# Source code for cvxpy.constraints.exponential

"""

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 typing import List, Tuple

import numpy as np

from cvxpy.constraints.constraint import Constraint
from cvxpy.expressions import cvxtypes
from cvxpy.utilities import scopes

[docs]class ExpCone(Constraint):
"""A reformulated exponential cone constraint.

Operates elementwise on :math:x, y, z.

Original cone:

.. math::

K = \\{(x,y,z) \\mid y > 0, ye^{x/y} <= z\\}
\\cup \\{(x,y,z) \\mid x \\leq 0, y = 0, z \\geq 0\\}

Reformulated cone:

.. math::

K = \\{(x,y,z) \\mid y, z > 0, y\\log(y) + x \\leq y\\log(z)\\}
\\cup \\{(x,y,z) \\mid x \\leq 0, y = 0, z \\geq 0\\}

Parameters
----------
x : Variable
x in the exponential cone.
y : Variable
y in the exponential cone.
z : Variable
z in the exponential cone.
"""

def __init__(self, x, y, z, constr_id=None) -> None:
Expression = cvxtypes.expression()
self.x = Expression.cast_to_const(x)
self.y = Expression.cast_to_const(y)
self.z = Expression.cast_to_const(z)
xs, ys, zs = self.x.shape, self.y.shape, self.z.shape
if xs != ys or xs != zs:
msg = ("All arguments must have the same shapes. Provided arguments have"
"shapes %s" % str((xs, ys, zs)))
raise ValueError(msg)
super(ExpCone, self).__init__([self.x, self.y, self.z],
constr_id)

def __str__(self) -> str:
return "ExpCone(%s, %s, %s)" % (self.x, self.y, self.z)

def __repr__(self) -> str:
return "ExpCone(%s, %s, %s)" % (self.x, self.y, self.z)

@property
def residual(self):
# TODO(akshayka): The projection should be implemented directly.
from cvxpy import Minimize, Problem, Variable, hstack, norm2
if self.x.value is None or self.y.value is None or self.z.value is None:
return None
x = Variable(self.x.shape)
y = Variable(self.y.shape)
z = Variable(self.z.shape)
constr = [ExpCone(x, y, z)]
obj = Minimize(norm2(hstack([x, y, z]) -
hstack([self.x.value, self.y.value, self.z.value])))
problem = Problem(obj, constr)
return problem.solve()

@property
def size(self) -> int:
"""The number of entries in the combined cones.
"""
return 3 * self.num_cones()

def num_cones(self):
"""The number of elementwise cones.
"""
return self.x.size

def cone_sizes(self) -> List[int]:
"""The dimensions of the exponential cones.

Returns
-------
list
A list of the sizes of the elementwise cones.
"""
return [3]*self.num_cones()

[docs]    def is_dcp(self, dpp: bool = False) -> bool:
"""An exponential constraint is DCP if each argument is affine.
"""
if dpp:
with scopes.dpp_scope():
return all(arg.is_affine() for arg in self.args)
return all(arg.is_affine() for arg in self.args)

def is_dgp(self, dpp: bool = False) -> bool:
return False

def is_dqcp(self) -> bool:
return self.is_dcp()

@property
def shape(self) -> Tuple[int, ...]:
s = (3,) + self.x.shape
return s

def save_dual_value(self, value) -> None:
# TODO(akshaya,SteveDiamond): verify that reshaping below works correctly
value = np.reshape(value, newshape=(-1, 3))
dv0 = np.reshape(value[:, 0], newshape=self.x.shape)
dv1 = np.reshape(value[:, 1], newshape=self.y.shape)
dv2 = np.reshape(value[:, 2], newshape=self.z.shape)
self.dual_variables[0].save_value(dv0)
self.dual_variables[1].save_value(dv1)
self.dual_variables[2].save_value(dv2)