# This code is part of a Qiskit project.
#
# (C) Copyright IBM 2019, 2023.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# 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.
"""Linear expression interface."""
from typing import List, Union, Dict, Any
from dataclasses import dataclass
from numpy import ndarray
from scipy.sparse import spmatrix, dok_matrix
from .quadratic_program_element import QuadraticProgramElement
from ..exceptions import QiskitOptimizationError
from ..infinity import INFINITY
@dataclass
class ExpressionBounds:
"""Lower bound and upper bound of a linear expression or a quadratic expression"""
lowerbound: float
"""Lower bound"""
upperbound: float
"""Upper bound"""
[docs]class LinearExpression(QuadraticProgramElement):
"""Representation of a linear expression by its coefficients."""
def __init__(
self,
quadratic_program: Any,
coefficients: Union[ndarray, spmatrix, List[float], Dict[Union[int, str], float]],
) -> None:
"""Creates a new linear expression.
The linear expression can be defined via an array, a list, a sparse matrix, or a dictionary
that uses variable names or indices as keys and stores the values internally as a
dok_matrix.
Args:
quadratic_program: The parent QuadraticProgram.
coefficients: The (sparse) representation of the coefficients.
"""
super().__init__(quadratic_program)
self.coefficients = coefficients
def __getitem__(self, i: Union[int, str]) -> float:
"""Returns the i-th coefficient where i can be a variable name or index.
Args:
i: the index or name of the variable corresponding to the coefficient.
Returns:
The coefficient corresponding to the addressed variable.
"""
if isinstance(i, str):
i = self.quadratic_program.variables_index[i]
return self.coefficients[0, i]
def __setitem__(self, i: Union[int, str], value: float) -> None:
if isinstance(i, str):
i = self.quadratic_program.variables_index[i]
self._coefficients[0, i] = value
def _coeffs_to_dok_matrix(
self, coefficients: Union[ndarray, spmatrix, List, Dict[Union[int, str], float]]
) -> dok_matrix:
"""Maps given 1d-coefficients to a dok_matrix.
Args:
coefficients: The 1d-coefficients to be mapped.
Returns:
The given 1d-coefficients as a dok_matrix
Raises:
QiskitOptimizationError: if coefficients are given in unsupported format.
"""
if (
isinstance(coefficients, list)
or isinstance(coefficients, ndarray)
and len(coefficients.shape) == 1
):
coefficients = dok_matrix([coefficients])
elif isinstance(coefficients, spmatrix):
coefficients = dok_matrix(coefficients)
elif isinstance(coefficients, dict):
coeffs = dok_matrix((1, self.quadratic_program.get_num_vars()))
for index, value in coefficients.items():
if isinstance(index, str):
index = self.quadratic_program.variables_index[index]
coeffs[0, index] = value
coefficients = coeffs
else:
raise QiskitOptimizationError("Unsupported format for coefficients.")
return coefficients
@property
def coefficients(self) -> dok_matrix:
"""Returns the coefficients of the linear expression.
Returns:
The coefficients of the linear expression.
"""
return self._coefficients
@coefficients.setter
def coefficients(
self,
coefficients: Union[ndarray, spmatrix, List[float], Dict[Union[str, int], float]],
) -> None:
"""Sets the coefficients of the linear expression.
Args:
coefficients: The coefficients of the linear expression.
"""
self._coefficients = self._coeffs_to_dok_matrix(coefficients)
[docs] def to_array(self) -> ndarray:
"""Returns the coefficients of the linear expression as array.
Returns:
An array with the coefficients corresponding to the linear expression.
"""
return self._coefficients.toarray()[0]
[docs] def to_dict(self, use_name: bool = False) -> Dict[Union[int, str], float]:
"""Returns the coefficients of the linear expression as dictionary, either using variable
names or indices as keys.
Args:
use_name: Determines whether to use index or names to refer to variables.
Returns:
An dictionary with the coefficients corresponding to the linear expression.
"""
if use_name:
return {
self.quadratic_program.variables[k].name: v
for (_, k), v in self._coefficients.items()
}
else:
return {k: v for (_, k), v in self._coefficients.items()}
[docs] def evaluate(self, x: Union[ndarray, List, Dict[Union[int, str], float]]) -> float:
"""Evaluate the linear expression for given variables.
Args:
x: The values of the variables to be evaluated.
Returns:
The value of the linear expression given the variable values.
"""
# cast input to dok_matrix if it is a dictionary
x = self._coeffs_to_dok_matrix(x)
# compute the dot-product of the input and the linear coefficients
val = (x @ self.coefficients.transpose())[0, 0]
# return the result
return val
# pylint: disable=unused-argument
[docs] def evaluate_gradient(self, x: Union[ndarray, List, Dict[Union[int, str], float]]) -> ndarray:
"""Evaluate the gradient of the linear expression for given variables.
Args:
x: The values of the variables to be evaluated.
Returns:
The value of the gradient of the linear expression given the variable values.
"""
# extract the coefficients as array and return it
return self.to_array()
@property
def bounds(self) -> ExpressionBounds:
"""Returns the lower bound and the upper bound of the linear expression
Returns:
The lower bound and the upper bound of the linear expression
Raises:
QiskitOptimizationError: if the linear expression contains any unbounded variable
"""
l_b = u_b = 0.0
for ind, coeff in self.to_dict().items():
x = self.quadratic_program.get_variable(ind)
if x.lowerbound == -INFINITY or x.upperbound == INFINITY:
raise QiskitOptimizationError(
f"Linear expression contains an unbounded variable: {x.name}"
)
lst = [coeff * x.lowerbound, coeff * x.upperbound]
l_b += min(lst)
u_b += max(lst)
return ExpressionBounds(lowerbound=l_b, upperbound=u_b)
def __repr__(self):
# pylint: disable=cyclic-import
from ..translators.prettyprint import expr2str, DEFAULT_TRUNCATE
return f"<{self.__class__.__name__}: {expr2str(linear=self, truncate=DEFAULT_TRUNCATE)}>"
def __str__(self):
# pylint: disable=cyclic-import
from ..translators.prettyprint import expr2str
return f"{expr2str(linear=self)}"