a Sic@sdZddlmZddlZddlmZgdZdZe gdZ d d e ee DZ dd d Z d dZddZddZdddZdS)z: Contains helper functions for opt_einsum testing scripts ) OrderedDictN) get_symbol) build_viewscompute_size_by_dictfind_contraction flop_countZabcdefghijklmopqABC)r r r r r r r r r r r r r cCsi|]\}}||qSr).0csrrN/var/www/html/django/DPS/env/lib/python3.9/site-packages/opt_einsum/helpers.py rcsVdur tg}|ddd}|D](}fdd|D}|tjj|q(|S)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) Nz->r,csg|] }|qSrr)rxdimension_dictrr 0rzbuild_views..)_default_dim_dictsplitappendnprandomrand)stringrviewstermstermdimsrrrrsrcCsd}|D]}|||9}q|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 rr)indicesidx_dictretirrrr5srcs\t|fddt|ddD}tj|}|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'}) c3s|]}|VqdSN)poprr) remainingrr ~rz#find_contraction..T)reverse)listsortedsetunionr) positions input_sets output_setinputs idx_contract idx_remain new_result idx_removedrr-rrRs+   rcCs,t||}td|d}|r$|d7}||S)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_factorrrrrs  rr Fcsx|durtj|||d}ddt|D} gtfddt|Dfdd} ttjt| D]\\} } | |kr| | | 7<q|tjd |} | | | vrtjd |} q| | | 7<q||r&t |}tjd |<t|D]} | | |7<q|7d tjd d | }fdd| D}||f}|rt|f7}|S)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)] Nr cSsg|]}dqS)r)r_rrrrrz!rand_equation..c3s(|] }t|tjdfVqdS)rN)rrrrandintr,)d_maxd_minrrr/rz rand_equation..c3s<tD].\}}|kr*||Vq|V|VqdSr*) enumerater)r)ix)n_outoutput size_dictrrgens  zrand_equation..genrrrEz{}->{}rcs"g|]}tfdd|DqS)c3s|]}|VqdSr*r)rrKrNrrr/rz+rand_equation...)tuple)roprPrrrr) rrseedrangerrJ permutationr1rGrjoinformat)nregrLrIrHrSZ global_dimZreturn_size_dictZnum_indsr8rOr)rKwhereZgdimeqshapesr(r)rHrIrLrMrNr rand_equations64     r])N)rr rDNFF)__doc__ collectionsrnumpyrparserr__all__Z _valid_charsarrayZ_sizesziprrrrrr]rrrrs   #7'