QuadraticExpression¶

class QuadraticExpression(quadratic_program, coefficients)[source]¶

Bases: QuadraticProgramElement

Representation of a quadratic expression by its coefficients.

Creates a new quadratic expression.

The quadratic 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. We stores values in a compressed way, i.e., values at symmetric positions are summed up in the upper triangle. For example, {(0, 1): 1, (1, 0): 2} -> {(0, 1): 3}.

Parameters:

quadratic_program (Any) – The parent QuadraticProgram.
coefficients (ndarray | spmatrix | list[list[float]] | dict[tuple[int | str, int | str], float]) – The (sparse) representation of the coefficients.

Attributes

bounds¶

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

Returns:: The lower bound and the upper bound of the quadratic expression
Raises:: QiskitOptimizationError – if the quadratic expression contains any unbounded variable

coefficients¶

Returns the coefficients of the quadratic expression.

Returns:: The coefficients of the quadratic expression.

quadratic_program¶

Returns the parent QuadraticProgram.

Returns:: The parent QuadraticProgram.

Methods

evaluate(x)[source]¶

Evaluate the quadratic expression for given variables: x * Q * x.

Parameters:: x (ndarray | list | dict[int | str, float]) – The values of the variables to be evaluated.
Returns:: The value of the quadratic expression given the variable values.
Return type:: float

evaluate_gradient(x)[source]¶

Evaluate the gradient of the quadratic expression for given variables.

Parameters:: x (ndarray | list | dict[int | str, float]) – The values of the variables to be evaluated.
Returns:: The value of the gradient quadratic expression given the variable values.
Return type:: ndarray

to_array(symmetric=False)[source]¶

Returns the coefficients of the quadratic expression as array.

Parameters:: symmetric (bool) – Determines whether the output is in a symmetric form or not.
Returns:: An array with the coefficients corresponding to the quadratic expression.
Return type:: ndarray

to_dict(symmetric=False, use_name=False)[source]¶

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

Parameters:

symmetric (bool) – Determines whether the output is in a symmetric form or not.
use_name (bool) – Determines whether to use index or names to refer to variables.

Returns:

An dictionary with the coefficients corresponding to the quadratic expression.

Return type:

dict[tuple[int, int] | tuple[str, str], float]