cotengra#

Submodules#

Package Contents#

Classes#

ContractionTree

Binary tree representing a tensor network contraction.

ContractionTreeCompressed

A contraction tree for compressed contractions. Currently the only

ContractionTreeMulti

Binary tree representing a tensor network contraction.

HyperGraph

Simple hypergraph builder and writer.

SliceFinder

An object to help find the best indices to slice over in order to reduce

SlicedContractor

A contraction where certain indices are explicitly summed over,

QuickBBOptimizer

Base class for different path optimizers to inherit from.

FlowCutterOptimizer

Base class for different path optimizers to inherit from.

HyperOptimizer

A path optimizer that samples a series of contraction trees

ReusableHyperOptimizer

Like HyperOptimizer but it will re-instantiate the optimizer

Functions#

get_hypergraph(inputs[, output, size_dict, accel])

Single entry-point for creating a, possibly accelerated, HyperGraph.

optimize_quickbb(inputs, output, size_dict[, ...])

optimize_flowcutter(inputs, output, size_dict[, ...])

list_hyper_functions()

Return a list of currently registered hyper contraction finders.

get_hyper_space()

hash_contraction(inputs, output, size_dict[, method])

Compute a hash for a particular contraction geometry.

plot_contractions(tree[, x, y, color, size, ...])

plot_contractions_alt(tree[, x, y, color, size, ...])

plot_scatter(self[, x, y, figsize, return_fig])

plot_scatter_alt(self[, x, y, color, color_scheme, ...])

Plot the trials total flops vs max size.

plot_slicings(slice_finder[, color_scheme, ...])

plot_slicings_alt(slice_finder[, color_scheme, ...])

plot_tree(tree[, layout, layout_hypergraph, k, ...])

Plot a contraction tree using matplotlib.

plot_tree_ring(tree, **kwargs)

plot_tree_tent(tree, **kwargs)

plot_tree_span(tree, **kwargs)

plot_trials(self[, y, figsize])

plot_trials_alt(self[, y, width, height])

Plot the trials interactively using altair.

HyperCompressedOptimizer([chi, methods, minimize])

Instantiates a HyperOptimizer but with default arguments applicable to

ReusableHyperCompressedOptimizer([chi, methods, ...])

Instantiates a HyperOptimizer but with default arguments applicable to

HyperMultiOptimizer(*args, **kwargs)

hyper_optimize(inputs, output, size_dict[, memory_limit])

Attributes#

UniformOptimizer

Does no gaussian process tuning by default, just randomly samples - requires

QuasiRandOptimizer

Does no gaussian process tuning by default, just randomly samples but in a

class cotengra.ContractionTree(inputs, output, size_dict, track_childless=False, track_flops=False, track_write=False, track_size=False)#

Binary tree representing a tensor network contraction.

Parameters:
  • inputs (sequence of str) – The list of input tensor’s indices.

  • output (str) – The output indices.

  • size_dict (dict[str, int]) – The size of each index.

  • track_childless (bool, optional) – Whether to dynamically keep track of which nodes are childless. Useful if you are ‘divisively’ building the tree.

  • track_flops (bool, optional) – Whether to dynamically keep track of the total number of flops. If False You can still compute this once the tree is complete.

  • track_size (bool, optional) – Whether to dynamically keep track of the largest tensor so far. If False You can still compute this once the tree is complete.

children#

Mapping of each node to two children.

Type:

dict[node, tuple[node]

info#

Information about the tree nodes. The key is the set of inputs (a set of inputs indices) the node contains. Or in other words, the subgraph of the node. The value is a dictionary to cache information about effective ‘leg’ indices, size, flops of formation etc.

Type:

dict[node, dict]

remove_ind_#
subtree_reconfigure_#
subtree_reconfigure_forest_#
slice_#
slice_and_reconfigure_#
slice_and_reconfigure_forest_#
compressed_reconfigure_#
path#
ssa_path#
path_surface#
ssa_path_surface#
plot_ring#
plot_tent#
plot_span#
plot_rubberband#
plot_contractions#
plot_contractions_alt#
set_state_from(other)#

Set the internal state of this tree to that of other.

copy()#

Create a copy of this ContractionTree.

property nslices#

Simple alias for how many independent contractions this tree represents overall.

property nchunks#

The number of ‘chunks’ - determined by the number of sliced output indices.

node_to_terms(node)#

Turn a node – a frozen set of ints – into the corresponding terms – a sequence of sets of str corresponding to input indices.

gen_leaves()#

Generate the nodes representing leaves of the contraction tree, i.e. of size 1 each corresponding to a single input tensor.

classmethod from_path(inputs, output, size_dict, *, path=None, ssa_path=None, check=False, **kwargs)#

Create a (completed) ContractionTree from the usual inputs plus a standard contraction path or ‘ssa_path’ - you need to supply one.

classmethod from_info(info, **kwargs)#

Create a ContractionTree from an opt_einsum.PathInfo object.

classmethod from_eq(eq, size_dict, **kwargs)#

Create a empty ContractionTree directly from an equation and set of shapes.

Parameters:
  • eq (str) – The einsum string equation.

  • size_dict (dict[str, int]) – The size of each index.

classmethod from_edge_path(edge_path, inputs, output, size_dict, check=False, **kwargs)#

Create a ContractionTree from an edge elimination ordering.

