2VhR0ddlmZddlmZddlmZddlmZddlmZddl m Z GddeZ ed d gd Z d Z Gd deZeddgdZdZGddeZeddgdZdZGddeZeddgdZdZGdd eZed!d"gd#Zd$ZGd%d&eZed'd(gd)Zd*ZGd+d,eZed-d.gdQd0ZGd1d2eZed3d4gdRd5Z Gd6d7eZ!ed8d9gd:Z"d;Z#Gd<d=eZ$ed>d?gdSd@Z%dSdAZ&GdBdCeZ'edDdEgdTdFZ(dTdGZ)GdHdIeZ*edJdKgdUdLZ+dMZ,dNZ-dOZ.dPZ/y/)V)backend) keras_export) KerasTensor)any_symbolic_tensors) Operation) reduce_shapec*eZdZfdZdZdZxZS)Choleskyc"t|yNsuper__init__self __class__s D/home/dcms/DCMS/lib/python3.12/site-packages/keras/src/ops/linalg.pyrzCholesky.__init__  ct|Sr ) _choleskyrxs rcallz Cholesky.call s |rcnt|t|t|j|jSr  _assert_2d_assert_squarershapedtypers rcompute_output_speczCholesky.compute_output_spec&1 q177AGG,,r__name__ __module__ __qualname__rrr! __classcell__rs@rr r s-rr zkeras.ops.choleskyzkeras.ops.linalg.choleskycbt|frtj|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!z''** Q<rctj|}t|t| tjj |S#t $r}td|d}~wwxYw)NzCholesky decomposition failed: )rconvert_to_tensorrrlinalgr, Exception ValueErrorres rrr'sa!!!$AqM1@~~&&q)) @:1#>??@sA A(A##A(c*eZdZfdZdZdZxZS)Detc"t|yr r rs rrz Det.__init__2rrct|Sr )_detrs rrzDet.call5 Awrctt|t|t|jdd|jSNrrs rr!zDet.compute_output_spec8s,1 q1773B<11rr#r(s@rr5r51s2rr5z keras.ops.detzkeras.ops.linalg.detcbt|frtj|St|S)zComputes the determinant of a square tensor. Args: x: Input tensor of shape `(..., M, M)`. Returns: A tensor of shape `(...,)` representing the determinant of `x`. )rr5r*r8r+s rdetr>>*QD!u""1%% 7Nrctj|}t|t|tjj |Sr )rr.rrr/r>r+s rr8r8N6!!!$AqM1 >>  a  rc*eZdZfdZdZdZxZS)Eigc"t|yr r rs rrz Eig.__init__Vrrct|Sr )_eigrs rrzEig.callYr9rct|t|t|jdd|jt|j|jfSNrrrrr rs rr!zEig.compute_output_spec\Eq1  agg .  )  rr#r(s@rrCrCUs rrCz keras.ops.eigzkeras.ops.linalg.eigcbt|frtj|St|S)a$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 reigrMer?rctj|}t|t|tjj |Sr )rr.rrr/rMr+s rrFrFus6!!!$A1qM >>  a  rc*eZdZfdZdZdZxZS)Eighc"t|yr r rs rrz Eigh.__init__}rrct|Sr )_eighrs rrz Eigh.calls Qxrct|t|t|jdd|jt|j|jfSrHrJrs rr!zEigh.compute_output_specrKrr#r(s@rrPrP|s rrPzkeras.ops.eighzkeras.ops.linalg.eighcbt|frtj|St|S)a)Computes the eigenvalues and eigenvectors of a complex Hermitian. Args: x: Input tensor of shape `(..., M, M)`. Returns: A tuple of two tensors: a tensor of shape `(..., M)` containing eigenvalues and a tensor of shape `(..., M, M)` containing eigenvectors. )rrPr*rSr+s reighrVs*QD!v##A&& 8Orctj|}t|t|tjj |Sr )rr.rrr/rVr+s rrSrSs6!!!$A1qM >>  q !!rc*eZdZfdZdZdZxZS)Invc"t|yr r rs rrz Inv.__init__rrct|Sr )_invrs rrzInv.callr9rcnt|t|t|j|jSr rrs rr!zInv.compute_output_specr"rr#r(s@rrYrYs-rrYz keras.ops.invzkeras.ops.linalg.invcbt|frtj|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|tjj |Sr )rr.rrr/r_r+s rr\r\rArc*eZdZfdZdZdZxZS)LuFactorc"t|yr r rs rrzLuFactor.__init__rrct|Sr ) _lu_factorrs rrz LuFactor.calls !