Source code for sympy.matrices.expressions.inverse

from __future__ import print_function, division

from sympy.core.sympify import _sympify
from sympy.core import S, Basic

from sympy.matrices.expressions.matexpr import ShapeError
from sympy.matrices.expressions.matpow import MatPow


[docs]class Inverse(MatPow): """ 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 """ is_Inverse = True exp = S(-1) def __new__(cls, mat): mat = _sympify(mat) if not mat.is_Matrix: raise TypeError("mat should be a matrix") if not mat.is_square: raise ShapeError("Inverse of non-square matrix %s" % mat) return Basic.__new__(cls, mat) @property def arg(self): return self.args[0] @property def shape(self): return self.arg.shape def _eval_inverse(self): return self.arg def _eval_determinant(self): from sympy.matrices.expressions.determinant import det return 1/det(self.arg) def doit(self, **hints): if hints.get('deep', True): return self.arg.doit(**hints).inverse() else: return self.arg.inverse()
from sympy.assumptions.ask import ask, Q from sympy.assumptions.refine import handlers_dict def refine_Inverse(expr, assumptions): """ >>> 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 """ if ask(Q.orthogonal(expr), assumptions): return expr.arg.T elif ask(Q.unitary(expr), assumptions): return expr.arg.conjugate() elif ask(Q.singular(expr), assumptions): raise ValueError("Inverse of singular matrix %s" % expr.arg) return expr handlers_dict['Inverse'] = refine_Inverse