Representation of a quadratic expression by its coefficients.

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:

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.

Returns:

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

Parameters:

x (ndarray | List | Dict[int | str, float]) – The values of the variables to be evaluated.

Returns:

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]