# Source code for cvxpy.atoms.log_sum_exp

"""

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
from cvxpy.atoms.axis_atom import AxisAtom
import numpy as np
from scipy.special import logsumexp

[docs]class log_sum_exp(AxisAtom):
""":math:\\log\\sum_i e^{x_i}

"""

def __init__(self, x, axis=None, keepdims=False):
super(log_sum_exp, self).__init__(x, axis=axis, keepdims=keepdims)

@Atom.numpy_numeric
def numeric(self, values):
"""Evaluates e^x elementwise, sums, and takes the log.
"""
return logsumexp(values[0], axis=self.axis, keepdims=self.keepdims)

"""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.
"""

"""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.
"""
denom = np.exp(logsumexp(value, axis=None, keepdims=True))
nom = np.exp(value)
D = nom/denom
return D

def sign_from_args(self):
"""Returns sign (is positive, is negative) of the expression.
"""
return (False, False)

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