3.0); h = x * tt; *p++ = std::complex (-h.imag (), h.real ()); // p = 4 tt *= t*(1.0/4.0); *p++ = x*tt; // p = 5 tt *= t*(-1.0/5.0); h = x * tt; *p++ = std::complex(-h.imag () ,h.real ()); // p = 6 tt *= t*(1.0/6.0); *p++ = x*tt; // p = 7 tt *= t*(-1.0/7.0); h = x * tt; *p++ = std::complex(-h.imag(),h.real()); // p = 8 tt *= t*(1.0/8.0); *p++ = x*tt; // p = 9 tt *= t*(-1.0/9.0); h = x * tt; *p++ = std::complex(-h.imag(),h.real()); // p = 10 tt *= t*(1.0/10.0); *p++ = x*tt; // p = 11 tt *= t*(-1.0/11.0); h = x * tt; *p++ = std::complex(-h.imag(),h.real()); } record_current->stored_data = true; for(k++; k < n && tvec_ptr[k] < te; k++) { x = std::complex (xvec_ptr[k]); { double t = mu * (tvec_ptr[k] - tau_h), tt; p = record_current->power_series; // p = 0 *p++ += std::complex(x); // p = 1 tt = -t; h = x * tt; *p++ += std::complex(- h.imag(), h.real()); // p = 2 tt *= t*(1.0/2.0); *p++ += x*tt; // p = 3 tt *= t*(-1.0/3.0); h = x * tt; *p++ += std::complex(-h.imag(),h.real()); // p = 4 tt *= t*(1.0/4.0); *p++ += x*tt; // p = 5 tt *= t*(-1.0/5.0); h = x * tt; *p++ += std::complex(-h.imag(),h.real()); // p = 6 tt *= t*(1.0/6.0); *p++ += x*tt; // p = 7 tt *= t*(-1.0/7.0); h = x * tt; *p++ += std::complex(-h.imag(),h.real()); // p = 8 tt *= t*(1.0/8.0); *p++ += x*tt; // p = 9 tt *= t*(-1.0/9.0); h = x * tt; *p++ += std::complex(-h.imag(),h.real()); // p = 10 tt *= t*(1.0/10.0); *p++ += x*tt; // p = 11 tt *= t*(-1.0/11.0); h = x * tt; *p++ += std::complex(-h.imag(),h.real()); } record_current->stored_data = true; } if (k >= n) break; tau_h = te + delta_tau; te = tau_h + delta_tau; record_current->next = new Precomputation_Record; record_current = record_current->next; } record_tail = record_current; record_current = precomp_records_head; record_tail->next = 0; /* Summation of coefficients for each frequency. As we have ncoeffs * noctaves elements, * it makes sense to work from the top down, as we have omega_max by default (maxfreq) */ omega_oct = maxfreq / mu; omega_multiplier = exp (-log(2) / coefficients); octavemax = maxfreq; loop_tau_0 = tau_0; loop_delta_tau = delta_tau; octave_idx_type iter = 0; // Loops need to first travel over octaves, then coefficients; for (octave_iter = octaves; ; omega_oct *= 0.5, octavemax *= 0.5, loop_tau_0 += loop_delta_tau, loop_delta_tau *= 2) { o = omega_oct; omega_working = octavemax; for (coeff_iter = 0; coeff_iter < coefficients; coeff_iter++, o *= omega_multiplier, omega_working *= omega_multiplier) { exp_term = std::complex (cos (- omega_working * loop_tau_0), sin (- omega_working * loop_tau_0)); exp_multiplier = std::complex (cos (- 2 * omega_working * loop_delta_tau) , sin (- 2 * omega_working * loop_delta_tau)); for (zeta = 0, record_current = precomp_records_head; record_current; record_current = record_current->next, exp_term *= exp_multiplier ) { if (record_current->stored_data) { int p; for (zz = 0, p = 0, on_1 = n_1; p < 12; p++) { zz += record_current->power_series[p] * on_1; on_1 *= o; } zeta += exp_term * zz; } } results(iter) = std::complex (zeta); iter++; } if (! (--octave_iter)) break; /* If we've already reached the lowest value, stop. * Otherwise, merge with the next computation range. */ double *exp_pse_ptr, *exp_ptr, exp_power_series_elements[12]; { double t = mu * loop_delta_tau, tt; exp_ptr = exp_power_series_elements; *exp_ptr++ = 1; *exp_ptr++ = t; tt = t * t * ( 1.0 / 2.0 ); *exp_ptr++ = tt; tt *= t * ( 1.0 / 3.0 ); *exp_ptr++ = tt; tt *= t * ( 1.0 / 4.0 ); *exp_ptr++ = tt; tt *= t * ( 1.0 / 5.0 ); *exp_ptr++ = tt; tt *= t * ( 1.0 / 6.0 ); *exp_ptr++ = tt; tt *= t * ( 1.0 / 7.0 ); *exp_ptr++ = tt; tt *= t * ( 1.0 / 8.0 ); *exp_ptr++ = tt; tt *= t * ( 1.0 / 9.0 ); *exp_ptr++ = tt; tt *= t * ( 1.0 / 10.0 ); *exp_ptr++ = tt; tt *= t * ( 1.0 / 11.0 ); *exp_ptr++ = tt; } exp_pse_ptr = exp_ptr = exp_power_series_elements; try { for (record_current = precomp_records_head; record_current; record_current = record_current->next) { if (! (record_ref = record_current->next ) || ! record_ref->stored_data ) { // In this case, there is no next record, but this record has data. if (record_current->stored_data) { int p = 0; for (exp_pse_ptr = exp_power_series_elements + 1, temp_ptr_alpha = temp_alpha; p < 12; p++ , exp_pse_ptr++) { tpra = temp_ptr_alpha; *(temp_ptr_alpha++) = std::complex(record_current->power_series[p]); for( exp_ptr = exp_power_series_elements, record_current->power_series[p] = *temp_ptr_alpha * *exp_ptr; ; ) { /* This next block is from Mathias' code, and it does a few * ... unsavoury things. First off, it uses conditionals with * break in order to avoid potentially accessing null regions * of memory, and then it does ... painful things with a few * numbers. However, remembering that most of these will not * actually be accessed for the first iterations, it's easier. */ if (++exp_ptr >= exp_pse_ptr) break; --tpra; h = *tpra * *exp_ptr; record_current->power_series[p].real ( record_current->power_series[p].real() - h.imag()); record_current->power_series[p].imag ( record_current->power_series[p].imag() + h.real()); if (++exp_ptr >= exp_pse_ptr ) break; --tpra; record_current->power_series[p] -= *tpra * *exp_ptr; if (++exp_ptr >= exp_pse_ptr) break; --tpra; h = -*tpra * *exp_ptr; record_current->power_series[p].real ( record_current->power_series[p].real() - h.imag()); record_current->power_series[p].imag ( record_current->power_series[p].imag() + h.real()); if (++exp_ptr >= exp_pse_ptr) break; --tpra; record_current->power_series[p] += *tpra * *exp_ptr; } } if ( ! record_ref ) break; // Last record was reached } else { record_next = record_ref; if ( record_current->stored_data ) { int p = 0, q = 0; for (exp_pse_ptr = exp_power_series_elements + 1, temp_ptr_alpha = temp_alpha, temp_ptr_beta = temp_beta; p < 12; p++, q++, exp_pse_ptr++) { tpra = temp_ptr_alpha; *temp_ptr_alpha++ = record_current->power_series[p] + record_next->power_series[q]; *temp_ptr_beta++ = record_current->power_series[p] - record_next->power_series[q]; tprb = temp_ptr_beta; for (exp_ptr = exp_power_series_elements, record_current->power_series[p] = *tpra * *exp_ptr; ;) { if (++exp_ptr >= exp_pse_ptr ) break; tprb -= 2; h = *tprb * *exp_ptr; record_current->power_series[p].real ( record_current->power_series[p].real() - h.imag()); record_current->power_series[p].imag ( record_current->power_series[p].imag() + h.real()); if ( ++exp_ptr >= exp_pse_ptr ) break; tpra -= 2; record_current->power_series[p] -= *tpra * *exp_ptr; if (++exp_ptr >= exp_pse_ptr) break; tprb -= 2; h = - *tprb * *exp_ptr; record_current->power_series[p].real ( record_current->power_series[p].real() - h.imag()); record_current->power_series[p].imag ( record_current->power_series[p].imag() + h.real()); if (++exp_ptr >= exp_pse_ptr) break; tpra -= 2; record_current->power_series[p] += *tpra * *exp_ptr; } } } else { int q = 0; for (exp_pse_ptr = exp_power_series_elements + 1, temp_ptr_alpha = temp_alpha, temp_ptr_beta = temp_beta; q < 12; q++, exp_pse_ptr++) { tpra = temp_ptr_alpha; *temp_ptr_alpha++ = std::complex(record_next->power_series[q]); for (exp_ptr = exp_power_series_elements, record_next->power_series[q] = *tpra * *exp_ptr; ;) { if (++exp_ptr >= exp_pse_ptr) break; --tpra; h = *tpra * *exp_ptr; record_next->power_series[q].real ( record_next->power_series[q].real() - h.imag()); record_next->power_series[q].imag ( record_next->power_series[q].imag() + h.real()); if (++exp_ptr >= exp_pse_ptr) break; --tpra; record_next->power_series[q] -= *tpra * *exp_ptr; if ( ++exp_ptr >= exp_pse_ptr ) break; --tpra; h = -*tpra * *exp_ptr; record_next->power_series[q].real ( record_next->power_series[q].real() - h.imag()); record_next->power_series[q].imag ( record_next->power_series[q].imag() + h.real()); if (++exp_ptr >= exp_pse_ptr) break; --tpra; record_next->power_series[q] += *tpra * *exp_ptr; } } } record_current->stored_data = true; record_ref = record_next; record_current->next = record_ref->next; delete record_ref; } } } } catch (std::exception & e) {//This section was part of my debugging, and may be removed. std::cout << "Exception thrown: " << e.what() << std::endl; return (false); } } return true; } /* %!xtest <48905> %! maxfreq = 4 / ( 2 * pi ); %! t = [0:0.008:8]; %! x = ( 2 .* sin (maxfreq .* t) + %! 3 .* sin ( (3 / 4) * maxfreq .* t)- %! 0.5 .* sin ((1/4) * maxfreq .* t) - %! 0.2 .* cos (maxfreq .* t) + %! cos ((1/4) * maxfreq .* t)); %! assert (fastlscomplex (t, x, maxfreq, 2, 2), %! [(-0.400924546169395 - 2.371555305867469i), ... %! (1.218065147708429 - 2.256125004156890i), ... %! (1.935428592212907 - 1.539488163739336i), ... %! (2.136692292751917 - 0.980532175174563i)], 5e-10); */ lssa-0.1.4/src/fastlsreal.cc0000644000000000000000000003720013743165726014122 0ustar0000000000000000/* Copyright (C) 2012 Benjamin Lewis * * This program is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 3 of the License, or * (at your option) any later version. * * This program is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License along * with this program; if not, write to the Free Software Foundation, Inc., * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */ #include #include #include #include #include #include #include ComplexRowVector flsreal( RowVector tvec , ComplexRowVector xvec , double maxfreq , int octaves , int coefficients); DEFUN_DLD(fastlsreal,args,nargout, "-*- texinfo -*-\n\ @deftypefn {Function File} { C = } fastlsreal(@var{time},@var{magnitude},@var{maximum_frequency},@var{octaves},@var{coefficients})\n\ \n\ Return the real least-sqaures spectral fit to the (@var{time},@var{magnitude})\n\ data supplied, using the fast algorithm.\n\ \n\ @seealso{lsreal, fastlscomplex}\n\ @end deftypefn") { if ( args.length() != 5 ) { print_usage(); return octave_value_list (); } RowVector tvals = args(0).row_vector_value(); ComplexRowVector xvals = args(1).complex_row_vector_value(); double omegamax = args(2).double_value(); int noctaves = args(3).int_value(); int ncoeff = args(4).int_value(); if ( tvals.numel() != xvals.numel() ){ if ( tvals.numel() > xvals.numel() ) { error("More time values than magnitude values."); } else { error("More magnitude values than time values."); } } if ( ncoeff == 0 ) error("No coefficients to compute."); if ( noctaves == 0 ) error("No octaves to compute over."); if ( omegamax == 0 ) error("No difference between minimal and maximal frequency."); octave_value_list retval; if ( !error_state) { ComplexRowVector results = flsreal(tvals,xvals,omegamax,noctaves,ncoeff); retval(0) = octave_value(results); } else { return octave_value_list (); } return retval; } ComplexRowVector flsreal( RowVector tvec , RowVector xvec , double maxfreq, int octaves, int