&VfGddlmZddlmZddlmZddlmZddlmZddl m Z GddeZ ed d gd Z d Z Gd deZeddgdZdZGddeZeddgdZdZGddeZeddgdZdZGdd eZed!d"gd#Zd$ZGd%d&eZed'd(gd)Zd*ZGd+d,eZed-d.gdOd1ZGd2d3eZed4d5gdPd7Z Gd8d9eZ!ed:d;gd<Z"d=Z#Gd>d?eZ$ed@dAgdQdBZ%dQdCZ&GdDdEeZ'edFdGgdRdIZ(dRdJZ)dKZ*dLZ+dMZ,dNZ-d/S)S)backend) keras_export) KerasTensor)any_symbolic_tensors) Operation) reduce_shapec*eZdZfdZdZdZxZS)CholeskycHtdSNsuper__init__self __class__s Q/var/www/html/software/conda/lib/python3.11/site-packages/keras/src/ops/linalg.pyrzCholesky.__init__  c t|Sr ) _choleskyrxs rcallz Cholesky.call s||rcrt|t|t|j|jSr  _assert_2d_assert_squarershapedtypers rcompute_output_speczCholesky.compute_output_spec/1 q17AG,,,r__name__ __module__ __qualname__rrr! __classcell__rs@rr r sV-------rr zkeras.ops.choleskyzkeras.ops.linalg.choleskyct|fr!t|St|S)aComputes the Cholesky decomposition of a positive semi-definite matrix. Args: x: Input tensor of shape `(..., M, M)`. Returns: A tensor of shape `(..., M, M)` representing the lower triangular Cholesky factor of `x`. )rr symbolic_callrrs rcholeskyr,s:QD!!+zz''*** Q<<rctj|}t|t| tj|S#t $r}td|d}~wwxYw)NzCholesky decomposition failed: )rconvert_to_tensorrrlinalgr, Exception ValueErrorres rrr's!!$$AqMMM1@~&&q))) @@@>1>>???@sA A4A//A4c*eZdZfdZdZdZxZS)DetcHtdSr r rs rrz Det.__init__3rrc t|Sr )_detrs rrzDet.call6 Awwrct|t|t|jdd|jSNrrs rr!zDet.compute_output_spec9s71 q173B3<111rr#r(s@rr5r51sV2222222rr5z keras.ops.detzkeras.ops.linalg.detct|fr!t|St|S)zComputes the determinant of a square tensor. Args: x: Input tensor of shape `(..., M, M)`. Returns: A tensor of shape `(...,)` represeting the determinant of `x`. )rr5r*r8r+s rdetr>?9QD!!&uu""1%%% 77Nrctj|}t|t|tj|Sr )rr.rrr/r>r+s rr8r8OA!!$$AqMMM1 >  a  rc*eZdZfdZdZdZxZS)EigcHtdSr r rs rrz Eig.__init__Xrrc t|Sr )_eigrs rrzEig.call[r9rct|t|t|jdd|jt|j|jfSNrrrrr rs rr!zEig.compute_output_spec^Oq1  ag . .  ) )  rr#r(s@rrCrCVsV       rrCz keras.ops.eigzkeras.ops.linalg.eigct|fr!t|St|S)a$Computes the eigenvalues and eigenvectors of a square matrix. Args: x: Input tensor of shape `(..., M, M)`. Returns: A tuple of two tensors: a tensor of shape `(..., M)` containing eigenvalues and a tensor of shape `(..., M, M)` containing eigenvectors. )rrCr*rFr+s reigrMgr?rctj|}t|t|tj|Sr )rr.rrr/rMr+s rrFrFwsA!!$$A1qMMM >  a  rc*eZdZfdZdZdZxZS)EighcHtdSr r rs rrz Eigh.__init__rrc t|Sr )_eighrs rrz Eigh.calls Qxxrct|t|t|jdd|jt|j|jfSrHrJrs rr!zEigh.compute_output_specrKrr#r(s@rrPrP~sV       rrPzkeras.ops.eighzkeras.ops.linalg.eighct|fr!t|St|S)a)Computes the eigenvalues and eigenvectors of a complex Hermitian. Args: x: Input tensor of shape `(..., M, M)`. Returns: A tuple of two tensors: a tensor of shape `(..., M)` containing eigenvalues and a tensor of shape `(..., M, M)` containing eigenvectors. )rrPr*rSr+s reighrVs9QD!!'vv##A&&& 88Orctj|}t|t|tj|Sr )rr.rrr/rVr+s rrSrSsA!!