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= true opt-level = 3 cotengrust-0.1.3/LICENSE000066400000000000000000001033331461675323200147310ustar00rootroot00000000000000 GNU AFFERO GENERAL PUBLIC LICENSE Version 3, 19 November 2007 Copyright (C) 2007 Free Software Foundation, Inc. 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There are many ways you could offer source, and different solutions will be better for different programs; see section 13 for the specific requirements. You should also get your employer (if you work as a programmer) or school, if any, to sign a "copyright disclaimer" for the program, if necessary. For more information on this, and how to apply and follow the GNU AGPL, see . cotengrust-0.1.3/README.md000066400000000000000000000260311461675323200152020ustar00rootroot00000000000000# cotengrust `cotengrust` provides fast rust implementations of contraction ordering primitives for tensor networks or einsum expressions. The two main functions are: - `optimize_optimal(inputs, output, size_dict, **kwargs)` - `optimize_greedy(inputs, output, size_dict, **kwargs)` The optimal algorithm is an optimized version of the `opt_einsum` 'dp' path - itself an implementation of https://arxiv.org/abs/1304.6112. There is also a variant of the greedy algorithm, which runs `ntrials` of greedy, randomized paths and computes and reports the flops cost (log10) simultaneously: - `optimize_random_greedy_track_flops(inputs, output, size_dict, **kwargs)` ## Installation `cotengrust` is available for most platforms from [PyPI](https://pypi.org/project/cotengrust/): ```bash pip install cotengrust ``` or if you want to develop locally (which requires [pyo3](https://github.com/PyO3/pyo3) and [maturin](https://github.com/PyO3/maturin)): ```bash git clone https://github.com/jcmgray/cotengrust.git cd cotengrust maturin develop --release ``` (the release flag is very important for assessing performance!). ## Usage If `cotengrust` is installed, then by default `cotengra` will use it for its greedy, random-greedy, and optimal subroutines, notably subtree reconfiguration. You can also call the routines directly: ```python import cotengra as ctg import cotengrust as ctgr # specify an 8x8 square lattice contraction inputs, output, shapes, size_dict = ctg.utils.lattice_equation([8, 8]) # find the optimal 'combo' contraction path %%time path = ctgr.optimize_optimal(inputs, output, size_dict, minimize='combo') # CPU times: user 13.7 s, sys: 83.4 ms, total: 13.7 s # Wall time: 13.7 s # construct a contraction tree for further introspection tree = ctg.ContractionTree.from_path( inputs, output, size_dict, path=path ) tree.plot_rubberband() ``` ![optimal-8x8-order](https://github.com/jcmgray/cotengrust/assets/8982598/f8e18ff2-5ace-4e46-81e1-06bffaef5e45) ## API The optimize functions follow the api of the python implementations in `cotengra.pathfinders.path_basic.py`. ```python def optimize_optimal( inputs, output, size_dict, minimize='flops', cost_cap=2, search_outer=False, simplify=True, use_ssa=False, ): """Find an optimal contraction ordering. Parameters ---------- inputs : Sequence[Sequence[str]] The indices of each input tensor. output : Sequence[str] The indices of the output tensor. size_dict : dict[str, int] The size of each index. minimize : str, optional The cost function to minimize. The options are: - "flops": minimize with respect to total operation count only (also known as contraction cost) - "size": minimize with respect to maximum intermediate size only (also known as contraction width) - 'write' : minimize the sum of all tensor sizes, i.e. memory written - 'combo' or 'combo={factor}` : minimize the sum of FLOPS + factor * WRITE, with a default factor of 64. - 'limit' or 'limit={factor}` : minimize the sum of MAX(FLOPS, alpha * WRITE) for each individual contraction, with a default factor of 64. 'combo' is generally a good default in term of practical hardware performance, where both memory bandwidth and compute are limited. cost_cap : float, optional The maximum cost of a contraction to initially consider. This acts like a sieve and is doubled at each iteration until the optimal path can be found, but supplying an accurate guess can speed up the algorithm. search_outer : bool, optional If True, consider outer product contractions. This is much slower but theoretically might be required to find the true optimal 'flops' ordering. In practical settings (i.e. with minimize='combo'), outer products should not be required. simplify : bool, optional Whether to perform simplifications before optimizing. These are: - ignore any indices that appear in all terms - combine any repeated indices within a single term - reduce any non-output indices that only appear on a single term - combine any scalar terms - combine any tensors with matching indices (hadamard products) Such simpifications may be required in the general case for the proper functioning of the core optimization, but may be skipped if the input indices are already in a simplified form. use_ssa : bool, optional Whether to return the contraction path in 'single static assignment' (SSA) format (i.e. as if each intermediate is appended to the list of inputs, without removals). This can be quicker and easier to work with than the 'linear recycled' format that `numpy` and `opt_einsum` use. Returns ------- path : list[list[int]] The contraction path, given as a sequence of pairs of node indices. It may also have single term contractions if `simplify=True`. """ ... def optimize_greedy( inputs, output, size_dict, costmod=1.0, temperature=0.0, simplify=True, use_ssa=False, ): """Find a contraction path using a (randomizable) greedy algorithm. Parameters ---------- inputs : Sequence[Sequence[str]] The indices of each input tensor. output : Sequence[str] The indices of the output tensor. size_dict : dict[str, int] A dictionary mapping indices to their dimension. costmod : float, optional When assessing local greedy scores how much to weight the size of the tensors removed compared to the size of the tensor added:: score = size_ab / costmod - (size_a + size_b) * costmod This can be a useful hyper-parameter to tune. temperature : float, optional When asessing local greedy scores, how much to randomly perturb the score. This is implemented as:: score -> sign(score) * log(|score|) - temperature * gumbel() which implements boltzmann sampling. simplify : bool, optional Whether to perform simplifications before optimizing. These are: - ignore any indices that appear in all terms - combine any repeated indices within a single term - reduce any non-output indices that only appear on a single term - combine any scalar terms - combine any tensors with matching indices (hadamard products) Such simpifications may be required in the general case for the proper functioning of the core optimization, but may be skipped if the input indices are already in a simplified form. use_ssa : bool, optional Whether to return the contraction path in 'single static assignment' (SSA) format (i.e. as if each intermediate is appended to the list of inputs, without removals). This can be quicker and easier to work with than the 'linear recycled' format that `numpy` and `opt_einsum` use. Returns ------- path : list[list[int]] The contraction path, given as a sequence of pairs of node indices. It may also have single term contractions if `simplify=True`. """ def optimize_simplify( inputs, output, size_dict, use_ssa=False, ): """Find the (partial) contracton path for simplifiactions only. Parameters ---------- inputs : Sequence[Sequence[str]] The indices of each input tensor. output : Sequence[str] The indices of the output tensor. size_dict : dict[str, int] A dictionary mapping indices to their dimension. use_ssa : bool, optional Whether to return the contraction path in 'single static assignment' (SSA) format (i.e. as if each intermediate is appended to the list of inputs, without removals). This can be quicker and easier to work with than the 'linear recycled' format that `numpy` and `opt_einsum` use. Returns ------- path : list[list[int]] The contraction path, given as a sequence of pairs of node indices. It may also have single term contractions. """ ... def optimize_random_greedy_track_flops( inputs, output, size_dict, ntrials=1, costmod=(0.1, 4.0), temperature=(0.001, 1.0), seed=None, simplify=True, use_ssa=False, ): """Perform a batch of random greedy optimizations, simulteneously tracking the best contraction path in terms of flops, so as to avoid constructing a separate contraction tree. Parameters ---------- inputs : tuple[tuple[str]] The indices of each input tensor. output : tuple[str] The indices of the output tensor. size_dict : dict[str, int] A dictionary mapping indices to their dimension. ntrials : int, optional The number of random greedy trials to perform. The default is 1. costmod : (float, float), optional When assessing local greedy scores how much to weight the size of the tensors removed compared to the size of the tensor added:: score = size_ab / costmod - (size_a + size_b) * costmod It is sampled uniformly from the given range. temperature : (float, float), optional When asessing local greedy scores, how much to randomly perturb the score. This is implemented as:: score -> sign(score) * log(|score|) - temperature * gumbel() which implements boltzmann sampling. It is sampled log-uniformly from the given range. seed : int, optional The seed for the random number generator. simplify : bool, optional Whether to perform simplifications before optimizing. These are: - ignore any indices that appear in all terms - combine any repeated indices within a single term - reduce any non-output indices that only appear on a single term - combine any scalar terms - combine any tensors with matching indices (hadamard products) Such simpifications may be required in the general case for the proper functioning of the core optimization, but may be skipped if the input indices are already in a simplified form. use_ssa : bool, optional Whether to return the contraction path in 'single static assignment' (SSA) format (i.e. as if each intermediate is appended to the list of inputs, without removals). This can be quicker and easier to work with than the 'linear recycled' format that `numpy` and `opt_einsum` use. Returns ------- path : list[list[int]] The best contraction path, given as a sequence of pairs of node indices. flops : float The flops (/ contraction cost / number of multiplications), of the best contraction path, given log10. """ ... def ssa_to_linear(ssa_path, n=None): """Convert a SSA path to linear format.""" ... def find_subgraphs(inputs, output, size_dict,): """Find all disconnected subgraphs of a specified contraction.""" ... ``` cotengrust-0.1.3/pyproject.toml000077500000000000000000000011161461675323200166370ustar00rootroot00000000000000[project] name = "cotengrust" version = "0.1.3" description = "Fast contraction ordering primitives for tensor networks." readme = "README.md" requires-python = ">=3.8" classifiers = [ "Programming Language :: Rust", "Programming Language :: Python :: Implementation :: CPython", "Programming Language :: Python :: Implementation :: PyPy", ] license = { file = "LICENSE" } authors = [ {name = "Johnnie Gray", email = "johnniemcgray@gmail.com"} ] [build-system] requires = ["maturin>=1.0,<2.0"] build-backend = "maturin" [tool.maturin] features = ["pyo3/extension-module"] cotengrust-0.1.3/src/000077500000000000000000000000001461675323200145105ustar00rootroot00000000000000cotengrust-0.1.3/src/lib.rs000077500000000000000000001117041461675323200156330ustar00rootroot00000000000000use bit_set::BitSet; use ordered_float::OrderedFloat; use pyo3::prelude::*; use rand::Rng; use rand::SeedableRng; use rustc_hash::FxHashMap; use std::collections::{BTreeSet, BinaryHeap, HashSet}; use std::f32; use FxHashMap as Dict; type Ix = u16; type Count = u8; type Legs = Vec<(Ix, Count)>; type Node = u16; type Score = f32; type SSAPath = Vec>; type GreedyScore = OrderedFloat; // types for optimal optimization type ONode = u32; type Subgraph = BitSet; type BitPath = Vec<(Subgraph, Subgraph)>; type SubContraction = (Legs, Score, BitPath); /// helper struct to build contractions from bottom up #[derive(Clone)] struct ContractionProcessor { nodes: Dict, edges: Dict>, appearances: Vec, sizes: Vec, ssa: Node, ssa_path: SSAPath, track_flops: bool, flops: Score, flops_limit: Score, } /// given log(x) and log(y) compute log(x + y), without exponentiating both fn logadd(lx: Score, ly: Score) -> Score { let max_val = lx.max(ly); max_val + f32::ln_1p(f32::exp(-f32::abs(lx - ly))) } /// given log(x) and log(y) compute log(x - y), without exponentiating both, /// if (x - y) is negative, return -log(x - y). fn logsub(lx: f32, ly: f32) -> f32 { if lx < ly { -ly - f32::ln_1p(-f32::exp(lx - ly)) } else { lx + f32::ln_1p(-f32::exp(ly - lx)) } } fn compute_legs(ilegs: &Legs, jlegs: &Legs, appearances: &Vec) -> Legs { let mut ip = 0; let mut jp = 0; let ni = ilegs.len(); let nj = jlegs.len(); let mut new_legs: Legs = Vec::with_capacity(ilegs.len() + jlegs.len()); loop { if ip == ni { new_legs.extend(jlegs[jp..].iter()); break; } if jp == nj { new_legs.extend(ilegs[ip..].iter()); break; } let (ix, ic) = ilegs[ip]; let (jx, jc) = jlegs[jp]; if ix < jx { // index only appears in ilegs new_legs.push((ix, ic)); ip += 1; } else if ix > jx { // index only appears in jlegs new_legs.push((jx, jc)); jp += 1; } else { // index appears in both let new_count = ic + jc; if new_count != appearances[ix as usize] { // not last appearance -> kept index contributes to new size new_legs.push((ix, new_count)); } ip += 1; jp += 1; } } new_legs } fn compute_size(legs: &Legs, sizes: &Vec) -> Score { legs.iter().map(|&(ix, _)| sizes[ix as usize]).sum() } fn compute_flops(ilegs: &Legs, jlegs: &Legs, sizes: &Vec) -> Score { let mut flops: Score = 0.0; let mut seen: HashSet = HashSet::with_capacity(ilegs.len()); for &(ix, _) in ilegs { seen.insert(ix); flops += sizes[ix as usize]; } for (ix, _) in jlegs { if !seen.contains(ix) { flops += sizes[*ix as usize]; } } flops } fn is_simplifiable(legs: &Legs, appearances: &Vec) -> bool { let mut prev_ix = Node::MAX; for &(ix, ix_count) in legs { if (ix == prev_ix) || (ix_count == appearances[ix as usize]) { return true; } prev_ix = ix; } false } fn compute_simplified(legs: &Legs, appearances: &Vec) -> Legs { if legs.len() == 0 { return legs.clone(); } let mut new_legs: Legs = Vec::with_capacity(legs.len()); let (mut cur_ix, mut cur_cnt) = legs[0]; for &(ix, ix_cnt) in legs.iter().skip(1) { if ix == cur_ix { cur_cnt += 1; } else { if cur_cnt != appearances[cur_ix as usize] { new_legs.push((cur_ix, cur_cnt)); } cur_ix = ix; cur_cnt = ix_cnt; } } new_legs } impl ContractionProcessor { fn new( inputs: Vec>, output: Vec, size_dict: Dict, track_flops: bool, ) -> ContractionProcessor { if size_dict.len() > Ix::MAX as usize { panic!("cotengrust: too many indices, maximum is {}", Ix::MAX); } let mut nodes: Dict = Dict::default(); let mut edges: Dict> = Dict::default(); let mut indmap: Dict = Dict::default(); let mut sizes: Vec = Vec::with_capacity(size_dict.len()); let mut appearances: Vec = Vec::with_capacity(size_dict.len()); // enumerate index labels as unsigned integers from 0 let mut c: Ix = 0; for (i, term) in inputs.into_iter().enumerate() { let mut legs = Vec::with_capacity(term.len()); for ind in term { match indmap.get(&ind) { None => { // index not parsed yet indmap.insert(ind, c); edges.insert(c, std::iter::once(i as Node).collect()); appearances.push(1); sizes.push(f32::ln(size_dict[&ind] as f32)); legs.push((c, 1)); c += 1; } Some(&ix) => { // index already present appearances[ix as usize] += 1; edges.get_mut(&ix).unwrap().insert(i as Node); legs.push((ix, 1)); } }; } legs.sort(); nodes.insert(i as Node, legs); } output.into_iter().for_each(|ind| { appearances[indmap[&ind] as usize] += 1; }); let ssa = nodes.len() as Node; let ssa_path: SSAPath = Vec::with_capacity(2 * ssa as usize - 1); let flops: Score = 0.0; let flops_limit: Score = Score::INFINITY; ContractionProcessor { nodes, edges, appearances, sizes, ssa, ssa_path, track_flops, flops, flops_limit, } } fn neighbors(&self, i: Node) -> BTreeSet { let mut js = BTreeSet::default(); for (ix, _) in self.nodes[&i].iter() { self.edges[&ix].iter().for_each(|&j| { if j != i { js.insert(j); }; }); } js } /// remove an index from the graph, updating all legs fn remove_ix(&mut self, ix: Ix) { for j in