_add_node(node, check=False)#
_remove_node(node)#

Remove node from this tree and update the flops and maximum size if tracking them respectively. Inplace operation.

get_keep(node)#

Get a set of at least the indices that should be explicitly kept if they appear on node (or below).

get_legs(node)#

Get the effective ‘outer’ indices for the collection of tensors in node.

get_involved(node)#

Get all the indices involved in the formation of subgraph node.

get_removed(node)#

Get the indices that will be removed by the creation of node.

get_size(node)#

Get the tensor size of node.

get_flops(node)#

Get the FLOPs for the pairwise contraction that will create node.

get_can_dot(node)#

Get whether this contraction can be performed as a dot product (i.e. with tensordot), or else requires einsum, as it has indices that don’t appear exactly twice in either the inputs or the output.

get_inds(node)#

Get the indices of this node - an ordered string version of get_legs that starts with tree.inputs and maintains the order they appear in each contraction ‘ABC,abc->ABCabc’, to match tensordot.

get_tensordot_axes(node)#

Get the axes arg for a tensordot ocontraction that produces node. The pairs are sorted in order of appearance on the left input.

get_tensordot_perm(node)#

Get the permutation required, if any, to bring the tensordot output of this nodes contraction into line with self.get_inds(node).

get_einsum_eq(node)#

Get the einsum string describing the contraction that produces node, unlike get_inds the characters are mapped into [a-zA-Z], for compatibility with numpy.einsum for example.

get_centrality(node)#
total_flops(dtype='float')#

Sum the flops contribution from every node in the tree.

Parameters:

dtype ({'float', 'complex', None}, optional) – Scale the answer depending on the assumed data type.

total_write()#

Sum the total amount of memory that will be created and operated on.

total_cost(factor=DEFAULT_COMBO_FACTOR, combine=sum)#
max_size()#

The size of the largest intermediate tensor.

peak_size(order=None)#

Get the peak concurrent size of tensors needed - this depends on the traversal order, i.e. the exact contraction path, not just the contraction tree.

total_size()#

Get the total sum of all intermediate tensor sizes, this is relevant when, for example, using autodiff on a contraction without checkpointing.

arithmetic_intensity()#

The ratio of total flops to total write - the higher the better for extracting good computational performance.

contraction_cost()#

Get the total number of scalar operations ~ time complexity.

contraction_width()#

Get log2 of the size of the largest tensor.

compressed_contract_stats(chi, order='surface_order', compress_late=True)#
max_size_compressed(chi, order='surface_order', compress_late=True)#

Compute the maximum sized tensor produced when a compressed contraction is performed with maximum bond size chi, ordered by order. This is close to the ideal space complexity if only tensors that are being directly operated on are kept in memory.

peak_size_compressed(chi, order='surface_order', compress_late=True, accel='auto')#

Compute the peak size of combined intermediate tensors when a compressed contraction is performed with maximum bond size chi, ordered by order. This is the practical space complexity if one is not swapping intermediates in and out of memory.

total_size_compressed(chi, order='surface_order', compress_late=True, accel='auto')#

Compute the total size of all intermediate tensors when a compressed contraction is performed with maximum bond size chi, ordered by order. This is relevant maybe for time complexity and e.g. autodiff space complexity (since every intermediate is kept).

contract_nodes_pair(x, y, check=False)#

Contract node x with node y in the tree to create a new parent node.

contract_nodes(nodes, optimize='auto-hq', check=False, extra_opts=None)#

Contract an arbitrary number of nodes in the tree to build up a subtree. The root of this subtree (a new intermediate) is returned.

is_complete()#

Check every node has two children, unless it is a leaf.

get_default_order()#
_traverse_ordered(order)#

Traverse the tree in the order that minimizes order(node), but still contrained to produce children before parents.

traverse(order=None)#

Generate, in order, all the node merges in this tree. Non-recursive! This ensures children are always visited before their parent.

Parameters:

order (None or callable, optional) – How to order the contractions within the tree. If a callable is given (which should take a node as its argument), try to contract nodes that minimize this function first.

Returns:

The bottom up ordered sequence of tree merges, each a tuple of (parent, left_child, right_child).

Return type:

generator[tuple[node]]

See also

descend

descend(mode='dfs')#

Generate, from root to leaves, all the node merges in this tree. Non-recursive! This ensures parents are visited before their children.

Parameters:

mode ({'dfs', bfs}, optional) – How expand from a parent.

Returns:

The top down ordered sequence of tree merges, each a tuple of (parent, left_child, right_child).

Return type:

generator[tuple[node]

See also

traverse

get_subtree(node, size, search='bfs')#

Get a subtree spanning down from node which will have size leaves (themselves not necessarily leaves of the actual tree).

Parameters:
  • node (node) – The node of the tree to start with.

  • size (int) – How many subtree leaves to aim for.

  • search ({'bfs', 'dfs', 'random'}, optional) –

    How to build the tree:

    • ’bfs’: breadth first expansion

    • ’dfs’: depth first expansion (largest nodes first)

    • ’random’: random expansion

Returns:

  • sub_leaves (tuple[node]) – Nodes which are subtree leaves.

  • branches (tuple[node]) – Nodes which are between the subtree leaves and root.

remove_ind(ind, inplace=False)#

Remove (i.e. slice) index ind from this contraction tree, taking care to update all relevant information about each node.

calc_subtree_candidates(pwr=2, what='flops')#
subtree_reconfigure(subtree_size=8, subtree_search='bfs', weight_what='flops', weight_pwr=2, select='max', maxiter=500, seed=None, minimize='flops', optimize=None, inplace=False, progbar=False)#

Reconfigure subtrees of this tree with locally optimal paths.

Parameters:
  • subtree_size (int, optional) – The size of subtree to consider. Cost is exponential in this.

  • subtree_search ({'bfs', 'dfs', 'random'}, optional) –

    How to build the subtrees:

    • ’bfs’: breadth-first-search creating balanced subtrees

    • ’dfs’: depth-first-search creating imbalanced subtrees

    • ’random’: random subtree building

  • weight_what ({'flops', 'size'}, optional) – When assessing nodes to build and optimize subtrees from whether to score them by the (local) contraction cost, or tensor size.

  • weight_pwr (int, optional) – When assessing nodes to build and optimize subtrees from, how to scale their score into a probability: score**(1 / weight_pwr). The larger this is the more explorative the algorithm is when select='random'.

