vh\nddlZddlmZmZmZmZddlZddlZddl m Z ddl m Z ddl m Z ddl mZmZddlmZddlmZdd lmZdd lmZdd lmZmZdd lmZmZmZdd lm Z m!Z!m"Z"e!dZ#GddejHjJZ&eddddejNddde(deddde(e)ze*e+e,dfzdededzdedefdefdZ-eddddejNdddedeedeeezddde(e)ze*e+e,dfzdededzdedefdefdZ-e#ddddejNddddde(e)ze*e+e,dfzdededzdedefdef d Z-iZ.d!Z/edd"d#e(dede)e(ze*e+e,dfzde+e*e+e,dfeffd$Z0edd"dedeedeeezde)e(ze*e+e,dfzde+e*e+e,dfeff d%Z0e#dd"de)e(ze*e+e,dfzde+e*e+e,dfeffd&Z0d'Z1ejNdfde*ed(ee+e+e,dfe2e(e(ffd)Z3ejhe.ejj<y)*N)overloadAnyCallableSequence)config)core)dtypes)jit named_call) shape_poly)lax) PrecisionLike)util)canonicalize_sharding NamedSharding)Array ArrayLike DTypeLike)partition_list set_moduleunzip2z jax.numpyceZdZdZdZy) UnoptimizedzUnoptimized path for einsum.c&dgt|dz zS)N)rr)len)selfinputsargskwargss P/opt/face_recognition/venv/lib/python3.12/site-packages/jax/_src/numpy/einsum.py__call__zUnoptimized.__call__'s 8s6{Q ''N)__name__ __module__ __qualname____doc__r"r#r!rr%s $(r#rauto)outoptimize precisionpreferred_element_type _dot_general out_sharding subscriptoperandsr*r+.r,r-r.returncyNr()r0r*r+r,r-r.r/r1s r!einsumr5*s r#arraxescyr4r() r6r7r*r+r,r-r.r/r1s r!r5r56s r#c|g|}| tdt|dtr|dnd}|durdn|dur tn|} t d|D}|D chc]M} t| trt j | D]"} tj| s t| $O} } } | stj} n.tt| }tj|t } | |dd| d\}}t d |D}t#t$d d }| t'|| }t)t+j,d |}|||||||Scc} } w)aYEinstein summation JAX implementation of :func:`numpy.einsum`. ``einsum`` is a powerful and generic API for computing various reductions, inner products, outer products, axis reorderings, and combinations thereof across one or more input arrays. It has a somewhat complicated overloaded API; the arguments below reflect the most common calling convention. The Examples section below demonstrates some of the alternative calling conventions. Args: subscripts: string containing axes names separated by commas. *operands: sequence of one or more arrays corresponding to the subscripts. optimize: specify how to optimize the order of computation. In JAX this defaults to ``"auto"`` which produces optimized expressions via the opt_einsum_ package. Other options are ``True`` (same as ``"optimal"``), ``False`` (unoptimized), or any string supported by ``opt_einsum``, which includes ``"optimal"``, ``"greedy"``, ``"eager"``, and others. It may also be a pre-computed path (see :func:`~jax.numpy.einsum_path`). precision: either ``None`` (default), which means the default precision for the backend, a :class:`~jax.lax.Precision` enum value (``Precision.DEFAULT``, ``Precision.HIGH`` or ``Precision.HIGHEST``). preferred_element_type: either ``None`` (default), which means the default accumulation type for the input types, or a datatype, indicating to accumulate results to and return a result with that datatype. out: unsupported by JAX _dot_general: optionally override the ``dot_general`` callable used by ``einsum``. This parameter is experimental, and may be removed without warning at