# Source code for cvxpy.atoms.pf_eigenvalue

"""

you may not use this file except in compliance with the License.
You may obtain a copy of the License at

Unless required by applicable law or agreed to in writing, software
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
"""

from cvxpy.atoms.atom import Atom
import numpy as np

[docs]class pf_eigenvalue(Atom):
"""The Perron-Frobenius eigenvalue of a positive matrix.

For an elementwise positive matrix :math:X, this atom represents its
spectral radius, i.e., the magnitude of its largest eigenvalue. Because
:math:X is positive, the spectral radius equals its largest eigenvalue,
which is guaranteed to be positive.

This atom is log-log convex.

Parameters
----------
X : cvxpy.Expression
A positive square matrix.
"""
def __init__(self, X):
super(pf_eigenvalue, self).__init__(X)
if len(X.shape) != 2 or X.shape[0] != X.shape[1]:
raise ValueError("Argument to spectral radius must be a "
self.args[0] = X

def numeric(self, values):
return np.max(np.abs(np.linalg.eig(values[0])[0]))

def name(self):
return "%s(%s)" % (self.__class__.__name__, self.args[0])

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.
"""
return (True, False)

def is_atom_convex(self):
"""Is the atom convex?
"""
return False

def is_atom_concave(self):
"""Is the atom concave?
"""
return False

def is_atom_log_log_convex(self):
"""Is the atom log-log convex?
"""
return True

def is_atom_log_log_concave(self):
"""Is the atom log-log concave?
"""
return False

# TODO(akshayka): Figure out monotonicity.
def is_incr(self, idx):
"""Is the composition non-decreasing in argument idx?
"""
return False

def is_decr(self, idx):
"""Is the composition non-increasing in argument idx?
"""
return False