  • select ({'max', 'min', 'random'}, optional) –

    What order to select node subtrees to optimize:

    • ’max’: choose the highest score first

    • ’min’: choose the lowest score first

    • ’random’: choose randomly weighted on score – see weight_pwr.

  • maxiter (int, optional) – How many subtree optimizations to perform, the algorithm can terminate before this if all subtrees have been optimized.

  • seed (int, optional) – A random seed (seeds python system random module).

  • minimize ({'flops', 'size'}, optional) – Whether to minimize with respect to contraction flops or size.

  • inplace (bool, optional) – Whether to perform the reconfiguration inplace or not.

  • progbar (bool, optional) – Whether to show live progress of the reconfiguration.

Return type:

ContractionTree

subtree_reconfigure_forest(num_trees=8, num_restarts=10, restart_fraction=0.5, subtree_maxiter=100, subtree_size=10, subtree_search=('random', 'bfs'), subtree_select=('random',), subtree_weight_what=('flops', 'size'), subtree_weight_pwr=(2,), parallel='auto', parallel_maxiter_steps=4, minimize='flops', progbar=False, inplace=False)#

‘Forested’ version of subtree_reconfigure which is more explorative and can be parallelized. It stochastically generates a ‘forest’ reconfigured trees, then only keeps some fraction of these to generate the next forest.

Parameters:
  • num_trees (int, optional) – The number of trees to reconfigure at each stage.

  • num_restarts (int, optional) – The number of times to halt, prune and then restart the tree reconfigurations.

  • restart_fraction (float, optional) – The fraction of trees to keep at each stage and generate the next forest from.

  • subtree_maxiter (int, optional) – Number of subtree reconfigurations per step. num_restarts * subtree_maxiter is the max number of total subtree reconfigurations for the final tree produced.

  • subtree_size (int, optional) – The size of subtrees to search for and reconfigure.

  • subtree_search (tuple[{'random', 'bfs', 'dfs'}], optional) – Tuple of options for the search kwarg of ContractionTree.subtree_reconfigure() to randomly sample.

  • subtree_select (tuple[{'random', 'max', 'min'}], optional) – Tuple of options for the select kwarg of ContractionTree.subtree_reconfigure() to randomly sample.

  • subtree_weight_what (tuple[{'flops', 'size'}], optional) – Tuple of options for the weight_what kwarg of ContractionTree.subtree_reconfigure() to randomly sample.

  • subtree_weight_pwr (tuple[int], optional) – Tuple of options for the weight_pwr kwarg of ContractionTree.subtree_reconfigure() to randomly sample.

  • parallel ('auto', False, True, int, or distributed.Client) – Whether to parallelize the search.

  • parallel_maxiter_steps (int, optional) – If parallelizing, how many steps to break each reconfiguration into in order to evenly saturate many processes.

  • minimize ({'flops', 'size'}, optional) – Whether to minimize the total flops or maximum size of the contraction tree.

  • progbar (bool, optional) – Whether to show live progress.

  • inplace (bool, optional) – Whether to perform the subtree reconfiguration inplace.

Return type:

ContractionTree

slice(target_size=None, target_overhead=None, target_slices=None, temperature=0.01, minimize='flops', allow_outer=True, max_repeats=16, inplace=False)#

Slice this tree (turn some indices into indices which are explicitly summed over rather than being part of contractions). The indices are stored in tree.sliced_inds, and the contraction width updated to take account of the slicing. Calling tree.contract(arrays) moreover which automatically perform the slicing and summation.

Parameters:
  • target_size (int, optional) – The target number of entries in the largest tensor of the sliced contraction. The search algorithm will terminate after this is reached.

  • target_slices (int, optional) – The target or minimum number of ‘slices’ to consider - individual contractions after slicing indices. The search algorithm will terminate after this is breached.

  • target_overhead (float, optional) – The target increase in total number of floating point operations. For example, a value of 2.0 will terminate the search just before the cost of computing all the slices individually breaches twice that of computing the original contraction all at once.

  • temperature (float, optional) – How much to randomize the repeated search.

  • minimize ({'flops', 'size', ...}, optional) – Which metric to score the overhead increase against.

  • allow_outer (bool, optional) – Whether to allow slicing of outer indices.

  • max_repeats (int, optional) – How many times to repeat the search with a slight randomization.

  • inplace (bool, optional) – Whether the remove the indices from this tree inplace or not.

Return type:

ContractionTree

slice_and_reconfigure(target_size, step_size=2, temperature=0.01, minimize='flops', allow_outer=True, max_repeats=16, reconf_opts=None, progbar=False, inplace=False)#

Interleave slicing (removing indices into an exterior sum) with subtree reconfiguration to minimize the overhead induced by this slicing.

Parameters:
  • target_size (int) – Slice the tree until the maximum intermediate size is this or smaller.

  • step_size (int, optional) – The minimum size reduction to try and achieve before switching to a round of subtree reconfiguration.

  • temperature (float, optional) – The temperature to supply to SliceFinder for searching for indices.

  • max_repeats (int, optional) – The number of slicing attempts to perform per search.

  • progbar (bool, optional) – Whether to show live progress.

  • inplace (bool, optional) – Whether to perform the slicing and reconfiguration inplace.

  • reconf_opts (None or dict, optional) – Supplied to ContractionTree.subtree_reconfigure() or ContractionTree.subtree_reconfigure_forest(), depending on ‘forested’ key value.

slice_and_reconfigure_forest(target_size, step_size=2, num_trees=8, restart_fraction=0.5, temperature=0.02, max_repeats=32, minimize='flops', allow_outer=True, parallel='auto', progbar=False, inplace=False, reconf_opts=None)#

‘Forested’ version of ContractionTree.slice_and_reconfigure(). This maintains a ‘forest’ of trees with different slicing and subtree reconfiguration attempts, pruning the worst at each step and generating a new forest from the best.

