o o h< @sddlmZmZddlmZddlmZmZmZddl m Z m Z ddl m Z mZddlmZddlmZddlmZmZmZmZmZmZmZdd lmZdd lmZdd lm Z dd l!m"Z#d dl$m%Z%d dl&m'Z'd dl(m)Z)d dl*m*Z*d dl+m,Z,d dl-m.Z.m/Z/m0Z0m1Z1Gddde'e Z2e 3e e2fe2ddZ4ddZ5ddZ6ddZ7ddZ8d d!Z9d"d#Z:d$d%Z;d&d'Zd*d+Z?d,d-Z@e@ed<d.S)/)askQ) handlers_dict)BasicsympifyS)mulMul)NumberIntegerDummyadjoint)rm_idunpacktypedflattenexhaustdo_onenew)NonInvertibleMatrixError) MatrixBase)sympy_deprecation_warning)validate_matmul_integer)Inverse) MatrixExpr)MatPow transpose)PermutationMatrix) ZeroMatrixIdentityGenericIdentity OneMatrixcseZdZdZdZeZddddddZedd Z e d d Z d$d d Z ddZ ddZfddZddZddZddZddZddZddZd%d d!Zd"d#ZZS)&MatMula A product of matrix expressions Examples ======== >>> from sympy import MatMul, MatrixSymbol >>> A = MatrixSymbol('A', 5, 4) >>> B = MatrixSymbol('B', 4, 3) >>> C = MatrixSymbol('C', 3, 6) >>> MatMul(A, B, C) A*B*C TFN)evaluatecheck_sympifycs|sjSttfdd|}|rttt|}tjg|R}|\}}|dur3tdddd|dur;t ||s?|S|rF |S|S)Ncs j|kSN)identity)iclsu/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/sympy/matrices/expressions/matmul.py0 z MatMul.__new__..zaPassing check to MatMul is deprecated and the check argument will be removed in a future version.z1.11z,remove-check-argument-from-matrix-operations)deprecated_since_versionactive_deprecations_targetF) r+listfiltermaprr__new__as_coeff_matricesrvalidate _evaluate)r.r'r(r)argsobjfactormatricesr/r-r0r8*s(  zMatMul.__new__cCst|Sr*) canonicalize)r.exprr/r/r0r;JszMatMul._evaluatecCs$dd|jD}|dj|djfS)NcSg|]}|jr|qSr/ is_Matrix.0argr/r/r0 Pz MatMul.shape..r)r<rowscols)selfr?r/r/r0shapeNsz MatMul.shapec  sjddlm}ddlm|\}}t|dkr"||d||fSdgt|ddgt|d}|d<|d<dd} |d| tdt|D]}t|<qNt |ddD] \}} | j dd||<q_fd d t |D}t |} t fd d |Drd }||| gtdddgt||R} t dd |Dsd}|r| S| S)Nr)SumImmutableMatrixrrJcss d} td|V|d7}q)NrTzi_%ir )counterr/r/r0fbs zMatMul._entry..fdummy_generatorcs,g|]\}}|j||ddqS)r)rT)_entryrFr,rG)rTindicesr/r0rHos,z!MatMul._entry..c3s|]}|VqdSr*hasrFvrPr/r0 qz MatMul._entry..Tcss|] }t|ttfVqdSr*) isinstancer intrZr/r/r0r\ysF)sympy.concrete.summationsrOsympy.matrices.immutablerQr9lengetrangenext enumeraterNr fromiteranyzipdoit) rMr,jexpandkwargsrOcoeffr? ind_rangesrSrG expr_in_sumresultr/)rQrTrWr0rUSs6      z MatMul._entrycCsBdd|jD}dd|jD}t|}|jdurtd||fS)NcSg|]}|js|qSr/rCrFxr/r/r0rH~rIz,MatMul.as_coeff_matrices..cSrBr/rCrsr/r/r0rHrIFz3noncommutative scalars in MatMul are not supported.)r<r is_commutativeNotImplementedError)rMscalarsr?rnr/r/r0r9}s  