Source code for sympy.matrices.expressions.transpose

from __future__ import print_function, division

from sympy import Basic
from sympy.functions import adjoint, conjugate

from sympy.matrices.expressions.matexpr import MatrixExpr

[docs]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.matrices import MatrixSymbol, Transpose >>> from sympy.functions import 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) try: result = arg._eval_transpose() return result if result is not None else Transpose(arg) except AttributeError: 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): return self.arg._entry(j, i, expand=expand) 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 transpose(expr): """ Matrix transpose """ return Transpose(expr).doit() 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