}rct||jdd}|jdd\}}t||}t|||fz|jt||fz|jfSr;)rrminrr )rr batch_shapemnks rr!zLuFactor.compute_output_specsl1 ggcrl wwrs|1 1I  q!f,agg 6  qd*AGG 4  rr#r(s@rrbrbs rrbzkeras.ops.lu_factorzkeras.ops.linalg.lu_factorcbt|frtj|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!z''** a=rctj|}t|tjdk(r t|tj j |S#t$r}t d|dd}~wwxYw)N tensorflowzLU decomposition failed: zG. LU decomposition is only supported for square matrices in Tensorflow.)rr.rrr1r/rmr2s rreres|!!!$AqML(  1  >> # #A &&  +A3/??  s A## B,A;;Bc,eZdZdfd ZdZdZxZS)Normct|t|tr|dvrt d|t|t r|g}||_||_||_y)N)fronuczXInvalid `ord` argument. Expected one of {'fro', 'nuc'} when using string. Received: ord=) rr isinstancestrr1intordaxiskeepdims)rrxryrzrs rrz Norm.__init__sd  c3 .( %%(E+ dC 6D   rc xtj|j}d|vs|dk(rtj}|j(t t t|j}n |j}t|}|dk(r2t|jtrtd|j|dk(rA|jdddtdtd dd dd f vrtd |jtt|j|j|j |S)Nrwboolz6Invalid `ord` argument for vector norm. Received: ord=rsrtinfz-infrIr<z6Invalid `ord` argument for matrix norm. Received: ord=)ryrzr )rstandardize_dtyper floatxrytuplerangelenrrurxrvr1floatrrrz)rr output_dtyperynum_axess rr!zNorm.compute_output_spec s 009 L LF$:">>+L 99 s177|,-D99Dt9 q=Z#6!!% , ]txx    %L &M   0 !!% ,  tyy4== I  rctj|}tjj||j|j |j S)Nrxryrz)rr.r/normrxryrzrs rrz Norm.call,sC  % %a (~~"" 488$))dmm#  rNNFr$r%r&rr!rr'r(s@rrqrqs !  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The following norms can be calculated: - For matrices: - `ord=None`: Frobenius norm - `ord="fro"`: Frobenius norm - `ord="nuc"`: nuclear norm - `ord=np.inf`: `max(sum(abs(x), axis=1))` - `ord=-np.inf`: `min(sum(abs(x), axis=1))` - `ord=0`: not supported - `ord=1`: `max(sum(abs(x), axis=0))` - `ord=-1`: `min(sum(abs(x), axis=0))` - `ord=2`: 2-norm (largest sing. value) - `ord=-2`: smallest singular value - other: not supported - For vectors: - `ord=None`: 2-norm - `ord="fro"`: not supported - `ord="nuc"`: not supported - `ord=np.inf`: `max(abs(x))` - `ord=-np.inf`: `min(abs(x))` - `ord=0`: `sum(x != 0)` - `ord=1`: as below - `ord=-1`: as below - `ord=2`: as below - `ord=-2`: as below - other: `sum(abs(x)**ord)**(1./ord)` Returns: Norm of the matrix or vector(s). Example: >>> x = keras.ops.reshape(keras.ops.arange(9, dtype="float32") - 4, (3, 3)) >>> keras.ops.linalg.norm(x) 7.7459664 r)rrqr*rr.r/r)rrxryrzs rrr3sWpQD!$:HHKK!!!$A >>  qcx  HHrc,eZdZdfd ZdZdZxZS)QrcTt||dvrtd|||_y)N>reducedcompletez]`mode` argument value not supported. Expected one of {'reduced', 'complete'}. Received: mode=)rrr1mode)rrrs rrz Qr.__init__rs<  . .""&)   rct|jdkrtd|j|jd}|jd}||td|jt||}t |jdd}|j dk(r8t |||fz|jt |||fz|jfSt |||fz|jt |||fz|jfS)Nr~z5Input should have rank >= 2. Received: input.shape = r<rIzOInput should have its last 2 dimensions fully-defined. Received: input.shape = r)rr )rrr1rgrrrr )rrrirjrkbases rr!zQr.compute_output_spec|s qww>> x = keras.ops.convert_to_tensor([[1., 2.], [3., 4.], [5., 6.]]) >>> q, r = qr(x) >>> print(q) array([[-0.16903079 0.897085] [-0.5070925 0.2760267 ] [-0.8451542 -0.34503305]], shape=(3, 2), dtype=float32) r)rrr*rr.r/r)rrs rrrsM0QD!t}**1--!!!$A >>  QT  **rc*eZdZfdZdZdZxZS)Solvec"t|yr r rs rrzSolve.