self.edges.remove(&ix).unwrap() { self.nodes.get_mut(&j).unwrap().retain(|(k, _)| *k != ix); } } /// remove a node from the graph, update the edgemap, return the legs fn pop_node(&mut self, i: Node) -> Legs { let legs = self.nodes.remove(&i).unwrap(); for (ix, _) in legs.iter() { let enodes = match self.edges.get_mut(&ix) { Some(enodes) => enodes, // if repeated index, might have already been removed None => continue, }; enodes.remove(&i); if enodes.len() == 0 { // last node with this index -> remove from map self.edges.remove(&ix); } } legs } /// add a new node to the graph, update the edgemap, return the new id fn add_node(&mut self, legs: Legs) -> Node { let i = self.ssa; self.ssa += 1; for (ix, _) in &legs { self.edges .entry(*ix) .and_modify(|nodes| { nodes.insert(i); }) .or_insert(std::iter::once(i as Node).collect()); } self.nodes.insert(i, legs); i } /// contract two nodes, return the new node id fn contract_nodes(&mut self, i: Node, j: Node) -> Node { let ilegs = self.pop_node(i); let jlegs = self.pop_node(j); if self.track_flops { self.flops = logadd(self.flops, compute_flops(&ilegs, &jlegs, &self.sizes)); } let new_legs = compute_legs(&ilegs, &jlegs, &self.appearances); let k = self.add_node(new_legs); self.ssa_path.push(vec![i, j]); k } /// contract two nodes (which we already know the legs for), return the new node id fn contract_nodes_given_legs(&mut self, i: Node, j: Node, new_legs: Legs) -> Node { let ilegs = self.pop_node(i); let jlegs = self.pop_node(j); if self.track_flops { self.flops = logadd(self.flops, compute_flops(&ilegs, &jlegs, &self.sizes)); } let k = self.add_node(new_legs); self.ssa_path.push(vec![i, j]); k } /// find any indices that appear in all terms and just remove/ignore them fn simplify_batch(&mut self) { let mut ix_to_remove = Vec::new(); let nterms = self.nodes.len(); for (ix, ix_nodes) in self.edges.iter() { if ix_nodes.len() >= nterms { ix_to_remove.push(*ix); } } for ix in ix_to_remove { self.remove_ix(ix); } } /// perform any simplifications involving single terms fn simplify_single_terms(&mut self) { for (i, legs) in self.nodes.clone().into_iter() { if is_simplifiable(&legs, &self.appearances) { self.pop_node(i); let legs_reduced = compute_simplified(&legs, &self.appearances); self.add_node(legs_reduced); self.ssa_path.push(vec![i]); } } } /// combine and remove all scalars fn simplify_scalars(&mut self) { let mut scalars = Vec::new(); let mut j: Option = None; let mut jndim: usize = 0; for (i, legs) in self.nodes.iter() { let ndim = legs.len(); if ndim == 0 { scalars.push(*i); } else { // also search for smallest other term to multiply into if j.is_none() || ndim < jndim { j = Some(*i); jndim = ndim; } } } if scalars.len() > 0 { for p in 0..scalars.len() - 1 { let i = scalars[p]; let j = scalars[p + 1]; let k = self.contract_nodes(i, j); scalars[p + 1] = k; } } } /// combine all terms that have the same legs fn simplify_hadamard(&mut self) { // group all nodes by their legs (including permutations) let mut groups: Dict, Vec> = Dict::default(); // keep track of groups with size >= 2 let mut hadamards: BTreeSet> = BTreeSet::default(); for (i, legs) in self.nodes.iter() { let key: BTreeSet = legs.iter().map(|&(ix, _)| ix).collect(); match groups.get_mut(&key) { Some(group) => { hadamards.insert(key); group.push(*i); } None => { groups.insert(key, vec![*i]); } } } for key in hadamards.into_iter() { let mut group = groups.remove(&key).unwrap(); while group.len() > 1 { let i = group.pop().unwrap(); let j = group.pop().unwrap(); let k = self.contract_nodes(i, j); group.push(k); } } } /// iteratively perform all simplifications until nothing left to do fn simplify(&mut self) { self.simplify_batch(); let mut should_run = true; while should_run { self.simplify_single_terms(); self.simplify_scalars(); let ssa_before = self.ssa; self.simplify_hadamard(); should_run = ssa_before != self.ssa; } } /// find disconnected subgraphs fn subgraphs(&self) -> Vec> { let mut remaining: BTreeSet = BTreeSet::default(); self.nodes.keys().for_each(|i| { remaining.insert(*i); }); let mut groups: Vec> = Vec::new(); while remaining.len() > 0 { let i = remaining.pop_first().unwrap(); let mut queue: Vec = vec![i]; let mut group: BTreeSet = vec![i].into_iter().collect(); while queue.len() > 0 { let i = queue.pop().unwrap(); for j in self.neighbors(i) { if !group.contains(&j) { group.insert(j); queue.push(j); } } } group.iter().for_each(|i| { remaining.remove(i); }); groups.push(group.into_iter().collect()); } groups } /// greedily optimize the contraction order of all terms fn optimize_greedy( &mut self, costmod: Option, temperature: Option, seed: Option, ) -> bool { let coeff_t = temperature.unwrap_or(0.0); let log_coeff_a = f32::ln(costmod.unwrap_or(1.0)); let mut rng = if coeff_t != 0.0 { Some(match seed { Some(seed) => rand::rngs::StdRng::seed_from_u64(seed), None => rand::rngs::StdRng::from_entropy(), }) } else { // zero temp - no need for rng None }; let mut local_score = |sa: Score, sb: Score, sab: Score| -> Score { let gumbel = if let Some(rng) = &mut rng { coeff_t * -f32::ln(-f32::ln(rng.gen())) } else { 0.0 as f32 }; logsub(sab - log_coeff_a, logadd(sa, sb) + log_coeff_a) - gumbel }; // cache all current nodes sizes as we go let mut node_sizes: Dict = Dict::default(); self.nodes.iter().for_each(|(&i, legs)| { node_sizes.insert(i, compute_size(&legs, &self.sizes)); }); // we will *deincrement* c, since its a max-heap let mut c: i32 = 0; let mut queue: BinaryHeap<(GreedyScore, i32)> = BinaryHeap::with_capacity(self.edges.len() * 