NonLinearFit.h

Classes

NonLinearFit -- Class for non-linear least-squares fit. (full description)

template<class T> class NonLinearFit : public GenericL2Fit<T>

Interface

Public Members
explicit NonLinearFit(Bool svd=False)
NonLinearFit(const NonLinearFit &other)
NonLinearFit &operator=(const NonLinearFit &other)
virtual ~NonLinearFit()
void setMaxIter(uInt maxIter=MAXITER)
uInt getMaxIter() const
uInt currentIteration() const
void setCriteria(const Double criteria=CRITERIUM)
Double getCriteria() const
Bool converged() const
Protected Members
virtual Bool fitIt (Vector<typename FunctionTraits<T>::BaseType> &sol, const T<typename FunctionTraits<T>::BaseType> &x, const Vector<typename FunctionTraits<T>::BaseType> &y, const Vector<typename FunctionTraits<T>::BaseType> *const sigma, const Vector<Bool> *const mask=0) = 0

Description

Review Status

Reviewed By:
wbrouw
Date Reviewed:
2006/06/15
Programs:
Tests:

Prerequisite

Etymology

A nonlinear function is used to fit a set of data points.

Synopsis

NOTE: Constraints added. Documentation out of date at moment, check the tLinearFitSVD and tNonLinearFirLM programs for examples.

The following is a brief summary of the non-linear least-squares fit problem. See module header, Fitting, for a more complete description.

Given a set of N data points (measurements), (x(i), y(i)) i = 0,...,N-1, along with a set of standard deviations, sigma(i), for the data points, and a specified non-linear function, f(x;a) where a = a(j) j = 0,...,M-1 are a set of parameters to be determined, the non-linear least-squares fit tries to minimize

    chi-square = [(y(0)-f(x(0);a)/sigma(0)]^2 + [(y(1)-f(x(1);a)/sigma(1)]^2 + 
                 ... + [(y(N-1)-f(x(N-1);a))/sigma(N-1)]^2.
    
by adjusting {a(j)} in the equation.

For multidimensional functions, x(i) is a vector, and

    f(x(i);a) = f(x(i,0), x(i,1), x(i,2), ...;a)
    

If the measurement errors (standard deviation sigma) are not known at all, they can all be set to one initially. In this case, we assume all measurements have the same standard deviation, after minimizing chi-square, we recompute

    sigma^2 = {(y(0)-z(0))^2 + (y(1)-z(1))^2 + ... 
              + (y(N-1)-z(N-1))^2}/(N-M) = chi-square/(N-M).
    

A statistic weight can be also be assigned to each measurement if the standard deviation is not available. sigma can be calculated from

    sigma = 1/ sqrt(weight)
    
Alternatively a 'weight' switch can be set with asWeight(). For best arithmetic performance, weight should be normalized to a maximum value of one. Having a large weight value can sometimes lead to overflow problems.

The function to be fitted to the data can be given as an instance of the Function class. One can also form a sum of functions using the CompoundFunction.

For small datasets the usage of the calls is:

Note that the fitter is reusable. An example is given in the following.

The solution of a fit always produces the total number of parameters given to the fitter. I.e. including any parameters that were fixed. In the latter case the solution returned will be the fixed value.

Template Type Argument Requirements (T)

If there are a large number of unknowns or a large number of data points machine memory limits (or timing reasons) may not allow a complete in-core fitting to be performed. In this case one can incrementally build the normal equation (see buildNormalMatrix()).

The normal operation of the class tests for real inversion problems only. If tests are needed for almost collinear columns in the solution matrix, the collinearity can be set as the square of the sine of the minimum angle allowed.

Singular Value Decomposition is supported by setting the 'svd' switch, which has a behaviour completely identical to, apart from a default collinearity check of 1e-8.

Other information (see a.o. LSQaips) can be set and obtained as well.

Motivation

The creation of the class module was driven by the need to write code to fit Gaussian functions to data points.

Example

Member Description

explicit NonLinearFit(Bool svd=False)

Create a fitter: the normal way to generate a fitter object. Necessary data will be deduced from the Functional provided with setFunction(). Create optionally a fitter with SVD behaviour specified.

NonLinearFit(const NonLinearFit &other)

Copy constructor (deep copy)

NonLinearFit &operator=(const NonLinearFit &other)

Assignment (deep copy)

virtual ~NonLinearFit()

Destructor

void setMaxIter(uInt maxIter=MAXITER)

setMaxIter() sets the maximum number of iterations to do before stopping. Default value is 30.

uInt getMaxIter() const

getMaxIter() queries what the maximum number of iterations currently is

uInt currentIteration() const

currentIteration() queries what the current iteration is

void setCriteria(const Double criteria=CRITERIUM)

setCriteria() sets the convergence criteria. The actual value and its interpretation depends on the derived class used to do the actual iteration. Default value is 0.001.

Double getCriteria() const

getCriteria() queries the current criteria

Bool converged() const

Check to see if the fit has converged

virtual Bool fitIt (Vector<typename FunctionTraits<T>::BaseType> &sol, const T<typename FunctionTraits<T>::BaseType> &x, const Vector<typename FunctionTraits<T>::BaseType> &y, const Vector<typename FunctionTraits<T>::BaseType> *const sigma, const Vector<Bool> *const mask=0) = 0

Generalised fitter