/
transpose.py
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/
transpose.py
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from ...functions import adjoint, conjugate
from .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
========
>>> 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):
arg = arg.doit(**hints)
result = arg._eval_transpose()
return result if result is not None else 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 .determinant import det
return det(self.arg)
def transpose(expr):
"""Matrix transpose."""
return Transpose(expr).doit()