2); // the heap keeps a reference to actual contraction info in this let mut contractions: Dict = Dict::default(); // get the initial candidate contractions for ix_nodes in self.edges.values() { // convert to vector for combinational indexing let ix_nodes: Vec = ix_nodes.iter().cloned().collect(); // for all combinations of nodes with a connected edge for ip in 0..ix_nodes.len() { let i = ix_nodes[ip]; let isize = node_sizes[&i]; for jp in (ip + 1)..ix_nodes.len() { let j = ix_nodes[jp]; let jsize = node_sizes[&j]; let klegs = compute_legs(&self.nodes[&i], &self.nodes[&j], &self.appearances); let ksize = compute_size(&klegs, &self.sizes); let score = local_score(isize, jsize, ksize); queue.push((OrderedFloat(-score), c)); contractions.insert(c, (i, j, ksize, klegs)); c -= 1; } } } // greedily contract remaining while let Some((_, c0)) = queue.pop() { let (i, j, ksize, klegs) = contractions.remove(&c0).unwrap(); if !self.nodes.contains_key(&i) || !self.nodes.contains_key(&j) { // one of the nodes has been removed -> skip continue; } // perform contraction: let k = self.contract_nodes_given_legs(i, j, klegs.clone()); if self.track_flops && self.flops >= self.flops_limit { // stop if we have reached the flops limit return false; } node_sizes.insert(k, ksize); for l in self.neighbors(k) { // assess all neighboring contractions of new node let llegs = &self.nodes[&l]; let lsize = node_sizes[&l]; // get candidate legs and size let mlegs = compute_legs(&klegs, llegs, &self.appearances); let msize = compute_size(&mlegs, &self.sizes); let score = local_score(ksize, lsize, msize); queue.push((OrderedFloat(-score), c)); contractions.insert(c, (k, l, msize, mlegs)); c -= 1; } } // success return true; } /// Optimize the contraction order of all terms using a greedy algorithm /// that contracts the smallest two terms. Typically only called once /// only disconnected subgraph terms (outer products) remain. fn optimize_remaining_by_size(&mut self) { if self.nodes.len() == 1 { // nothing to do return; }; let mut nodes_sizes: BinaryHeap<(GreedyScore, Node)> = BinaryHeap::default(); self.nodes.iter().for_each(|(node, legs)| { nodes_sizes.push((OrderedFloat(-compute_size(&legs, &self.sizes)), *node)); }); let (_, mut i) = nodes_sizes.pop().unwrap(); let (_, mut j) = nodes_sizes.pop().unwrap(); let mut k = self.contract_nodes(i, j); while self.nodes.len() > 1 { // contract the smallest two nodes until only one remains let ksize = compute_size(&self.nodes[&k], &self.sizes); nodes_sizes.push((OrderedFloat(-ksize), k)); (_, i) = nodes_sizes.pop().unwrap(); (_, j) = nodes_sizes.pop().unwrap(); k = self.contract_nodes(i, j); } } } fn single_el_bitset(x: usize, n: usize) -> BitSet { let mut a: BitSet = BitSet::with_capacity(n); a.insert(x); a } fn compute_con_cost_flops( temp_legs: Legs, appearances: &Vec, sizes: &Vec, iscore: Score, jscore: Score, _factor: Score, ) -> (Legs, Score) { // remove indices that have reached final appearance // and compute cost and size of local contraction let mut new_legs: Legs = Legs::with_capacity(temp_legs.len()); let mut cost: Score = 0.0; for (ix, ix_count) in temp_legs.into_iter() { // all involved indices contribute to the cost let d = sizes[ix as usize]; cost += d; if ix_count != appearances[ix as usize] { // not last appearance -> kept index contributes to new size new_legs.push((ix, ix_count)); } } let new_score = logadd(logadd(iscore, jscore), cost); (new_legs, new_score) } fn compute_con_cost_size( temp_legs: Legs, appearances: &Vec, sizes: &Vec, iscore: Score, jscore: Score, _factor: Score, ) -> (Legs, Score) { // remove indices that have reached final appearance // and compute cost and size of local contraction let mut new_legs: Legs = Legs::with_capacity(temp_legs.len()); let mut size: Score = 0.0; for (ix, ix_count) in temp_legs.into_iter() { if ix_count != appearances[ix as usize] { // not last appearance -> kept index contributes to new size new_legs.push((ix, ix_count)); size += sizes[ix as usize]; } } let new_score = iscore.max(jscore).max(size); (new_legs, new_score) } fn compute_con_cost_write( temp_legs: Legs, appearances: &Vec, sizes: &Vec, iscore: Score, jscore: Score, _factor: Score, ) -> (Legs, Score) { // remove indices that have reached final appearance // and compute cost and size of local contraction let mut new_legs: Legs = Legs::with_capacity(temp_legs.len()); let mut size: Score = 0.0; for (ix, ix_count) in temp_legs.into_iter() { if ix_count != appearances[ix as usize] { // not last appearance -> kept index contributes to new size new_legs.push((ix, ix_count)); size += sizes[ix as usize]; } } let new_score = logadd(logadd(iscore, jscore), size); (new_legs, new_score) } fn compute_con_cost_combo( temp_legs: Legs, appearances: &Vec, sizes: &Vec, iscore: Score, jscore: Score, factor: Score, ) -> (Legs, Score) { // remove indices that have reached final appearance // and compute cost and size of local contraction let mut new_legs: Legs = Legs::with_capacity(temp_legs.len()); let mut size: Score = 0.0; let mut cost: Score = 0.0; for (ix, ix_count) in temp_legs.into_iter() { // all involved indices contribute to the cost let d = sizes[ix as usize]; cost += d; if ix_count != appearances[ix as usize] { // not last appearance -> kept index contributes to new size new_legs.push((ix, ix_count)); size += d; } } // the score just for this contraction let new_local_score = logadd(cost, factor + size); // the total score including history