__init__rrct||Sr )_solverabs rrz Solve.callsa|rct|t|t|t||t |j |j Sr rr _assert_1d_assert_a_b_compatrrr rs rr!zSolve.compute_output_spec71 q1 1a 177AGG,,rr#r(s@rrrs-rrzkeras.ops.solvezkeras.ops.linalg.solvecht||frtj||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)` representing 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 rsolvers1QF#w$$Q** !Q<rctj|}tj|}t|t|t |t ||tj j||Sr )rr.rrrrr/rrs rrrsY!!!$A!!!$AqM1qMq! >>  1 %%rc,eZdZdfd ZdZdZxZS)SolveTriangularc0t|||_yr )rrlower)rrrs rrzSolveTriangular.__init__  rc0t|||jSr )_solve_triangularrrs rrzSolveTriangular.calls Atzz22rct|t|t|t||t |j |j Sr rrs rr!z#SolveTriangular.compute_output_specrrFr#r(s@rrrs3-rrzkeras.ops.solve_triangularz!keras.ops.linalg.solve_triangularclt||frt|j||St|||Sr)rrr*rrrrs rsolve_triangularrs7 QF#u%33Aq99 Q5 ))rctj|}tj|}t|t|t |t ||tj j|||Sr )rr.rrrrr/rrs rrr s[!!!$A!!!$AqM1qMq! >> * *1a 77rc,eZdZdfd ZdZdZxZS)SVDc>t|||_||_yr )rr full_matrices compute_uv)rrrrs rrz SVD.__init__s *$rcDt||j|jSr )_svdrrrs rrzSVD.callsAt))4??;;rct||jdd\}}|jdd}|t||fz}|jr|||fz}|||fz}n"||t||fz}|t|||fz}|jrAt ||j t ||j t ||j fSt ||j Sr;)rrrgrrrr )rrrowscolumnsbatchess_shapeu_shapev_shapes rr!zSVD.compute_output_specs1  g''#2,Sw/11   t ,G' 22Gs4'9 ::GT7!3W ==G ??GQWW-GQWW-GQWW-  7AGG,,rTTr#r(s@rrrs% <-rrz keras.ops.svdzkeras.ops.linalg.svdcjt|frt||j|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 rsvdr3s5QD!=*-;;A>> =* --rctj|}t|tjj |||Sr )rr.rr/rrs rrrFs2!!!$AqM >>  a ;;rc,eZdZdfd ZdZdZxZS)Lstsqc0t|||_yr )rrrcond)rrrs rrzLstsq.__init__MrrcZtjj|||jS)Nr)rr/lstsqrrs rrz Lstsq.callQs"~~##Aq #;;rct|jdk7rtd|jt|jdvrtd|j|j\}}|jd|k7r%td|jd|jt|jdk(r*|jd}t||f|j }|St|f|j }|S) Nr~z-Expected a to have rank 2. Received: a.shape=)r}r~z2Expected b to have rank 1 or 2. Received: b.shape=rzAExpected b.shape[0] to be equal to a.shape[0]. Received: a.shape= , b.shape=r}r)rrr1rr )rrrrirjrkrs rr!zLstsq.compute_output_specTs qww<1 ?yI  qww>  1E  22rcN|D] }|jdkstd|dy)Nr}z8Expected input to have rank >= 1. Received scalar input .)ndimr1arraysrs rrrs5  66A:J1#QO rcb|D]*}|jdkstd|jdy)Nr~z= 2. Received input with shape r)rr1rrs rrrs>  66A:--.WWIQ8 rcp|D]1}|jdd\}}||k7std|jy)Nr<z?Expected a square matrix. Received non-square input with shape )rr1)rrrirjs rrrsL wwrs|1 6889yB rc|j|jk(rE|jd|jdk7r%td|jd|jy|j|jdz k(rE|jd|jdk7r%td|jd|jyy)Nr<zbIncompatible shapes between `a` and `b`. Expected `a.shape[-2] == b.shape[-2]`. Received: a.shape=rr}rIzbIncompatible shapes between `a` and `b`. Expected `a.shape[-1] == b.shape[-1]`. Received: a.shape=)rrr1rs rrrsvv 772;!''"+ %%%&WWIZyB  & 166A:  772;!''"+ %%%&WWIZyB  & rrrrrr )0 keras.srcrkeras.src.api_exportrkeras.src.backendrrkeras.src.ops.operationrkeras.src.ops.operation_utilsrr r,rr5r>r8rCrMrFrPrVrSrYr_r\rbrmrerqrrrrrrrrrrrrrrrrrrrrrso-)2-6 -y -#%@AB C  @ 2) 2 678 9 !  )   678 9 !  9  !89: ;  " -) - 678 9 ! y $$&BCDE" '6 96 r!89::I;:Iz(4(4V~456+7+: -I - ":;<=$& -i - !#FG**$8-)-< 678.9.$< I@ ":;<(3=(3Vr