ó ~9­\c @ sÞddlmZmZddlmZddlmZmZmZddl m Z ddl m Z ddl mZddlmZmZmZmZmZmZmZddlmZmZmZmZmZdd lmZdd lm Z d eefd „ƒYZ!d „Z"d„Z#d„Z$d„Z%d„Z&d„Z'd„Z(d„Z)e$e'e&eed„ƒe%e(ee)f Z*eeiee*Œe!6ƒƒZ+d„Z,ddl-m.Z.m/Z/ddl0m1Z1d„Z2e2e1d >> from sympy import MatMul, MatrixSymbol >>> A = MatrixSymbol('A', 5, 4) >>> B = MatrixSymbol('B', 4, 3) >>> C = MatrixSymbol('C', 3, 6) >>> MatMul(A, B, C) A*B*C cO s‹|jdtƒ}|stƒStd„|ƒ}ttt|ƒƒ}tj||Œ}|j ƒ\}}|r}t |Œn|s‡|S|S(NtcheckcS s tƒ|kS(N(R(ti((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pyt(t( tgettTrueRtfiltertlisttmapRRt__new__tas_coeff_matricestvalidate(tclstargstkwargsRtobjtfactortmatrices((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pyR! s cC s=g|jD]}|jr |^q }|dj|djfS(Niiÿÿÿÿ(R%t is_Matrixtrowstcols(tselftargR)((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pytshape5s%c séddlm}m}m}m‰m‰|jƒ\}}t|ƒdkrb||d||fSdgt|ƒd} dgt|ƒd} || d<|| dLsc3 s$|]}t|ˆtfƒVqdS(N(t isinstancetint(R5R6(R3(s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pys Ts(tsympyR0R1RR2R3R"tlentNoneRt enumerateR/tfromitertanyRtziptFalsetdoit(R-RtjtexpandR0R1RtcoeffR)tindicest ind_rangesR.t expr_in_sumtresult((R2R3s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pyt_entry:s,(  ; * cC s~g|jD]}|js |^q }g|jD]}|jr/|^q/}t|Œ}|jtkrttdƒ‚n||fS(Ns3noncommutative scalars in MatMul are not supported.(R%R*Rtis_commutativeR@tNotImplementedError(R-txtscalarsR)RD((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pyR"Xs %% cC s"|jƒ\}}|t|ŒfS(N(R"R(R-RDR)((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pyt as_coeff_mmulascC s9tg|jddd…D]}t|ƒ^qŒjƒS(Niÿÿÿÿ(RR%RRA(R-R.((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pyt_eval_transposeescC s9tg|jddd…D]}t|ƒ^qŒjƒS(Niÿÿÿÿ(RR%RRA(R-R.((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pyt _eval_adjointhscC sR|jƒ\}}|dkrBddlm}|||jƒƒStdƒ‚dS(Ni(ttracesCan't simplify any further(RNRQRARK(R-R(tmmulRQ((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pyt _eval_traceks  cC sRddlm}|jƒ\}}t|Œ}||jttt||ƒƒŒS(Niÿÿÿÿ(t Determinant(t&sympy.matrices.expressions.determinantRTR"t only_squaresR+RRR (R-RTR(R)tsquare_matrices((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pyt_eval_determinantss cC s…yVtg|jddd…D]+}t|tƒr>|jƒn|d^qŒjƒSWn(tk r€ddlm}||ƒSXdS(Niÿÿÿÿ(tInverse( RR%R7RtinverseRARt"sympy.matrices.expressions.inverseRY(R-R.RY((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pyt _eval_inverseysP cK s„|jdtƒ}|r@g|jD]}|j|^q"}n |j}g|jD]}|jrS|^qS}tt|Œƒ}|S(Ntdeep(RRR%RAR*t canonicalizeR(R-R&R]R.R%tmatstexpr((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pyRA‚s( %cK sTg|jD]}|jr |^q }g|jD]}|js/|^q/}||gS(N(R%RJ(R-R&RLtcoeff_ctcoeff_nc((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pytargs_cncŽs%%cC szddlm}gt|jƒD]!\}}|j|ƒr |^q }g}x&|D]}|j| }|j|d} tj| ƒ} tjgt| ƒD]}||ƒjƒ^qšƒ} tj|ƒ} tjgt|ƒD]}||ƒjƒ^q݃} |j|j |ƒ}x[|D]S}|j rG|j | ƒ|j | ƒn|j | ƒ|j | ƒ|j |ƒqWqTW|S(Ni(t Transpose(RRdR<R%R4RR=treversedRAt_eval_derivative_matrix_linest transposedt append_firstt append_secondtappend(R-RLRdRR.t with_x_indtlinestindt left_argst right_argst right_matt right_revtleft_mattleft_revtd((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pyRf“s&7  44     (t__name__t __module__t__doc__Rt is_MatMulR!tpropertyR/RIR"RNRORPRSRXR\RARcRf(((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pyRs         cG sgx`tt|ƒdƒD]H}|||d!\}}|j|jkrtd||fƒ‚qqWdS(s, Checks for valid shapes for args of MatMul iis"Matrices %s and %s are not alignedN(RR:R,R+R(R)RtAtB((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pyR#­scG s*|ddkr|d}ntt|ŒS(Nii(RR(R%((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pytnewmul·s cC s{tg|jD]!