Source code for sympy.matrices.expressions.transpose
from __future__ import print_function, division
from sympy import Basic, Q
from sympy.functions import adjoint, conjugate
from sympy.matrices.expressions.matexpr import MatrixExpr
from sympy.matrices import MatrixBase
[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'
>>> A.T == transpose(A) == Transpose(A)
True
>>> Transpose(A*B)
(A*B)'
>>> transpose(A*B)
B'*A'
"""
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):
return self.arg._entry(j, i)
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()