g`6ddlmZddlmZmZddlmZddlmZddl m Z ddl m Z ddl mZddlmZdd lmZmZdd lmZmZmZmZmZmZdd lmZd ZGd deZdZ dZ!GddeZ"dS))Counter)Mulsympify)Add) ExprBuilder)default_sort_key)log) MatrixExpr)validate_matadd_integer) ZeroMatrix OneMatrix)unpackflatten conditionexhaustrm_idsort)sympy_deprecation_warningc|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)matricess _/var/www/html/ai-engine/env/lib/python3.11/site-packages/sympy/matrices/expressions/hadamard.pyhadamard_productrsM" ?=>>> 8}}{ H % * * , ,,cbeZdZdZdZdddfd ZedZdZd Z d Z d Z d Z xZ 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)evaluatecheckcttt|}t|dkrt dt d|Dst d|tddd|d ur t|tj |g|R}|r| d }|S) Nrz+HadamardProduct needs at least one argumentc3@K|]}t|tVdSN) isinstancer ).0args r z*HadamardProduct.__new__..Gs,??3:c:..??????rz 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)clsr r!argsobj __class__s rr2zHadamardProduct.__new__AsC&&'' t99>>JKK K??$????? @>?? ?   %|)/+Y [ [ [ [    dOOeggoc)D)))  '(((&&C rc&|jdjSNr)r4shapeselfs rr9zHadamardProduct.shapeXsy|!!rc @tfd|jDS)Nc.g|]}|jfiS)_entry)r&r'ijkwargss r z*HadamardProduct._entry..]s/EEECZSZ1////EEEr)rr4)r;r@rArBs ```rr?zHadamardProduct._entry\s-EEEEEE49EEEFFrc`ddlm}ttt ||jSNr) transpose)$sympy.matrices.expressions.transposerFrr,r-r4r;rFs r_eval_transposezHadamardProduct._eval_transpose_s3BBBBBBSDI%>%> ? ?@@rc 0|jfd|jD}ddlmddlm}fd|jDrIfd|jD}|dt Dj|j}t|g|z}t|S)Nc32K|]}|jdiVdS)Nr>)r)r&r@hintss rr(z'HadamardProduct.doit..ds1>>q616??E??>>>>>>rr) MatrixBase)ImmutableMatrixc4g|]}t||Sr>)r%)r&r@rMs rrCz(HadamardProduct.doit..is(FFF!Jq*,E,EFAFFFrcg|]}|v| Sr>r>)r&r@explicits rrCz(HadamardProduct.doit..ks#CCCq(1B1B1B1B1Brc6g|]}tj|Sr>)rfromiter)r&r@s rrCz(HadamardProduct.doit..ls-((($% Q(((r) funcr4sympy.matrices.matrixbaserMsympy.matrices.immutablerNzipreshaper9r canonicalize)r;rLexprrN remainderexpl_matrMrQs ` @@rrzHadamardProduct.doitcsty>>>>DI>>>?888888<<<<<<FFFFtyFFF  >CCCCDICCCI((),h((( $H#hZ)%;=DD!!!rc6g}t|j}tt|D]S}|d||||gz||dzdz}|t |Ttj|SNr) r,r4rangerdiffappendrrrS)r;xtermsr4r@factorss r_eval_derivativez HadamardProduct._eval_derivativessDIs4yy!! 5 5A2A2h$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)r&r@r'rbs rrCzAHadamardProduct._eval_derivative_matrix_lines..s,IIIFAscggajjIaIIIrr)rc<g|]\}}j|dk|Sr)r9r&rAer;s rrCzAHadamardProduct._eval_derivative_matrix_lines..s-PPPdaTZ]a=O=O=O=O=Orro)0sympy.tensor.array.expressions.array_expressionsrhrj"sympy.matrices.expressions.matexprrl enumerater4_eval_derivative_matrix_linesr_lines_first_line_index_second_line_indexr_first_pointer_parent_first_pointer_index_second_pointer_parent_second_pointer_indexra)r;rbrhrjrl with_x_indlinesind left_args right_argsdhadamdiagonalr@l1l2subexprs`` rrzz-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_HadamardProductr2propertyr9r?rIrrerz __classcell__r6s@rrr)s*%*$.""X"GGGAAA""" ###'''''''rrctdt}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|tSr$r%rrbs rzcanonicalize..jO44rc,t|tSr$rrs rrzcanonicalize..rrc,t|tSr$)r%r rs rrzcanonicalize..sJq)44rc^td|jDrt|jS|S)Nc3@K|]}t|tVdSr$)r%r )r&cs rr(z/canonicalize..absorb.. s,99Qz!Z((999999r)anyr4r r9rs rabsorbzcanonicalize..absorb s5 99!&999 9 9 qw' 'Hrc,t|tSr$rrs rrzcanonicalize..rrrc,t|tSr$rrs rrzcanonicalize..#rr)rrrrr%rrr4itemsra HadamardPowerrrr)rbrulefunrtallynew_argbaseexps rrYrYspf  4 4   D $--C AA  4 4 44 5 5  C AA  4 4   C AA!_%% & 9 9ID#axxt$$$$}T3778888 W %  4 4 ! " "  C AA q A Hrct|}t|}|dkr|S|js||zS|jrtdt||S)Nrz#cannot raise expression to a matrix)r is_Matrixr.r)rrs rhadamard_powerr-sd 4==D #,,C axx >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 c$t|}t|}|jr |jr||zSt|tr%t|trt ||t |||}|Sr$)r is_scalarr%r r0r1r2)r3rrr5r6s rr2zHadamardPower.__new__rst}}cll > cm 3;  dJ ' ' JsJ,G,G T3   ggooc4-- rc|jdSr8_argsr:s rrzHadamardPower.basez!}rc|jdSr^rr:s rrzHadamardPower.exprrcJ|jjr |jjS|jjSr$)rrr9rr:s rr9zHadamardPower.shapes# 9  #9? 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