Class GaussNewtonOptimizer

java.lang.Object

org.apache.commons.math3.fitting.leastsquares.GaussNewtonOptimizer

All Implemented Interfaces:

LeastSquaresOptimizer

public class GaussNewtonOptimizer
extends Object
implements LeastSquaresOptimizer

Gauss-Newton least-squares solver.

This class solve a least-square problem by solving the normal equations of the linearized problem at each iteration. Either LU decomposition or Cholesky decomposition can be used to solve the normal equations, or QR decomposition or SVD decomposition can be used to solve the linear system. LU decomposition is faster but QR decomposition is more robust for difficult problems, and SVD can compute a solution for rank-deficient problems.

Since:

3.3

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static enum	GaussNewtonOptimizer.Decomposition	The decomposition algorithm to use to solve the normal equations.

Nested classes/interfaces inherited from interface LeastSquaresOptimizer

LeastSquaresOptimizer.Optimum

Field Summary

Fields

Modifier and Type	Field	Description
private final GaussNewtonOptimizer.Decomposition	decomposition	Indicator for using LU decomposition.
private static final double	SINGULARITY_THRESHOLD	The singularity threshold for matrix decompositions.

Constructor Summary

Constructors

Constructor	Description
GaussNewtonOptimizer()	Creates a Gauss Newton optimizer.
GaussNewtonOptimizer(GaussNewtonOptimizer.Decomposition decomposition)	Create a Gauss Newton optimizer that uses the given decomposition algorithm to solve the normal equations.

Method Summary

Modifier and Type	Method	Description
private static Pair<RealMatrix, RealVector>	computeNormalMatrix(RealMatrix jacobian, RealVector residuals)	Compute the normal matrix, JTJ.
GaussNewtonOptimizer.Decomposition	getDecomposition()	Get the matrix decomposition algorithm used to solve the normal equations.
LeastSquaresOptimizer.Optimum	optimize(LeastSquaresProblem lsp)	Solve the non-linear least squares problem.
String	toString()
GaussNewtonOptimizer	withDecomposition(GaussNewtonOptimizer.Decomposition newDecomposition)	Configure the decomposition algorithm.

Methods inherited from class Object

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

Field Details

SINGULARITY_THRESHOLD

private static final double SINGULARITY_THRESHOLD

The singularity threshold for matrix decompositions. Determines when a ConvergenceException is thrown. The current value was the default value for LUDecomposition.

See Also:

• Constant Field Values

decomposition

private final GaussNewtonOptimizer.Decomposition decomposition

Indicator for using LU decomposition.

Constructor Details

GaussNewtonOptimizer

public GaussNewtonOptimizer()

Creates a Gauss Newton optimizer.

The default for the algorithm is to solve the normal equations using QR decomposition.

GaussNewtonOptimizer

public GaussNewtonOptimizer(GaussNewtonOptimizer.Decomposition decomposition)

Create a Gauss Newton optimizer that uses the given decomposition algorithm to solve the normal equations.

Parameters:

decomposition - the GaussNewtonOptimizer.Decomposition algorithm.

Method Details

getDecomposition

public GaussNewtonOptimizer.Decomposition getDecomposition()

Get the matrix decomposition algorithm used to solve the normal equations.

Returns:

the matrix GaussNewtonOptimizer.Decomposition algoritm.

withDecomposition

public GaussNewtonOptimizer withDecomposition(GaussNewtonOptimizer.Decomposition newDecomposition)

Configure the decomposition algorithm.

Parameters:

newDecomposition - the GaussNewtonOptimizer.Decomposition algorithm to use.

Returns:

a new instance.

optimize

public LeastSquaresOptimizer.Optimum optimize(LeastSquaresProblem lsp)

Solve the non-linear least squares problem.

Specified by:

optimize in interface LeastSquaresOptimizer

Parameters:

lsp - the problem definition, including model function and convergence criteria.

Returns:

The optimum.

toString

public String toString()

Overrides:

toString in class Object

computeNormalMatrix

private static Pair<RealMatrix, RealVector> computeNormalMatrix(RealMatrix jacobian,
 RealVector residuals)

Compute the normal matrix, J^TJ.

Parameters:

jacobian - the m by n jacobian matrix, J. Input.

residuals - the m by 1 residual vector, r. Input.

Returns:

the n by n normal matrix and the n by 1 J^{Tr vector.}