# Source code for sympy.matrices.expressions.trace

from __future__ import print_function, division

from sympy import Basic, Expr, sympify
from sympy.matrices.matrices import MatrixBase
from .matexpr import ShapeError

[docs]class Trace(Expr):
"""Matrix Trace

Represents the trace of a matrix expression.

>>> from sympy import MatrixSymbol, Trace, eye
>>> A = MatrixSymbol('A', 3, 3)
>>> Trace(A)
Trace(A)

trace
"""
is_Trace = True

def __new__(cls, mat):
mat = sympify(mat)

if not mat.is_Matrix:
raise TypeError("input to Trace, %s, is not a matrix" % str(mat))

if not mat.is_square:
raise ShapeError("Trace of a non-square matrix")

return Basic.__new__(cls, mat)

def _eval_transpose(self):
return self

@property
def arg(self):
return self.args[0]

def doit(self, **kwargs):
if kwargs.get('deep', True):
arg = self.arg.doit(**kwargs)
try:
return arg._eval_trace()
except (AttributeError, NotImplementedError):
return Trace(arg)
else:
# _eval_trace would go too deep here
if isinstance(self.arg, MatrixBase):
return trace(self.arg)
else:
return Trace(self.arg)

def _eval_rewrite_as_Sum(self):
from sympy import Sum, Dummy
i = Dummy('i')
return Sum(self.arg[i, i], (i, 0, self.arg.rows-1)).doit()

def trace(expr):
""" Trace of a Matrix.  Sum of the diagonal elements

>>> from sympy import trace, Symbol, MatrixSymbol, pprint, eye
>>> n = Symbol('n')
>>> X = MatrixSymbol('X', n, n)  # A square matrix
>>> trace(2*X)
2*Trace(X)

>>> trace(eye(3))
3