o *ήc^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_warningcGsB|stdt|t|dkr|dSdd|D}t|S)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.0irrJ/tmp/pip-target-vg8gfxp4/lib/python/sympy/matrices/expressions/hadamard.py (sz$hadamard_product..) TypeErrorvalidatelenHadamardProductdoit)matricesrrrhadamard_products  r"cs`eZdZdZdZdddfdd Zedd Zd d Zd d Z ddZ ddZ ddZ Z S)ra( Elementwise product of matrix expressions Examples ======== Hadamard product for matrix symbols: >>> from sympy import hadamard_product, HadamardProduct, MatrixSymbol >>> A = MatrixSymbol('A', 5, 5) >>> B = MatrixSymbol('B', 5, 5) >>> isinstance(hadamard_product(A, B), HadamardProduct) True Notes ===== This is a symbolic object that simply stores its argument without evaluating it. To actually compute the product, use the function ``hadamard_product()`` or ``HadamardProduct.doit`` TFN)evaluatecheckcslttt|}|durtdddd|dvrt|ntddddtj|g|R}|r4|jdd}|S) NzjPassing check to HadamardProduct is deprecated and the check argument will be removed in a future version.z1.11z,remove-check-argument-from-matrix-operations)deprecated_since_versionactive_deprecations_target)TNzpPassing check=False to HadamardProduct is deprecated and the check argument will be removed in a future version.F)deep)listmaprrrsuper__new__r )clsr#r$argsobj __class__rrr+Ds$  zHadamardProduct.__new__cCs |jdjSNr)r-shapeselfrrrr2Ys zHadamardProduct.shapec stfdd|jDS)Ncs g|] }|jfiqSr)_entryrargrjkwargsrrr^s z*HadamardProduct._entry..)rr-)r4rr9r:rr8rr5]szHadamardProduct._entrycCs ddlm}ttt||jSNr) transpose)$sympy.matrices.expressions.transposer<rr(r)r-r4r<rrr_eval_transpose`s zHadamardProduct._eval_transposec s|jfdd|jD}ddlmddlm}fdd|jDrEfdd|jD}|ddtDj|j}t |g|}t |S) Ncsg|] }|jdiqS)r)r r)hintsrrresz(HadamardProduct.doit..r MatrixBase)ImmutableMatrixcsg|] }t|r|qSr) isinstancerrArrriscsg|]}|vr|qSrrr)explicitrrrkscSsg|]}t|qSr)rfromiterrrrrrls ) funcr-sympy.matrices.matricesrBsympy.matrices.immutablerCzipreshaper2r canonicalize)r4r@exprrC remainderexpl_matr)rBrEr@rr ds  zHadamardProduct.doitcCsdg}t|j}tt|D]}|d||||g||dd}|t|q t|SNr) r(r-rangerdiffappendr"rrF)r4xtermsr-rfactorsrrr_eval_derivativess  , z HadamardProduct._eval_derivativec s<ddlm}ddlm}ddlm}fddtjD}g}|D]y}jd|}j|dd} j|} t| |} dd g} fd dt| D} | D]G} | j | j }| j | j }t |t |t ||g| t ||ggg| }|jdjdj| _ d| _|jdjd j| _d| _|g| _ || qSq"|S) Nr ArrayDiagonalArrayTensorProduct _make_matrixcsg|] \}}|r|qSr)has)rrr7rTrrrszAHadamardProduct._eval_derivative_matrix_lines..r)rcs"g|] \}}j|dkr|qSr)r2rr9er3rrrs"r`)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)r4rTrYr[r] with_x_indlinesind left_args right_argsdhadamdiagonalrl1l2subexprr)r4rTrrj{sH          z-HadamardProduct._eval_derivative_matrix_lines)__name__ __module__ __qualname____doc__is_HadamardProductr+propertyr2r5r?r rWrj __classcell__rrr/rr,s rcGsTtdd|Ds td|d}|ddD]}|j|jkr'td||fqdS)Ncss|]}|jVqdSN) is_Matrixr6rrr szvalidate..z Mix of Matrix and Scalar symbolsrrz"Matrices %s and %s are not aligned)allrr2r )r-ABrrrrs rcCstddt}t|}||}tddtdd}||}dd}tdd|}||}t|trXt|j}g}|D]\}}|dkrK| |q=| t ||q=t|}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) cS t|tSrrDrr_rrr zcanonicalize..cSrrrr_rrrr rcSrr)rDr r_rrrr rcSs"tdd|jDrt|jS|S)Ncss|]}t|tVqdSr)rDr )rcrrrrsz/canonicalize..absorb..)anyr-r r2r_rrrabsorbs zcanonicalize..absorbcSrrrr_rrrrrrcSrrrr_rrrr,r)rrrrrDrrr-itemsrS HadamardPowerrrr )rTrulefunrtallynew_argbaseexprrrrLs@S    rLcCsBt|}t|}|dkr|S|js||S|jrtdt||S)Nrz#cannot raise expression to a matrix)rr ValueErrorr)rrrrrhadamard_power6s rcsdeZdZdZfddZeddZeddZedd 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|jr(|jr(|j|jkr(td|j|jt|||}|S)NzGThe shape of the base {} and the shape of the exponent {} do not match.)r is_scalarrr2rformatr*r+)r,rrr.r/rrr+{s  zHadamardPower.__new__cC |jdSr1_argsr3rrrr zHadamardPower.basecCrrPrr3rrrrrzHadamardPower.expcCs|jjr|jjS|jjSr)rrr2rr3rrrr2szHadamardPower.shapecKs|j}|j}|jr|j||fi|}n |jr|}ntd||jr2|j||fi|}||S|jr;|}||Std|)Nz)The base {} must be a scalar or a matrix.z-The exponent {} must be a scalar or a matrix.)rrrr5rrr)r4rr9r:rrabrrrr5s$zHadamardPower._entrycCsddlm}t||j|jSr;)r=r<rrrr>rrrr?s zHadamardPower._eval_transposecCs:|j|}|jt}||}t|||j||Sr)rrRr applyfuncrr")r4rTdexplogbasedlbaserrrrWs   zHadamardPower._eval_derivativec sddlm}ddlm}ddlm}j|}|D]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|_q|S) NrrZrXr\)rr`racs$g|]\}}jj|dkr|qSrd)rr2rer3rrrs$z?HadamardPower._eval_derivative_matrix_lines..r) validatorr`)rgr[rYrhr]rrjrirkrlrmrrr _validater-rnrorprq) r4rTr[rYr]lrrryrzr{r|rr3rrjs>           z+HadamardPower._eval_derivative_matrix_lines)r}r~rrr+rrrr2r5r?rWrjrrrr/rrBs 8    rN)# collectionsr sympy.corerrsympy.core.addrsympy.core.exprrsympy.core.sortingr&sympy.functions.elementary.exponentialrsympy.matrices.commonr rhr "sympy.matrices.expressions.specialr r sympy.strategiesr rrrrrsympy.utilities.exceptionsrr"rrrLrrrrrrs$         y