coefficients ) { struct XTElem { double x, t; }; struct Precomputation_Record { Precomputation_Record *next; XTElem power_series[12]; // I'm using 12 as a matter of compatibility, only. bool stored_data; }; ComplexRowVector results = ComplexRowVector (coefficients * octaves ); double tau, delta_tau, tau_0, tau_h, n_inv, mu, omega_oct, omega_multiplier, octavemax, omega_working, loop_tau_0, loop_delta_tau, x; double length = ( tvec((tvec.numel()-1)) - tvec( octave_idx_type (0))); int octave_iter, coeff_iter; std::complex zeta, z_accumulator, zeta_exp_term, zeta_exp_multiplier, alpha, iota, i_accumulator, iota_exp_term, iota_exp_multiplier, exp_squared, exp_squared_multiplier; octave_idx_type n = tvec.numel(); XTElem *tpra, *temp_ptr_alpha, temp_alpha[12], *tprb, *temp_ptr_beta, temp_beta[12], temp_array[12]; int factorial_array[12]; factorial_array[0] = 1; for ( int i = 1 ; i < 12 ; i++ ) { factorial_array[i] = factorial_array[i-1] * i; } n_inv = 1.0 / n; mu = (0.5 * M_PI)/length; // Per the article; this is in place to improve numerical accuracy if desired. /* Viz. the paper, in which Dtau = c / omega_max, and c is stated as pi/2 for floating point processors, * In the case of this computation, I'll go by the recommendation. */ delta_tau = M_PI / ( 2 * maxfreq ); tau_0 = tvec(0) + delta_tau; tau_h = tau_0; size_t precomp_subset_count = (size_t) ceil( ( tvec(tvec.numel()-1) - tvec(0) ) / ( 2 * delta_tau ) ); // I've used size_t because it will work for my purposes without threatening undefined behaviour. const std::complex im = std::complex ( 0 , 1 ); //I seriously prefer C99's complex numbers. octave_idx_type k ( 0 ); // Iterator for accessing xvec, tvec. Precomputation_Record * precomp_records_head, *record_current, *record_tail, *record_ref, *record_next; record_current = precomp_records_head = new Precomputation_Record; for ( te = tvec(k) + (2 * delta_tau) ; ; ) { x = xvec(k); { double t = mu*(tvec(k)-tau_h), tt; p = record_current->power_series; // p = 0 p->x = x; (p++)->t = 1; // p = 1 tt = -t; p->x = x * tt; (p++)->t = tt; // p = 2 tt *= t*(1.0/2.0); p->x = x*tt; (p++)->t = tt; // p = 3 tt *= t*(-1.0/3.0); p->x = x * tt; (p++)->t = tt; // p = 4 tt *= t*(1.0/4.0); p->x = x * tt; (p++)->t = tt; // p = 5 tt *= t*(-1.0/5.0); p->x = x * tt; (p++)->t = tt; // p = 6 tt *= t*(1.0/6.0); p->x = x * tt; (p++)->t = tt; // p = 7 tt *= t*(-1.0/7.0); p->x = x * tt; (p++)->t = tt; // p = 8 tt *= t*(1.0/8.0); p->x = x * tt; (p++)->t = tt; // p = 9 tt *= t*(-1.0/9.0); p->x = x * tt; (p++)->t = tt; // p = 10 tt *= t*(1.0/10.0); p->x = x * tt; (p++)->t = tt; // p = 11 tt *= t*(-1.0/11.0); p->x = x * tt; (p++)->t = tt; } record_current->stored_data = true; for(k++; ( k < n ) && tvec(k) < te ; k++ ) { x = xvec(k); { double t = mu*(tvec(k)-tau_h), tt; p = record_current->power_series; // p = 0 p->x += x; (p++)->t += 1; // p = 1 tt = -t; p->x += x * tt; (p++)->t += tt; // p = 2 tt *= t*(1.0/2.0); p->x += x * tt; (p++)->t += tt; // p = 3 tt *= t*(-1.0/3.0); p->x += x * tt; (p++)->t += tt; // p = 4 tt *= t*(1.0/4.0); p->x += x * tt; (p++)->t += tt; // p = 5 tt *= t*(-1.0/5.0); p->x += x * tt; (p++)->t += tt; // p = 6 tt *= t*(1.0/6.0); p->x += x * tt; (p++)->t += tt; // p = 7 tt *= t*(-1.0/7.0); p->x += x * tt; (p++)->t += tt; // p = 8 tt *= t*(1.0/8.0); p->x += x * tt; (p++)->t += tt; // p = 9 tt *= t*(-1.0/9.0); p->x += x * tt; (p++)->t += tt; // p = 10 tt *= t*(1.0/10.0); p->x += x * tt; (p++)->t += tt; // p = 11 tt *= t*(-1.0/11.0); p->x += x * tt; (p++)->t += tt; } record_current->stored_data = true; } if( k >= n ) break; tau_h = te + delta_tau; te = tau_h + delta_tau; record_current->next = new Precomputation_Record; record_current = record_current->next; } record_tail = record_current; record_current = precomp_records_head; record_tail->next = 0; /* Summation of coefficients for each frequency. As we have ncoeffs * noctaves elements, * it makes sense to work from the top down, as we have omega_max by default (maxfreq) */ omega_oct = maxfreq / mu; omega_multiplier = exp(-log(2)/coefficients); octavemax = maxfreq; loop_tau_0 = tau_0; loop_delta_tau = delta_tau; octave_idx_type iter ( 0 ); // Loops need to first travel over octaves, then coefficients; for ( octave_iter = octaves ; ; omega_oct *= 0.5 , octavemax *= 0.5 , loop_tau_0 += loop_delta_tau , loop_delta_tau *= 2 ) { o = omega_oct; omega_working = octavemax; for ( coeff_iter = 0 ; coeff_iter < coefficients ; coeff_iter++, o *= omega_multiplier, omega_working *= omega_multiplier){ exp_term = std::complex ( cos( - omega_working * loop_tau_0 ) , sin ( - omega_working * loop_tau_0 ) ); exp_squared = exp_term * exp_term; exp_multiplier = std::complex ( cos ( - 2 * omega_working * loop_delta_tau ) , sin ( - 2 * omega_working * loop_delta_tau ) ); exp_squared_multiplier = exp_multiplier * exp_multiplier; for ( zeta = iota = 0, record_current = precomp_records_head ; record_current ; record_current = record_current->next, exp_term *= exp_multiplier, exp_squared *= exp_squared_multiplier ) { if ( record_current->stored_data ) { int p; for ( zz = ii = 0 , p = 0, on_1 = n_1 ; p < 12 ; ) { zz.real() += record_current->power_series[p]->x * on_1; ii.real() += record_current->power_series[p++]-> t * o2n_1; on_1 *= o; o2n_1 *= o2; zz.imag() += record_current->power_series[p]->x * on_1; ii.imag() += record_current->power_series[p++]-> t * o2n_1; on_1 *= o; o2n_1 *= o2; } zeta += exp_term * zz; iota += exp_squared * ii; } } results(iter) = 2 / ( 1 - ( iota.real() * iota.real() ) - (iota.imag() * iota.imag() ) * ( conj(zeta) - conj(iota) * zeta ); iter++; } if ( !(--octave_iter) ) break; /* If we've already reached the lowest value, stop. * Otherwise, merge with the next computation range. */ double *exp_pse_ptr, *exp_ptr, exp_power_series_elements[12]; exp_power_series_elements[0] = 1; exp_pse_ptr = exp_ptr = exp_power_series_elements; for ( int r_iter = 1 ; r_iter < 12 ; r_iter++ ) { exp_power_series_elements[r_iter] = exp_power_series_elements[r_iter-1] * ( mu * loop_delta_tau) * ( 1.0 / ( (double) r_iter ) ); } try{ for ( record_current = precomp_records_head ; record_current ; record_current = record_current->next ) { if ( ! ( record_ref = record_current->next ) || ! record_ref->stored_data ) { // In this case, there is no next record, but this record has data. if ( record_current->stored_data ) { int p = 0; for( exp_pse_ptr = exp_power_series_elements , temp_ptr_alpha = temp_alpha ; ; ) { tpra = temp_ptr_alpha; temp_ptr_alpha->x = record_current->power_series[p]->x; (temp_ptr_alpha++)->t = record_current->power_series[p]->t; temp_ptr_beta->x = -record_current->power_series[p]->x; (temp_ptr_beta++)->t = -record_current->power_series[p]->t; for( exp_ptr = exp_pse_ptr++, record_current->power_series[p]->x = tpra->x * *exp_ptr, record_current->power_series[p]->t = tpra->t * *exp_ptr ; ; ) { /* This next block is from Mathias' code, and it does a few * ... unsavoury things. First off, it uses conditionals with * break in order to avoid potentially accessing null regions * of memory, and then it does ... painful things with a few * numbers. However, remembering that