a Юм>> 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 TF)┌evaluate┌check┌_sympifycst|s ИjSttЗfddД|ГГ}|r2ttt|ГГ}tjИg|вRО}|аб\}}|r\t|О|sd|S|rpt |ГS|S)Ncs Иj|kSйN)┌identity)┌iй┌clsй·q/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/sympy/matrices/expressions/matmul.py┌.єz MatMul.__new__..) r*┌list┌filter┌maprr┌__new__┌as_coeff_matrices┌validate┌canonicalize)r-r&r'r(┌args┌obj┌factor┌matricesr.r,r/r5(szMatMul.__new__cCs$ddД|jDГ}|dj|djfS)NcSsg|]}|jr|СqSr.й┌ is_Matrixй┌.0┌argr.r.r/┌ Dr1z MatMul.shape..rщ )r9┌rows┌cols)┌selfr<r.r.r/┌shapeBszMatMul.shapecCs|jdабS)Nr)r9┌could_extract_minus_signйrFr.r.r/rHGszMatMul.could_extract_minus_signc spddlm}ddlmЙ|аб\}}t|ГdkrD||d||fSdgt|ГdЙdgt|Гd}|Иd<|Иd<ddД} |аd| ГбЙtdt|ГГD]}tИГИ|<qЬt |ddЕГD]\}} | j dd||<q╛ЗЗfd d Дt |ГDГ}tа|б}t ЗfddД|DГГРrd }|||gtИddЕdgt|Г|ГвRО}t ddД|DГГРs^d}|Рrl|абS|S)Nr)┌Sumй┌ImmutableMatrixrrCcss d}td|ГV|d7}qdS)Nrzi_%ir)┌counterr.r.r/┌fYszMatMul._entry..f┌dummy_generatorcs,g|]$\}}|jИ|И|dИdНСqS)r)rO)┌_entryйr@r+rA)rO┌indicesr.r/rBfr1z!MatMul._entry..c3s|]}|аИбVqdSr)йZhasйr@┌vrKr.r/┌ hr1z MatMul._entry..Tcss|]}t|ttfГVqdSr))┌ isinstancer┌intrTr.r.r/rVpr1F)Zsympy.concrete.summationsrJZsympy.matrices.immutablerLr6┌len┌get┌range┌next┌ enumeraterGr ┌fromiter┌any┌zip┌doit) rFr+┌j┌expand┌kwargsrJ┌coeffr<Z ind_rangesrNrAZexpr_in_sum┌resultr.)rLrOrRr/rPJs6 ■ z MatMul._entrycCsBddД|jDГ}ddД|jDГ}t|О}|jdur:tdГВ||fS)NcSsg|]}|js|СqSr.r=йr@┌xr.r.r/rBur1z,MatMul.as_coeff_matrices..cSsg|]}|jr|СqSr.r=rgr.r.r/rBvr1Fz3noncommutative scalars in MatMul are not supported.)r9r ┌is_commutative┌NotImplementedError)rFZscalarsr<rer.r.r/r6ts zMatMul.as_coeff_matricescCs|аб\}}|t|ОfSr))r6r%йrFrer<r.r.r/┌ as_coeff_mmul}szMatMul.as_coeff_mmulcCs4|аб\}}t|gddД|dddЕDГвRОабS)aиTransposition of matrix multiplication. Notes ===== The following rules are applied. Transposition for matrix multiplied with another matrix: `\left(A B\right)^{T} = B^{T} A^{T}` Transposition for matrix multiplied with scalar: `\left(c A\right)^{T} = c A^{T}` References ========== .. 