any time. Returns: array containing the result of the einstein summation. See also: :func:`jax.numpy.einsum_path` Examples: The mechanics of ``einsum`` are perhaps best demonstrated by example. Here we show how to use ``einsum`` to compute a number of quantities from one or more arrays. For more discussion and examples of ``einsum``, see the documentation of :func:`numpy.einsum`. >>> M = jnp.arange(16).reshape(4, 4) >>> x = jnp.arange(4) >>> y = jnp.array([5, 4, 3, 2]) **Vector product** >>> jnp.einsum('i,i', x, y) Array(16, dtype=int32) >>> jnp.vecdot(x, y) Array(16, dtype=int32) Here are some alternative ``einsum`` calling conventions to compute the same result: >>> jnp.einsum('i,i->', x, y) # explicit form Array(16, dtype=int32) >>> jnp.einsum(x, (0,), y, (0,)) # implicit form via indices Array(16, dtype=int32) >>> jnp.einsum(x, (0,), y, (0,), ()) # explicit form via indices Array(16, dtype=int32) **Matrix product** >>> jnp.einsum('ij,j->i', M, x) # explicit form Array([14, 38, 62, 86], dtype=int32) >>> jnp.matmul(M, x) Array([14, 38, 62, 86], dtype=int32) Here are some alternative ``einsum`` calling conventions to compute the same result: >>> jnp.einsum('ij,j', M, x) # implicit form Array([14, 38, 62, 86], dtype=int32) >>> jnp.einsum(M, (0, 1), x, (1,), (0,)) # explicit form via indices Array([14, 38, 62, 86], dtype=int32) >>> jnp.einsum(M, (0, 1), x, (1,)) # implicit form via indices Array([14, 38, 62, 86], dtype=int32) **Outer product** >>> jnp.einsum("i,j->ij", x, y) Array([[ 0, 0, 0, 0], [ 5, 4, 3, 2], [10, 8, 6, 4], [15, 12, 9, 6]], dtype=int32) >>> jnp.outer(x, y) Array([[ 0, 0, 0, 0], [ 5, 4, 3, 2], [10, 8, 6, 4], [15, 12, 9, 6]], dtype=int32) Some other ways of computing outer products: >>> jnp.einsum("i,j", x, y) # implicit form Array([[ 0, 0, 0, 0], [ 5, 4, 3, 2], [10, 8, 6, 4], [15, 12, 9, 6]], dtype=int32) >>> jnp.einsum(x, (0,), y, (1,), (0, 1)) # explicit form via indices Array([[ 0, 0, 0, 0], [ 5, 4, 3, 2], [10, 8, 6, 4], [15, 12, 9, 6]], dtype=int32) >>> jnp.einsum(x, (0,), y, (1,)) # implicit form via indices Array([[ 0, 0, 0, 0], [ 5, 4, 3, 2], [10, 8, 6, 4], [15, 12, 9, 6]], dtype=int32) **1D array sum** >>> jnp.einsum("i->", x) # requires explicit form Array(6, dtype=int32) >>> jnp.einsum(x, (0,), ()) # explicit form via indices Array(6, dtype=int32) >>> jnp.sum(x) Array(6, dtype=int32) **Sum along an axis** >>> jnp.einsum("...j->...", M) # requires explicit form Array([ 6, 22, 38, 54], dtype=int32) >>> jnp.einsum(M, (..., 0), (...,)) # explicit form via indices Array([ 6, 22, 38, 54], dtype=int32) >>> M.sum(-1) Array([ 6, 22, 38, 54], dtype=int32) **Matrix transpose** >>> y = jnp.array([[1, 2, 3], ... [4, 5, 6]]) >>> jnp.einsum("ij->ji", y) # explicit form Array([[1, 4], [2, 5], [3, 6]], dtype=int32) >>> jnp.einsum("ji", y) # implicit form Array([[1, 4], [2, 5], [3, 6]], dtype=int32) >>> jnp.einsum(y, (1, 0)) # implicit