zMatMul.as_coeff_matricescCs|\}}|t|fSr*)r9r&rMrnr?r/r/r0 as_coeff_mmuls  zMatMul.as_coeff_mmulc s tt|jdi|}||SNr/)superr&rlr;)rMrmexpanded __class__r/r0rls z MatMul.expandcCs4|\}}t|gdd|dddDRS)aTransposition 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 ========== .. [1] https://en.wikipedia.org/wiki/Transpose cSg|]}t|qSr/rrEr/r/r0rHz*MatMul._eval_transpose..NrJ)r9r&rjrxr/r/r0_eval_transposes zMatMul._eval_transposecCs"tdd|jdddDS)NcSrr/rrEr/r/r0rHrz(MatMul._eval_adjoint..rJ)r&r<rjrMr/r/r0 _eval_adjoints"zMatMul._eval_adjointcCs4|\}}|dkrddlm}|||SdS)Nr)trace)ryrrj)rMr>mmulrr/r/r0 _eval_traces  zMatMul._eval_tracecCs<ddlm}|\}}t|}||jttt||S)Nr) Determinant)&sympy.matrices.expressions.determinantrr9 only_squaresrKr r5r7)rMrr>r?square_matricesr/r/r0_eval_determinants  zMatMul._eval_determinantcCs>tdd|jDrtdd|jdddDSt|S)Ncss |] }t|tr|jVqdSr*)r^r is_squarerEr/r/r0r\z'MatMul._eval_inverse..css*|]}t|tr |n|dVqdS)rJN)r^rinverserEr/r/r0r\s  rJ)allr<r&rjrrr/r/r0 _eval_inverseszMatMul._eval_inversec s@dd}|rtfdd|jD}n|j}tt|}|S)NdeepTc3s |] }|jdiVqdSrz)rjrEhintsr/r0r\rzMatMul.doit..)rctupler<r@r&)rMrrr<rAr/rr0rjs  z MatMul.doitc sjddjD}ddjD}|r1t|}t|}|r1|r1t||kr1tdfdd|D||gS)NcSrBr/rursr/r/r0rHrIz#MatMul.args_cnc..cSrrr/rrsr/r/r0rHrIz"repeated commutative arguments: %scs$g|]}tj|dkr|qSr)r5r<count)rFcirr/r0rHs$)r<rbset ValueError)rMcsetwarnrmcoeff_ccoeff_ncclenr/rr0args_cncszMatMul.args_cncc sddlmfddt|jD}g}|D]U}|jd|}|j|dd}|r0t|}nt|jd}|rHtfddt|D}nt|jd}|j| } | D]} | || || | qYq|S)Nr Transposecsg|] \}}|r|qSr/rXrVrtr/r0rHz8MatMul._eval_derivative_matrix_lines..cs"g|] }|jr |n|qSr/)rDrj)rFr,rr/r0rHs"r) r rrfr<r&rgr#rNreversed_eval_derivative_matrix_lines append_first append_secondappend) rMrt with_x_indlinesind left_args right_args right_matleft_revdr,r/)rrtr0rs&     z$MatMul._eval_derivative_matrix_lines)T)FT)__name__ __module__ __qualname____doc__ is_MatMulr$r+r8 classmethodr;propertyrNrUr9ryrlrrrrrrjrr __classcell__r/r/r}r0r&s*    *   r&cGs(|ddkr |dd}ttg|RS)Nrr)rr&r<r/r/r0newmuls  rcCs>tdd|jDrdd|jD}t|dj|djS|S)Ncss"|] }|jp |jo |jVqdSr*)is_zerorD is_ZeroMatrixrEr/r/r0r\szany_zeros..cSrBr/rCrEr/r/r0rHrIzany_zeros..rrJ)rhr<r"rKrL)rr?r/r/r0 any_zeross rcCstdd|jDs |Sg}|jd}|jddD]}t|ttfr/t|ttfr/||}q|||}q||t|S)a Merge explicit MatrixBase arguments >>> from sympy import MatrixSymbol, 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] css|]}t|tVqdSr*)r^rrEr/r/r0r\r]z!merge_explicit..rrN)rhr<r^rr rr&)matmulnewargslastrGr/r/r0merge_explicits    rcCs:|\}}tdd|}||krt|g|jRS|S)z 