Source code for cvxpy.atoms.sum_largest

"""
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 cvxpy.interface as intf
import numpy as np
import scipy.sparse as sp


[docs]class sum_largest(Atom): """Sum of the largest k values in the matrix X. """ def __init__(self, x, k): self.k = k super(sum_largest, self).__init__(x) def validate_arguments(self): """Verify that k is a positive integer. """ if int(self.k) != self.k or self.k <= 0: raise ValueError("Second argument must be a positive integer.") super(sum_largest, self).validate_arguments() def numeric(self, values): """Returns the sum of the k largest entries of the matrix. """ value = values[0].flatten() indices = np.argsort(-value)[:int(self.k)] return value[indices].sum() 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: 1 for each of k largest indices. value = intf.from_2D_to_1D(values[0].flatten().T) indices = np.argsort(-value)[:int(self.k)] D = np.zeros((self.args[0].shape[0]*self.args[0].shape[1], 1)) D[indices] = 1 return [sp.csc_matrix(D)] 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. """ # Same as argument. return (self.args[0].is_nonneg(), self.args[0].is_nonpos()) 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 True def is_decr(self, idx): """Is the composition non-increasing in argument idx? """ return False def get_data(self): """Returns the parameter k. """ return [self.k]