most of these will not * actually be accessed for the first iterations, it's easier. */ if ( --exp_ptr < exp_power_series_elements ) break; ++tpra; record_current->power_series[p]->x -= tpra->x * *exp_ptr; record_current->power_series[p]->t -= tpra->t * *exp_ptr; if ( --exp_ptr < exp_power_series_elements ) break; ++tpra; record_current->power_series[p]->x += tpra->x * *exp_ptr; record_current->power_series[p]->t += tpra->x * *exp_ptr; } if ( ++p >= 12 ) break; temp_ptr_alpha->x = -record_current->power_series[p]->x; (temp_ptr_alpha++)->t = -record_current->power_series[p]->t; temp_ptr_beta->x = record_current->power_series[p]->x; (temp_ptr_beta++)->t = record_current->power_series[p]->t; for( tprb = temp_beta, exp_ptr = exp_pse_ptr++, record_current->power_series[p]->t = tprb->t * *exp_ptr; exp_ptr > exp_power_series_elements ; ) { ++tprb; --exp_ptr; record_current->power_series[p]->t += tprb->t * *exp_ptr; } if ( ++p >= 12 ) break; } } if ( ! record_ref ) break; // Last record was reached } else { record_next = record_ref; if ( record_current->stored_data ) { int p = 0; for( exp_pse_ptr = exp_power_series_elements, temp_ptr_alpha = temp_alpha, temp_ptr_beta = temp_beta; ; ) { temp_ptr_alpha->x = record_current->power_series[p]->x + record_next->power_series[p]->x; (temp_ptr_alpha++)->t = record_current->power_series[p]->t + record_next->power_series[p]->t; temp_ptr_beta->x = record_ref->power_series[p]->x - record_current->power_series[p]->x; (temp_ptr_beta++)->t = record_ref->power_series[p]->t - record_current->power_series[p]->t; for( tpra = temp_alpha, exp_ptr = exp_pse_ptr++, record_current->power_series[p]->x = tpra->x * *exp_ptr, record_current->power_series[p]->t = tpra->x * *exp_ptr; ; ) { if ( --exp_ptr < exp_pse_ptr ) break; ++tpra; record_current->power_series[p]->x -= tpra->x * *exp_ptr; record_current->power_series[p]->t -= tpra->t * *exp_ptr; if ( --exp_ptr < exp_pse_ptr ) break; ++tpra; record_current->power_series[p]->x += tpra->x * *exp_ptr; record_current->power_series[p]->t += tpra->t * *exp_ptr; } if ( ++p >= 12 ) break; temp_ptr_alpha->x = record_next->power_series[p]->x - record_current->power_series[p]->x; (temp_ptr_alpha++)->t = record_next->power_series[p]->t - record_current->power_series[p]->t; temp_ptr_beta->x = record_current->power_series[p]->x + record_next->power_series[p]->x; (temp_ptr_beta++)->t = record_current->power_series[p]->t + record_next->power_series[p]->t; for(tprb = temp_beta, exp_ptr = exp_pse_ptr++, record_current->power_series[p]->x = tprb->x * *exp_ptr, record_current->power_series[p]->t = tprb->x * *exp_ptr; exp_ptr > exp_power_series_elements; ) { ++tprb; --exp_ptr; record_current->power_series[p]->x += tprb->x * *exp_ptr; record_current->power_series[p]->t += tprb->t * *exp_ptr; } if ( ++p >= 12 ) break; } } else { int q = 0; for( exp_pse_ptr = exp_power_series_elements, temp_ptr_alpha = temp_alpha, temp_ptr_beta = temp_beta; ; ) { temp_ptr_alpha->x = record_next->power_series[q]->x; temp_ptr_alpha->t = record_next->power_series[q]->t; for(tpra = temp_alpha, exp_ptr = exp_pse_ptr++, record_next->power_series[q]->x = tpra->x * *exp_ptr, record_next->power_series[q]->t = tpra->t * *exp_ptr; exp_ptr > exp_power_series_elements; ) { ++tpra; --exp_ptr; record_next->power_series[q]->x += tpra->x * *exp_ptr; record_next->power_series[q]->t += tpra->t * *exp_ptr; } if ( ++q >= 12 ) break; } record_current->stored_data = true; record_ref = record_next; record_current->next = record_ref->next; record_next = 0; delete record_ref; } } } return results; }