Parameters:
  • target_size (int) – Slice the tree until the maximum intermediate size is this or smaller.

  • step_size (int, optional) – The minimum size reduction to try and achieve before switching to a round of subtree reconfiguration.

  • num_restarts (int, optional) – The number of times to halt, prune and then restart the tree reconfigurations.

  • restart_fraction (float, optional) – The fraction of trees to keep at each stage and generate the next forest from.

  • temperature (float, optional) – The temperature at which to randomize the sliced index search.

  • max_repeats (int, optional) – The number of slicing attempts to perform per search.

  • parallel ('auto', False, True, int, or distributed.Client) – Whether to parallelize the search.

  • progbar (bool, optional) – Whether to show live progress.

  • inplace (bool, optional) – Whether to perform the slicing and reconfiguration inplace.

  • reconf_opts (None or dict, optional) – Supplied to ContractionTree.slice_and_reconfigure().

Return type:

ContractionTree

compressed_reconfigure(chi, minimize='peak', order_only=False, max_nodes='auto', max_time=None, local_score=None, exploration_power=0, best_score=None, progbar=False, inplace=False)#

Reconfigure this tree according to peak_size_compressed.

Parameters:
  • chi (int) – The maximum bond dimension to consider.

  • order_only (bool, optional) – Whether to only consider the ordering of the current tree contractions, or all possible contractions, starting with the current.

  • max_nodes (int, optional) – Set the maximum number of contraction steps to consider.

  • max_time (float, optional) – Set the maximum time to spend on the search.

  • local_score (callable, optional) –

    A function that assigns a score to a potential contraction, with a lower score giving more priority to explore that contraction earlier. It should have signature:

    local_score(step, new_score, dsize, new_size)
    

    where step is the number of steps so far, new_score is the score of the contraction so far, dsize is the change in memory by the current step, and new_size is the new memory size after contraction.

  • exploration_power (float, optional) – If not 0.0, the inverse power to which the step is raised in the default local score function. Higher values favor exploring more promising branches early on - at the cost of increased memory. Ignored if local_score is supplied.

  • best_score (float, optional) – Manually specify an upper bound for best score found so far.

  • progbar (bool, optional) – If True, display a progress bar.

  • inplace (bool, optional) – Whether to perform the reconfiguration inplace on this tree.

Return type:

ContractionTree

flat_tree(order=None)#

Create a nested tuple representation of the contraction tree like:

((0, (1, 2)), ((3, 4), ((5, (6, 7)), (8, 9))))

Such that the contraction will progress like:

((0, (1, 2)), ((3, 4), ((5, (6, 7)), (8, 9))))
((0, 12), (34, ((5, 67), 89)))
(012, (34, (567, 89)))
(012, (34, 56789))
(012, 3456789)
0123456789

Where each integer represents a leaf (i.e. single element node).

get_leaves_ordered()#

Return the list of leaves as ordered by the contraction tree.

Return type:

tuple[frozenset[str]]

get_path(order=None)#

Generate a standard path from the contraction tree.

get_numpy_path(order=None)#

Generate a path compatible with the optimize kwarg of numpy.einsum.

get_ssa_path(order=None)#

Generate a ssa path from the contraction tree.

surface_order(node)#
set_surface_order_from_path(ssa_path)#
get_path_surface()#
get_ssa_path_surface()#
get_spans()#

Get all (which could mean none) potential embeddings of this contraction tree into a spanning tree of the original graph.

Return type:

tuple[dict[frozenset[int], frozenset[int]]]

compute_centralities(combine='mean')#

Compute a centrality for every node in this contraction tree.

get_hypergraph(accel=False)#

Get a hypergraph representing the uncontracted network (i.e. the leaves).

reset_contraction_indices()#

Reset all information regarding the explicit contraction indices ordering.

sort_contraction_indices(priority='flops', make_output_contig=True, make_contracted_contig=True, reset=True)#

Set explicit orders for the contraction indices of this self to optimize for one of two things: contiguity in contracted (‘k’) indices, or contiguity of left and right output (‘m’ and ‘n’) indices.

Parameters:
  • priority ({'flops', 'size', 'root', 'leaves'}, optional) – Which order to process the intermediate nodes in. Later nodes re-sort previous nodes so are more likely to keep their ordering. E.g. for ‘flops’ the mostly costly contracton will be process last and thus will be guaranteed to have its indices exactly sorted.

  • make_output_contig (bool, optional) – When processing a pairwise contraction, sort the parent contraction indices so that the order of indices is the order they appear from left to right in the two child (input) tensors.

  • make_contracted_contig (bool, optional) – When processing a pairwise contraction, sort the child (input) tensor indices so that all contracted indices appear contiguously.

  • reset (bool, optional) – Reset all indices to the default order before sorting.

print_contractions(sort=None, show_brackets=True)#

Print each pairwise contraction, with colorized indices (if colorama is installed), and other information.

_contract_core(arrays, order=None, prefer_einsum=False, strip_exponent=False, backend=None, check=False, progbar=False)#
contract_core(arrays, order=None, prefer_einsum=False, strip_exponent=False, backend=None, autojit=False, check=False, progbar=False)#

Contract arrays with this tree. The order of the axes and output is assumed to be that of tree.inputs and tree.output, but with sliced indices removed. This functon contracts the core tree and thus if indices have been sliced the arrays supplied need to be sliced as well.

Parameters:
  • arrays (sequence of array) – The arrays to contract.

  • order (str or callable, optional) – Supplied to ContractionTree.traverse().

  • prefer_einsum (bool, optional) – Prefer to use einsum for pairwise contractions, even if tensordot can perform the contraction.

