Source code for cvxpy.atoms.mixed_norm

"""
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.expressions.expression import Expression
from cvxpy.atoms.norm import norm


[docs]def mixed_norm(X, p=2, q=1): """Lp,q norm; :math:`(\\sum_k (\\sum_l \\lvert x_{k,l} \\rvert^p)^{q/p})^{1/q}`. Parameters ---------- X : Expression or numeric constant The matrix to take the l_{p,q} norm of. p : int or str, optional The type of inner norm. q : int or str, optional The type of outer norm. Returns ------- Expression An Expression representing the mixed norm. """ X = Expression.cast_to_const(X) # inner norms vecnorms = norm(X, p, axis=1) # outer norm return norm(vecnorms, q)