Source code for cvxpy.atoms.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 cvxpy.atoms.axis_atom import AxisAtom
import cvxpy.lin_ops.lin_utils as lu
import numpy as np


[docs]class max(AxisAtom): """:math:`\max_{i,j}\{X_{i,j}\}`. """ def __init__(self, x, axis=None, keepdims=False): super(max, self).__init__(x, axis=axis, keepdims=keepdims) @Atom.numpy_numeric def numeric(self, values): """Returns the largest entry in x. """ return values[0].max(axis=self.axis, keepdims=self.keepdims) 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. """ return self._axis_grad(values) def _column_grad(self, value): """Gives the (sub/super)gradient of the atom w.r.t. a column argument. Matrix expressions are vectorized, so the gradient is a matrix. Args: value: A numeric value for a column. Returns: A NumPy ndarray or None. """ # Grad: 1 for a largest index. value = np.matrix(value).A.ravel(order='F') idx = np.argmax(value) D = np.zeros((value.size, 1)) D[idx] = 1 return D 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 is_pwl(self): """Is the atom piecewise linear? """ return self.args[0].is_pwl() @staticmethod def graph_implementation(arg_objs, shape, data=None): """Reduces the atom to an affine expression and list of constraints. Parameters ---------- arg_objs : list LinExpr for each argument. shape : tuple The shape of the resulting expression. data : Additional data required by the atom. Returns ------- tuple (LinOp for objective, list of constraints) """ axis = data[0] if axis is None: t = lu.create_var((1, 1)) promoted_t = lu.promote(t, arg_objs[0].shape) elif axis == 0: t = lu.create_var((1, arg_objs[0].shape[1])) const_shape = (arg_objs[0].shape[0], 1) ones = lu.create_const(np.ones(const_shape), const_shape) promoted_t = lu.mul_expr(ones, t, arg_objs[0].shape) else: # axis == 1 t = lu.create_var((arg_objs[0].shape[0], 1)) const_shape = (1, arg_objs[0].shape[1]) ones = lu.create_const(np.ones(const_shape), const_shape) promoted_t = lu.rmul_expr(t, ones, arg_objs[0].shape) constraints = [lu.create_leq(arg_objs[0], promoted_t)] return (t, constraints)