}|jp+|jo+|j^q ƒrwg|jD]}|jrA|^qA}t|dj|djƒS|S(Niiÿÿÿÿ(R>R%tis_zeroR*t is_ZeroMatrixRR+R,(tmulR.R)((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pyt any_zeros¼s 1%cC s©td„|jDƒƒs|Sg}|jd}x_|jdD]P}t|ttfƒr{t|ttfƒr{||}q>|j|ƒ|}q>W|j|ƒt|ŒS(s Merge explicit MatrixBase arguments >>> from sympy import MatrixSymbol, eye, Matrix, MatMul, pprint >>> from sympy.matrices.expressions.matmul import merge_explicit >>> A = MatrixSymbol('A', 2, 2) >>> B = Matrix([[1, 1], [1, 1]]) >>> C = Matrix([[1, 2], [3, 4]]) >>> X = MatMul(A, B, C) >>> pprint(X) [1 1] [1 2] A*[ ]*[ ] [1 1] [3 4] >>> pprint(merge_explicit(X)) [4 6] A*[ ] [4 6] >>> X = MatMul(B, A, C) >>> pprint(X) [1 1] [1 2] [ ]*A*[ ] [1 1] [3 4] >>> pprint(merge_explicit(X)) [1 1] [1 2] [ ]*A*[ ] [1 1] [3 4] cs s|]}t|tƒVqdS(N(R7R(R5R.((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pys ßsii(R>R%R7RRRjR(tmatmultnewargstlastR.((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pytmerge_explicitÃs *    c C shddlm}|jƒ\}}x?tt|d |dƒƒD] \}\}}yú|jrK|jrK|d}}|d} } t|tƒr²t||ƒ r²|j\}}nt|tƒrãt||ƒ rã|j\} } n|| j ƒkrK|| dkr||| } n| | |} t ||| | g||dŒSnWq@t k r_q@Xq@W|S(s Y * X * X.I -> Y iÿÿÿÿ(RYiii( R[RYR"R<R?t is_squareR7RR%RZR|t ValueError( RRYR(R)RtXtYt_Xtx_expt_Yty_exptI((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pytxxinvís&0  + cC sK|jƒ\}}td„ƒ|ƒ}||krCt||jŒS|SdS(sñ Remove Identities from a MatMul This is a modified version of sympy.strategies.rm_id. This is necesssary because MatMul may contain both MatrixExprs and Exprs as args. See Also ======== sympy.strategies.rm_id cS s |jtkS(N(t is_IdentityR(RL((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pyRRN(RNR R|R%(RR(RRRH((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pyt remove_idss  cC s/|jƒ\}}|dkr+t||ŒS|S(Ni(R"R|(RR(R)((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pytfactor_in_fronts  c C sddlm}|jƒ\}}g}d}d}xª|jD]Ÿ}t||ƒrp|jd}|jd} n |}d} ||kr•|| 7}q>|dk rÑ|dkr½|j|ƒqÑ|j||ƒn| }|}q>W|dkrý|j|ƒn|j||ƒt||ŒS(Niÿÿÿÿ(Rii(tsympy.matrices.expressionsRRNR;R%R7RjR|( RRR(RRR%tbasetexpR.t current_baset current_exp((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pytcombine_powerss.       cC s |dkS(Ni((RL((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pyR?RcG s|dj|djkr)tdƒ‚ng}d}xat|ƒD]S\}}|j||jkrB|jt|||d!Œjƒƒ|d}qBqBW|S(s'factor matrices only if they are squareiiÿÿÿÿs!Invalid matrices being multipliedi(R+R,t RuntimeErrorR<RjRRA(R)touttstartRtM((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pyRVCs$(tasktQ(t handlers_dictcC s g}g}x7|jD],}|jr5|j|ƒq|j|ƒqW|d}x¢|dD]–}||jkržttj|ƒ|ƒržt|jdƒ}q[||j ƒkrÞttj |ƒ|ƒrÞt|jdƒ}q[|j|ƒ|}q[W|j|ƒt |ŒS(sè >>> from sympy import MatrixSymbol, Q, assuming, refine >>> X = MatrixSymbol('X', 2, 2) >>> expr = X * X.T >>> print(expr) X*X.T >>> with assuming(Q.orthogonal(X)): ... print(refine(expr)) I ii( R%R*RjtTRœRt orthogonalRR/t conjugatetunitaryR(R`t assumptionsR‚texprargsR%RƒR.((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pyt refine_MatMulTs   '*   N(3t __future__RRR9Rt sympy.coreRRRtsympy.core.compatibilityRtsympy.functionsRt$sympy.matrices.expressions.transposeRtsympy.strategiesR R R R R RRt"sympy.matrices.expressions.matexprRRRRRt!sympy.matrices.expressions.matpowRtsympy.matrices.matricesRRR#R|R€R„RŽRR‘R—trulesR^RVtsympy.assumptions.askRœRtsympy.assumptions.refineRžR¥(((s@lib/python2.7/site-packages/sympy/matrices/expressions/matmul.pyts44(   *      "