o i @stddlmZddlmZmZddlmZddlmZGdddeZ ddl m Z m Z ddl mZd d Zeed<d S) )_sympify)SBasic)NonSquareMatrixError)MatPowc@sxeZdZdZdZejZejfddZe ddZ e ddZ d d Z d d Z d dZddZddZddZddZdS)Inversea The multiplicative inverse of a matrix expression This is a symbolic object that simply stores its argument without evaluating it. To actually compute the inverse, use the ``.inverse()`` method of matrices. Examples ======== >>> from sympy import MatrixSymbol, Inverse >>> A = MatrixSymbol('A', 3, 3) >>> B = MatrixSymbol('B', 3, 3) >>> Inverse(A) A**(-1) >>> A.inverse() == Inverse(A) True >>> (A*B).inverse() B**(-1)*A**(-1) >>> Inverse(A*B) (A*B)**(-1) TcCsBt|}t|}|jstd|jdurtd|t|||S)Nzmat should be a matrixFzInverse of non-square matrix %s)rZ is_Matrix TypeErrorZ is_squarerr__new__)clsmatexpr q/var/www/html/eduruby.in/lip-sync/lip-sync-env/lib/python3.10/site-packages/sympy/matrices/expressions/inverse.pyr #s  zInverse.__new__cCs |jdSNr)argsselfr r rarg.s z Inverse.argcCs|jjSN)rshaperr r rr2sz Inverse.shapecCs|jSr)rrr r r _eval_inverse6szInverse._eval_inversecCt|jSr)rrZ transposerr r r_eval_transpose9zInverse._eval_transposecCrr)rrZadjointrr r r _eval_adjoint<rzInverse._eval_adjointcCrr)rr conjugaterr r r_eval_conjugate?rzInverse._eval_conjugatecCsddlm}d||jS)Nr)det)Z&sympy.matrices.expressions.determinantrr)rrr r r_eval_determinantBs zInverse._eval_determinantcKsBd|vr |ddkr |S|j}|ddr|jdi|}|S)NZ inv_expandFdeepTr )rgetdoitZinverse)rhintsrr r rr"Fs  z Inverse.doitcCsB|jd}||}|D]}|j|j 9_|j|9_q |Sr)r_eval_derivative_matrix_linesZ first_pointerTZsecond_pointer)rxrlinesliner r rr$Ps  z%Inverse._eval_derivative_matrix_linesN)__name__ __module__ __qualname____doc__Z is_InverserZ NegativeOner r propertyrrrrrrrr"r$r r r rrs    r)askQ) handlers_dictcCsTtt||r |jjStt||r|jStt||r(td|j|S)z >>> from sympy import MatrixSymbol, Q, assuming, refine >>> X = MatrixSymbol('X', 2, 2) >>> X.I X**(-1) >>> with assuming(Q.orthogonal(X)): ... print(refine(X.I)) X.T zInverse of singular matrix %s) r.r/Z orthogonalrr%ZunitaryrZsingular ValueError)exprZ assumptionsr r rrefine_Inverse]s  r3N)Zsympy.core.sympifyrZ sympy.corerrZsympy.matrices.exceptionsrZ!sympy.matrices.expressions.matpowrrZsympy.assumptions.askr.r/Zsympy.assumptions.refiner0r3r r r rs   Q