smile.math

Class LevenbergMarquardt

java.lang.Object

smile.math.LevenbergMarquardt

public class LevenbergMarquardt
extends java.lang.Object

The Levenberg–Marquardt algorithm. The Levenberg–Marquardt algorithm (LMA), also known as the Damped least-squares method, is used to solve non-linear least squares problems for generic curve-fitting problems. However, as with many fitting algorithms, the LMA finds only a local minimum, which is not necessarily the global minimum. The LMA interpolates between the Gauss–Newton algorithm (GNA) and the method of gradient descent. The LMA is more robust than the GNA, which means that in many cases it finds a solution even if it starts very far off the final minimum. For well-behaved functions and reasonable starting parameters, the LMA tends to be a bit slower than the GNA. LMA can also be viewed as Gauss–Newton using a trust region approach.

Field Summary

Fields

Modifier and Type	Field and Description
double[]	fittedValues The fitted values.
double[]	parameters The fitted parameters.
double[]	residuals The residuals.
double	sse The sum of squares due to error.

Method Summary

Modifier and Type	Method and Description
static LevenbergMarquardt	fit(DifferentiableMultivariateFunction func, double[][] x, double[] y, double[] p) Fits the nonlinear least squares.
static LevenbergMarquardt	fit(DifferentiableMultivariateFunction func, double[][] x, double[] y, double[] p, double stol, int maxIter) Fits the nonlinear least squares.
static LevenbergMarquardt	fit(DifferentiableMultivariateFunction func, double[] x, double[] y, double[] p) Fits the nonlinear least squares.
static LevenbergMarquardt	fit(DifferentiableMultivariateFunction func, double[] x, double[] y, double[] p, double stol, int maxIter) Fits the nonlinear least squares.

Methods inherited from class java.lang.Object

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

Field Detail

parameters

public final double[] parameters

The fitted parameters.

fittedValues

public final double[] fittedValues

The fitted values.

residuals

public final double[] residuals

The residuals.

sse

public final double sse

The sum of squares due to error.

Method Detail

fit

public static LevenbergMarquardt fit(DifferentiableMultivariateFunction func,
                                     double[] x,
                                     double[] y,
                                     double[] p)

Fits the nonlinear least squares.

Parameters:

func - the curve function.

x - independent variable.

y - the observations.

p - the initial parameters.

Returns:

the sum of squared errors.

fit

public static LevenbergMarquardt fit(DifferentiableMultivariateFunction func,
                                     double[] x,
                                     double[] y,
                                     double[] p,
                                     double stol,
                                     int maxIter)

Fits the nonlinear least squares.

Parameters:

func - the curve function. Of the input variable x, the first d elements are hyper-parameters to be fit. The rest is the independent variable.

x - independent variable.

y - the observations.

p - the initial parameters.

stol - the scalar tolerances on fractional improvement in sum of squares

maxIter - the maximum number of allowed iterations.

Returns:

the sum of squared errors.

fit

public static LevenbergMarquardt fit(DifferentiableMultivariateFunction func,
                                     double[][] x,
                                     double[] y,
                                     double[] p)

Fits the nonlinear least squares.

Parameters:

func - the curve function.

x - independent variables.

y - the observations.

p - the initial parameters.

Returns:

the sum of squared errors.

fit

public static LevenbergMarquardt fit(DifferentiableMultivariateFunction func,
                                     double[][] x,
                                     double[] y,
                                     double[] p,
                                     double stol,
                                     int maxIter)

Fits the nonlinear least squares.

Parameters:

func - the curve function. Of the input variable x, the first d elements are hyper-parameters to be fit. The rest is the independent variable.

x - independent variables.

y - the observations.

p - the initial parameters.

stol - the scalar tolerances on fractional improvement in sum of squares

maxIter - the maximum number of allowed iterations.

Returns:

the sum of squared errors.