form via indices Array([[1, 4], [2, 5], [3, 6]], dtype=int32) >>> jnp.einsum(y, (0, 1), (1, 0)) # explicit form via indices Array([[1, 4], [2, 5], [3, 6]], dtype=int32) >>> jnp.transpose(y) Array([[1, 4], [2, 5], [3, 6]], dtype=int32) **Matrix diagonal** >>> jnp.einsum("ii->i", M) Array([ 0, 5, 10, 15], dtype=int32) >>> jnp.diagonal(M) Array([ 0, 5, 10, 15], dtype=int32) **Matrix trace** >>> jnp.einsum("ii", M) Array(30, dtype=int32) >>> jnp.trace(M) Array(30, dtype=int32) **Tensor products** >>> x = jnp.arange(30).reshape(2, 3, 5) >>> y = jnp.arange(60).reshape(3, 4, 5) >>> jnp.einsum('ijk,jlk->il', x, y) # explicit form Array([[ 3340, 3865, 4390, 4915], [ 8290, 9940, 11590, 13240]], dtype=int32) >>> jnp.tensordot(x, y, axes=[(1, 2), (0, 2)]) Array([[ 3340, 3865, 4390, 4915], [ 8290, 9940, 11590, 13240]], dtype=int32) >>> jnp.einsum('ijk,jlk', x, y) # implicit form Array([[ 3340, 3865, 4390, 4915], [ 8290, 9940, 11590, 13240]], dtype=int32) >>> jnp.einsum(x, (0, 1, 2), y, (1, 3, 2), (0, 3)) # explicit form via indices Array([[ 3340, 3865, 4390, 4915], [ 8290, 9940, 11590, 13240]], dtype=int32) >>> jnp.einsum(x, (0, 1, 2), y, (1, 3, 2)) # implicit form via indices Array([[ 3340, 3865, 4390, 4915], [ 8290, 9940, 11590, 13240]], dtype=int32) **Chained dot products** >>> w = jnp.arange(5, 9).reshape(2, 2) >>> x = jnp.arange(6).reshape(2, 3) >>> y = jnp.arange(-2, 4).reshape(3, 2) >>> z = jnp.array([[2, 4, 6], [3, 5, 7]]) >>> jnp.einsum('ij,jk,kl,lm->im', w, x, y, z) Array([[ 481, 831, 1181], [ 651, 1125, 1599]], dtype=int32) >>> jnp.einsum(w, (0, 1), x, (1, 2), y, (2, 3), z, (3, 4)) # implicit, via indices Array([[ 481, 831, 1181], [ 651, 1125, 1599]], dtype=int32) >>> w @ x @ y @ z # direct chain of matmuls Array([[ 481, 831, 1181], [ 651, 1125, 1599]], dtype=int32) >>> jnp.linalg.multi_dot([w, x, y, z]) Array([[ 481, 831, 1181], [ 651, 1125, 1599]], dtype=int32) .. _opt_einsum: https://github.com/dgasmith/opt_einsum Nz2The 'out' argument to jnp.einsum is not supported.rToptimalFc3XK|]"}t|dr|jn|$yw) __jax_array__N)hasattrr<).0ops r! zeinsum..%s/'*1_)E2##%2M's(*) einsum_calluse_blasr+c3@K|]^}}}}|t||fywr4) frozenset)r>abc_s r!r@zeinsum..6s#L 1a!9Q<+Ls)r)static_argnumsinline)namer5)NotImplementedError isinstancestrrtuplenpshaperis_constant_dimtype opt_einsum contract_pathnextiter_poly_einsum_handlersget_default_poly_einsum_handlerr _einsumr listrensure_arraylike_tuple) subscriptsr*r+r,r-r.r/r1spec path_typer?dnon_constant_dim_typesrYty contractions jit_einsumoperand_arrayss r!r5r5Csyv $8 $(_ R SS"8A;4!$$#t+i(eBSYa)'%''( ! 