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- from sympy.core.basic import Basic
- from sympy.functions import adjoint, conjugate
- from sympy.matrices.expressions.matexpr import MatrixExpr
- class Transpose(MatrixExpr):
- """
- The transpose of a matrix expression.
- This is a symbolic object that simply stores its argument without
- evaluating it. To actually compute the transpose, use the ``transpose()``
- function, or the ``.T`` attribute of matrices.
- Examples
- ========
- >>> from sympy import MatrixSymbol, Transpose, transpose
- >>> A = MatrixSymbol('A', 3, 5)
- >>> B = MatrixSymbol('B', 5, 3)
- >>> Transpose(A)
- A.T
- >>> A.T == transpose(A) == Transpose(A)
- True
- >>> Transpose(A*B)
- (A*B).T
- >>> transpose(A*B)
- B.T*A.T
- """
- is_Transpose = True
- def doit(self, **hints):
- arg = self.arg
- if hints.get('deep', True) and isinstance(arg, Basic):
- arg = arg.doit(**hints)
- _eval_transpose = getattr(arg, '_eval_transpose', None)
- if _eval_transpose is not None:
- result = _eval_transpose()
- return result if result is not None else Transpose(arg)
- else:
- return Transpose(arg)
- @property
- def arg(self):
- return self.args[0]
- @property
- def shape(self):
- return self.arg.shape[::-1]
- def _entry(self, i, j, expand=False, **kwargs):
- return self.arg._entry(j, i, expand=expand, **kwargs)
- def _eval_adjoint(self):
- return conjugate(self.arg)
- def _eval_conjugate(self):
- return adjoint(self.arg)
- def _eval_transpose(self):
- return self.arg
- def _eval_trace(self):
- from .trace import Trace
- return Trace(self.arg) # Trace(X.T) => Trace(X)
- def _eval_determinant(self):
- from sympy.matrices.expressions.determinant import det
- return det(self.arg)
- def _eval_derivative(self, x):
- # x is a scalar:
- return self.arg._eval_derivative(x)
- def _eval_derivative_matrix_lines(self, x):
- lines = self.args[0]._eval_derivative_matrix_lines(x)
- return [i.transpose() for i in lines]
- def transpose(expr):
- """Matrix transpose"""
- return Transpose(expr).doit(deep=False)
- from sympy.assumptions.ask import ask, Q
- from sympy.assumptions.refine import handlers_dict
- def refine_Transpose(expr, assumptions):
- """
- >>> from sympy import MatrixSymbol, Q, assuming, refine
- >>> X = MatrixSymbol('X', 2, 2)
- >>> X.T
- X.T
- >>> with assuming(Q.symmetric(X)):
- ... print(refine(X.T))
- X
- """
- if ask(Q.symmetric(expr), assumptions):
- return expr.arg
- return expr
- handlers_dict['Transpose'] = refine_Transpose
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