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


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, exp=S(-1)):
        # exp is there to make it consistent with
        # inverse.func(*inverse.args) == inverse
        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, exp)

    @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 'inv_expand' in hints and hints['inv_expand'] == False:
            return self
        if hints.get('deep', True):
            return self.arg.doit(**hints).inverse()
        else:
            return self.arg.inverse()

    def _eval_derivative_matrix_lines(self, x):
        arg = self.args[0]
        lines = arg._eval_derivative_matrix_lines(x)
        for line in lines:
            if line.transposed:
                line.first *= self
                line.second *= -self.T
            else:
                line.first *= -self.T
                line.second *= self
        return lines


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