opt_einsum.paths.optimal

opt_einsum.paths.optimal(input_sets, output_set, idx_dict, memory_limit)[source]

Computes all possible pair contractions, sieves the results based on memory_limit and returns the lowest cost path. This algorithm scales factorial with respect to the elements in the list input_sets.

Parameters:
  • input_sets (list) – List of sets that represent the lhs side of the einsum subscript
  • output_set (set) – Set that represents the rhs side of the overall einsum subscript
  • idx_dict (dictionary) – Dictionary of index sizes
  • memory_limit (int) – The maximum number of elements in a temporary array
Returns:

path – The optimal contraction order within the memory limit constraint.

Return type:

list

Examples

>>> isets = [set('abd'), set('ac'), set('bdc')]
>>> oset = set('')
>>> idx_sizes = {'a': 1, 'b':2, 'c':3, 'd':4}
>>> optimal(isets, oset, idx_sizes, 5000)
[(0, 2), (0, 1)]