$$A1qMMM >  q ! !!rc*eZdZfdZdZdZxZS)InvcHtdSr r rs rrz Inv.__init__rrc t|Sr )_invrs rrzInv.callr9rcrt|t|t|j|jSr rrs rr!zInv.compute_output_specr"rr#r(s@rrYrYsV-------rrYz keras.ops.invzkeras.ops.linalg.invct|fr!t|St|S)zComputes the inverse of a square tensor. Args: x: Input tensor of shape `(..., M, M)`. Returns: A tensor of shape `(..., M, M)` representing the inverse of `x`. )rrYr*r\r+s rinvr_r?rctj|}t|t|tj|Sr )rr.rrr/r_r+s rr\r\rArc*eZdZfdZdZdZxZS)LuFactorcHtdSr r rs rrzLuFactor.__init__rrc t|Sr ) _lu_factorrs rrz LuFactor.calls!}}rct||jdd}|jdd\}}t||}t|||fz|jt||fz|jfSr;)rrminrr )rr batch_shapemnks rr!zLuFactor.compute_output_specst1 gcrcl wrss|1 1II  q!f,ag 6 6  qd*AG 4 4  rr#r(s@rrbrbsV       rrbzkeras.ops.lu_factorzkeras.ops.linalg.lu_factorct|fr!t|St|S)a@Computes the lower-upper decomposition of a square matrix. Args: x: A tensor of shape `(..., M, M)`. Returns: A tuple of two tensors: a tensor of shape `(..., M, M)` containing the lower and upper triangular matrices and a tensor of shape `(..., M)` containing the pivots. )rrbr*rer+s r lu_factorrms:QD!!+zz''*** a==rc tj|}t|tjdkr6 t|n%#t$r}t d|dd}~wwxYwtj|S)N tensorflowzLU decomposition failed: zG. LU decomposition is only supported for square matrices in Tensorflow.)rr.rrr1r/rmr2s rreres!!$$AqMMML((  1       ?A???   > # #A & &&sA A.A))A.c,eZdZdfd ZdZdZxZS)NormNFctt|tr|dvrt d|t|t r|g}||_||_||_dS)N)fronuczXInvalid `ord` argument. Expected one of {'fro', 'nuc'} when using string. Received: ord=) rr isinstancestrr1intordaxiskeepdims)rrxryrzrs rrz Norm.__init__s  c3   .(( +%(++ dC  6D   rc ftj|j}d|vs|dkrtj}|j/t t t|j}n|j}t|}|dkr1t|j trtd|j |dkrC|j dddtdtd dd dd f vrtd |j tt|j|j|j |S)Nrwboolz6Invalid `ord` argument for vector norm. Received: ord=rsrtinfz-infrIr<z6Invalid `ord` argument for matrix norm. Received: ord=)ryrz)r )rstandardize_dtyper floatxrytuplerangelenrrurxrvr1floatrrrz)rr output_dtyperynum_axess rr!zNorm.compute_output_specsO099 L LF$:$:">++L 9 s17||,,--DD9Dt99 q==Z#66=,!%,, ]]tx    %LL &MM   0 ,!%,,  ty4= I I I    rctj|}tj||j|j|jS)Nrxryrz)rr.r/normrxryrzrs rrz Norm.call1s@  %a ( (~"" 48$)dm#   rNNFr$r%r&rr!rr'r(s@rrqrqs\ ! ! ! ! ! !    D       rrqzkeras.ops.normzkeras.ops.linalg.normNFct|fr%t||||Stj|}tj||||S)aMMatrix or vector norm. This function is able to return one of eight different matrix norms, or one of an infinite number of vector norms (described below), depending on the value of the `ord` parameter. Args: x: Input tensor. ord: Order of the norm (see table under Notes). The default is `None`. axis: If `axis` is an integer, it specifies the axis of `x` along which to compute the vector