Ed^8ddlmZddlmZmZddlmZddlmZddl m Z ddl m Z ddl mZddlmZdd lmZmZdd lmZmZmZmZmZmZdd lmZd ZGd deZdZdZ dZ!GddeZ"dS))Counter)Mulsympify)Add) ExprBuilder)default_sort_key)log) ShapeError) MatrixExpr) ZeroMatrix OneMatrix)unpackflatten conditionexhaustrm_idsort)sympy_deprecation_warningc|stdt|t|dkr|dSd|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 undefinedrc g|] }|j | S) is_Identity.0is Clib/python3.11/site-packages/sympy/matrices/expressions/hadamard.py z$hadamard_product..(s===!q}=A===) TypeErrorvalidatelenHadamardProductdoit)matricess rhadamard_productr&sm" ?=>>> h 8}}1{==x===)..000rcbeZdZdZdZdddfd ZedZdZd Z d Z d Z d Z xZ S) r#a( Elementwise product of matrix expressions Examples ======== Hadamard product for matrix symbols: >>> from sympy import hadamard_product, HadamardProduct, MatrixSymbol >>> A = MatrixSymbol('A', 5, 5) >>> B = MatrixSymbol('B', 5, 5) >>> isinstance(hadamard_product(A, B), HadamardProduct) True Notes ===== This is a symbolic object that simply stores its argument without evaluating it. To actually compute the product, use the function ``hadamard_product()`` or ``HadamardProduct.doit`` TFN)evaluatecheckcttt|}|tddd|dvr t |ntdddt j|g|R}|r|d}|S) NzjPassing check to HadamardProduct is deprecated and the check argument will be removed in a future version.z1.11z,remove-check-argument-from-matrix-operations)deprecated_since_versionactive_deprecations_target)TNzpPassing check=False to HadamardProduct is deprecated and the check argument will be removed in a future version.F)deep)listmaprrr!super__new__r$)clsr(r)argsobj __class__s rr1zHadamardProduct.__new__DsC&&''  [ %|)/+Y [ [ [ [ L  [ dOOO %C)/+Y [ [ [ [ eggoc)D)))  '(((&&C rc&|jdjSNr)r3shapeselfs rr8zHadamardProduct.shapeYsy|!!rc @tfd|jDS)Nc.g|]}|jfiSr)_entry)rargrjkwargss rrz*HadamardProduct._entry..^s/EEECZSZ1////EEEr)rr3)r:rr?r@s ```rr=zHadamardProduct._entry]s-EEEEEE49EEEFFrc`ddlm}ttt ||jSNr) transpose)$sympy.matrices.expressions.transposerCr#r.r/r3r:rCs r_eval_transposezHadamardProduct._eval_transpose`s3BBBBBBSDI%>%> ? ?@@rc 0|jfd|jD}ddlmddlm}fd|jDrIfd|jD}|dt Dj|j}t|g|z}t|S)Nc*g|]}|jdiS)r)r$)rrhintss rrz(HadamardProduct.doit..es'>>>q616??E??>>>rr) MatrixBase)ImmutableMatrixc4g|]}t||Sr) isinstance)rrrJs rrz(HadamardProduct.doit..is(FFF!Jq*,E,EFAFFFrcg|]}|v| Srr)rrexplicits rrz(HadamardProduct.doit..ks#CCCq(1BCCCCrc6g|]}tj|Sr)rfromiterrs rrz(HadamardProduct.doit..ls-((($% Q(((r) funcr3sympy.matrices.matricesrJsympy.matrices.immutablerKzipreshaper8r# canonicalize)r:rIexprrK remainderexpl_matrJrOs ` @@rr$zHadamardProduct.doitdsty>>>>DI>>>?666666<<<<<<FFFFtyFFF  >CCCCDICCCI((),h((( $H#hZ)%;=DD!!!rc6g}t|j}tt|D]S}|d||||gz||dzdz}|t |Ttj|SNr) r.r3ranger"diffappendr&rrQ)r:xtermsr3rfactorss r_eval_derivativez HadamardProduct._eval_derivativessDIs4yy!! 5 5A2A2h$q',,q//!22T!A#$$Z?G LL)73 4 4 4 4|E"""rc ddlm}ddlm}ddlm}fdt jD}g}|D]I}jd|}j|dzd} j|} t| |z} ddg} fd t | D} | D]} | j | j }| j | j }t|t|t||g| t||ggg| }|jdjdj| _ d| _|jdjd j| _d| _|g| _ || ؐK|S) Nr ArrayDiagonalArrayTensorProduct _make_matrixcDg|]\}}||Sr)has)rrr>r`s rrzAHadamardProduct._eval_derivative_matrix_lines..s,IIIFAscggajjIaIIIrr)rc<g|]\}}j|dk|Sr)r8rr?er:s rrzAHadamardProduct._eval_derivative_matrix_lines..s-PPPdaTZ]a=OPPPPrrm)0sympy.tensor.array.expressions.array_expressionsrfrh"sympy.matrices.expressions.matexprrj enumerater3_eval_derivative_matrix_linesr&_lines_first_line_index_second_line_indexr_first_pointer_parent_first_pointer_index_second_pointer_parent_second_pointer_indexr_)r:r`rfrhrj with_x_indlinesind left_args right_argsdhadamdiagonalrl1l2subexprs`` rrxz-HadamardProduct._eval_derivative_matrix_lines{sRRRRRRWWWWWWCCCCCCIIIIi &:&:III   C $3$I3q566*J #<q*A*F')*&+2<?+?+B+G(*+'#9 Q- 0 r)__name__ __module__ __qualname____doc__is_HadamardProductr1propertyr8r=rFr$rcrx __classcell__r5s@rr#r#,s*%*$*""X"GGGAAA " " "###'''''''rr#ctd|Dstd|d}|ddD](}|j|jkrtd|d|d)dS)Nc3$K|] }|jV dSN) is_Matrix)rr>s r zvalidate..s$--s}------rz Mix of Matrix and Scalar symbolsrrz Matrices z and z are not aligned)allr r8r )r3ABs rr!r!s ----- - -<:;;; QA !""XLL 7ag  L*QQQJKK K LLLrctdt}t|}||}tdtd}||}d}td|}||}t |t rxt |j}g}|D]D\}}|dkr| |!| t||Et |}tdtt}||}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) c,t|tSrrMr#r`s rzcanonicalize..jO44rc,t|tSrrrs rrzcanonicalize.. rrc,t|tSr)rMr rs rrzcanonicalize.. sJq)44rc^td|jDrt|jS|S)Nc3@K|]}t|tVdSr)rMr )rcs rrz/canonicalize..absorb..s,99Qz!Z((999999r)anyr3r r8rs rabsorbzcanonicalize..absorbs5 99!&999 9 9 qw' 'Hrc,t|tSrrrs rrzcanonicalize..rrrc,t|tSrrrs rrzcanonicalize..,rr)rrrrrMr#rr3itemsr_ HadamardPowerrrr)r`rulefunrtallynew_argbaseexps rrWrWssf  4 4   D $--C AA  4 4 44 5 5  C AA  4 4   C AA!_%% & 9 9ID#ax 9t$$$$}T3778888 W %  4 4 ! " "  C AA q A Hrct|}t|}|dkr|S|js||zS|jrtdt||S)Nrz#cannot raise expression to a matrix)rr ValueErrorr)rrs rhadamard_powerr6sg 4==D #,,C ax >Sy }@>??? s # ##rc|eZdZdZfdZedZedZedZdZ dZ dZ d Z xZ 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 cFt|}t|}|jr |jr||zS|jrD|jr=|j|jkr-t d|j|jt |||}|S)NzGThe shape of the base {} and the shape of the exponent {} do not match.)r is_scalarrr8rformatr0r1)r2rrr4r5s rr1zHadamardPower.__new__{st}}cll > cm 3;  > cm  ci0G = CI..  ggooc4-- rc|jdSr7_argsr9s rrzHadamardPower.basez!}rc|jdSr\rr9s rrzHadamardPower.exprrcJ|jjr |jjS|jjSr)rrr8rr9s rr8zHadamardPower.shapes# 9  #9? 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