,Vh XdZddlmZmZmZmZmZmZmZm Z ddl m Z m Z gdZ dZgdZeeeeZe deedeed efd Ze deedeeefd efd Zdeded efd Zd eedee de d eeeee e e ffdZdeedededeeefd ef dZde d e fdZy)z9Contains helper functions for opt_einsum testing scripts.)Any CollectionDict FrozenSetIterableListTupleoverload)ArrayIndexType ArrayType)compute_size_by_dictfind_contraction flop_countabcdefghijklmopqABC)rrrrrrrrrrrrrindicesidx_dictreturncyNrrs B/home/dcms/DCMS/lib/python3.12/site-packages/opt_einsum/helpers.pyr r sNQcyrrrs rr r sUXrc(d}|D] }|||z} |S)aComputes the product of the elements in indices based on the dictionary idx_dict. Parameters ---------- indices : iterable Indices to base the product on. idx_dict : dictionary Dictionary of index _sizes Returns: ------- ret : int The resulting product. Examples: -------- >>> compute_size_by_dict('abbc', {'a': 2, 'b':3, 'c':5}) 90 r)rrretis rr r s+, C  x{ Jr positions input_sets output_setct|fdt|dD}tj|}|j}||z}||z }j ||||fS)aFinds the contraction for a given set of input and output sets. Parameters ---------- positions : iterable Integer positions of terms used in the contraction. 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 Returns: ------- new_result : set The indices of the resulting contraction remaining : list List of sets that have not been contracted, the new set is appended to the end of this list idx_removed : set Indices removed from the entire contraction idx_contraction : set The indices used in the current contraction Examples: -------- # A simple dot product test case >>> pos = (0, 1) >>> isets = [set('ab'), set('bc')] >>> oset = set('ac') >>> find_contraction(pos, isets, oset) ({'a', 'c'}, [{'a', 'c'}], {'b'}, {'a', 'b', 'c'}) # A more complex case with additional terms in the contraction >>> pos = (0, 2) >>> isets = [set('abd'), set('ac'), set('bdc')] >>> oset = set('ac') >>> find_contraction(pos, isets, oset) ({'a', 'c'}, [{'a', 'c'}, {'a', 'c'}], {'b', 'd'}, {'a', 'b', 'c', 'd'}) c3@K|]}j|ywr)pop).0r$ remainings r z#find_contraction.._s H1immA HsT)reverse)listsorted frozensetunionappend) r%r&r'inputs idx_contract idx_remain new_result idx_removedr,s @rrr2srXZ I Hy$(G HF??F+L!!!9-Jl*J+K Z y+| ;;ridx_contractioninner num_termssize_dictionarycPt||}td|dz }|r|dz }||zS)aComputes the number of FLOPS in the contraction. Parameters ---------- idx_contraction : iterable The indices involved in the contraction inner : bool Does this contraction require an inner product? num_terms : int The number of terms in a contraction size_dictionary : dict The size of each of the indices in idx_contraction Returns: ------- flop_count : int The total number of FLOPS required for the contraction. Examples: -------- >>> flop_count('abc', False, 1, {'a': 2, 'b':3, 'c':5}) 30 >>> flop_count('abc', True, 2, {'a': 2, 'b':3, 'c':5}) 60 r")r max)r9r:r;r< overall_size op_factors rrrjs8B(ILAy1}%I Q ) ##rarrayct|dryy)N__array_interface__TF)hasattr)rAs rhas_array_interfacerEsu+,rN)__doc__typingrrrrrrr r opt_einsum.typingr r __all__ _valid_chars_sizesdictzip_default_dim_dictintr strrboolrrErrrrRs??TTT7 D$ B\623 Q(3-Q49QQ Q X*S/XT#s(^XPSX X#85<#5<^$5<5< 9S>4/ OP 5