  • backend (str, optional) – What library to use for einsum and transpose, will be automatically inferred from the arrays if not given.

  • autojit (bool, optional) – Whether to use autoray.autojit to jit compile the expression.

  • check (bool, optional) – Perform some basic error checks.

  • progbar (bool, optional) – Show progress through the contraction.

slice_arrays(arrays, i)#

Take arrays and slice the relevant inputs according to tree.sliced_inds and the dynary representation of i.

contract_slice(arrays, i, **kwargs)#

Get slices i of arrays and then contract them.

gather_slices(slices, backend=None, progbar=False)#

Gather all the output contracted slices into a single full result. If none of the sliced indices appear in the output, then this is a simple sum - otherwise the slices need to be partially summed and partially stacked.

gen_output_chunks(arrays, **contract_opts)#

Generate each output chunk of the contraction - i.e. take care of summing internally sliced indices only first. This assumes that the sliced_inds are sorted by whether they appear in the output or not (the default order). Useful for performing some kind of reduction over the final tensor object like fn(x).sum() without constructing the entire thing.

contract(arrays, order=None, prefer_einsum=False, strip_exponent=False, backend=None, autojit=False, check=False, progbar=False)#

Contract arrays with this tree. This function takes unsliced arrays and handles the slicing, contractions and gathering. The order of the axes and output is assumed to match that of tree.inputs and tree.output.

Parameters:
  • arrays (sequence of array) – The arrays to contract.

  • order (str or callable, optional) – Supplied to ContractionTree.traverse().

  • prefer_einsum (bool, optional) – Prefer to use einsum for pairwise contractions, even if tensordot can perform the contraction.

  • strip_exponent (bool, optional) – If True, eagerly strip the exponent (in log10) from intermediate tensors to control numerical problems from leaving the range of the datatype. This method then returns the scaled ‘mantissa’ output array and the exponent separately.

  • backend (str, optional) – What library to use for tensordot, einsum and transpose, it will be automatically inferred from the input arrays if not given.

  • autojit (bool, optional) – Whether to use the ‘autojit’ feature of autoray to compile the contraction expression.

  • check (bool, optional) – Perform some basic error checks.

  • progbar (bool, optional) – Whether to show a progress bar.

Returns:

  • output (array) – The contracted output, it will be scaled if strip_exponent==True.

  • exponent (float) – The exponent of the output in base 10, returned only if strip_exponent==True.

contract_mpi(arrays, comm=None, root=None, **kwargs)#

Contract the slices of this tree and sum them in parallel - assuming we are already running under MPI.

Parameters:
  • arrays (sequence of array) – The input (unsliced arrays)

  • comm (None or mpi4py communicator) – Defaults to mpi4py.MPI.COMM_WORLD if not given.

  • root (None or int, optional) – If root=None, an Allreduce will be performed such that every process has the resulting tensor, else if an integer e.g. root=0, the result will be exclusively gathered to that process using Reduce, with every other process returning None.

  • kwargs – Supplied to contract_slice().

plot_hypergraph(**kwargs)#
__repr__()#

Return repr(self).

class cotengra.ContractionTreeCompressed(inputs, output, size_dict, track_childless=False, track_flops=False, track_write=False, track_size=False)#

Bases: ContractionTree

A contraction tree for compressed contractions. Currently the only difference is that this defaults to the ‘surface’ traversal ordering.

classmethod from_path(inputs, output, size_dict, *, path=None, ssa_path=None, check=False, **kwargs)#

Create a (completed) ContractionTreeCompressed from the usual inputs plus a standard contraction path or ‘ssa_path’ - you need to supply one. This also set the default ‘surface’ traversal ordering to be the initial path.

get_default_order()#
class cotengra.ContractionTreeMulti(inputs, output, size_dict, track_childless=False, track_flops=False, track_write=False, track_size=False)#

Bases: ContractionTree

Binary tree representing a tensor network contraction.

Parameters:
  • inputs (sequence of str) – The list of input tensor’s indices.

  • output (str) – The output indices.

  • size_dict (dict[str, int]) – The size of each index.

  • track_childless (bool, optional) – Whether to dynamically keep track of which nodes are childless. Useful if you are ‘divisively’ building the tree.

  • track_flops (bool, optional) – Whether to dynamically keep track of the total number of flops. If False You can still compute this once the tree is complete.

  • track_size (bool, optional) – Whether to dynamically keep track of the largest tensor so far. If False You can still compute this once the tree is complete.

children#

Mapping of each node to two children.

Type:

dict[node, tuple[node]

info#

Information about the tree nodes. The key is the set of inputs (a set of inputs indices) the node contains. Or in other words, the subgraph of the node. The value is a dictionary to cache information about effective ‘leg’ indices, size, flops of formation etc.

Type:

dict[node, dict]

set_varmults(varmults)#
get_varmults()#
set_numconfigs(numconfigs)#
get_numconfigs()#
class cotengra.HyperGraph(inputs, output=None, size_dict=None)#

Simple hypergraph builder and writer.

Parameters:
  • inputs (sequence of list[str] or dict[int, list[str]]) – The nodes. If given as a dict, the keys will be taken as the node enumeration rather than range(len(inputs)).

  • output (str, optional) – Output indices.

  • size_dict (dict[str, int], optional) – Size of each index.

nodes#

Mapping of node to the list of edges incident to it.

Type:

dict[int, list[str]]

edges#

Mapping of hyper edges to list of nodes it is incident to.

Type:

dict[str, list[int]]

num_nodes#

The number of nodes.

Type:

int

num_edges#

The number of hyper-edges.

