U me @stddlmZddlmZmZddlmZddlmZGdddeZ ddl m Z m Z ddl mZd d Zeed<d S) )_sympify)SBasic)NonSquareMatrixError)MatPowc@s`eZdZdZdZejZejfddZe ddZ e ddZ d d Z d d Z d dZddZdS)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|jdkr4td|t|||S)Nzmat should be a matrixFzInverse of non-square matrix %s)rZ is_Matrix TypeErrorZ is_squarerr__new__)clsmatexpr F/tmp/pip-unpacked-wheel-rdz2gdd2/sympy/matrices/expressions/inverse.pyr #s  zInverse.__new__cCs |jdSNr)argsselfr r rarg.sz Inverse.argcCs|jjSN)rshaperr r rr2sz Inverse.shapecCs|jSr)rrr r r _eval_inverse6szInverse._eval_inversecCsddlm}d||jS)Nr)det)Z&sympy.matrices.expressions.determinantrr)rrr r r_eval_determinant9s zInverse._eval_determinantcKs>d|kr|ddkr|S|j}|ddr6|jf|}|S)NZ inv_expandFdeepT)rgetdoitZinverse)rhintsrr r rr=s   z Inverse.doitcCsB|jd}||}|D]$}|j|j 9_|j|9_q|Sr)r_eval_derivative_matrix_linesZ first_pointerTZsecond_pointer)rxrlinesliner r rrGs   z%Inverse._eval_derivative_matrix_linesN)__name__ __module__ __qualname____doc__Z is_InverserZ NegativeOner r propertyrrrrrrr r r rrs    r)askQ) handlers_dictcCsTtt||r|jjStt||r2|jStt||rPtd|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 orthogonalrrZunitary conjugateZsingular ValueError)exprZ assumptionsr r rrefine_InverseTs  r.N)Zsympy.core.sympifyrZ sympy.corerrZsympy.matrices.commonrZ!sympy.matrices.expressions.matpowrrZsympy.assumptions.askr(r)Zsympy.assumptions.refiner*r.r r r rs   H