Source code for cvxpy.atoms.log_det

"""
Copyright 2013 Steven Diamond

This file is part of CVXPY.

CVXPY is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
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.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): n, m = self.args[0].shape if n != m: 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 def _grad(self, values): """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 = np.matrix(values[0]) eigen_val = LA.eigvals(X) if np.min(eigen_val) > 0: # Grad: X^{-1}.T D = np.linalg.inv(X).T return [sp.csc_matrix(D.A.ravel(order='F')).T] # Outside domain. else: return [None] def _domain(self): """Returns constraints describing the domain of the node. """ return [self.args[0] >> 0]