~\;jdZddlmZddlZddlmZgdZdZejgdZ e ee Dcic]\}}|| c}}Z dd Z d Zd Zd Zdd Zycc}}w)z: Contains helper functions for opt_einsum testing scripts ) OrderedDictN) get_symbol) build_viewscompute_size_by_dictfind_contraction flop_countabcdefghijklmopqABC)r r r rr r r rr r r r r c|t}g}|jddjd}|D]?}|Dcgc]}|| }}|jtjj |A|Scc}w)a Builds random numpy arrays for testing. Parameters ---------- string : list of str List of tensor strings to build dimension_dict : dictionary Dictionary of index _sizes Returns ------- ret : list of np.ndarry's The resulting views. Examples -------- >>> view = build_views(['abbc'], {'a': 2, 'b':3, 'c':5}) >>> view[0].shape (2, 3, 3, 5) z->r,)_default_dim_dictsplitappendnprandomrand)stringdimension_dictviewstermstermxdimss [G:\00. PROJECTS\API\Inventory\templateJSON\kerjaOCR\Lib\site-packages\opt_einsum/helpers.pyrrsz0* E LL q ! ' ' ,E+/04aq!40 RYY^^T*+ L1s A4c(d}|D] }|||z} |S)a Computes 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)indicesidx_dictretis r rr5s&. C  x{ Jct|fdt|dD}tj|}|j}||z}||z }j ||||fS)a Finds 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|ywN)pop).0r& remainings r z#find_contraction..~s H(G1immA(GsT)reverse)listsortedsetunionr) positions input_sets output_setinputs idx_contract idx_remain new_result idx_removedr-s @r rrRsrVZ I Hy$(G HF99f%L!!!9-Jl*J*,K Z y+| ;;r'cPt||}td|dz }|r|dz }||zS)a Computes 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}) 90 >>> flop_count('abc', True, 2, {'a': 2, 'b':3, 'c':5}) 270 r)rmax)idx_contractioninner num_termssize_dictionary overall_size op_factors r r r s7>(ILAy1}%I Q ) ##r'c|tjj|||zdzz}t|D cgc]} d} } gt fdt|Dfd} t tjj t| D]t\} } | |kr| | xx| z cc<tjjd|}| | |vr(tjjd|}| | |vr(| |xx| z cc<v|rSt|}tjjdz|<t|D]} | | xx|z cc<|z djtjj djdj| }| Dcgc]}tfd |D}}||f}|r|fz }|Scc} wcc}w) aGenerate a random contraction and shapes. Parameters ---------- n : int Number of array arguments. reg : int 'Regularity' of the contraction graph. This essentially determines how many indices each tensor shares with others on average. n_out : int, optional Number of output indices (i.e. the number of non-contracted indices). Defaults to 0, i.e., a contraction resulting in a scalar. d_min : int, optional Minimum dimension size. d_max : int, optional Maximum dimension size. seed: int, optional If not None, seed numpy's random generator with this. global_dim : bool, optional Add a global, 'broadcast', dimension to every operand. return_size_dict : bool, optional Return the mapping of indices to sizes. Returns ------- eq : str The equation string. shapes : list[tuple[int]] The array shapes. size_dict : dict[str, int] The dict of index sizes, only returned if ``return_size_dict=True``. Examples -------- >>> eq, shapes = rand_equation(n=10, reg=4, n_out=5, seed=42) >>> eq 'oyeqn,tmaq,skpo,vg,hxui,n,fwxmr,hitplcj,kudlgfv,rywjsb->cebda' >>> shapes [(9, 5, 4, 5, 4), (4, 4, 8, 5), (9, 4, 6, 9), (6, 6), (6, 9, 7, 8), (4,), (9, 3, 9, 4, 9), (6, 8, 4, 6, 8, 6, 3), (4, 7, 8, 8, 6, 9, 6), (9, 5, 3, 3, 9, 5)] r c3zK|]2}t|tjjdzf4yw)rN)rrrrandint)r,r&d_maxd_mins r r.z rand_equation..s3jZiUVZ]BII,=,=eUQY,OPZi8;c3zKtD](\}}|krj||!||*ywr*) enumerater)r&ixn_outoutput size_dicts r genzrand_equation..gens>y)EAr5y b!*rJrrz{}->{}rc3(K|] }| ywr*r")r,rMrPs r r.z rand_equation..s/BbIbMBs) rrseedrangerrL permutationr0rGrjoinformattuple)nregrNrIrHrS global_dimreturn_size_dictnum_inds_r7rQr&rMwheregdimeqopshapesr%rOrPs ``` @@r rand_equationrdsh  t3w!|e#H( #(Qb(F # FjZ_`hZijjI 29900ce=>2 q5 1IOIII%%a+Eu % ))!Q/u % 5MR M?(#))++E519= $qA 1I I$WWRYY**62 3F &)6 2B;A A&Be/B//&F A v,C } Je$VBs G1G6r*)rr NFF)__doc__ collectionsrnumpyrparserr__all__ _valid_charsarray_sizesziprrrrr rd)css00r rqsz$ S$ K L&),&?@&?daQT&?@ F:4