# Source code for cvxpy.atoms.affine.diag

"""

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

[docs]def diag(expr):
"""Extracts the diagonal from a matrix or makes a vector a diagonal matrix.

Parameters
----------
expr : Expression or numeric constant
A vector or square matrix.

Returns
-------
Expression
An Expression representing the diagonal vector/matrix.
"""
expr = AffAtom.cast_to_const(expr)
if expr.is_vector():
return diag_vec(vec(expr))
elif expr.ndim == 2 and expr.shape[0] == expr.shape[1]:
return diag_mat(expr)
else:
raise ValueError("Argument to diag must be a vector or square matrix.")

class diag_vec(AffAtom):
"""Converts a vector into a diagonal matrix.
"""

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

def numeric(self, values):
"""Convert the vector constant into a diagonal matrix.
"""
return np.diag(values[0])

def shape_from_args(self):
"""A square matrix.
"""
rows = self.args[0].shape[0]
return (rows, rows)

def is_symmetric(self):
"""Is the expression symmetric?
"""
return True

def is_hermitian(self):
"""Is the expression symmetric?
"""
return True

@staticmethod
def graph_implementation(arg_objs, shape, data=None):
"""Convolve two vectors.

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.diag_vec(arg_objs[0]), [])

class diag_mat(AffAtom):
"""Extracts the diagonal from a square matrix.
"""

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

@AffAtom.numpy_numeric
def numeric(self, values):
"""Extract the diagonal from a square matrix constant.
"""
# The return type in numpy versions < 1.10 was ndarray.
v = np.diag(values[0])
if isinstance(v, np.matrix):
v = v.A[0]
return v

def shape_from_args(self):
"""A column vector.
"""
rows, _ = self.args[0].shape
return (rows,)

@staticmethod
def graph_implementation(arg_objs, shape, data=None):
"""Extracts the diagonal of a matrix.

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.diag_mat(arg_objs[0]), [])