let new_score = logadd(logadd(iscore, jscore), new_local_score); (new_legs, new_score) } fn compute_con_cost_limit( temp_legs: Legs, appearances: &Vec, sizes: &Vec, iscore: Score, jscore: Score, factor: Score, ) -> (Legs, Score) { // remove indices that have reached final appearance // and compute cost and size of local contraction let mut new_legs: Legs = Legs::with_capacity(temp_legs.len()); let mut size: Score = 0.0; let mut cost: Score = 0.0; for (ix, ix_count) in temp_legs.into_iter() { // all involved indices contribute to the cost let d = sizes[ix as usize]; cost += d; if ix_count != appearances[ix as usize] { // not last appearance -> kept index contributes to new size new_legs.push((ix, ix_count)); size += d; } } // whichever is more expensive, the cost or the scaled write let new_local_score = cost.max(factor + size); // the total score including history let new_score = logadd(logadd(iscore, jscore), new_local_score); (new_legs, new_score) } impl ContractionProcessor { fn optimize_optimal_connected( &mut self, subgraph: Vec, minimize: Option, cost_cap: Option, search_outer: Option, ) { // parse the minimize argument let minimize = minimize.unwrap_or("flops".to_string()); let mut minimize_split = minimize.split('-'); let minimize_type = minimize_split.next().unwrap(); let factor = minimize_split .next() .map_or(64.0, |s| s.parse::().unwrap()) .ln(); if minimize_split.next().is_some() { // multiple hyphens -> raise error panic!("invalid minimize: {:?}", minimize); } let compute_cost = match minimize_type { "flops" => compute_con_cost_flops, "size" => compute_con_cost_size, "write" => compute_con_cost_write, "combo" => compute_con_cost_combo, "limit" => compute_con_cost_limit, _ => panic!( "minimize must be one of 'flops', 'size', 'write', 'combo', or 'limit', got {}", minimize ), }; let search_outer = search_outer.unwrap_or(false); // storage for each possible contraction to reach subgraph of size m let mut contractions: Vec> = vec![Dict::default(); subgraph.len() + 1]; // intermediate storage for the entries we are expanding let mut contractions_m_temp: Vec<(Subgraph, SubContraction)> = Vec::new(); // need to keep these separately let mut best_scores: Dict = Dict::default(); // we use linear index within terms given during optimization, this maps // back to the original node index let nterms = subgraph.len(); let mut termmap: Dict = Dict::default(); for (i, node) in subgraph.into_iter().enumerate() { let isubgraph = single_el_bitset(i, nterms); termmap.insert(isubgraph.clone(), node); let ilegs = self.nodes[&node].clone(); let iscore: Score = 0.0; let ipath: BitPath = Vec::new(); contractions[1].insert(isubgraph, (ilegs, iscore, ipath)); } let mut ip: usize; let mut jp: usize; let mut skip_because_outer: bool; let cost_cap_incr = f32::ln(2.0); let mut cost_cap = cost_cap.unwrap_or(cost_cap_incr); while contractions[nterms].len() == 0 { // try building subgraphs of size m for m in 2..=nterms { // out of bipartitions of size (k, m - k) for k in 1..=m / 2 { for (isubgraph, (ilegs, iscore, ipath)) in contractions[k].iter() { for (jsubgraph, (jlegs, jscore, jpath)) in contractions[m - k].iter() { // filter invalid combinations first if !isubgraph.is_disjoint(&jsubgraph) || { (k == m - k) && isubgraph.gt(&jsubgraph) } { // subgraphs overlap -> not valid, or // equal subgraph size -> only process sorted pairs continue; } let mut temp_legs: Legs = Vec::with_capacity(ilegs.len() + jlegs.len()); ip = 0; jp = 0; // if search_outer -> we will never skip skip_because_outer = !search_outer; while ip < ilegs.len() && jp < jlegs.len() { if ilegs[ip].0 < jlegs[jp].0 { // index only appears in ilegs temp_legs.push(ilegs[ip]); ip += 1; } else if ilegs[ip].0 > jlegs[jp].0 { // index only appears in jlegs temp_legs.push(jlegs[jp]); jp += 1; } else { // index appears in both temp_legs.push((ilegs[ip].0, ilegs[ip].1 + jlegs[jp].1)); ip += 1; jp += 1; skip_because_outer = false; } } if skip_because_outer { // no shared indices -> outer product continue; } // add any remaining indices temp_legs.extend(ilegs[ip..].iter().chain(jlegs[jp..].iter())); // compute candidate contraction result and score let (new_legs, new_score) = compute_cost( temp_legs, &self.appearances, &self.sizes, *iscore, *jscore, factor, ); if new_score > cost_cap { // contraction not allowed yet due to 'sieve' continue; } // check candidate against current best subgraph path let new_subgraph: Subgraph = isubgraph.union(&jsubgraph).collect(); // because we have to do a delayed update of // contractions[m] for borrowing reasons, we check // against a non-delayed score lookup so we don't // overwrite best scores within the same iteration let found_new_best = match best_scores.get(&new_subgraph) { Some(current_score) => new_score < *current_score, None => true, }; if found_new_best { best_scores.insert(new_subgraph.clone(), new_score); // only need the path if updating let mut new_path: BitPath = Vec::with_capacity(ipath.len() + jpath.len() + 1); new_path.extend_from_slice(&ipath); new_path.extend_from_slice(&jpath); new_path.push((isubgraph.clone(), jsubgraph.clone())); contractions_m_temp .push((new_subgraph, (new_legs, new_score, new_path))); } } } // move new contractions from temp into the main storage, // there might be contractions for the same subgraph in // this, but because we check eagerly best_scores above, // later entries are guaranteed to be better contractions_m_temp.drain(..).for_each(|(k, v)| { contractions[m].insert(k, v); }); } } cost_cap += cost_cap_incr; } // can only ever be a single entry in contractions[nterms] -> the best let (_, _, best_path) = contractions[nterms].values().next().unwrap(); // convert from the bitpath to the actual (subgraph) node ids for (isubgraph, jsubgraph) in best_path.into_iter() { let i = termmap[&isubgraph]; let j = termmap[&jsubgraph]; let k = self.contract_nodes(i, j); let ksubgraph: Subgraph = isubgraph.union(&jsubgraph).collect(); termmap.insert(ksubgraph, k); } } fn optimize_optimal( &mut self, minimize: Option, cost_cap: Option, search_outer: Option, ) { for subgraph in self.subgraphs() { self.optimize_optimal_connected(subgraph, minimize.clone(), cost_cap, search_outer); } } } // --------------------------- PYTHON FUNCTIONS ---------------------------- // #[pyfunction] fn ssa_to_linear(ssa_path: SSAPath, n: Option) -> SSAPath { let n = match n { Some(n) => n, None => ssa_path.iter().map(|v| v.len()).sum::() + ssa_path.len() + 1, }; let mut ids: Vec = (0..n).map(|i| i as Node).collect(); let mut path: SSAPath = Vec::with_capacity(2 * n - 1); let mut ssa = n as Node; for scon in ssa_path { // find the locations of the ssa ids in the list of ids let mut con: Vec = scon .iter() .map(|s| ids.binary_search(s).unwrap() as Node) .collect(); // remove the ssa ids from the list con.sort(); for j in con.iter().rev() { ids.remove(*j as usize); } path.push(con); ids.push(ssa); ssa += 1; } path } #[pyfunction] fn find_subgraphs( inputs: Vec>, output: Vec, size_dict: Dict, ) -> Vec> { let cp = ContractionProcessor::new(inputs, output, size_dict, false); cp.subgraphs() } #[pyfunction] fn optimize_simplify( inputs: Vec>, output: Vec, size_dict: Dict, use_ssa: Option, ) -> SSAPath { let n = inputs.len(); let mut cp = ContractionProcessor::new(inputs, output, size_dict, false); cp.simplify(); if use_ssa.unwrap_or(false) { cp.ssa_path } else { ssa_to_linear(cp.ssa_path, Some(n)) } } #[pyfunction] fn optimize_greedy( py: Python, inputs: Vec>, output: Vec, size_dict: Dict, costmod: Option, temperature: Option, seed: Option, simplify: Option, use_ssa: Option, ) -> Vec> { py.allow_threads(|| { let n = inputs.len(); let mut cp = ContractionProcessor::new(inputs, output, size_dict, false); if simplify.unwrap_or(true) { // perform simplifications cp.simplify(); } // greedily contract each connected subgraph cp.optimize_greedy(costmod, temperature, seed); // optimize any remaining disconnected terms cp.optimize_remaining_by_size(); if use_ssa.unwrap_or(false) { cp.ssa_path } else { ssa_to_linear(cp.ssa_path, Some(n)) } }) } #[pyfunction] fn optimize_random_greedy_track_flops( py: Python, inputs: Vec>, output: Vec, size_dict: Dict, ntrials: usize, costmod: Option<(f32, f32)>, temperature: Option<(f32, f32)>, seed: Option, simplify: Option, use_ssa: Option, ) -> (Vec>, Score) { py.allow_threads(|| { let (costmod_min, costmod_max) = costmod.unwrap_or((0.1, 4.0)); let costmod_diff = (costmod_max - costmod_min).abs(); let is_const_costmod = costmod_diff < Score::EPSILON; let (temp_min, temp_max) = temperature.unwrap_or((0.001, 1.0)); let log_temp_min = Score::ln(temp_min); let log_temp_max = Score::ln(temp_max); let log_temp_diff = (log_temp_max - log_temp_min).abs(); let is_const_temp = log_temp_diff < Score::EPSILON; let mut rng = match seed { Some(seed) => rand::rngs::StdRng::seed_from_u64(seed), None => rand::rngs::StdRng::from_entropy(), }; let seeds = (0..ntrials).map(|_| rng.gen()).collect::>(); let n: usize = inputs.len(); // construct processor and perform simplifications once let mut cp0 = ContractionProcessor::new(inputs, output, size_dict, true); if simplify.unwrap_or(true) { cp0.simplify(); } let mut best_path = None; let mut best_flops = f32::INFINITY; for seed in seeds { let mut cp = cp0.clone(); // uniform sample for costmod let costmod = if is_const_costmod { costmod_min } else { costmod_min + rng.gen::() * costmod_diff }; // log-uniform sample for temperature let temperature = if is_const_temp { temp_min } else { f32::exp(log_temp_min + rng.gen::() * log_temp_diff) }; // greedily contract each connected subgraph let success = cp.optimize_greedy(Some(costmod), Some(temperature), Some(seed)); if !success { continue; } // optimize any remaining disconnected terms cp.optimize_remaining_by_size(); if cp.flops < best_flops { best_path = Some(cp.ssa_path); best_flops = cp.flops; cp0.flops_limit = cp.flops; } } // convert to base 10 for easier comparison best_flops *= f32::consts::LOG10_E; if use_ssa.unwrap_or(false) { (best_path.unwrap(), best_flops) } else { (ssa_to_linear(best_path.unwrap(), Some(n)), best_flops) } }) } #[pyfunction] fn optimize_optimal( py: Python, inputs: Vec>, output: Vec, size_dict: Dict, minimize: Option, cost_cap: Option, search_outer: Option, simplify: Option, use_ssa: Option, ) -> Vec> { py.allow_threads(|| { let n = inputs.len(); let mut cp = ContractionProcessor::new(inputs, output, size_dict, false); if simplify.unwrap_or(true) { // perform simplifications cp.simplify(); } // optimally contract each connected subgraph cp.optimize_optimal(minimize, cost_cap, search_outer); // optimize any remaining disconnected terms cp.optimize_remaining_by_size(); if use_ssa.unwrap_or(false) { cp.ssa_path } else { ssa_to_linear(cp.ssa_path, Some(n)) } }) } /// A Python module implemented in Rust. #[pymodule] fn cotengrust(m: &Bound<'_, PyModule>) -> PyResult<()> { m.add_function(wrap_pyfunction!(ssa_to_linear, m)?)?; m.add_function(wrap_pyfunction!(find_subgraphs, m)?)?; m.add_function(wrap_pyfunction!