# Source code for qiskit_optimization.converters.linear_equality_to_penalty

```# This code is part of a Qiskit project.
#
# (C) Copyright IBM 2020, 2023.
#
# obtain a copy of this license in the LICENSE.txt file in the root directory
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.

"""Converter to convert a problem with equality constraints to unconstrained with penalty terms."""

import logging
from typing import Optional, cast, Union, Tuple, List

import numpy as np

from ..exceptions import QiskitOptimizationError
from ..problems.constraint import Constraint
from ..problems.variable import Variable

logger = logging.getLogger(__name__)

"""Convert a problem with only equality constraints to unconstrained with penalty terms."""

def __init__(self, penalty: Optional[float] = None) -> None:
"""
Args:
penalty: Penalty factor to scale equality constraints that are added to objective.
If None is passed, a penalty factor will be automatically calculated on
every conversion.
"""
self._src_num_vars: Optional[int] = None
self._penalty: Optional[float] = penalty
self._should_define_penalty: bool = penalty is None

"""Convert a problem with equality constraints into an unconstrained problem.

Args:
problem: The problem to be solved, that does not contain inequality constraints.

Returns:
The converted problem, that is an unconstrained problem.

Raises:
QiskitOptimizationError: If an inequality constraint exists.
"""

self._src_num_vars = problem.get_num_vars()

# If no penalty was given, set the penalty coefficient by _auto_define_penalty()
if self._should_define_penalty:
penalty = self._auto_define_penalty(problem)
else:
penalty = self._penalty

# Set variables
for x in problem.variables:
if x.vartype == Variable.Type.CONTINUOUS:
dst.continuous_var(x.lowerbound, x.upperbound, x.name)
elif x.vartype == Variable.Type.BINARY:
dst.binary_var(x.name)
elif x.vartype == Variable.Type.INTEGER:
dst.integer_var(x.lowerbound, x.upperbound, x.name)
else:
raise QiskitOptimizationError(f"Unsupported vartype: {x.vartype}")

# get original objective terms
offset = problem.objective.constant
linear = problem.objective.linear.to_dict()
sense = problem.objective.sense.value

# convert linear constraints into penalty terms
for constraint in problem.linear_constraints:

if constraint.sense != Constraint.Sense.EQ:
raise QiskitOptimizationError(
"An inequality constraint exists. "
"The method supports only equality constraints."
)

constant = constraint.rhs
row = constraint.linear.to_dict()

# constant parts of penalty*(Constant-func)**2: penalty*(Constant**2)
offset += sense * penalty * constant**2

# linear parts of penalty*(Constant-func)**2: penalty*(-2*Constant*func)
for j, coef in row.items():
# if j already exists in the linear terms dic, add a penalty term
# into existing value else create new key and value in the linear_term dict
linear[j] = linear.get(j, 0.0) + sense * penalty * -2 * coef * constant

# quadratic parts of penalty*(Constant-func)**2: penalty*(func**2)
for j, coef_1 in row.items():
for k, coef_2 in row.items():
# if j and k already exist in the quadratic terms dict,
# add a penalty term into existing value
# else create new key and value in the quadratic term dict

# according to implementation of quadratic terms in OptimizationModel,
# don't need to multiply by 2, since loops run over (x, y) and (y, x).
tup = cast(Union[Tuple[int, int], Tuple[str, str]], (j, k))
quadratic[tup] = quadratic.get(tup, 0.0) + sense * penalty * coef_1 * coef_2

else:

# Update the penalty to the one just used
self._penalty = penalty

return dst

@staticmethod
"""Automatically define the penalty coefficient.

Returns:
Return the minimum valid penalty factor calculated
from the upper bound and the lower bound of the objective function.
If a constraint has a float coefficient,
return the default value for the penalty factor.
"""
default_penalty = 1e5

# Check coefficients of constraints.
# If a constraint has a float coefficient, return the default value for the penalty factor.
terms = []
for constraint in problem.linear_constraints:
terms.append(constraint.rhs)
terms.extend(constraint.linear.to_array().tolist())
if any(isinstance(term, float) and not term.is_integer() for term in terms):
logger.warning(
"Warning: Using %f for the penalty coefficient because "
"a float coefficient exists in constraints. \n"
"The value could be too small. "
"If so, set the penalty coefficient manually.",
default_penalty,
)
return default_penalty

lin_b = problem.objective.linear.bounds

[docs]    def interpret(self, x: Union[np.ndarray, List[float]]) -> np.ndarray:
"""Convert the result of the converted problem back to that of the original problem

Args:
x: The result of the converted problem or the given result in case of FAILURE.

Returns:
The result of the original problem.

Raises:
QiskitOptimizationError: if the number of variables in the result differs from
that of the original problem.
"""
if len(x) != self._src_num_vars:
raise QiskitOptimizationError(
"The number of variables in the passed result differs from "
"that of the original problem."
)
return np.asarray(x)

@property
def penalty(self) -> Optional[float]:
"""Returns the penalty factor used in conversion.

Returns:
The penalty factor used in conversion.
"""
return self._penalty

@penalty.setter
def penalty(self, penalty: Optional[float]) -> None:
"""Set a new penalty factor.

Args:
penalty: The new penalty factor.
If None is passed, a penalty factor will be automatically calculated
on every conversion.
"""
self._penalty = penalty
self._should_define_penalty = penalty is None
```