Type:

int

__slots__ = ['inputs', 'output', 'size_dict', 'nodes', 'edges', 'compressed', 'node_counter']#
plot#
copy()#

Copy this HyperGraph.

classmethod from_edges(edges, output=(), size_dict=())#
get_num_nodes()#
property num_nodes#
get_num_edges()#
property num_edges#
__len__()#
edges_size(es)#

Get the combined, i.e. product, size of all edges in es.

bond_size(i, j)#

Get the combined, i.e. product, size of edges shared by nodes i and j.

node_size(i)#

Get the size of the term represented by node i.

neighborhood_size(nodes)#

Get the size of nodes in the immediate neighborhood of nodes.

contract_pair_cost(i, j)#

Get the cost of contracting nodes i and j - the product of the dimensions of the indices involved.

total_node_size()#

Get the total size of all nodes.

output_nodes()#

Get the nodes with output indices.

neighbors(i)#

Get the neighbors of node i.

neighbor_edges(i)#

Get the edges incident to all neighbors of node i, (including its own edges).

has_node(i)#

Does this hypergraph have node i?

get_node(i)#

Get the edges node i is incident to.

get_edge(e)#

Get the nodes edge e is incident to.

has_edge(e)#

Does this hypergraph have edge e?

next_node()#

Get the next available node identifier.

add_node(inds, node=None)#

Add a node with inds, and optional identifier node. The identifier will be generated if not given and returned.

remove_node(i)#

Remove node i from this hypergraph.

remove_edge(e)#

Remove edge e from this hypergraph.

contract(i, j, node=None)#

Combine node i and node j.

compress(chi, edges=None)#

‘Compress’ multiedges, combining their size up to a maximum of chi.

candidate_contraction_size(i, j, chi=None)#

Get the size of the node created if i and j were contracted, optionally including the effect of first compressing bonds to size chi.

simple_distance(region, p=2)#

Compute a simple distance metric from nodes in region to all others. Unlike graph distance, relative connectedness is taken into account.

simple_closeness(p=0.75, mu=0.5)#

Compute a rough hypergraph ‘closeness’.

Parameters:
  • p (float, optional) – Once any node has had H.num_nodes**p visitors terminate. Set greater than 1.0 for no limit (slower).

  • mu (float, optional) – Let the visitor score decay with this power. The higher this is, the more local connectivity is favored.

Returns:

scores – The simple hypergraph closenesses - higher being more central.

Return type:

dict[int, float]

simple_centrality(r=None, smoothness=2, **closeness_opts)#

A simple algorithm for large hypergraph centrality. First we find a rough closeness centrality, then relax / smooth this by nodes iteratively radiating their centrality to their neighbors.

Parameters:
  • r (None or int, optional) – Number of iterations. Defaults to max(10, int(self.num_nodes**0.5)).

  • smoothness (float, optional) – The smoothness. In conjunction with a high value of r this will create a smooth gradient from one of the hypergraph to the other.

  • closeness_opts – Supplied to HyperGraph.simple_closeness as the starting point.

Return type:

dict[int, float]

compute_loops(max_loop_length=None)#

Generate all loops up to a certain length in this hypergraph.

Parameters:

max_loop_length (None or int, optional) – The maximum loop length to search for. If None, then this is set automatically by the length of the first loop found.

Yields:

loop (tuple[int]) – A set of nodes that form a loop.

get_laplacian()#

Get the graph Laplacian.

get_resistance_distances()#

Get the resistance distance between all nodes of the raw graph.

resistance_centrality(rescale=True)#

Compute the centrality in terms of the total resistance distance to all other nodes.

to_networkx(as_tree_leaves=False)#

Convert to a networkx Graph, with hyperedges represented as nodes.

Parameters:

as_tree_leaves (bool, optional) – If true, then the nodes are converted to ‘tree leaf’ form, i.e. map node i to frozenset([i]), to match the nodes in a ContractionTree.

compute_weights(weight_edges='const', weight_nodes='const')#
__repr__()#

Return repr(self).

cotengra.get_hypergraph(inputs, output=None, size_dict=None, accel=False)#

Single entry-point for creating a, possibly accelerated, HyperGraph.

class cotengra.SliceFinder(tree_or_info, target_size=None, target_overhead=None, target_slices=None, temperature=0.01, minimize='flops', allow_outer=True)#

An object to help find the best indices to slice over in order to reduce the memory footprint of a contraction as much as possible whilst introducing as little extra overhead. It searches for and stores ContractionCosts.

Parameters:
  • tree_or_info (ContractionTree or PathInfo) – Object describing the target full contraction to slice, generated for example from a call to contract_path().

  • target_size (int, optional) – The target number of entries in the largest tensor of the sliced contraction. The search algorithm will terminate after this is reached.

  • target_slices (int, optional) – The target or minimum number of ‘slices’ to consider - individual contractions after slicing indices. The search algorithm will terminate after this is breached.

  • target_overhead (float, optional) – The target increase in total number of floating point operations. For example, a value of 2.0 will terminate the search just before the cost of computing all the slices individually breaches twice that of computing the original contraction all at once.

  • temperature (float, optional) – When sampling combinations of indices, how far to randomly stray from what looks like the best (local) choice.

plot_slicings#
plot_slicings_alt#
_maybe_default(attr, value)#
best(k=None, target_size=None, target_overhead=None, target_slices=None)#

Return the best contraction slicing, subject to target filters.

trial(target_size=None, target_overhead=None, target_slices=None, temperature=None)#

A single slicing attempt, greedily select indices from the popular pool, subject to the score function, terminating when any of the target criteria are met.

search(max_repeats=16, temperature=None, target_size=None, target_overhead=None, target_slices=None)#

Repeat trial several times and return the best found so far.

SlicedContractor(arrays, target_size=None, target_overhead=None, target_slices=None, **kwargs)#

Generate a sliced contraction using the best indices found by this SliceFinder and by default the original contraction path as well.

class cotengra.SlicedContractor(eq, arrays, sliced, optimize='auto', size_dict=None)#

A contraction where certain indices are explicitly summed over, corresponding to taking different ‘slices’ of the input arrays, each of which can be contracted independently with hopefully a lower memory requirement. The recommended way of instantiating this is from a directly from SliceFinder which already.

