# Source code for cvxpy.atoms.log_det

"""

you may not use this file except in compliance with the License.
You may obtain a copy of the License at

Unless required by applicable law or agreed to in writing, software
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
"""

from cvxpy.atoms.atom import Atom
import numpy as np
from numpy import linalg as LA
import scipy.sparse as sp

[docs]class log_det(Atom):
""":math:\\log\\det A

"""

def __init__(self, A):
super(log_det, self).__init__(A)

def numeric(self, values):
"""Returns the logdet of PSD matrix A.

For PSD matrix A, this is the sum of logs of eigenvalues of A
and is equivalent to the nuclear norm of the matrix logarithm of A.
"""
sign, logdet = LA.slogdet(values[0])
if sign == 1:
return logdet
else:
return -np.inf

# Any argument shape is valid.
def validate_arguments(self):
shape = self.args[0].shape
if len(shape) == 1 or shape[0] != shape[1]:
raise TypeError("The argument to log_det must be a square matrix.")

def shape_from_args(self):
"""Returns the (row, col) shape of the expression.
"""
return tuple()

def sign_from_args(self):
"""Returns sign (is positive, is negative) of the expression.
"""
return (True, False)

def is_atom_convex(self):
"""Is the atom convex?
"""
return False

def is_atom_concave(self):
"""Is the atom concave?
"""
return True

def is_incr(self, idx):
"""Is the composition non-decreasing in argument idx?
"""
return False

def is_decr(self, idx):
"""Is the composition non-increasing in argument idx?
"""
return False

"""Gives the (sub/super)gradient of the atom w.r.t. each argument.

Matrix expressions are vectorized, so the gradient is a matrix.

Args:
values: A list of numeric values for the arguments.

Returns:
A list of SciPy CSC sparse matrices or None.
"""
X = values[0]
eigen_val = LA.eigvals(X)
if np.min(eigen_val) > 0: