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)
assert mat.is_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()