Parameters:
  • eq (str) – The overall contraction to perform.

  • arrays (sequence of array) – The arrays to contract.

  • sliced (sequence of str) – Which indices in eq to slice over.

  • optimize (str or path or PathOptimizer, optional) – How to optimize the sliced contraction path - the contraction with sliced indices removed. If these sliced indices were found automatically is it generally best to supply the full path they were found with respect to rather than trying to re-optimize the path.

  • size_dict (dict[str, int], optional) – If already known, the sizes of each index.

classmethod from_info(info, arrays, sliced, optimize=None, **kwargs)#

Creat a SlicedContractor directly from a PathInfo object.

property individual_flops#

FLOP cost of a single contraction slice.

property total_flops#

FLOP cost of performing all sliced contractions.

property max_size#

The largest size tensor produced in an individual contraction.

get_sliced_arrays(i)#

Generate the tuple of array inputs corresponding to slice i.

contract_slice(i, **kwargs)#

Contraction of just slice i.

gather_slices(slices)#

Gather all the output contracted slices into the single full result.

contract_all(**kwargs)#

Contract (and sum) all slices at once.

get_dask_chunked(**kwargs)#
get_mars_chunked(**kwargs)#
class cotengra.QuickBBOptimizer(max_time=10, executable='quickbb_64', seed=None)#

Bases: opt_einsum.paths.PathOptimizer

Base class for different path optimizers to inherit from.

Subclassed optimizers should define a call method with signature:

def __call__(self, inputs, output, size_dict, memory_limit=None):
    """
    Parameters
    ----------
    inputs : list[set[str]]
        The indices of each input array.
    outputs : set[str]
        The output indices
    size_dict : dict[str, int]
        The size of each index
    memory_limit : int, optional
        If given, the maximum allowed memory.
    """
    # ... compute path here ...
    return path

where path is a list of int-tuples specifiying a contraction order.

run_quickbb(fname, outfile, statfile, max_time=None)#
build_tree(inputs, output, size_dict)#
__call__(inputs, output, size_dict, memory_limit=None)#
cotengra.optimize_quickbb(inputs, output, size_dict, memory_limit=None, max_time=60, seed=None)#
class cotengra.FlowCutterOptimizer(max_time=10, seed=None, executable='flow_cutter_pace17')#

Bases: opt_einsum.paths.PathOptimizer

Base class for different path optimizers to inherit from.

Subclassed optimizers should define a call method with signature:

def __call__(self, inputs, output, size_dict, memory_limit=None):
    """
    Parameters
    ----------
    inputs : list[set[str]]
        The indices of each input array.
    outputs : set[str]
        The output indices
    size_dict : dict[str, int]
        The size of each index
    memory_limit : int, optional
        If given, the maximum allowed memory.
    """
    # ... compute path here ...
    return path

where path is a list of int-tuples specifiying a contraction order.

run_flowcutter(file, max_time=None)#
compute_edge_path(lg)#
build_tree(inputs, output, size_dict, memory_limit=None)#
__call__(inputs, output, size_dict, memory_limit=None)#
cotengra.optimize_flowcutter(inputs, output, size_dict, memory_limit=None, max_time=10, seed=None)#
cotengra.list_hyper_functions()#

Return a list of currently registered hyper contraction finders.

cotengra.get_hyper_space()#
class cotengra.HyperOptimizer(methods=None, minimize='flops', max_repeats=128, max_time=None, parallel='auto', slicing_opts=None, slicing_reconf_opts=None, reconf_opts=None, optlib=DEFAULT_OPTLIB, space=None, score_compression=0.75, max_training_steps=None, compressed=False, multicontraction=False, progbar=False, **optlib_opts)#

Bases: opt_einsum.paths.PathOptimizer

A path optimizer that samples a series of contraction trees while optimizing the hyper parameters used to generate them.

Parameters:
  • methods (None or sequence[str] or str, optional) – Which method(s) to use from list_hyper_functions().

  • minimize ({'flops', 'write', 'size', 'combo' or callable}, optional) – How to score each trial, used to train the optimizer and rank the results. If a custom callable, it should take a trial dict as its argument and return a single float.

  • max_repeats (int, optional) – The maximum number of trial contraction trees to generate. Default: 128.

  • max_time (None or float, optional) – The maximum amount of time to run for. Use None for no limit. You can also set an estimated execution ‘rate’ here like 'rate:1e9' that will terminate the search when the estimated FLOPs of the best contraction found divided by the rate is greater than the time spent searching, allowing quick termination on easy contractions.

  • parallel ('auto', False, True, int, or distributed.Client) – Whether to parallelize the search.

  • slicing_opts (dict, optional) – If supplied, once a trial contraction path is found, try slicing with the given options, and then update the flops and size of the trial with the sliced versions.

  • slicing_reconf_opts (dict, optional) – If supplied, once a trial contraction path is found, try slicing interleaved with subtree reconfiguation with the given options, and then update the flops and size of the trial with the sliced and reconfigured versions.

  • reconf_opts (dict, optional) – If supplied, once a trial contraction path is found, try subtree reconfiguation with the given options, and then update the flops and size of the trial with the reconfigured versions.

  • optlib ({'baytune', 'nevergrad', 'chocolate', 'skopt'}, optional) – Which optimizer to sample and train with.

  • space (dict, optional) – The hyper space to search, see get_hyper_space for the default.

  • score_compression (float, optional) – Raise scores to this power in order to compress or accentuate the differences. The lower this is, the more the selector will sample from various optimizers rather than quickly specializing.

  • max_training_steps (int, optional) – The maximum number of trials to train the optimizer with. Setting this can be helpful when the optimizer itself becomes costly to train (e.g. for Gaussian Processes).