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 cSs |jduS)NT) is_Identityrr/r/r0r16r2zremove_ids..)ryrrr<)rr>rrqr/r/r0 remove_ids's rcCs(|\}}|dkrt|g|RS|SNr)r9r)rr>r?r/r/r0factor_in_front<s rc Cs |\}}|dg}tdt|D]}|d}||}t|trJt|jtrJ|jj}t|}t||| dkrJ|d| t |j dg}qt|trt|jtr|jj} t| }t| ||||krt |j d} | |d<t|||D]} | || <q{q|j dks|j dkr| |qt|t r|j\} } n|tj} } t|t r|j\}}n|tj}}| |kr| |}t | |jdd|d<qt|tsz|}Wn tyd}Ynw|dur| |kr| |}t | |jdd|d<q| |qt|g|RS)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., $$ Y \times X \times X^{-1} \Rightarrow Y $$ rrrJNF)r)r9rdrbr^rrGr&r<r5r#rNrrrrOnerjrrrr)rr>r<new_argsr,ABBargslAargsr+rkA_baseA_expB_baseB_expnew_exp B_base_invr/r/r0combine_powersBsZ              rc Cs|j}t|}|dkr |S|dg}td|D],}|d}||}t|tr>t|tr>|jd}|jd}t|||d<q||qt|S)zGRefine products of permutation matrices as the products of cycles. rrrJ)r<rbrdr^r!rr&) rr<rrqr,rrcycle_1cycle_2r/r/r0combine_permutationss      rcCs|\}}|dg}|ddD]/}|d}t|tr!t|ts'||q||t|jd|jd||jd9}qt|g|RS)zj Combine products of OneMatrix e.g. OneMatrix(2, 3) * OneMatrix(3, 4) -> 3 * OneMatrix(2, 4) rrNrJ)r9r^r%rpoprNr)rr>r<rrrr/r/r0combine_one_matricess   rcs|jtdkr?ddlm}djr'djr'|fdddjDSdjr?djr?|fdddjDS|S)zr Simplify MatMul expressions but distributing rational term to MatMul. e.g. 2*(A+B) -> 2*A + 2*B rr)MatAddrcsg|] }t|dqSrr&rjrFmatrr/r0rHrz$distribute_monom..csg|] }td|qS)rrrrr/r0rHr)r<rbmataddr is_MatAdd is_Rational)rrr/rr0distribute_monoms  rcCs|dkSrr/rr/r/r0r1sr1cGsp|dj|djkrtdg}d}t|D]\}}|j||jkr5|t|||d|d}q|S)z'factor matrices only if they are squarerrJz!Invalid matrices being multipliedr)rKrL RuntimeErrorrfrr&rj)r?outstartr,Mr/r/r0rsrcCsg}g}|jD]}|jr||q||q|d}|ddD]4}||jkr9tt||r9t|jd}q"|| krOtt ||rOt|jd}q"|||}q"||t |S)z >>> from sympy import MatrixSymbol, Q, assuming, refine >>> X = MatrixSymbol('X', 2, 2) >>> expr = X * X.T >>> print(expr) X*X.T >>> with assuming(Q.orthogonal(X)): ... print(refine(expr)) I rrN) r<rDrTrr orthogonalr#rN conjugateunitaryr&)rA assumptionsrexprargsr<rrGr/r/r0 refine_MatMuls       rN)Asympy.assumptions.askrrsympy.assumptions.refiner sympy.corerrrsympy.core.mulrr sympy.core.numbersr r sympy.core.symbolr sympy.functionsrsympy.strategiesrrrrrrrsympy.matrices.exceptionsrsympy.matrices.matrixbasersympy.utilities.exceptionsr!sympy.matrices.expressions._shaperr:rrmatexprrmatpowrr permutationr!specialr"r#r$r%r&register_handlerclassrrrrrrrrrrulesr@rrr/r/r/r0sJ   $         V*? 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