2s(;xx| 4#7#7#: 1g  ,,M d)* +B)--b2NOM( tdYH(LL|LL,7?4H* JT2J33HhGH. NL)*L, HH's E1res r!r@z/_default_poly_einsum_handler..FsEd1gn!3Es!) collections namedtupler=rSrUrm enumerateidrXrY) r1r rlxdummiesiremapping out_dummiesrhcontract_operandss r!r^r^Ds  7G*< =%4< >/07#5EQWWEEqww O)*+ >' >"+G"4 5$!QRUAX 5' 5(66J6J+|9DEAx1/EE L ((  > 5EsAC/C$C )r+rbcyr4r(rbr+r1s r! einsum_pathr}Ms ),r#cyr4r()r6r7r+r1s r!r}r}Ts ),r#c^|durd}n|dur t}tj|g|d|iS)aEvaluates the optimal contraction path without evaluating the einsum. JAX implementation of :func:`numpy.einsum_path`. This function calls into the opt_einsum_ package, and makes use of its optimization routines. Args: subscripts: string containing axes names separated by commas. *operands: sequence of one or more arrays corresponding to the subscripts. optimize: specify how to optimize the order of computation. In JAX this defaults to ``"auto"``. Other options are ``True`` (same as ``"optimize"``), ``False`` (unoptimized), or any string supported by ``opt_einsum``, which includes ``"optimize"``,, ``"greedy"``, ``"eager"``, and others. Returns: A tuple containing the path that may be passed to :func:`~jax.numpy.einsum`, and a printable object representing this optimal path. Examples: >>> key1, key2, key3 = jax.random.split(jax.random.key(0), 3) >>> x = jax.random.randint(key1, minval=-5, maxval=5, shape=(2, 3)) >>> y = jax.random.randint(key2, minval=-5, maxval=5, shape=(3, 100)) >>> z = jax.random.randint(key3, minval=-5, maxval=5, shape=(100, 5)) >>> path, path_info = jnp.einsum_path("ij,jk,kl", x, y, z, optimize="optimal") >>> print(path) [(1, 2), (0, 1)] >>> print(path_info) Complete contraction: ij,jk,kl->il Naive scaling: 4 Optimized scaling: 3 Naive FLOP count: 9.000e+3 Optimized FLOP count: 3.060e+3 Theoretical speedup: 2.941e+0 Largest intermediate: 1.500e+1 elements -------------------------------------------------------------------------------- scaling BLAS current remaining -------------------------------------------------------------------------------- 3 GEMM kl,jk->lj ij,lj->il 3 GEMM lj,ij->il il->il Use the computed path in :func:`~jax.numpy.einsum`: >>> jnp.einsum("ij,jk,kl", x, y, z, optimize=path) Array([[-754, 324, -142, 82, 50], [ 408, -50, 87, -29, 7]], dtype=int32) .. _opt_einsum: https://github.com/dgasmith/opt_einsum Tr:Fr+)rrXrYr|s r!r}r}\s<jH5}H  ! !* Kx K( KKr#cp|jtjtj |Sr4) translaterR maketransdictfromkeys)scharss r! _removecharsrs# S]]4==#78 99r#rhc h +,-./012t|d}|t|ts tdt j dt j |ddi\}nd}fd22fd}2fd}d } t|D]z\} \} } } | t|d z k(}t| }| jd \}.|jd }t| d k(rb|j| d }|\-tj-}|Dcgc] }||d k(s |}}||-|\}-||-|.\}-n2t| dk(rt|j| \+/|\,0| +,tj /0\+,| /0tj +,\/0tj,}tj0}|Dcgc]}||d k(r ||d k(r|}}|+,|\+,|Dcgc]}||d k(r ||d k(r|}}|/0|\/0|+,|.0z\+,|/0|.,z\/0t#,t#0z}|Dcgc] }||vs| }}t#,t#0z}.Dcgc] }||vs| }}t%,0fd|D\}}t&j(j*s>t-+,/0fd|Ds'Jd+j d,d/j d0dj/|} t%,0fd|D\}!}"| dj/|z}#t1,|#}$t10|#}%| |%z|$z--.k(r|"|!f||ff}&|ind|i}'|/+|&|fdi|'}n| |$z|%z-|sd}(n|-.k7rt.t|j2kDr4|j5|j2j7t.}|j21t9.1fd-D})t|j:1j5|)}(n|}(|!