Matrix¶

class Matrix¶

This class represents a quadratic objective in coefficient-matrix form, expressed as \(x^\top Q x + p^\top x + c\).

Methods

`__init__`
`evaluate`	Evaluate the matrix objective using the provided variable assignments.
`to_poly`	Convert this matrix form to `Poly`.

Attributes

`constant`	Constant term `c`.
`linear`	Linear coefficient array `p`.
`quadratic`	Quadratic coefficient array `Q`.
`variable_array`	Variable array `x` used in the matrix representation.

__add__(self, arg: Constraint | ConstraintList, /) → Model¶

Create a Model whose objective is this matrix form, with the given constraints.

Parameters:: arg (Constraint | ConstraintList) – Constraints to include.
Returns:: Model containing this objective and the given constraints.
Return type:: Model

__eq__(self, arg: object, /) → bool¶

Parameters:: arg (object)
Return type:: bool

__init__(*args, **kwargs)¶

__ne__(self, arg: object, /) → bool¶

Parameters:: arg (object)
Return type:: bool

__radd__(self, arg: Constraint | ConstraintList, /) → Model¶

Create a Model whose objective is this matrix form, with the given constraints.

Parameters:: arg (Constraint | ConstraintList) – Constraints to include.
Returns:: Model containing this objective and the given constraints.
Return type:: Model

__repr__(self) → str¶

Return a developer-friendly string representation of the matrix form.

Return type:: str

__str__(self) → str¶

Return a human-readable string representation of the matrix form.

Return type:: str

evaluate(self, values: Values) → float¶

evaluate(self, values: Values, default: float) → float

Evaluate the matrix objective using the provided variable assignments.

Substitute variables in x with the given values and evaluate x^\top Q x + p^\top x + c. If default is not specified, a variable that values does not give takes the default value of its type: 0 for a binary variable, -1 for an Ising variable, and, for an integer or a real variable, 0 if the bounds hold 0, else the upper bound, or the lower bound when the variable has no upper bound.

Overload 1.

Args:

values (amplify.Values): Variable values obtained from optimization results, e.g. result.best.values.

Returns:

float: Evaluated objective value.

Overload 2.

Args:

values (amplify.Values): Variable values obtained from optimization results, e.g. result.best.values.
default (float): Default value used for variables not included in values.

Returns:

float: Evaluated objective value.

to_poly(self) → Poly¶

Convert this matrix form to Poly.

Returns:: Polynomial converted from this matrix form.
Return type:: Poly

property constant¶

Constant term c.

Return type:: float

property linear¶

Linear coefficient array p.

For a variable array x with n dimensions, the linear coefficient array p also has n dimensions. When x is one-dimensional, p is a 1D vector.

Return type:: ndarray

property quadratic¶

Quadratic coefficient array Q.

For a variable array x with n dimensions, the quadratic coefficient array Q has 2n dimensions. When x is one-dimensional, Q is a 2D matrix.

Return type:: ndarray

property variable_array¶

Variable array x used in the matrix representation.

Use this array when constructing constraints for a matrix objective.

Returns:: Variable array used in this representation.
Return type:: PolyArray[Dim]