# Source code for cvxpy.constraints.zero

```"""

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
"""

import numpy as np

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

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

The preferred way of creating a ``Zero`` constraint is through
simply write ``x == 0``. The former creates a ``Zero`` constraint with
``x`` as its argument.
"""
def __init__(self, expr, constr_id=None) -> None:
super(Zero, self).__init__([expr], constr_id)

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

def __repr__(self) -> str:
"""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) -> str:
return "%s == 0" % self.args[0]

[docs]    def is_dcp(self, dpp: bool = False) -> bool:
"""A zero constraint is DCP if its argument is affine."""
if dpp:
with scopes.dpp_scope():
return self.args[0].is_affine()
return self.args[0].is_affine()

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

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

@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)

# 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

def save_dual_value(self, value) -> None:
"""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) -> 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) -> str:
"""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) -> None:
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) -> str:
return "%s == %s" % (self.args[0], self.args[1])

def is_dcp(self, dpp: bool = False) -> bool:
"""An equality constraint is DCP if its argument is affine."""
if dpp:
with scopes.dpp_scope():
return self.expr.is_affine()
return self.expr.is_affine()

def is_dgp(self, dpp: bool = False) -> bool:
if dpp:
with scopes.dpp_scope():
return (self.args[0].is_log_log_affine() and
self.args[1].is_log_log_affine())
return (self.args[0].is_log_log_affine() and
self.args[1].is_log_log_affine())

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

@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_dual_value(self, value) -> None:
"""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)
```