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104 lines
2.7 KiB
104 lines
2.7 KiB
5 months ago
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from sympy.core.sympify import _sympify
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from sympy.core import S, Basic
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from sympy.matrices.common import NonSquareMatrixError
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from sympy.matrices.expressions.matpow import MatPow
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class Inverse(MatPow):
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"""
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The multiplicative inverse of a matrix expression
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This is a symbolic object that simply stores its argument without
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evaluating it. To actually compute the inverse, use the ``.inverse()``
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method of matrices.
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Examples
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========
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>>> from sympy import MatrixSymbol, Inverse
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>>> A = MatrixSymbol('A', 3, 3)
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>>> B = MatrixSymbol('B', 3, 3)
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>>> Inverse(A)
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A**(-1)
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>>> A.inverse() == Inverse(A)
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True
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>>> (A*B).inverse()
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B**(-1)*A**(-1)
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>>> Inverse(A*B)
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(A*B)**(-1)
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"""
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is_Inverse = True
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exp = S.NegativeOne
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def __new__(cls, mat, exp=S.NegativeOne):
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# exp is there to make it consistent with
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# inverse.func(*inverse.args) == inverse
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mat = _sympify(mat)
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exp = _sympify(exp)
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if not mat.is_Matrix:
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raise TypeError("mat should be a matrix")
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if mat.is_square is False:
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raise NonSquareMatrixError("Inverse of non-square matrix %s" % mat)
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return Basic.__new__(cls, mat, exp)
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@property
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def arg(self):
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return self.args[0]
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@property
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def shape(self):
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return self.arg.shape
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def _eval_inverse(self):
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return self.arg
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def _eval_determinant(self):
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from sympy.matrices.expressions.determinant import det
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return 1/det(self.arg)
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def doit(self, **hints):
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if 'inv_expand' in hints and hints['inv_expand'] == False:
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return self
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arg = self.arg
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if hints.get('deep', True):
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arg = arg.doit(**hints)
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return arg.inverse()
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def _eval_derivative_matrix_lines(self, x):
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arg = self.args[0]
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lines = arg._eval_derivative_matrix_lines(x)
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for line in lines:
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line.first_pointer *= -self.T
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line.second_pointer *= self
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return lines
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from sympy.assumptions.ask import ask, Q
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from sympy.assumptions.refine import handlers_dict
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def refine_Inverse(expr, assumptions):
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"""
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>>> from sympy import MatrixSymbol, Q, assuming, refine
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>>> X = MatrixSymbol('X', 2, 2)
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>>> X.I
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X**(-1)
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>>> with assuming(Q.orthogonal(X)):
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... print(refine(X.I))
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X.T
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"""
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if ask(Q.orthogonal(expr), assumptions):
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return expr.arg.T
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elif ask(Q.unitary(expr), assumptions):
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return expr.arg.conjugate()
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elif ask(Q.singular(expr), assumptions):
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raise ValueError("Inverse of singular matrix %s" % expr.arg)
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return expr
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handlers_dict['Inverse'] = refine_Inverse
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