Module ojalgo

Package org.ojalgo.function.multiary

Class QuadraticFunction<N extends java.lang.Comparable<N>>

java.lang.Object

org.ojalgo.function.multiary.QuadraticFunction<N>

All Implemented Interfaces:

BasicFunction, BasicFunction.PlainUnary<Access1D<N>,N>, MultiaryFunction<N>, MultiaryFunction.Constant<N>, MultiaryFunction.Linear<N>, MultiaryFunction.PureQuadratic<N>, MultiaryFunction.Quadratic<N>, MultiaryFunction.TwiceDifferentiable<N>

public final class QuadraticFunction<N extends java.lang.Comparable<N>>
extends java.lang.Object
implements MultiaryFunction.TwiceDifferentiable<N>, MultiaryFunction.Quadratic<N>

[x]^T[Q][x] + [l]^T[x] + c

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	QuadraticFunction.Factory<N extends java.lang.Comparable<N>>

Nested classes/interfaces inherited from interface org.ojalgo.function.BasicFunction

BasicFunction.Differentiable<N extends java.lang.Comparable<N>,F extends BasicFunction>, BasicFunction.Integratable<N extends java.lang.Comparable<N>,F extends BasicFunction>, BasicFunction.PlainUnary<T,R>

Nested classes/interfaces inherited from interface org.ojalgo.function.multiary.MultiaryFunction

MultiaryFunction.Affine<N extends java.lang.Comparable<N>>, MultiaryFunction.Constant<N extends java.lang.Comparable<N>>, MultiaryFunction.Convex<N extends java.lang.Comparable<N>>, MultiaryFunction.Linear<N extends java.lang.Comparable<N>>, MultiaryFunction.PureQuadratic<N extends java.lang.Comparable<N>>, MultiaryFunction.Quadratic<N extends java.lang.Comparable<N>>, MultiaryFunction.TwiceDifferentiable<N extends java.lang.Comparable<N>>

Field Summary

Fields

Modifier and Type	Field	Description
private LinearFunction<N>	myLinear
private PureQuadraticFunction<N>	myPureQuadratic

Constructor Summary

Constructors

Constructor	Description
QuadraticFunction(PureQuadraticFunction<N> pureQuadratic, LinearFunction<N> linear)
QuadraticFunction(MatrixStore<N> quadratic, MatrixStore<N> linear)

Method Summary

Modifier and Type	Method	Description
int	arity()
(package private) PhysicalStore.Factory<N,?>	factory()
static <N extends java.lang.Comparable<N>> QuadraticFunction.Factory<N>	factory(PhysicalStore.Factory<N,?> factory)
N	getConstant()
MatrixStore<N>	getGradient(Access1D<N> point)	The gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is that rate of increase.
MatrixStore<N>	getHessian(Access1D<N> point)	The Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a function.
MatrixStore<N>	getLinearFactors(boolean negated)
(package private) Scalar<N>	getScalarValue(Access1D<N> arg)
N	invoke(Access1D<N> arg)
PhysicalStore<N>	linear()
PhysicalStore<N>	quadratic()
void	setConstant(java.lang.Comparable<?> constant)
static <N extends java.lang.Comparable<N>> QuadraticFunction<N>	wrap(PhysicalStore<N> quadratic, PhysicalStore<N> linear)

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.ojalgo.function.multiary.MultiaryFunction

andThen

Methods inherited from interface org.ojalgo.function.multiary.MultiaryFunction.TwiceDifferentiable

toFirstOrderApproximation, toSecondOrderApproximation

Field Detail

myLinear

private final LinearFunction<N extends java.lang.Comparable<N>> myLinear

myPureQuadratic

private final PureQuadraticFunction<N extends java.lang.Comparable<N>> myPureQuadratic

Constructor Detail

QuadraticFunction

QuadraticFunction(MatrixStore<N> quadratic,
                  MatrixStore<N> linear)

QuadraticFunction

QuadraticFunction(PureQuadraticFunction<N> pureQuadratic,
                  LinearFunction<N> linear)

Method Detail

factory

public static <N extends java.lang.Comparable<N>> QuadraticFunction.Factory<N> factory(PhysicalStore.Factory<N,?> factory)

wrap

public static <N extends java.lang.Comparable<N>> QuadraticFunction<N> wrap(PhysicalStore<N> quadratic,
                                                                            PhysicalStore<N> linear)

arity

public int arity()

Specified by:

arity in interface MultiaryFunction<N extends java.lang.Comparable<N>>

getConstant

public N getConstant()

Specified by:

getConstant in interface MultiaryFunction.Constant<N extends java.lang.Comparable<N>>

getGradient

public MatrixStore<N> getGradient(Access1D<N> point)

Description copied from interface: MultiaryFunction.TwiceDifferentiable

The gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is that rate of increase.

The Jacobian is a generalization of the gradient. Gradients are only defined on scalar-valued functions, but Jacobians are defined on vector- valued functions. When f is real-valued (i.e., f : Rn → R) the derivative Df(x) is a 1 × n matrix, i.e., it is a row vector. Its transpose is called the gradient of the function: ∇f(x) = Df(x)^T , which is a (column) vector, i.e., in Rn. Its components are the partial derivatives of f:

The first-order approximation of f at a point x ∈ int dom f can be expressed as (the affine function of z) f(z) = f(x) + ∇f(x)T (z − x).

Specified by:

getGradient in interface MultiaryFunction.TwiceDifferentiable<N extends java.lang.Comparable<N>>

getHessian

public MatrixStore<N> getHessian(Access1D<N> point)

Description copied from interface: MultiaryFunction.TwiceDifferentiable

The Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a function. It describes the local curvature of a function of many variables. The Hessian is the Jacobian of the gradient.

The second-order approximation of f, at or near x, is the quadratic function of z defined by f(z) = f(x) + ∇f(x)T (z − x) + (1/2)(z − x)T ∇2f(x)(z − x)

Specified by:

getHessian in interface MultiaryFunction.TwiceDifferentiable<N extends java.lang.Comparable<N>>

getLinearFactors

public MatrixStore<N> getLinearFactors(boolean negated)

Specified by:

getLinearFactors in interface MultiaryFunction.TwiceDifferentiable<N extends java.lang.Comparable<N>>

Returns:

The gradient at origin (0-vector), negated or not

invoke

public N invoke(Access1D<N> arg)

Specified by:

invoke in interface BasicFunction.PlainUnary<Access1D<N extends java.lang.Comparable<N>>,N extends java.lang.Comparable<N>>

Specified by:

invoke in interface MultiaryFunction<N extends java.lang.Comparable<N>>

linear

public PhysicalStore<N> linear()

Specified by:

linear in interface MultiaryFunction.Linear<N extends java.lang.Comparable<N>>

quadratic

public PhysicalStore<N> quadratic()

Specified by:

quadratic in interface MultiaryFunction.PureQuadratic<N extends java.lang.Comparable<N>>

setConstant

public void setConstant(java.lang.Comparable<?> constant)

Specified by:

setConstant in interface MultiaryFunction.Constant<N extends java.lang.Comparable<N>>

factory

PhysicalStore.Factory<N,?> factory()

getScalarValue

Scalar<N> getScalarValue(Access1D<N> arg)