com.numericalmethod.suanshu.analysis.function.rn2r1

Class QuadraticFunction

java.lang.Object

com.numericalmethod.suanshu.analysis.function.rn2r1.QuadraticFunction

All Implemented Interfaces:

Function<Vector,java.lang.Double>, RealScalarFunction, java.io.Serializable

Direct Known Subclasses:

QPProblemOnlyEqualityConstraints

public class QuadraticFunction
extends java.lang.Object
implements RealScalarFunction

A quadratic function takes this form: \(f(x) = \frac{1}{2} \times x'Hx + x'p + c\).

See Also:

• "Andreas Antoniou, Wu-Sheng Lu, "Section 13.2, Convex QP Problems with Equality Constraints," Practical Optimization: Algorithms and Engineering Applications."
• Wikipedia: Quadratic function

, Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from interface com.numericalmethod.suanshu.analysis.function.Function

Function.EvaluationException

Constructor Summary

Constructors

Constructor and Description
QuadraticFunction(Matrix H, Vector p) Construct a quadratic function of this form: \(f(x) = \frac{1}{2} \times x'Hx + x'p\).
QuadraticFunction(Matrix H, Vector p, double c) Construct a quadratic function of this form: \(f(x) = \frac{1}{2} \times x'Hx + x'p + c\).
QuadraticFunction(QuadraticFunction f) Copy constructor.

Method Summary

Modifier and Type	Method and Description
int	dimensionOfDomain() Get the number of variables the function has.
int	dimensionOfRange() Get the dimension of the range space of the function.
java.lang.Double	evaluate(Vector z) Evaluate the function f at x, where x is from the domain.
ImmutableMatrix	Hessian()
ImmutableVector	p()
java.lang.String	toString()

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

QuadraticFunction

public QuadraticFunction(Matrix H,
                         Vector p,
                         double c)

Construct a quadratic function of this form: \(f(x) = \frac{1}{2} \times x'Hx + x'p + c\).

Parameters:

H - a symmetric, positive semi-definite matrix

p - a vector

c - a constant

QuadraticFunction

public QuadraticFunction(Matrix H,
                         Vector p)

Construct a quadratic function of this form: \(f(x) = \frac{1}{2} \times x'Hx + x'p\).

Parameters:

H - a symmetric, positive semi-definite matrix

p - a vector

QuadraticFunction

public QuadraticFunction(QuadraticFunction f)

Copy constructor.

Parameters:

f - a quadratic function

Method Detail

Hessian

public ImmutableMatrix Hessian()

p

public ImmutableVector p()

evaluate

public java.lang.Double evaluate(Vector z)

Description copied from interface: Function

Evaluate the function f at x, where x is from the domain.

Specified by:

evaluate in interface Function<Vector,java.lang.Double>

Parameters:

z - x

Returns:

f(x)

dimensionOfDomain

public int dimensionOfDomain()

Description copied from interface: Function

Get the number of variables the function has. For example, for a univariate function, the domain dimension is 1; for a bivariate function, the domain dimension is 2.

Specified by:

dimensionOfDomain in interface Function<Vector,java.lang.Double>

Returns:

the number of variables

dimensionOfRange

public int dimensionOfRange()

Description copied from interface: Function

Get the dimension of the range space of the function. For example, for a Rⁿ->R^m function, the dimension of the range is m.

Specified by:

dimensionOfRange in interface Function<Vector,java.lang.Double>

Returns:

the dimension of the range

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object