# Source code for cvxpy.atoms.mixed_norm

"""

This file is part of CVXPY.

CVXPY is free software: you can redistribute it and/or modify
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)