qiskit.optimization.problems.QuadraticExpression

class QuadraticExpression(quadratic_program, coefficients)

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}.

Parameter

• quadratic_program (Any) – The parent QuadraticProgram.

• coefficients (Union[ndarray, spmatrix, List[List[float]], Dict[Tuple[Union[int, str], Union[int, str]], float]]) – The (sparse) representation of the coefficients.

__init__(quadratic_program, 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}.

Parameter

• quadratic_program (Any) – The parent QuadraticProgram.

• coefficients (Union[ndarray, spmatrix, List[List[float]], Dict[Tuple[Union[int, str], Union[int, str]], float]]) – The (sparse) representation of the coefficients.

Methods

__init__(quadratic_program, coefficients)	Creates a new quadratic expression.
evaluate(x)	Evaluate the quadratic expression for given variables: x * Q * x.
evaluate_gradient(x)	Evaluate the gradient of the quadratic expression for given variables.
to_array([symmetric])	Returns the coefficients of the quadratic expression as array.
to_dict([symmetric, use_name])	Returns the coefficients of the quadratic expression as dictionary, either using tuples of variable names or indices as keys.

Attributes

coefficients	Returns the coefficients of the quadratic expression.
quadratic_program	Returns the parent QuadraticProgram.

property coefficients

Returns the coefficients of the quadratic expression.

Rückgabetyp

dok_matrix

Rückgabe

The coefficients of the quadratic expression.

evaluate(x)

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

Parameter

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

Rückgabetyp

float

Rückgabe

The value of the quadratic expression given the variable values.

evaluate_gradient(x)

Evaluate the gradient of the quadratic expression for given variables.

Parameter

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

Rückgabetyp

ndarray

Rückgabe

The value of the gradient quadratic expression given the variable values.

property quadratic_program

Returns the parent QuadraticProgram.

Rückgabetyp

Any

Rückgabe

The parent QuadraticProgram.

to_array(symmetric=False)

Returns the coefficients of the quadratic expression as array.

Parameter

symmetric (bool) – Determines whether the output is in a symmetric form or not.

Rückgabetyp

ndarray

Rückgabe

An array with the coefficients corresponding to the quadratic expression.

to_dict(symmetric=False, use_name=False)

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

Parameter

• 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.

Rückgabetyp

Dict[Union[Tuple[int, int], Tuple[str, str]], float]

Rückgabe

An dictionary with the coefficients corresponding to the quadratic expression.