org.ddogleg.optimization.impl

Class DoglegStepFtF

java.lang.Object

org.ddogleg.optimization.impl.DoglegStepFtF

All Implemented Interfaces:

TrustRegionStep

public class DoglegStepFtF
extends java.lang.Object
implements TrustRegionStep

Approximates the optimal step within the trust region using the so called dogleg. The Gauss Newton step is computed by squaring the Jacobian. In systems where the number of functions is much larger than the number of parameters this can be faster, but slightly less precise.

This implementation is based off the description found in [1,2], but some of the equations have been modified for simplicity and correctness.

• [1] K. Madsen, H.B. Nielson,and O. Tingleff, "Methods for Non-Linear Least Squares Problems" 2nd Ed, April 2004
• [2] Jorge Nocedal,and Stephen J. Wright "Numerical Optimization" 2nd Ed. Springer 2006

Constructor Summary

Constructors

Constructor and Description
DoglegStepFtF() Default solver
DoglegStepFtF(org.ejml.interfaces.linsol.LinearSolver<org.ejml.data.DenseMatrix64F> pinv) Specify configuration

Method Summary

Modifier and Type	Method and Description
void	computeStep(double regionRadius, org.ejml.data.DenseMatrix64F step) Uses the Cauchy point, Gauss-Newton point, or a linear combination of both depending on the regionRadius.
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

DoglegStepFtF

public DoglegStepFtF(org.ejml.interfaces.linsol.LinearSolver<org.ejml.data.DenseMatrix64F> pinv)

Specify configuration

Parameters:

pinv - Linear solver for a positive semi-definite symmetric system

DoglegStepFtF

public DoglegStepFtF()

Default solver

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)

Uses the Cauchy point, Gauss-Newton point, or a linear combination of both depending on the regionRadius. The predicted reduction is computed differently depending on which of the 3 cases is active.

Specified by:

computeStep in interface TrustRegionStep

Parameters:

regionRadius - Size of the trust region.

step - Output, the computed 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