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106 lines
2.6 KiB
106 lines
2.6 KiB
5 months ago
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from sympy.core.basic import Basic
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from sympy.functions import adjoint, conjugate
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from sympy.matrices.expressions.matexpr import MatrixExpr
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class Transpose(MatrixExpr):
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"""
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The transpose 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 transpose, use the ``transpose()``
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function, or the ``.T`` attribute of matrices.
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Examples
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========
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>>> from sympy import MatrixSymbol, Transpose, transpose
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>>> A = MatrixSymbol('A', 3, 5)
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>>> B = MatrixSymbol('B', 5, 3)
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>>> Transpose(A)
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A.T
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>>> A.T == transpose(A) == Transpose(A)
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True
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>>> Transpose(A*B)
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(A*B).T
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>>> transpose(A*B)
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B.T*A.T
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"""
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is_Transpose = True
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def doit(self, **hints):
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arg = self.arg
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if hints.get('deep', True) and isinstance(arg, Basic):
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arg = arg.doit(**hints)
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_eval_transpose = getattr(arg, '_eval_transpose', None)
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if _eval_transpose is not None:
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result = _eval_transpose()
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return result if result is not None else Transpose(arg)
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else:
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return Transpose(arg)
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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[::-1]
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def _entry(self, i, j, expand=False, **kwargs):
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return self.arg._entry(j, i, expand=expand, **kwargs)
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def _eval_adjoint(self):
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return conjugate(self.arg)
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def _eval_conjugate(self):
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return adjoint(self.arg)
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def _eval_transpose(self):
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return self.arg
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def _eval_trace(self):
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from .trace import Trace
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return Trace(self.arg) # Trace(X.T) => Trace(X)
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def _eval_determinant(self):
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from sympy.matrices.expressions.determinant import det
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return det(self.arg)
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def _eval_derivative(self, x):
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# x is a scalar:
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return self.arg._eval_derivative(x)
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def _eval_derivative_matrix_lines(self, x):
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lines = self.args[0]._eval_derivative_matrix_lines(x)
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return [i.transpose() for i in lines]
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def transpose(expr):
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"""Matrix transpose"""
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return Transpose(expr).doit(deep=False)
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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_Transpose(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.T
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X.T
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>>> with assuming(Q.symmetric(X)):
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... print(refine(X.T))
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X
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"""
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if ask(Q.symmetric(expr), assumptions):
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return expr.arg
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return expr
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handlers_dict['Transpose'] = refine_Transpose
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