norms. If `axis` is a 2-tuple, it specifies the axes that hold 2-D matrices, and the matrix norms of these matrices are computed. keepdims: If this is set to `True`, the axes which are reduced are left in the result as dimensions with size one. Note: For values of `ord < 1`, the result is, strictly speaking, not a mathematical 'norm', but it may still be useful for various numerical purposes. The following norms can be calculated: - For matrices: - `ord=None`: Frobenius norm - `ord="fro"`: Frobenius norm - `ord="nuc"`: nuclear norm - `ord=np.inf`: `max(sum(abs(x), axis=1))` - `ord=-np.inf`: `min(sum(abs(x), axis=1))` - `ord=0`: not supported - `ord=1`: `max(sum(abs(x), axis=0))` - `ord=-1`: `min(sum(abs(x), axis=0))` - `ord=2`: 2-norm (largest sing. value) - `ord=-2`: smallest singular value - other: not supported - For vectors: - `ord=None`: 2-norm - `ord="fro"`: not supported - `ord="nuc"`: not supported - `ord=np.inf`: `max(abs(x))` - `ord=-np.inf`: `min(abs(x))` - `ord=0`: `sum(x != 0)` - `ord=1`: as below - `ord=-1`: as below - `ord=2`: as below - `ord=-2`: as below - other: `sum(abs(x)**ord)**(1./ord)` Returns: Norm of the matrix or vector(s). Example: >>> x = keras.ops.reshape(keras.ops.arange(9, dtype="float32") - 4, (3, 3)) >>> keras.ops.linalg.norm(x) 7.7459664 r)rrqr*rr.r/r)rrxryrzs rrr8sjpQD!!L$:::HHKKK!!$$A >  qcx  H HHrc,eZdZdfd ZdZdZxZS)Qrreducedct|dvrtd|||_dS)N>rcompletez]`mode` argument value not supported. Expected one of {'reduced', 'complete'}. Received: mode=)rrr1mode)rrrs rrz Qr.__init__wsV  . . .)"&))   rct|jdkrtd|j|jd}|jd}||td|jt||}t |jdd}|jdkr6t |||fz|jt |||fz|jfSt |||fz|jt |||fz|jfS)Nr~z5Input should have rank >= 2. Received: input.shape = r<rIzOInput should have its last 2 dimensions fully-defined. Received: input.shape = r)rr )rrr1rgrrrr )rrrirjrkbases rr!zQr.compute_output_specs3 qw<>> x = keras.ops.convert_to_tensor([[1., 2.], [3., 4.], [5., 6.]]) >>> q, r = qr(x) >>> print(q) array([[-0.16903079 0.897085] [-0.5070925 0.2760267 ] [-0.8451542 -0.34503305]], shape=(3, 2), dtype=float32) r)rrr*rr.r/r)rrs rrrs]0QD!!.t}}}**1---!!$$A >  QT  * **rc*eZdZfdZdZdZxZS)SolvecHtdSr r rs rrzSolve.__init__rrc"t||Sr )_solverabs rrz Solve.callsa||rct|t|t|t||t |j|jSr rr _assert_1d_assert_a_b_compatrrr rs rr!zSolve.compute_output_specJ1 q1 1a   17AG,,,rr#r(s@rrrsV-------rrzkeras.ops.solvezkeras.ops.linalg.solvect||fr"t||St||SaSolves a linear system of equations given by `a x = b`. Args: a: A tensor of shape `(..., M, M)` representing the coefficients matrix. b: A tensor of shape `(..., M)` or `(..., M, N)` represeting the right-hand side or "dependent variable" matrix. Returns: A tensor of shape `(..., M)` or `(..., M, N)` representing the solution of the linear system. Returned shape is identical to `b`. )rrr*rrrs rsolvers@QF##+ww$$Q*** !Q<<rc tj|}tj|}t|t|t |t ||tj||Sr )rr.rrrrr/rrs rrrsn!!