U ;qLe^6@sddlmZddlmZmZddlmZddlmZddl m Z ddl m Z ddl mZddlmZdd lmZmZdd lmZmZmZmZmZmZdd lmZd d ZGdddeZddZ ddZ!GdddeZ"dS))Counter)Mulsympify)Add) ExprBuilder)default_sort_key)log) MatrixExpr)validate_matadd_integer) ZeroMatrix OneMatrix)unpackflatten conditionexhaustrm_idsort)sympy_deprecation_warningcGs,|s tdt|dkr |dSt|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 undefinedr) TypeErrorlenHadamardProductdoit)matricesrz/home/p21-0144/sympy/latex2sympy2solve-back-end/sympyEq/lib/python3.8/site-packages/sympy/matrices/expressions/hadamard.pyhadamard_products  rcs`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)evaluatecheckcsttt|}t|dkr"tdtdd|DsGsz*HadamardProduct.__new__..z Mix of Matrix and Scalar symbolszjPassing 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_targetF)deep) listmaprr ValueErrorallrrvalidatesuper__new__r)clsrrargsobj __class__rrr.As"  zHadamardProduct.__new__cCs |jdjSNr)r0shapeselfrrrr5XszHadamardProduct.shapec stfdd|jDS)Ncsg|]}|jfqSr)_entryr!ijkwargsrr ]sz*HadamardProduct._entry..)rr0)r7r:r;r<rr9rr8\szHadamardProduct._entrycCs ddlm}ttt||jSNr) transpose)$sympy.matrices.expressions.transposer?rr(r)r0r7r?rrr_eval_transpose_s zHadamardProduct._eval_transposec s|jfdd|jD}ddlmddlm}fdd|jDrfdd|jD}|d dtDj|j}t |g|}t |S) Nc3s|]}|jfVqdSr)rr"r:)hintsrrr$dsz'HadamardProduct.doit..r MatrixBase)ImmutableMatrixcsg|]}t|r|qSr)r rCrErrr=is z(HadamardProduct.doit..csg|]}|kr|qSrrrC)explicitrrr=kscSsg|]}t|qSr)rfromiterrCrrrr=ls) funcr0sympy.matrices.matricesrFsympy.matrices.immutablerGzipreshaper5r canonicalize)r7rDexprrG remainderZexpl_matr)rFrHrDrrcs  zHadamardProduct.doitcCsdg}t|j}tt|D]>}|d||||g||dd}|t|qt|SNr) r(r0rangerdiffappendrrrI)r7xtermsr0r:factorsrrr_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 ||ggf| }|jdjdj| _ d| _|jdjd j| _d| _|g| _ || qqD|S) Nr ArrayDiagonalArrayTensorProduct _make_matrixcsg|]\}}|r|qSr)has)r"r:r#rVrrr=s zAHadamardProduct._eval_derivative_matrix_lines..r)rcs"g|]\}}j|dkr|qSr)r5r"r;er6rrr=srb)0sympy.tensor.array.expressions.array_expressionsr[r]"sympy.matrices.expressions.matexprr_ enumerater0_eval_derivative_matrix_linesr_lines_first_line_index_second_line_indexr_first_pointer_parent_first_pointer_index_second_pointer_parent_second_pointer_indexrU)r7rVr[r]r_ with_x_indlinesind left_args right_argsdZhadamdiagonalr:l1l2subexprr)r7rVrrl{sF         z-HadamardProduct._eval_derivative_matrix_lines)__name__ __module__ __qualname____doc__Zis_HadamardProductr.propertyr5r8rBrrYrl __classcell__rrr2rr)s 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|tSrr rrarrrzcanonicalize..cSs t|tSrrrarrrrrcSs t|tSr)r r rarrrrrcSs&tdd|jDrt|jS|SdS)Ncss|]}t|tVqdSr)r r )r"crrrr$ sz/canonicalize..absorb..)anyr0r r5rarrrabsorb s zcanonicalize..absorbcSs t|tSrrrarrrrrrcSs t|tSrrrarrrr#r)rrrrr rrr0itemsrU HadamardPowerrrr )rVrulefunrZtallyZnew_argbaseexprrrrOs@S    rOcCsBt|}t|}|dkr|S|js*||S|jr8tdt||S)Nrz#cannot raise expression to a matrix)r is_Matrixr*r)rrrrrhadamard_power-srcsdeZdZdZfddZeddZeddZedd 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 csVt|}t|}|jr$|jr$||St|trBt|trBt||t|||}|Sr)r is_scalarr r r,r-r.)r/rrr1r2rrr.rs  zHadamardPower.__new__cCs |jdSr4_argsr6rrrrszHadamardPower.basecCs |jdSrRrr6rrrrszHadamardPower.expcCs|jjr|jjS|jjSr)rrr5rr6rrrr5szHadamardPower.shapecKsx|j}|j}|jr$|j||f|}n|jr0|}ntd||jrV|j||f|}n|jrb|}ntd|||S)Nz)The base {} must be a scalar or a matrix.z-The exponent {} must be a scalar or a matrix.)rrrr8rr*format)r7r:r;r<rrabrrrr8s"zHadamardPower._entrycCsddlm}t||j|jSr>)r@r?rrrrArrrrBs zHadamardPower._eval_transposecCs:|j|}|jt}||}t|||j||Sr)rrTr applyfuncrr)r7rVdexpZlogbaseZdlbaserrrrYs   zHadamardPower._eval_derivativec sddlm}ddlm}ddlm}j|}|D]}ddg}fddt|D}|j|j }|j|j } t |t |t ||gj t jj d t || ggf||jd } | jdjdj|_d|_d|_ | jdjd j|_d|_d|_ | g|_q4|S) Nrr\rZr^)rrbrccs$g|]\}}jj|dkr|qSrf)rr5rgr6rrr=sz?HadamardPower._eval_derivative_matrix_lines..r) validatorrb)rir]r[rjr_rrlrkrmrnrorrr _validater0rprqrrrs) r7rVr]r[r_lrr:rzr{r|r}rr6rrls>           z+HadamardPower._eval_derivative_matrix_lines)r~rrrr.rrrr5r8rBrYrlrrrr2rr9s8     rN)# collectionsr sympy.corerrZsympy.core.addrsympy.core.exprrsympy.core.sortingr&sympy.functions.elementary.exponentialrrjr !sympy.matrices.expressions._shaper r,Z"sympy.matrices.expressions.specialr r sympy.strategiesr rrrrrsympy.utilities.exceptionsrrrrOrrrrrrs         ~