Source code for cvxpy.atoms.sigma_max

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


[docs]class sigma_max(Atom): """ Maximum singular value. """ _allow_complex = True def __init__(self, A): super(sigma_max, self).__init__(A) @Atom.numpy_numeric def numeric(self, values): """Returns the largest singular value of A. """ return LA.norm(values[0], 2) 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. """ # Grad: U diag(e_1) V.T U, s, V = LA.svd(values[0]) ds = np.zeros(len(s)) ds[0] = 1 D = U.dot(np.diag(ds)).dot(V) return [sp.csc_matrix(D.ravel(order='F')).T] 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. """ # Always positive. return (True, False) def is_atom_convex(self): """Is the atom convex? """ return True def is_atom_concave(self): """Is the atom concave? """ return False 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