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See Also ======== sympy.strategies.rm_id cSs |jduS)NT)Zis_Identityrr.r.r/r0,r1zremove_ids..N)rlrrОr9)rr;rprfr.r.r/┌ remove_idss rХcCs(|аб\}}|dkr$t|g|вRОS|SйNr)r6rО)rr;r<r.r.r/┌factor_in_front2srЧc Cs>|аб\}}|dg}|ddЕDР]}|d}|jdksD|jdkrP|а|бq"t|tГrf|j\}}n|tj}}t|tГrИ|j\}} n|tj}} ||kr╛|| } t|| ГjddН|d<q"ndt|t ГРs"z|а б}Wntyьd}Yn0|duРr"||kРr"|| } t|| ГjddН|d<q"|а|бq"t|g|вRОS)aCombine consecutive powers with the same base into one, e.g. $$A \times A^2 \Rightarrow A^3$$ This also cancels out the possible matrix inverses using the knowledgebase of :class:`~.Inverse`, e.g., $$ Y \times X \times X^{-1} \Rightarrow Y $$ rrNrCF)rw) r6Z is_squarerВrWrr9rZOnerarrurrО)rr;r9┌new_argsrНrМZA_baseZA_expZB_baseZB_expZnew_expZ B_base_invr.r.r/┌combine_powers8s8 rЩc CsР|j}t|Г}|dkr|S|dg}td|ГD]X}|d}||}t|tГr|t|tГr||jd}|jd}t||Г|d<q.|а|бq.t|ОS)zGRefine products of permutation matrices as the products of cycles. rЛrrrC)r9rYr[rWr rВr%) rr9┌lrfr+rМrНZcycle_1Zcycle_2r.r.r/┌combine_permutationsds rЫcCsТ|аб\}}|dg}|ddЕD]^}|d}t|tГrBt|tГsN|а|бq"|аб|аt|jd|jdГб||jd9}q"t|g|вRОS)zj Combine products of OneMatrix e.g. OneMatrix(2, 3) * OneMatrix(3, 4) -> 3 * OneMatrix(2, 4) rrNrC)r6rWr$rВ┌poprGrО)rr;r9rШrНrМr.r.r/┌combine_one_matriceszs rЭcsВ|jЙtИГdkr~ddlm}ИdjrNИdjrN|ЗfddДИdjDГОSИdjr~Иdjr~|ЗfddДИdjDГОS|S)zr Simplify MatMul expressions but distributing rational term to MatMul. e.g. 2*(A+B) -> 2*A + 2*B rЛr)┌MatAddrcsg|]}t|ИdГабСqS)rйr%raйr@┌matr{r.r/rBЩr1z$distribute_monom..csg|]}tИd|ГабСqS)rrЯrаr{r.r/rBЫr1)r9rYZmataddrЮZ is_MatAddZis_Rational)rrЮr.r{r/┌distribute_monomОsrвcCs|dkSrЦr.rr.r.r/r0Яr1r0cGsp|dj|djkrtdГВg}d}t|ГD]>\}}|j||jkr,|аt|||dЕОабб|d}q,|S)z'factor matrices only if they are squarerrCz!Invalid matrices being multipliedr)rDrE┌RuntimeErrorr]rВr%ra)r<┌out┌startr+┌Mr.r.r/rsдs rscCs└g}g}|jD] }|jr$|а|бq|а|бq|d}|ddЕD]h}||jkrrttа|б|Гrrt|jdГ}qD||а бkrЮttа |б|ГrЮt|jdГ}qD|а|б|}qD|а|бt|ОS)zш >>> from sympy import MatrixSymbol, Q, assuming, refine >>> X = MatrixSymbol('X', 2, 2) >>> expr = X * X.T >>> print(expr) X*X.T >>> with assuming(Q.orthogonal(X)): ... print(refine(expr)) I rrN)r9r>rВ┌TrrZ orthogonalr"rG┌ conjugateZunitaryr%)ryZassumptionsrТZexprargsr9rУrAr.r.r/┌ refine_MatMul▒s rйN)>Zsympy.assumptions.askrrZsympy.assumptions.refinerZ sympy.corerrrZsympy.core.mulrr Zsympy.core.numbersr rZsympy.core.symbolr Zsympy.functionsrZsympy.strategiesrrrrrrrZsympy.matrices.commonrrZsympy.matrices.matricesrrurZmatexprrZmatpowrrZpermutationr Zspecialr!r"r#r$r%Zregister_handlerclassr7rОrРrФrХrЧrЩrЫrЭrв┌rulesr8rsrйr.r.r.r/┌sF$F *,■ "