Source code for cvxpy.atoms.log_det

"""
Copyright 2013 Steven Diamond

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
"""

from typing import List, Tuple

import numpy as np
import scipy.sparse as sp
from numpy import linalg as LA

import cvxpy.settings as s
from cvxpy.atoms.atom import Atom
from cvxpy.constraints.constraint import Constraint


class log_det(Atom):
    """:math:`\\log\\det A`

    """

    def __init__(self, A) -> None:
        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.
        """
        # take Hermitian part of the input.
        symm = (values[0] + np.conj(values[0].T))/2
        sign, logdet = LA.slogdet(symm)
        if np.isclose(np.real(sign), 1):
            return logdet
        else:
            return -np.inf

    # Any argument shape is valid.
    def validate_arguments(self) -> None:
        X = self.args[0]
        if len(X.shape) == 1 or X.shape[0] != X.shape[1]:
            raise TypeError("The argument to log_det must be a square matrix.")

    def shape_from_args(self) -> Tuple[int, ...]:
        """Returns the (row, col) shape of the expression.
        """
        return tuple()

    def sign_from_args(self) -> Tuple[bool, bool]:
        """Returns sign (is positive, is negative) of the expression.
        """
        return (True, False)

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

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

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

    def is_decr(self, idx) -> bool:
        """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 = values[0]
        eigen_val = LA.eigvalsh(X)
        if np.min(eigen_val) > 0:
            # Grad: X^{-1}.T
            D = np.linalg.inv(X).T
            return [sp.csc_matrix(D.ravel(order='F')).T]
        # Outside domain.
        else:
            return [None]

    def _domain(self) -> List[Constraint]:
        """Returns constraints describing the domain of the node.
        """
        return [self.args[0] >> 0]

    @property
    def value(self) -> float:
        if not np.allclose(self.args[0].value,
                           self.args[0].value.T.conj(),
                           rtol=s.ATOM_EVAL_TOL,
                           atol=s.ATOM_EVAL_TOL):
            raise ValueError("Input matrix was not Hermitian/symmetric.")
        if any([p.value is None for p in self.parameters()]):
            return None
        return self._value_impl()