a RG5d^8@sddlmZddlmZmZddlmZddlmZddl m Z ddl m Z ddl mZddlmZdd lmZmZdd lmZmZmZmZmZmZdd lmZd d ZGdddeZddZddZ ddZ!GdddeZ"dS))Counter)Mulsympify)Add) ExprBuilder)default_sort_key)log) ShapeError) MatrixExpr) ZeroMatrix OneMatrix)unpackflatten conditionexhaustrm_idsort)sympy_deprecation_warningcGsF|s tdt|t|dkr(|dSdd|D}t|SdS)au Return the elementwise (aka Hadamard) product of matrices. Examples ======== >>> from sympy import hadamard_product, MatrixSymbol >>> A = MatrixSymbol('A', 2, 3) >>> B = MatrixSymbol('B', 2, 3) >>> hadamard_product(A) A >>> hadamard_product(A, B) HadamardProduct(A, B) >>> hadamard_product(A, B)[0, 1] A[0, 1]*B[0, 1] z#Empty Hadamard product is undefinedrcSsg|]}|js|qS) is_Identity.0irr_/var/www/html/django/DPS/env/lib/python3.9/site-packages/sympy/matrices/expressions/hadamard.py (z$hadamard_product..N) TypeErrorvalidatelenHadamardProductdoit)matricesrrrhadamard_products r#cs`eZdZdZdZdddfdd Zedd Zd d Zd d Z ddZ ddZ ddZ Z S)r a( Elementwise product of matrix expressions Examples ======== Hadamard product for matrix symbols: >>> from sympy import hadamard_product, HadamardProduct, MatrixSymbol >>> A = MatrixSymbol('A', 5, 5) >>> B = MatrixSymbol('B', 5, 5) >>> isinstance(hadamard_product(A, B), HadamardProduct) True Notes ===== This is a symbolic object that simply stores its argument without evaluating it. To actually compute the product, use the function ``hadamard_product()`` or ``HadamardProduct.doit`` TFN)evaluatecheckcslttt|}|dur$tdddd|dvr6t|ntddddtj|g|R}|rh|jdd}|S) NzjPassing check to HadamardProduct is deprecated and the check argument will be removed in a future version.z1.11z,remove-check-argument-from-matrix-operations)deprecated_since_versionactive_deprecations_target)TNzpPassing check=False to HadamardProduct is deprecated and the check argument will be removed in a future version.F)deep)listmaprrrsuper__new__r!)clsr$r%argsobj __class__rrr,Ds$  zHadamardProduct.__new__cCs |jdjSNr)r.shapeselfrrrr3YszHadamardProduct.shapec stfdd|jDS)Ncs g|]}|jfiqSr)_entryrargrjkwargsrrr^rz*HadamardProduct._entry..)rr.)r5rr:r;rr9rr6]szHadamardProduct._entrycCs ddlm}ttt||jSNr) transpose)$sympy.matrices.expressions.transposer=r r)r*r.r5r=rrr_eval_transpose`s zHadamardProduct._eval_transposec s|jfdd|jD}ddlmddlm}fdd|jDrfdd|jD}|ddtDj|j}t |g|}t |S) Ncsg|]}|jfiqSr)r!r)hintsrrrerz(HadamardProduct.doit..r MatrixBase)ImmutableMatrixcsg|]}t|r|qSr) isinstancerrBrrrircsg|]}|vr|qSrrr)explicitrrrkrcSsg|]}t|qSr)rfromiterrrrrrls) funcr.sympy.matrices.matricesrCsympy.matrices.immutablerDzipreshaper3r canonicalize)r5rAexprrD remainderZexpl_matr)rCrFrArr!ds  zHadamardProduct.doitcCsdg}t|j}tt|D]>}|d||||g||dd}|t|qt|SNr) r)r.rangerdiffappendr#rrG)r5xtermsr.rfactorsrrr_eval_derivativess  ,z HadamardProduct._eval_derivativec s<ddlm}ddlm}ddlm}fddtjD}g}|D]}jd|}j|dd} j|} t| |} dd g} fd dt| D} | D]} | j | j }| j | j }t |t |t ||g| t ||ggg| }|jdjdj| _ d| _|jdjd j| _d| _|g| _ || qqD|S) Nr ArrayDiagonalArrayTensorProduct _make_matrixcsg|]\}}|r|qSr)has)rrr8rTrrrrzAHadamardProduct._eval_derivative_matrix_lines..r)rcs"g|]\}}j|dkr|qSr)r3rr:er4rrrrr`)0sympy.tensor.array.expressions.array_expressionsrYr["sympy.matrices.expressions.matexprr] enumerater._eval_derivative_matrix_linesr#_lines_first_line_index_second_line_indexr_first_pointer_parent_first_pointer_index_second_pointer_parent_second_pointer_indexrS)r5rTrYr[r] with_x_indlinesind left_args right_argsdZhadamdiagonalrl1l2subexprr)r5rTrrj{sF         z-HadamardProduct._eval_derivative_matrix_lines)__name__ __module__ __qualname____doc__Zis_HadamardProductr,propertyr3r6r@r!rWrj __classcell__rrr0rr ,s r cGsTtdd|Dstd|d}|ddD] }|j|jkr.td||fq.dS)Ncss|] }|jVqdSN) is_Matrixr7rrr rzvalidate..z Mix of Matrix and Scalar symbolsrrz"Matrices %s and %s are not aligned)allrr3r )r.ABrrrrs  rcCstddt}t|}||}tddtdd}||}dd}tdd|}||}t|trt|j}g}|D],\}}|dkr| |qz| t ||qzt|}td dt t }||}t |}|S) aCanonicalize the Hadamard product ``x`` with mathematical properties. Examples ======== >>> from sympy import MatrixSymbol, HadamardProduct >>> from sympy import OneMatrix, ZeroMatrix >>> from sympy.matrices.expressions.hadamard import canonicalize >>> from sympy import init_printing >>> init_printing(use_unicode=False) >>> A = MatrixSymbol('A', 2, 2) >>> B = MatrixSymbol('B', 2, 2) >>> C = MatrixSymbol('C', 2, 2) Hadamard product associativity: >>> X = HadamardProduct(A, HadamardProduct(B, C)) >>> X A.*(B.*C) >>> canonicalize(X) A.*B.*C Hadamard product commutativity: >>> X = HadamardProduct(A, B) >>> Y = HadamardProduct(B, A) >>> X A.*B >>> Y B.*A >>> canonicalize(X) A.*B >>> canonicalize(Y) A.*B Hadamard product identity: >>> X = HadamardProduct(A, OneMatrix(2, 2)) >>> X A.*1 >>> canonicalize(X) A Absorbing element of Hadamard product: >>> X = HadamardProduct(A, ZeroMatrix(2, 2)) >>> X A.*0 >>> canonicalize(X) 0 Rewriting to Hadamard Power >>> X = HadamardProduct(A, A, A) >>> X A.*A.*A >>> canonicalize(X) .3 A Notes ===== As the Hadamard product is associative, nested products can be flattened. The Hadamard product is commutative so that factors can be sorted for canonical form. A matrix of only ones is an identity for Hadamard product, so every matrices of only ones can be removed. Any zero matrix will make the whole product a zero matrix. Duplicate elements can be collected and rewritten as HadamardPower References ========== .. [1] https://en.wikipedia.org/wiki/Hadamard_product_(matrices) cSs t|tSrrEr r_rrrrzcanonicalize..cSs t|tSrrr_rrrr rcSs t|tSr)rEr r_rrrr rcSs&tdd|jDrt|jS|SdS)Ncss|]}t|tVqdSr)rEr )rcrrrrrz/canonicalize..absorb..)anyr.r r3r_rrrabsorbs zcanonicalize..absorbcSs t|tSrrr_rrrrrrcSs t|tSrrr_rrrr,r)rrrrrEr rr.itemsrS HadamardPowerrrr )rTrulefunrZtallyZnew_argbaseexprrrrMs@S    rMcCsBt|}t|}|dkr|S|js*||S|jr8tdt||S)Nrz#cannot raise expression to a matrix)rr ValueErrorr)rrrrrhadamard_power6srcsdeZdZdZfddZeddZeddZedd Zd d Z d d Z ddZ ddZ Z S)ra Elementwise power of matrix expressions Parameters ========== base : scalar or matrix exp : scalar or matrix Notes ===== There are four definitions for the hadamard power which can be used. Let's consider `A, B` as `(m, n)` matrices, and `a, b` as scalars. Matrix raised to a scalar exponent: .. math:: A^{\circ b} = \begin{bmatrix} A_{0, 0}^b & A_{0, 1}^b & \cdots & A_{0, n-1}^b \\ A_{1, 0}^b & A_{1, 1}^b & \cdots & A_{1, n-1}^b \\ \vdots & \vdots & \ddots & \vdots \\ A_{m-1, 0}^b & A_{m-1, 1}^b & \cdots & A_{m-1, n-1}^b \end{bmatrix} Scalar raised to a matrix exponent: .. math:: a^{\circ B} = \begin{bmatrix} a^{B_{0, 0}} & a^{B_{0, 1}} & \cdots & a^{B_{0, n-1}} \\ a^{B_{1, 0}} & a^{B_{1, 1}} & \cdots & a^{B_{1, n-1}} \\ \vdots & \vdots & \ddots & \vdots \\ a^{B_{m-1, 0}} & a^{B_{m-1, 1}} & \cdots & a^{B_{m-1, n-1}} \end{bmatrix} Matrix raised to a matrix exponent: .. math:: A^{\circ B} = \begin{bmatrix} A_{0, 0}^{B_{0, 0}} & A_{0, 1}^{B_{0, 1}} & \cdots & A_{0, n-1}^{B_{0, n-1}} \\ A_{1, 0}^{B_{1, 0}} & A_{1, 1}^{B_{1, 1}} & \cdots & A_{1, n-1}^{B_{1, n-1}} \\ \vdots & \vdots & \ddots & \vdots \\ A_{m-1, 0}^{B_{m-1, 0}} & A_{m-1, 1}^{B_{m-1, 1}} & \cdots & A_{m-1, n-1}^{B_{m-1, n-1}} \end{bmatrix} Scalar raised to a scalar exponent: .. math:: a^{\circ b} = a^b csdt|}t|}|jr$|jr$||S|jrP|jrP|j|jkrPtd|j|jt|||}|S)NzGThe shape of the base {} and the shape of the exponent {} do not match.)r is_scalarrr3rformatr+r,)r-rrr/r0rrr,{s zHadamardPower.__new__cCs |jdSr2_argsr4rrrrszHadamardPower.basecCs |jdSrPrr4rrrrszHadamardPower.expcCs|jjr|jjS|jjSr)rrr3rr4rrrr3szHadamardPower.shapecKs|j}|j}|jr(|j||fi|}n|jr4|}ntd||jr^|j||fi|}n|jrj|}ntd|||S)Nz)The base {} must be a scalar or a matrix.z-The exponent {} must be a scalar or a matrix.)rrrr6rrr)r5rr:r;rrabrrrr6s"zHadamardPower._entrycCsddlm}t||j|jSr<)r>r=rrrr?rrrr@s zHadamardPower._eval_transposecCs:|j|}|jt}||}t|||j||Sr)rrRr applyfuncrr#)r5rTdexpZlogbaseZdlbaserrrrWs   zHadamardPower._eval_derivativec sddlm}ddlm}ddlm}j|}|D]}ddg}fddt|D}|j|j }|j|j } t |t |t ||gj t jj d t || ggg||jd } | jdjdj|_d|_d|_ | jdjd j|_d|_d|_ | g|_q4|S) NrrZrXr\)rr`racs$g|]\}}jj|dkr|qSrd)rr3rer4rrrrz?HadamardPower._eval_derivative_matrix_lines..r) validatorr`)rgr[rYrhr]rrjrirkrlrmrrr _validater.rnrorprq) r5rTr[rYr]lrrrxryrzr{rr4rrjs>           z+HadamardPower._eval_derivative_matrix_lines)r|r}r~rr,rrrr3r6r@rWrjrrrr0rrBs8     rN)# collectionsr sympy.corerrZsympy.core.addrsympy.core.exprrsympy.core.sortingr&sympy.functions.elementary.exponentialrsympy.matrices.commonr rhr Z"sympy.matrices.expressions.specialr r sympy.strategiesr rrrrrsympy.utilities.exceptionsrr#r rrMrrrrrrs"         y