Skip to content

LinearExpression

Bases: QuadraticProgramElement

Representation of a linear expression by its coefficients.

Source code in q3as/quadratic/problems/linear_expression.py 
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
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)

    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]

    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()}

    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
    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)}"

bounds: ExpressionBounds property

Returns the lower bound and the upper bound of the linear expression

Returns:

Type Description
ExpressionBounds

The lower bound and the upper bound of the linear expression

Raises:

Type Description
QiskitOptimizationError

if the linear expression contains any unbounded variable

coefficients: dok_matrix property writable

Returns the coefficients of the linear expression.

Returns:

Type Description
dok_matrix

The coefficients of the linear expression.

__getitem__(i)

Returns the i-th coefficient where i can be a variable name or index.

Parameters:

Name Type Description Default
i Union[int, str]

the index or name of the variable corresponding to the coefficient.

 required

Returns:

Type Description
float

The coefficient corresponding to the addressed variable.
Source code in q3as/quadratic/problems/linear_expression.py 
61
62
63
64
65
66
67
68
69
70
71
72
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]

__init__(quadratic_program, coefficients)

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.

Parameters:

Name Type Description Default
quadratic_program Any

The parent QuadraticProgram.

 required
coefficients Union[ndarray, spmatrix, List[float], Dict[Union[int, str], float]]

The (sparse) representation of the coefficients.

 required
Source code in q3as/quadratic/problems/linear_expression.py 
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
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

evaluate(x)

Evaluate the linear expression for given variables.

Parameters:

Name Type Description Default
x Union[ndarray, List, Dict[Union[int, str], float]]

The values of the variables to be evaluated.

 required

Returns:

Type Description
float

The value of the linear expression given the variable values.
Source code in q3as/quadratic/problems/linear_expression.py 
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
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

evaluate_gradient(x)

Evaluate the gradient of the linear expression for given variables.

Parameters:

Name Type Description Default
x Union[ndarray, List, Dict[Union[int, str], float]]

The values of the variables to be evaluated.

 required

Returns:

Type Description
ndarray

The value of the gradient of the linear expression given the variable values.
Source code in q3as/quadratic/problems/linear_expression.py 
180
181
182
183
184
185
186
187
188
189
190
191
192
193
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()

to_array()

Returns the coefficients of the linear expression as array.

Returns:

Type Description
ndarray

An array with the coefficients corresponding to the linear expression.
Source code in q3as/quadratic/problems/linear_expression.py 
135
136
137
138
139
140
141
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]

to_dict(use_name=False)

Returns the coefficients of the linear expression as dictionary, either using variable names or indices as keys.

Parameters:

Name Type Description Default
use_name bool

Determines whether to use index or names to refer to variables.

 False

Returns:

Type Description
Dict[Union[int, str], float]

An dictionary with the coefficients corresponding to the linear expression.
Source code in q3as/quadratic/problems/linear_expression.py 
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
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()}