org.ddogleg.optimization.impl

Class CauchyStep

java.lang.Object

org.ddogleg.optimization.impl.CauchyStep

All Implemented Interfaces:

TrustRegionStep

public class CauchyStep
extends java.lang.Object
implements TrustRegionStep

Selects the optimal point along the gradient line within the trust region's constraint.

The negative definite case is not considered because it is impossible when the Hessian is approximated by squaring the Jacobian. For a matrix to be negative definite there must be a vector 'x' which will produce a negative result:
x'*H*x < 0 --> x'*J'*J*x --> (J*x)'*(J*x)
which is clearly always ≥ 0

Constructor Summary

Constructors

Constructor and Description
CauchyStep()

Method Summary

Modifier and Type	Method and Description
void	computeStep(double regionRadius, org.ejml.data.DenseMatrix64F step) Computes the Cauchy step.
void	init(int numParam, int numFunctions) Initialize internal data structures.
boolean	isMaxStep() Was a step equal to the regionRadius taken?
double	predictedReduction() Returns the predicted reduction for the step.
void	setInputs(org.ejml.data.DenseMatrix64F x, org.ejml.data.DenseMatrix64F residuals, org.ejml.data.DenseMatrix64F J, org.ejml.data.DenseMatrix64F gradient, double fx) Specifies the state of the system being optimized.

Methods inherited from class java.lang.Object

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

Constructor Detail

CauchyStep

public CauchyStep()

Method Detail

init

public void init(int numParam,
                 int numFunctions)

Description copied from interface: TrustRegionStep

Initialize internal data structures. Only needs to be called once.

Specified by:

init in interface TrustRegionStep

Parameters:

numParam - Number of parameters being optimizes. This is the length of 'x'

numFunctions - Number of functions. Number of outputs to f(x)

setInputs

public void setInputs(org.ejml.data.DenseMatrix64F x,
                      org.ejml.data.DenseMatrix64F residuals,
                      org.ejml.data.DenseMatrix64F J,
                      org.ejml.data.DenseMatrix64F gradient,
                      double fx)

Description copied from interface: TrustRegionStep

Specifies the state of the system being optimized. Call before TrustRegionStep.computeStep(double, org.ejml.data.DenseMatrix64F).

Specified by:

setInputs in interface TrustRegionStep

Parameters:

x - Sample point being considered.

residuals - Function output: f(x)

J - Jacobian: J(x)

gradient - Gradient: J^T(x)*f(x)

fx - Residual at x: 0.5*f^T(x)*f(x)

computeStep

public void computeStep(double regionRadius,
                        org.ejml.data.DenseMatrix64F step)

Computes the Cauchy step. See comment in class description for why negative definite case is not considered.

Specified by:

computeStep in interface TrustRegionStep

Parameters:

regionRadius -

step -

predictedReduction

public double predictedReduction()

Description copied from interface: TrustRegionStep

Returns the predicted reduction for the step. A linear model is used to predict the reduction. See class description for

Specified by:

predictedReduction in interface TrustRegionStep

Returns:

The predicted reduction.

isMaxStep

public boolean isMaxStep()

Description copied from interface: TrustRegionStep

Was a step equal to the regionRadius taken?

Specified by:

isMaxStep in interface TrustRegionStep

Returns:

true if maximum step and false if less than the maximum step