org.ddogleg.optimization

Interface UnconstrainedLeastSquares

All Superinterfaces:

IterativeOptimization, java.io.Serializable

All Known Implementing Classes:

LevenbergDampened_to_UnconstrainedLeastSquares, TrustRegionLeastSquares_to_UnconstrainedLeastSquares

public interface UnconstrainedLeastSquares
extends IterativeOptimization

Non-linear least squares problems have a special structure which can be taken advantage of for optimization. The least squares problem is defined below:
F(x) = 0.5*sum( i=1:M ; f_i(x)² )
where f_i(x) is a function from ℜ^N to ℜ. M is number of functions, and N is number of fit parameters. M ≥ N
f_i(x) = observed - predicted, which is known as the residual error.

Convergence is tested using the g-test, which is based off the gradient's norm.
G-test: gtol ≤ ||g(x)||_inf
A relative f-test is not provided since that test breaks down when the expected function output is zero. An absolute f-test can be done by checking the value of getFunctionValue() in each iteration.

NOTE: The function computes the M outputs of the f_i(x), residual error functions, NOT [f_i(x)]²

FORMATS:
Input functions are specified using FunctionNtoM for the set of M functions, and FunctionNtoMxN for the Jacobian. The function's output is a vector of length M, where element i correspond to function i's output. The Jacobian is an array containing the partial derivatives of each function. Element J(i,j) corresponds to the partial of function i and parameter j. The array is stored in a row major format. The partial for F(i,j) would be stored at index = i*N+j in the data array.

NOTE: If you need to modify the optimization parameters this can be done inside the 'function'.

Method Summary

Modifier and Type	Method and Description
double	getFunctionValue() Returns the value of the objective function being evaluated at the current parameters value.
double[]	getParameters() After each iteration this function can be called to get the current best set of parameters.
void	initialize(double[] initial, double ftol, double gtol) Specify the initial set of parameters from which to start from.
void	setFunction(FunctionNtoM function, FunctionNtoMxN jacobian) Specifies a set of functions and their Jacobian.

Methods inherited from interface org.ddogleg.optimization.IterativeOptimization

getWarning, isConverged, isUpdated, iterate

Method Detail

setFunction

void setFunction(FunctionNtoM function,
                 FunctionNtoMxN jacobian)

Specifies a set of functions and their Jacobian. See class description for documentation on output data format.

Parameters:

function - Computes the output of M functions f_i(x) which take in N fit parameters as input.

jacobian - Computes the Jacobian of the M functions. If null a numerical Jacobian will be used.

initialize

void initialize(double[] initial,
                double ftol,
                double gtol)

Specify the initial set of parameters from which to start from. Call after setFunction(org.ddogleg.optimization.functions.FunctionNtoM, org.ddogleg.optimization.functions.FunctionNtoMxN) has been called.

Parameters:

initial - Initial parameters or guess with N elements..

ftol - Relative threshold for change in function value between iterations. 0 ≤ ftol ≤ 1. Try 1e-12

gtol - Absolute threshold for convergence based on the gradient's norm. 0 disables test. 0 ≤ gtol. Try 1e-12

getParameters

double[] getParameters()

After each iteration this function can be called to get the current best set of parameters.

getFunctionValue

double getFunctionValue()

Returns the value of the objective function being evaluated at the current parameters value. If not supported then an exception is thrown.

Returns:

Objective function's value.