(optimize_simplify, m)?)?; m.add_function(wrap_pyfunction!(optimize_greedy, m)?)?; m.add_function(wrap_pyfunction!(optimize_random_greedy_track_flops, m)?)?; m.add_function(wrap_pyfunction!(optimize_optimal, m)?)?; Ok(()) } cotengrust-0.1.3/tests/000077500000000000000000000000001461675323200150635ustar00rootroot00000000000000cotengrust-0.1.3/tests/test_cotengrust.py000066400000000000000000000134641461675323200207010ustar00rootroot00000000000000import pytest try: import cotengra as ctg ctg_missing = False except ImportError: ctg_missing = True ctg = None import cotengrust as ctgr requires_cotengra = pytest.mark.skipif(ctg_missing, reason="requires cotengra") @pytest.mark.parametrize("which", ["greedy", "optimal"]) def test_basic_call(which): inputs = [('a', 'b'), ('b', 'c'), ('c', 'd'), ('d', 'a')] output = ('b', 'd') size_dict = {'a': 2, 'b': 3, 'c': 4, 'd': 5} path = { "greedy": ctgr.optimize_greedy, "optimal": ctgr.optimize_optimal, }[ which ](inputs, output, size_dict) assert all(len(con) <= 2 for con in path) def find_output_str(lhs): tmp_lhs = lhs.replace(",", "") return "".join(s for s in sorted(set(tmp_lhs)) if tmp_lhs.count(s) == 1) def eq_to_inputs_output(eq): if "->" not in eq: eq += "->" + find_output_str(eq) inputs, output = eq.split("->") inputs = inputs.split(",") inputs = [list(s) for s in inputs] output = list(output) return inputs, output def get_rand_size_dict(inputs, d_min=2, d_max=3): import random size_dict = {} for term in inputs: for ix in term: if ix not in size_dict: size_dict[ix] = random.randint(d_min, d_max) return size_dict # these are taken from opt_einsum test_case_eqs = [ # Test single-term equations "->", "a->a", "ab->ab", "ab->ba", "abc->bca", "abc->b", "baa->ba", "aba->b", # Test scalar-like operations "a,->a", "ab,->ab", ",ab,->ab", ",,->", # Test hadamard-like products "a,ab,abc->abc", "a,b,ab->ab", # Test index-transformations "ea,fb,gc,hd,abcd->efgh", "ea,fb,abcd,gc,hd->efgh", "abcd,ea,fb,gc,hd->efgh", # Test complex contractions "acdf,jbje,gihb,hfac,gfac,gifabc,hfac", "cd,bdhe,aidb,hgca,gc,hgibcd,hgac", "abhe,hidj,jgba,hiab,gab", "bde,cdh,agdb,hica,ibd,hgicd,hiac", "chd,bde,agbc,hiad,hgc,hgi,hiad", "chd,bde,agbc,hiad,bdi,cgh,agdb", "bdhe,acad,hiab,agac,hibd", # Test collapse "ab,ab,c->", "ab,ab,c->c", "ab,ab,cd,cd->", "ab,ab,cd,cd->ac", "ab,ab,cd,cd->cd", "ab,ab,cd,cd,ef,ef->", # Test outer prodcuts "ab,cd,ef->abcdef", "ab,cd,ef->acdf", "ab,cd,de->abcde", "ab,cd,de->be", "ab,bcd,cd->abcd", "ab,bcd,cd->abd", # Random test cases that have previously failed "eb,cb,fb->cef", "dd,fb,be,cdb->cef", "bca,cdb,dbf,afc->", "dcc,fce,ea,dbf->ab", "fdf,cdd,ccd,afe->ae", "abcd,ad", "ed,fcd,ff,bcf->be", "baa,dcf,af,cde->be", "bd,db,eac->ace", "fff,fae,bef,def->abd", "efc,dbc,acf,fd->abe", # Inner products "ab,ab", "ab,ba", "abc,abc", "abc,bac", "abc,cba", # GEMM test cases "ab,bc", "ab,cb", "ba,bc", "ba,cb", "abcd,cd", "abcd,ab", "abcd,cdef", "abcd,cdef->feba", "abcd,efdc", # Inner than dot "aab,bc->ac", "ab,bcc->ac", "aab,bcc->ac", "baa,bcc->ac", "aab,ccb->ac", # Randomly built test caes "aab,fa,df,ecc->bde", "ecb,fef,bad,ed->ac", "bcf,bbb,fbf,fc->", "bb,ff,be->e", "bcb,bb,fc,fff->", "fbb,dfd,fc,fc->", "afd,ba,cc,dc->bf", "adb,bc,fa,cfc->d", "bbd,bda,fc,db->acf", "dba,ead,cad->bce", "aef,fbc,dca->bde", ] @requires_cotengra @pytest.mark.parametrize("eq", test_case_eqs) @pytest.mark.parametrize("which", ["greedy", "optimal"]) def test_manual_cases(eq, which): inputs, output = eq_to_inputs_output(eq) size_dict = get_rand_size_dict(inputs) path = { "greedy": ctgr.optimize_greedy, "optimal": ctgr.optimize_optimal, }[ which ](inputs, output, size_dict) assert all(len(con) <= 2 for con in path) tree = ctg.ContractionTree.from_path( inputs, output, size_dict, path=path, check=True ) assert tree.is_complete() @requires_cotengra @pytest.mark.parametrize("seed", range(10)) @pytest.mark.parametrize("which", ["greedy", "optimal"]) def test_basic_rand(seed, which): inputs, output, shapes, size_dict = ctg.utils.rand_equation( n=10, reg=4, n_out=2, n_hyper_in=1, n_hyper_out=1, d_min=2, d_max=3, seed=seed, ) path = { "greedy": ctgr.optimize_greedy, "optimal": ctgr.optimize_optimal, }[ which ](inputs, output, size_dict) assert all(len(con) <= 2 for con in path) tree = ctg.ContractionTree.from_path( inputs, output, size_dict, path=path, check=True ) assert tree.is_complete() @requires_cotengra def test_optimal_lattice_eq(): inputs, output, _, size_dict = ctg.utils.lattice_equation( [4, 5], d_max=2, seed=42 ) path = ctgr.optimize_optimal(inputs, output, size_dict, minimize='flops') tree = ctg.ContractionTree.from_path( inputs, output, size_dict, path=path ) assert tree.is_complete() assert tree.contraction_cost() == 964 path = ctgr.optimize_optimal(inputs, output, size_dict, minimize='size') assert all(len(con) <= 2 for con in path) tree = ctg.ContractionTree.from_path( inputs, output, size_dict, path=path ) assert tree.contraction_width() == pytest.approx(5) @requires_cotengra def test_optimize_random_greedy_log_flops(): inputs, output, _, size_dict = ctg.utils.lattice_equation( [10, 10], d_max=3, seed=42 ) path, cost1 = ctgr.optimize_random_greedy_track_flops( inputs, output, size_dict, ntrials=4, seed=42 ) _, cost2 = ctgr.optimize_random_greedy_track_flops( inputs, output, size_dict, ntrials=4, seed=42 ) assert cost1 == cost2 tree = ctg.ContractionTree.from_path( inputs, output, size_dict, path=path ) assert tree.is_complete() assert tree.contraction_cost(log=10) == pytest.approx(cost1)