Source code for cvxpy.atoms.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/>.
"""

import numpy as np
import cvxpy
from cvxpy.expressions.expression import Expression
from cvxpy.atoms.norm_nuc import normNuc
from cvxpy.atoms.sigma_max import sigma_max
from cvxpy.atoms.pnorm import pnorm
from cvxpy.atoms.norm1 import norm1
from cvxpy.atoms.norm_inf import norm_inf
from cvxpy.atoms.affine.vec import vec


[docs]def norm(x, p=2, axis=None): """Wrapper on the different norm atoms. Parameters ---------- x : Expression or numeric constant The value to take the norm of. p : int or str, optional The type of norm. Returns ------- Expression An Expression representing the norm. """ x = Expression.cast_to_const(x) # matrix norms take precedence if axis is None and x.ndim == 2: if p == 1: # matrix 1-norm return cvxpy.atoms.max(norm1(x, axis=0)) elif p == 2: # matrix 2-norm is largest singular value return sigma_max(x) elif p == 'nuc': # the nuclear norm (sum of singular values) return normNuc(x) elif p == 'fro': # Frobenius norm return pnorm(vec(x), 2) elif p in [np.inf, "inf", "Inf"]: # the matrix infinity-norm return cvxpy.atoms.max(norm1(x, axis=1)) else: raise RuntimeError('Unsupported matrix norm.') else: if p == 1 or x.is_scalar(): return norm1(x, axis=axis) elif p in [np.inf, "inf", "Inf"]: return norm_inf(x, axis) else: return pnorm(x, p, axis)