# Source code for cvxpy.atoms.affine.trace

"""

This file is part of CVXPY.

CVXPY is free software: you can redistribute it and/or modify
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

CVXPY is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with CVXPY.  If not, see <http://www.gnu.org/licenses/>.
"""

from cvxpy.atoms.affine.affine_atom import AffAtom
import cvxpy.lin_ops.lin_utils as lu
import numpy as np

[docs]class trace(AffAtom):
"""The sum of the diagonal entries of a matrix.

Parameters
----------
expr : Expression
The expression to sum the diagonal of.
"""

def __init__(self, expr):
super(trace, self).__init__(expr)

@AffAtom.numpy_numeric
def numeric(self, values):
"""Sums the diagonal entries.
"""
return np.trace(values[0])

def validate_arguments(self):
"""Checks that the argument is a square matrix.
"""
shape = self.args[0].shape
if self.args[0].ndim != 2 or shape[0] != shape[1]:
raise ValueError("Argument to trace must be a square matrix.")

def shape_from_args(self):
"""Always scalar.
"""
return tuple()

@staticmethod
def graph_implementation(arg_objs, shape, data=None):
"""Sum the diagonal entries of the linear expression.

Parameters
----------
arg_objs : list
LinExpr for each argument.
shape : tuple
The shape of the resulting expression.
data :
Additional data required by the atom.

Returns
-------
tuple
(LinOp for objective, list of constraints)
"""
return (lu.trace(arg_objs[0]), [])