$$A!!$$AqMMM1qMMMq! >  1 % %%rc,eZdZdfd ZdZdZxZS)SolveTriangularFcVt||_dSr )rrlower)rrrs rrzSolveTriangular.__init__s$  rc.t|||jSr )_solve_triangularrrs rrzSolveTriangular.calls Atz222rct|t|t|t||t |j|jSr rrs rr!z#SolveTriangular.compute_output_specrrFr#r(s@rrrs[333-------rrzkeras.ops.solve_triangularz!keras.ops.linalg.solve_triangularct||fr#t|||St|||Sr)rrr*rrrrs rsolve_triangularrsH QF##:u%%33Aq999 Q5 ) ))rctj|}tj|}t|t|t |t ||tj|||Sr )rr.rrrrr/rrs rrrsp!!$$A!!$$AqMMM1qMMMq! > * *1a 7 77rc,eZdZdfd ZdZdZxZS)SVDTcdt||_||_dSr )rr full_matrices compute_uv)rrrrs rrz SVD.__init__s, *$rc8t||j|jSr )_svdrrrs rrzSVD.call#sAt)4?;;;rct||jdd\}}|jdd}|t||fz}|jr|||fz}|||fz}n*||t||fz}|t|||fz}|jr>t ||jt ||jt ||jfSt ||jSr;)rrrgrrrr )rrrowscolumnsbatchess_shapeu_shapev_shapes rr!zSVD.compute_output_spec&s1  g'#2#,Sw//11   >t ,G' 22GGs4'9'9 ::GT7!3!3W ==G ? GQW--GQW--GQW--  7AG,,,rTTr#r(s@rrrs[%%%%%% <<<-------rrz keras.ops.svdzkeras.ops.linalg.svdTct|fr#t|||St|||S)aComputes the singular value decomposition of a matrix. Args: x: Input tensor of shape `(..., M, N)`. Returns: A tuple of three tensors: a tensor of shape `(..., M, M)` containing the left singular vectors, a tensor of shape `(..., M, N)` containing the singular values and a tensor of shape `(..., N, N)` containing the right singular vectors. )rrr*rrrrs rsvdr;sFQD!!?=*--;;A>>> =* - --rctj|}t|tj|||Sr )rr.rr/rrs rrrNs7!!$$AqMMM >  a ; ;;rcD|D]}|jdkrtddS)Nr}z= 1. Received scalar input {a}.ndimr1arraysrs rrrTsB  6A::-  rcD|D]}|jdkrtddS)Nr~zFExpected input to have rank >= 2. Received input with shape {a.shape}.rrs rrr]sB  6A::7  rcn|D]1}|jdd\}}||krtd|j2dS)Nr<z?Expected a square matrix. Received non-square input with shape )rr1)rrrirjs rrrfse wrss|1 66B89BB  rc@|j|jkr=|jd|jdkrtd|jd|jdS|j|jdz kr;|jd|jdkr!td|jd|jdSdS)Nr<zbIncompatible shapes between `a` and `b`. Expected `a.shape[-2] == b.shape[-2]`. Received: a.shape=z , b.shape=r}rIzbIncompatible shapes between `a` and `b`. Expected `a.shape[-1] == b.shape[-1]`. Received: a.shape=)rrr1rs rrrpsv 72;!'"+ % %B%&WBB89BB  & % 16A:   72;!'"+ % %B%&WBB89BB    % %rrrrr). keras.srcrkeras.src.api_exportrkeras.src.backendrrkeras.src.ops.operationrkeras.src.ops.operation_utilsrr r,rr5r>r8rCrMrFrPrVrSrYr_r\rbrmrerqrrrrrrrrrrrrrrrrrrrs&------))))))222222------666666 - - - - -y - - -#%@ABB  CB  @@@ 2 2 2 2 2) 2 2 2 6788  98 !!!     )   " 6788  98 !!!     9   "!89::  ;:  """ - - - - -) - - - 6788  98 !!!     y   &$&BCDDED" ' ' '6 6 6 6 6 96 6 6 r!89:::I:I:I;::Iz(4(4(4(4(4(4(4(4V~4566+++76+: - - - - -I - - -  ":;<<=<$&&&-----i---"!#FG****$8888-----)---> 6788...98.$<<<< r