o GZh`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,|stdt|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)ZmatricesrR/var/www/auris/lib/python3.10/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|dkrtdtdd|Dstd|dur)tdddd |d ur1t|t j |g|R}|rC|j d d }|S) Nrz+HadamardProduct needs at least one argumentcs|]}t|tVqdSN) isinstancer .0argrrr Gz*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)Zdeprecated_since_versionZactive_deprecations_targetF)deep) listmaprr ValueErrorallrrvalidatesuper__new__r)clsrrargsobj __class__rrr-As"  zHadamardProduct.__new__cCs |jdjSNr)r/shapeselfrrrr4Xs zHadamardProduct.shapec stfdd|jDS)Ncs g|] }|jfiqSr)_entryr!ijkwargsrr ]s z*HadamardProduct._entry..)rr/)r6r9r:r;rr8rr7\szHadamardProduct._entrycCs ddlm}ttt||jSNr) transpose)$sympy.matrices.expressions.transposer>rr'r(r/r6r>rrr_eval_transpose_s zHadamardProduct._eval_transposec s|jfdd|jD}ddlmddlm}fdd|jDrEfdd|jD}|d dtDj|j}t |g|}t |S) Nc3s |] }|jdiVqdS)Nr)rr"r9)hintsrrr$dsz'HadamardProduct.doit..r MatrixBase)ImmutableMatrixcsg|] }t|r|qSr)r rBrDrrr<isz(HadamardProduct.doit..csg|]}|vr|qSrrrB)explicitrrr<kscSsg|]}t|qSr)rfromiterrBrrrr<ls ) funcr/Zsympy.matrices.matrixbaserEZsympy.matrices.immutablerFzipZreshaper4r canonicalize)r6rCexprrF remainderZexpl_matr)rErGrCrrcs  zHadamardProduct.doitcCsdg}t|j}tt|D]}|d||||g||dd}|t|q t|SNr) r'r/rangerdiffappendrrrH)r6xZtermsr/r9Zfactorsrrr_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)r"r9r#rRrrr<szAHadamardProduct._eval_derivative_matrix_lines..r)rcs"g|] \}}j|dkr|qSr)r4r"r:er5rrr<s"r\)0sympy.tensor.array.expressions.array_expressionsrUrW"sympy.matrices.expressions.matexprrY enumerater/_eval_derivative_matrix_linesr_lines_first_line_index_second_line_indexr_first_pointer_parent_first_pointer_index_second_pointer_parent_second_pointer_indexrQ)r6rRrUrWrYZ with_x_indlinesindZ left_argsZ right_argsdZhadamdiagonalr9l1l2subexprr)r6rRrrf{sH          z-HadamardProduct._eval_derivative_matrix_lines)__name__ __module__ __qualname____doc__Zis_HadamardProductr-propertyr4r7rArrSrf __classcell__rrr1rr)s 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|tSrr rr[rrr zcanonicalize..cSr{rr|r[rrrr}r~cSr{r)r r r[rrrr}r~cSs"tdd|jDrt|jS|S)Ncsrr)r r )r"crrrr$ r%z/canonicalize..absorb..)anyr/r r4r[rrrabsorb s zcanonicalize..absorbcSr{rr|r[rrrr}r~rcSr{rr|r[rrrr}#r~)rrrrr rrr/itemsrQ HadamardPowerrrr )rRruleZfunrZtallyZnew_argbaseexprrrrKs@S    rKcCsBt|}t|}|dkr|S|js||S|jrtdt||S)Nrz#cannot raise expression to a matrix)r is_Matrixr)r)rrrrrhadamard_power-s 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 csVt|}t|}|jr|jr||St|tr!t|tr!t||t|||}|Sr)r is_scalarr r r+r,r-)r.rrr0r1rrr-rs  zHadamardPower.__new__cC |jdSr3_argsr5rrrr zHadamardPower.basecCrrNrr5rrrrrzHadamardPower.expcCs|jjr|jjS|jjSr)rrr4rr5rrrr4szHadamardPower.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.)rrrr7rr)format)r6r9r:r;rrabrrrr7s$zHadamardPower._entrycCsddlm}t||j|jSr=)r?r>rrrr@rrrrAs zHadamardPower._eval_transposecCs:|j|}|jt}||}t|||j||Sr)rrPrZ applyfuncrr)r6rRZdexpZlogbaseZdlbaserrrrSs   zHadamardPower._eval_derivativec sddlm}ddlm}ddlm}j|}|D]d}ddg}fddt|D}|j|j }|j|j } t |t |t ||gj t jj d t || ggg||jd } | jdjdj|_d|_d|_ | jdjd j|_d|_d|_ | g|_q|S) NrrVrTrX)rr\r]cs$g|]\}}jj|dkr|qSr`)rr4rar5rrr<s$z?HadamardPower._eval_derivative_matrix_lines..r) validatorr\)rcrWrUrdrYrrfrergrhrirrr _validater/rjrkrlrm) r6rRrWrUrYlrr9rqrrrsrtrr5rrfs>           z+HadamardPower._eval_derivative_matrix_lines)rurvrwrxr-ryrrr4r7rArSrfrzrrr1rr9s 8    rN)# collectionsrZ sympy.corerrZsympy.core.addrZsympy.core.exprrZsympy.core.sortingrZ&sympy.functions.elementary.exponentialrrdr Z!sympy.matrices.expressions._shaper r+Z"sympy.matrices.expressions.specialr r Zsympy.strategiesr rrrrrZsympy.utilities.exceptionsrrrrKrrrrrrs"         ~