ķ ~9­\c@ sddlmZmZddlmZddlmZddlmZm Z m Z ddl m Z ddl mZddlmZddlmZmZmZmZmZmZmZmZdd lmZmZmZmZdd lm Z m!Z!d eefd „ƒYZ"d „Z#d„Z$d„Z%d„Z&d„Z'ed„ƒeeee%e$e&ƒe'ee ƒfZ(eed„ee(ŒƒƒZ)dS(i˙˙˙˙(tprint_functiontdivision(treduce(tadd(tAddtBasictsympify(tadjoint(t MatrixBase(t transpose(trm_idtunpacktflattentsortt conditiontexhausttdo_onetglom(t MatrixExprt ShapeErrort ZeroMatrixtGenericZeroMatrix(tdefault_sort_keytsifttMatAddcB seeZdZeZd„Zed„ƒZd d„Z d„Z d„Z d„Z d„Z d„ZRS( s3A Sum of Matrix Expressions MatAdd inherits from and operates like SymPy Add Examples ======== >>> from sympy import MatAdd, MatrixSymbol >>> A = MatrixSymbol('A', 5, 5) >>> B = MatrixSymbol('B', 5, 5) >>> C = MatrixSymbol('C', 5, 5) >>> MatAdd(A, B, C) A + B + C cO s’|s tƒStd„|ƒ}ttt|ƒƒ}|jdtƒ}tj||Œ}|rŽt d„|Dƒƒrt j |ƒSt |Œn|S(NcS s tƒ|kS(N(R(ti((s@lib/python2.7/site-packages/sympy/matrices/expressions/matadd.pyt(ttcheckcs s|]}t|tƒ VqdS(N(t isinstanceR(t.0R((s@lib/python2.7/site-packages/sympy/matrices/expressions/matadd.pys .s( RtfiltertlisttmapRtgettFalseRt__new__tallRtfromitertvalidate(tclstargstkwargsRtobj((s@lib/python2.7/site-packages/sympy/matrices/expressions/matadd.pyR$"s  cC s|jdjS(Ni(R)tshape(tself((s@lib/python2.7/site-packages/sympy/matrices/expressions/matadd.pyR,3scC s,tg|jD]}|j||ƒ^q ŒS(N(RR)t_entry(R-Rtjtexpandtarg((s@lib/python2.7/site-packages/sympy/matrices/expressions/matadd.pyR.7scC s,tg|jD]}t|ƒ^q ŒjƒS(N(RR)R tdoit(R-R1((s@lib/python2.7/site-packages/sympy/matrices/expressions/matadd.pyt_eval_transpose:scC s,tg|jD]}t|ƒ^q ŒjƒS(N(RR)RR2(R-R1((s@lib/python2.7/site-packages/sympy/matrices/expressions/matadd.pyt _eval_adjoint=scC s<ddlm}tg|jD]}||ƒ^qŒjƒS(Ni(ttrace(R5RR)R2(R-R5R1((s@lib/python2.7/site-packages/sympy/matrices/expressions/matadd.pyt _eval_trace@scK sY|jdtƒ}|r@g|jD]}|j|^q"}n |j}tt|ŒƒS(Ntdeep(R"tTrueR)R2t canonicalizeR(R-R*R7R1R)((s@lib/python2.7/site-packages/sympy/matrices/expressions/matadd.pyR2Ds ( cC sIg|jD]}|j|ƒ^q }g|D]}|D] }|^q6q,S(N(R)t_eval_derivative_matrix_lines(R-txR1t add_linesRR/((s@lib/python2.7/site-packages/sympy/matrices/expressions/matadd.pyR:Ls%N(t__name__t __module__t__doc__R8t is_MatAddR$tpropertyR,tNoneR.R3R4R6R2R:(((s@lib/python2.7/site-packages/sympy/matrices/expressions/matadd.pyRs      cG sstd„|Dƒƒs%tdƒ‚n|d}x=|dD]1}|j|jkr:td||fƒ‚q:q:WdS(Ncs s|]}|jVqdS(N(t is_Matrix(RR1((s@lib/python2.7/site-packages/sympy/matrices/expressions/matadd.pys Rss Mix of Matrix and Scalar symbolsiis"Matrices %s and %s are not aligned(R%t TypeErrorR,R(R)tAtB((s@lib/python2.7/site-packages/sympy/matrices/expressions/matadd.pyR'Qs  cC s|jƒdS(Ni(t as_coeff_mmul(R1((s@lib/python2.7/site-packages/sympy/matrices/expressions/matadd.pyRZRcC st|jƒdƒS(Ni(R RG(R1((s@lib/python2.7/site-packages/sympy/matrices/expressions/matadd.pyR[RcC s|dkr|S||SdS(Ni((tcnttmat((s@lib/python2.7/site-packages/sympy/matrices/expressions/matadd.pytcombine\s cC sUt|jd„ƒ}t|tƒdkrMt|ttt|tƒgŒS|SdS(sī Merge explicit MatrixBase arguments Examples ======== >>> from sympy import MatrixSymbol, eye, Matrix, MatAdd, pprint >>> from sympy.matrices.expressions.matadd import merge_explicit >>> A = MatrixSymbol('A', 2, 2) >>> B = eye(2) >>> C = Matrix([[1, 2], [3, 4]]) >>> X = MatAdd(A, B, C) >>> pprint(X) [1 0] [1 2] A + [ ] + [ ] [0 1] [3 4] >>> pprint(merge_explicit(X)) [2 2] A + [ ] [3 5] cS s t|tƒS(N(RR(R1((s@lib/python2.7/site-packages/sympy/matrices/expressions/matadd.pyRxRiN(RR)tlenR8RR#RR(tmataddtgroups((s@lib/python2.7/site-packages/sympy/matrices/expressions/matadd.pytmerge_explicitcs"cC s|dkpt|tƒS(Ni(RR(R;((s@lib/python2.7/site-packages/sympy/matrices/expressions/matadd.pyRRcC s t|tƒS(N(RR(R;((s@lib/python2.7/site-packages/sympy/matrices/expressions/matadd.pyR†RN(*t __future__RRtsympy.core.compatibilityRtoperatorRt sympy.coreRRRtsympy.functionsRtsympy.matrices.matricesRt$sympy.matrices.expressions.transposeR tsympy.strategiesR R R R RRRRt"sympy.matrices.expressions.matexprRRRRtsympy.utilitiesRRRR't factor_oft matrix_ofRJRNtrulesR9(((s@lib/python2.7/site-packages/sympy/matrices/expressions/matadd.pyts.:"@