|"f||ff}&|(ind|(i}(|+/|&|fdi|(}ntt-t.cxk(rtt#-k(sJJt#-t#.k(sJ-.k7r*t9-fd.D}*t=j>||*}|jA|}t=jB|d |Scc}wcc}wcc}wcc}wcc}w)Nr5z`out_sharding` argument of `einsum` only supports NamedSharding instances. Please file a bug if this is not enough for your use case.return_weak_type_flagTFcDtj||jk7r|j}t j |t jd|j|jtk7rtj|Stj|S)Nr) r result_typermastyper reducerTarraybooladd bitwise_or)rur7r-s r!sumz_einsum..sumsz !34? (() *a ::a!QWW-!"Dcggd LL69nnd LLr#c|r3|Dcgc]}|j|}}||}t||}||fScc}wr4)indexr)operandnamesuniquesrOr7rs r! sum_uniquesz_einsum..sum_uniquessI,3 4Dekk$ 4d 4GT"g5'*e E>5s;c |jD]\}}|dkDs t|Dcgc] \}}||k(s |}}}tjt j d|j |} tj| |tj|d}||vr ||}|j|d} ||dd}|j|d|dz }||fScc}}w)Nrrr) itemsrsr _deltarTrmrUselect full_likereplace) rrcounts keep_namesrOcountrwnr7eyers r! sum_repeatsz_einsum..sum_repeatss||~ 5 e '.=s C(C(ctj}tt|jDcgc]1\}}||j |d xs|dk(xs |||d3}}}t |tt|j\}} tj||djfd| DfScc}}w)Nrrrc3(K|] }| ywr4r()r>rwrs r!r@z9_einsum..filter_singleton_dims..s3PE!H3Ps) rdefinitely_equalrsmapfindrUrr`rangendimr squeezejoin) rr other_shape other_nameseqrwjkeep sqez_axes keep_axess ` r!filter_singleton_dimsz&_einsum..filter_singleton_dimss  B!#k&6&6">? A17==#Q' ' K17 KbQ6K K AD A)$U7<<5H0IJIy ;;w *BGG3Pi3P,P PP As6Crz->,rrIc3bK|]&}j|j|f(ywr4)rr>r lhs_names rhs_namess r!r@z_einsum..s0$:()&/^^A%6 q8I$J$:,/c3K|]M}|vxrC|vxr=jj|jj|k(Oywr4)rUr)r>rOlhsrrhsrs r!r@z_einsum.. se0&   Mdi/ M )//$'(CIIiood6K,LL M0&sAAz-Incompatible reduction dimensions: lhs.shape=z lhs_names=z rhs.shape=z rhs_names=rc3bK|]&}j|j|f(ywr4rrs r!r@z_einsum..s0"=&'$-??1#5yq7I"J"=rr/r-)rcc3FK|]}j|ywr4r)r>rO result_namesrcs r!r@z_einsum..0s!P$tL$6$6t$<=Ps!) partitionsc3@K|]}j|ywr4r)r>rOrs r!r@z_einsum..Cs>5;;t$>s)"rrQrrPr check_user_dtype_supportedrrsrsortedsplitpoprqCounterrrTrUsetrrdynamic_shapesvalueallrrrcupdate_normalized_spec_for_avalrSmeshr transposeappend_convert_element_type)3r1rhr,r-r.r/output_weak_typerrrrwoperand_indicescontracted_names_seteinstrlast_contractioncontracted_names input_str input_namesrrrOr lhs_counts rhs_counts lhs_uniques rhs_uniqueslhs_or_rhs_namesrulhs_and_rhs_names batch_names lhs_batch rhs_batchbatch_names_strlhs_contrhs_cont deleted_namesremaining_lhs_namesremaining_rhs_namesdimension_numbersk_out_shardingdot_general_out_sharding inverse_specpermrrrrrrrcrs3 ` @@@@@@@@r!r_r_s6'|X>,j}&M  Q RR ##$:HE#/5/A/A 0/)-0/,,L  Q=FlN9N!OOi.3y>9 ,G15F0FQGkG#$:-8$::i  " " ( (C0&%0&-&: yykYK8yykYK 9 :& ,o!"=+;"==h%0@(AAm(MB(MB  336IIe , &1Iy3IJ , 4")<8 sC):I16L1!/1 "558KK%) "  %%<*?  \%6%6!7 7'..!!;;C > >d gt,g OOGitl " "8A;0F#3 55QI*IIPGs0 TTT T%- T*7T* T/"T/)6rqtypingrrrrnumpyrTrXjax._srcrrr jax._src.apir r jax._src.exportr jax._src.laxr jax._src.lax.laxrjax._src.numpyrjax._src.sharding_implsrrjax._src.typingrrr jax._src.utilrrrexportpaths PathOptimizerr dot_generalrRrr`rSrpr5r\r^r}rrDr__einsum_contract_path_DimExprr(r#r!rs44(&*H77<< K (*""00(  39#/3),     Dj4c3h00    &, 3:&      39#/3),    3- 8C=(    Dj4c3h00   &, 3:&     39#/3),yH yHDj4c3h00 yH  yH &, yH3:&yH yHyH|) 58,,,Sj4c3h00, 4c3h # %& , ,  58 , , 3-,8C=(,Sj4c3h00 ,  4c3h # %& , ,4:8LSj4c3h008L T%S/ "C '( 8L8Lt: m55km55sCx)C.#!EFGm5^.8-M-Mj))*r#