Source code for cvxpy.atoms.lambda_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
from scipy import linalg as LA
import numpy as np
import scipy.sparse as sp


[docs]class lambda_max(Atom): """ Maximum eigenvalue; :math:`\lambda_{\max}(A)`. """ def __init__(self, A): super(lambda_max, self).__init__(A) def numeric(self, values): """Returns the largest eigenvalue of A. Requires that A be symmetric. """ lo = hi = self.args[0].shape[0]-1 return LA.eigvalsh(values[0], eigvals=(lo, hi))[0] def _domain(self): """Returns constraints describing the domain of the node. """ return [self.args[0].H == self.args[0]] 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. """ w, v = LA.eigh(values[0]) d = np.zeros(w.shape) d[-1] = 1 d = np.diag(d) D = v.dot(d).dot(v.T) return [sp.csc_matrix(D.ravel(order='F')).T] def validate_arguments(self): """Verify that the argument A is square. """ if not self.args[0].ndim == 2 or self.args[0].shape[0] != self.args[0].shape[1]: raise ValueError("The argument '%s' to lambda_max must resolve to a square matrix." % self.args[0].name()) 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 (False, 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