  • progbar (bool, optional) – Show live progress of the best contraction found so far.

  • optlib_opts – Supplied to the hyper-optimizer library initialization.

plot_trials#
plot_trials_alt#
plot_scatter#
plot_scatter_alt#
property minimize#
property parallel#
property tree#
property path#
setup(inputs, output, size_dict)#
get_score(trial)#
_maybe_cancel_futures()#
_maybe_report_result(setting, trial)#
_gen_results(repeats, trial_fn, trial_args)#
_get_and_report_next_future()#
_gen_results_parallel(repeats, trial_fn, trial_args)#
search(inputs, output, size_dict)#

Run this optimizer and return the ContractionTree for the best path it finds.

get_tree()#

Return the ContractionTree for the best path found.

__call__(inputs, output, size_dict, memory_limit=None)#

opt_einsum interface, returns direct path.

get_trials(sort=None)#
print_trials(sort=None)#
to_df()#
class cotengra.ReusableHyperOptimizer(*opt_args, directory=None, overwrite=False, set_surface_order=False, hash_method='a', cache_only=False, **opt_kwargs)#

Bases: opt_einsum.paths.PathOptimizer

Like HyperOptimizer but it will re-instantiate the optimizer whenever a new contraction is detected, and also cache the paths found.

Parameters:
  • opt_args – Supplied to HyperOptimizer.

  • directory (None or str, optional) – If specified use this directory as a persistent cache.

  • overwrite (bool, optional) – If True, the optimizer will always run, overwriting old results in the cache. This can be used to update paths with deleting the whole cache.

  • set_surface_order (bool, optional) – If True, when reloading a path to turn into a ContractionTree, the ‘surface order’ of the path (used for compressed paths), will be set manually to the order the disk path is.

  • hash_method ({'a', ...}, optional) – The method used to hash the contraction tree. The default, 'a', is faster but doesn’t recognize when indices are permuted.

  • cache_only (bool, optional) – If True, the optimizer will only use the cache, and will raise KeyError if a contraction is not found.

  • opt_kwargs – Supplied to HyperOptimizer.

property last_opt#
hash_query(inputs, output, size_dict)#

Hash the contraction specification, returning this and whether the contraction is already present as a tuple.

_compute_path(inputs, output, size_dict)#
update_from_tree(tree, overwrite=True)#

Explicitly add the contraction that tree represents into the cache. For example, if you have manually improved it via reconfing. If overwrite=False and the contracton is present already then do nothing.

__call__(inputs, output, size_dict, memory_limit=None)#
search(inputs, output, size_dict)#
cleanup()#
cotengra.hash_contraction(inputs, output, size_dict, method='a')#

Compute a hash for a particular contraction geometry.

cotengra.plot_contractions(tree, x='peak-size', y='flops', color='stage', size='scaling', point_opacity=0.8, color_scheme='viridis_r', x_scale='log', y_scale='log', figsize=(6, 4), return_fig=False)#
cotengra.plot_contractions_alt(tree, x='peak-size', y='flops', color='stage', size='scaling', width=400, height=400, point_opacity=0.8, color_scheme='lightmulti', x_scale='log', y_scale='log', color_scale='log', size_scale='linear')#
cotengra.plot_scatter(self, x='size', y='flops', figsize=(5, 5), return_fig=False)#
cotengra.plot_scatter_alt(self, x='size', y='flops', color='run:Q', color_scheme='purplebluegreen', shape='method:N', width=400, height=400)#

Plot the trials total flops vs max size.

cotengra.plot_slicings(slice_finder, color_scheme='RdYlBu_r', relative_flops=False, figsize=(6, 3), point_opacity=0.8, return_fig=False)#
cotengra.plot_slicings_alt(slice_finder, color_scheme='redyellowblue', relative_flops=False)#
cotengra.plot_tree(tree, layout='ring', layout_hypergraph=None, k=0.01, iterations=500, span=None, order=None, order_y_pow=1.0, edge_scale=1.0, node_scale=1.0, highlight=(), edge_colormap='GnBu', node_colormap='YlOrRd', edge_max_width=None, node_max_size=None, figsize=(5, 5), return_fig=False, raw_edge_color=None, raw_edge_alpha=None, tree_root_height=True, tree_alpha=0.8, colorbars=True, plot_raw_graph=True, plot_leaf_labels=False, ax=None)#

Plot a contraction tree using matplotlib.

cotengra.plot_tree_ring(tree, **kwargs)#
cotengra.plot_tree_tent(tree, **kwargs)#
cotengra.plot_tree_span(tree, **kwargs)#
cotengra.plot_trials(self, y='score', figsize=(8, 3), **kwargs)#
cotengra.plot_trials_alt(self, y=None, width=800, height=300)#

Plot the trials interactively using altair.

cotengra.UniformOptimizer#

Does no gaussian process tuning by default, just randomly samples - requires no optimization library.

cotengra.QuasiRandOptimizer#

Does no gaussian process tuning by default, just randomly samples but in a more ‘even’ way than purely random - requires chocolate.

cotengra.HyperCompressedOptimizer(chi=None, methods=('greedy-compressed', 'greedy-span', 'kahypar-agglom'), minimize='max-compressed', **kwargs)#

Instantiates a HyperOptimizer but with default arguments applicable to compressed path finding.

cotengra.ReusableHyperCompressedOptimizer(chi=None, methods=('greedy-compressed', 'greedy-span', 'kahypar-agglom'), set_surface_order=True, minimize='max-compressed', **kwargs)#

Instantiates a HyperOptimizer but with default arguments applicable to compressed path finding.

cotengra.HyperMultiOptimizer(*args, **kwargs)#
cotengra.hyper_optimize(inputs, output, size_dict, memory_limit=None, **opts)#