# Source code for cvxpy.constraints.zero

"""
Copyright 2013 Steven Diamond

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
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
"""

from cvxpy.constraints.constraint import Constraint
import cvxpy.lin_ops.lin_utils as lu
import numpy as np

[docs]class Zero(Constraint):
"""A constraint of the form :math:x = 0.

The preferred way of creating a Zero constraint is through
operator overloading. To constrain an expression x to be zero,
simply write x == 0. The former creates a Zero constraint with
x as its argument.
"""
def __init__(self, expr, constr_id=None):
super(Zero, self).__init__([expr], constr_id)

def __str__(self):
"""Returns a string showing the mathematical constraint.
"""
return self.name()

def __repr__(self):
"""Returns a string with information about the constraint.
"""
return "%s(%s)" % (self.__class__.__name__,
repr(self.args[0]))

@property
def shape(self):
"""int : The shape of the constrained expression."""
return self.args[0].shape

@property
def size(self):
"""int : The size of the constrained expression."""
return self.args[0].size

def name(self):
return "%s == 0" % self.args[0]

[docs]    def is_dcp(self):
"""A zero constraint is DCP if its argument is affine."""
return self.args[0].is_affine()

def is_dgp(self):
return False

@property
def residual(self):
"""The residual of the constraint.

Returns
-------
Expression
"""
if self.expr.value is None:
return None
return np.abs(self.expr.value)

def canonicalize(self):
"""Returns the graph implementation of the object.

Marks the top level constraint as the dual_holder,
so the dual value will be saved to the EqConstraint.

Returns:
A tuple of (affine expression, [constraints]).
"""
obj, constraints = self.args[0].canonical_form
dual_holder = lu.create_eq(obj, constr_id=self.id)
return (None, constraints + [dual_holder])

# The value of the dual variable.
@property
def dual_value(self):
"""NumPy.ndarray : The value of the dual variable.
"""
return self.dual_variables[0].value

# TODO(akshayka): Rename to save_dual_value to avoid collision with
# value as defined above.
def save_value(self, value):
"""Save the value of the dual variable for the constraint's parent.

Args:
value: The value of the dual variable.
"""
self.dual_variables[0].save_value(value)

class Equality(Constraint):
"""A constraint of the form :math:x = y.
"""
def __init__(self, lhs, rhs, constr_id=None):
self._expr = lhs - rhs
super(Equality, self).__init__([lhs, rhs], constr_id)

def __str__(self):
"""Returns a string showing the mathematical constraint.
"""
return self.name()

def __repr__(self):
"""Returns a string with information about the constraint.
"""
return "%s(%s, %s)" % (self.__class__.__name__,
repr(self.args[0]), repr(self.args[1]))

def _construct_dual_variables(self, args):
super(Equality, self)._construct_dual_variables([self._expr])

@property
def expr(self):
return self._expr

@property
def shape(self):
"""int : The shape of the constrained expression."""
return self.expr.shape

@property
def size(self):
"""int : The size of the constrained expression."""
return self.expr.size

def name(self):
return "%s == %s" % (self.args[0], self.args[1])

def is_dcp(self):
"""An equality constraint is DCP if its argument is affine."""
return self.expr.is_affine()

def is_dgp(self):
return (self.args[0].is_log_log_affine() and
self.args[1].is_log_log_affine())

@property
def residual(self):
"""The residual of the constraint.

Returns
-------
Expression
"""
if self.expr.value is None:
return None
return np.abs(self.expr.value)

@property
def dual_value(self):
"""NumPy.ndarray : The value of the dual variable.
"""
return self.dual_variables[0].value

def save_value(self, value):
"""Save the value of the dual variable for the constraint's parent.

Args:
value: The value of the dual variable.
"""
self.dual_variables[0].save_value(value)