Module imagingbook.common

Package imagingbook.common.math.nonlinear

Class NonlinearLeastSquares

java.lang.Object

imagingbook.common.math.nonlinear.NonlinearLeastSquares

public abstract class NonlinearLeastSquares
extends Object

This class defines static methods for simplified access to nonlinear least-squares solvers in Apache Commons Math, hiding much of the available configuration options. If other than default settings are needed, the original (Apache Commons Math) API should be used. See the Appendix C of [1] for additional details and examples.

[1] W. Burger, M.J. Burge, Digital Image Processing – An Algorithmic Introduction, 3rd ed, Springer (2022).

Field Summary

Fields

Modifier and Type	Field	Description
static int	MaxEvaluations
static int	MaxIterations
static double	Tolerance

Method Summary

Modifier and Type	Method	Description
static RealVector	solveGaussNewton(MultivariateVectorFunction V, MultivariateMatrixFunction J, RealVector z, RealVector p0)	Solves the nonlinear least-squares problem defined by the arguments using Gauss-Newton optimization.
static RealVector	solveLevenvergMarquardt(MultivariateVectorFunction V, MultivariateMatrixFunction J, RealVector z, RealVector p0)	Solves the nonlinear least-squares problem defined by the arguments using Levenberg-Marquardt optimization.
static RealVector	solveNLS(MultivariateVectorFunction V, MultivariateMatrixFunction J, RealVector z, RealVector p0)	Solves the nonlinear least-squares problem defined by the arguments.
static RealVector	solveNLS2(MultivariateVectorFunction V, MultivariateMatrixFunction J, RealVector z, RealVector p0)

Methods inherited from class java.lang.Object

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

Field Details

MaxEvaluations

public static int MaxEvaluations

MaxIterations

public static int MaxIterations

Tolerance

public static double Tolerance

Method Details

solveNLS

public static RealVector solveNLS(MultivariateVectorFunction V,
 MultivariateMatrixFunction J,
 RealVector z,
 RealVector p0)

Solves the nonlinear least-squares problem defined by the arguments. Delegates to the Levenberg-Marquardt method.

Parameters:

V - the "value" function, V(p) must return a vector for the current parameters p

J - the "Jacobian" function, J(p) must return a matrix for the current parameters p

z - the vector of observed ("target") values

p0 - initial parameter vector

Returns:

the vector of optimal parameters

solveLevenvergMarquardt

public static RealVector solveLevenvergMarquardt(MultivariateVectorFunction V,
 MultivariateMatrixFunction J,
 RealVector z,
 RealVector p0)

Solves the nonlinear least-squares problem defined by the arguments using Levenberg-Marquardt optimization.

Parameters:

V - the "value" function, V(p) must return a vector for the current parameters p

J - the "Jacobian" function, J(p) must return a matrix for the current parameters p

z - the vector of observed ("target") values

p0 - initial parameter vector

Returns:

the vector of optimal parameters

solveGaussNewton

public static RealVector solveGaussNewton(MultivariateVectorFunction V,
 MultivariateMatrixFunction J,
 RealVector z,
 RealVector p0)

Solves the nonlinear least-squares problem defined by the arguments using Gauss-Newton optimization.

Parameters:

V - the "value" function, V(p) must return a vector for the current parameters p

J - the "Jacobian" function, J(p) must return a matrix for the current parameters p

z - the vector of observed ("target") values

p0 - initial parameter vector

Returns:

the vector of optimal parameters

solveNLS2

public static RealVector solveNLS2(MultivariateVectorFunction V,
 MultivariateMatrixFunction J,
 RealVector z,
 RealVector p0)