Multidimensional fitter class for Gaussians. More...

#include <FitGaussian.h>

Public Member Functions
	FitGaussian ()
	Create the fitter. More...

	FitGaussian (uInt dimension)

	FitGaussian (uInt dimension, uInt numgaussians)

void	setDimensions (uInt dimensions)
	Adjust the number of dimensions. More...

void	setNumGaussians (uInt numgaussians)
	Adjust the number of gaussians to fit. More...

void	setFirstEstimate (const Matrix< T > &estimate)
	Set the initial estimate (the starting point of the first fit.) More...

void	setMaxRetries (uInt nretries)
	Set the maximum number of retries. More...

void	setMaxTime (Double maxtime)
	Set the maximum amount of time to spend (in seconds). More...

void	setRetryFactors ()
	Set the retry factors, the values that are added/multiplied with the first estimate on subsequent attempts if the first attempt fails. More...

void	setRetryFactors (const Matrix< T > &retryfactors)

uInt	nRetryFactors ()
	Return the number of retry options available. More...

Bool &	mask (uInt gaussian, uInt parameter)
	Mask out some parameters so that they are not modified during fitting. More...

const Bool &	mask (uInt gaussian, uInt parameter) const

Matrix< T >	fit (const Matrix< T > &pos, const Vector< T > &f, T maximumRMS=1.0, uInt maxiter=1024, T convcriteria=0.0001)
	Run the fit, using the data provided in the arguments pos and f. More...

Matrix< T >	fit (const Matrix< T > &pos, const Vector< T > &f, const Vector< T > &sigma, T maximumRMS=1.0, uInt maxiter=1024, T convcriteria=0.0001)

const Matrix< T > &	solution ()
	Allow access to the fit parameters from this class. More...

const Matrix< T > &	errors ()

void	correctParameters (Matrix< T > &parameters)
	Internal function for ensuring that parameters stay within their stated domains (see `Gaussian2D` and `Gaussian3D`.) More...

T	chisquared ()
	Return the chi squared of the fit. More...

T	RMS ()
	Return the RMS of the fit. More...

Bool	converged ()
	Returns True if the fit (eventually) converged to a value. More...

Private Member Functions
Matrix< T >	defaultRetryMatrix ()
	Sets the retry matrix to a default value. More...

void	expandRetryMatrix (uInt rowstoadd)
	Add one or more rows to the retry matrix. More...

uInt	countFreeParameters ()
	Find the number of unmasked parameters to be fit. More...

Private Attributes
uInt	itsDimension

uInt	itsNGaussians

uInt	itsMaxRetries

Double	itsMaxTime

T	itsChisquare

T	itsRMS

Bool	itsSuccess

LogIO	os

Matrix< T >	itsFirstEstimate

Matrix< T >	itsRetryFctr

Matrix< Bool >	itsMask

Matrix< T >	itsSolutionParameters
	The solutions to the fit. More...

Matrix< T >	itsSolutionErrors
	The errors on the solution parameters. More...

Detailed Description

template<class T>
class casacore::FitGaussian< T >

Multidimensional fitter class for Gaussians.

Review Status

Test programs:: tFitGaussian

Prerequisite

Gaussian1D class
Gaussian2D class
Gaussian3D class
NonLinearFitLM class

Etymology

Fits Gaussians to data.

Synopsis

FitGaussian is specially designed for fitting procedures in code that must be generalized for general dimensionality and number of components, and for complicated fits where the failure rate of the standard nonlinear fitter is unacceptibly high.

FitGaussian essentially provides a Gaussian-adapted interface for NonLinearFitLM. The user specifies the dimension, number of gaussians, initial estimate, retry factors, and the data, and the fitting proceeds automatically. Upon failure of the fitter it will retry the fit according to the retry factors until a fit is completed successfully. The user can optionally require as a criterion for success that the RMS of the fit residuals not exceed some maximum value.

The retry factors are applied in different ways: the height and widths are multiplied by the retry factors while the center and angles are increased by their factors. As of 2002/07/12 these are applied randomly (instead of sequentially) to different components and combinations of components. The factors can be specified by the user, but a default set is available. This random method is better than the sequential method for a limited number of retries, but true optimization of the retry system would demand the use of a more sophisticated method.

Example

FitGaussian<Double> fitgauss(1,1);
Matrix<Double> x(5,1); x(0,0) = 0; x(1,0) = 1; x(2,0) = 2; x(3,0) = 3; x(4,0) = 4;
Vector<Double> y(5); y(0) = 0; y(1) = 1; y(2) = 4; y(3) = 1; y(4) = 1;
Matrix<Double> estimate(1,3);
estimate(0,0) = 1; estimate(0,1) = 1; estimate(0,2) = 1;
fitgauss.setFirstEstimate(estimate);
Matrix<Double> solution;
solution = fitgauss.fit(x,y);
cout << solution;

Motivation

Fitting multiple Gaussians is required for many different applications, but requires a substantial amount of coding - especially if the dimensionality of the image is not known to the programmer. Furthermore, fitting multiple Gaussians has a very high failure rate. So, a specialized Gaussian fitting class that retries from different initial estimates until an acceptible fit was found was needed.

Template Type Argument Requirements (T)

T must be a real data type compatible with NonLinearFitLM - Float or Double.

Thrown Exceptions

AipsError if dimension is not 1, 2, or 3
AipsError if incorrect parameter number specified.
AipsError if estimate/retry/data arrays are of wrong dimension

To Do

Optimize the default retry matrix
Send fitting messages to logger instead of console
Consider using a more sophisticated retry ststem (above).
Check the estimates for reasonability, especially on failure of fit.
Consider adding other models (polynomial, etc) to make this a Fit3D class.

Definition at line 125 of file FitGaussian.h.

Constructor & Destructor Documentation

template<class T >

casacore::FitGaussian< T >::FitGaussian ( )

Create the fitter.

The dimension and the number of gaussians to fit can be modified later if necessary.

template<class T >

casacore::FitGaussian< T >::FitGaussian ( uInt dimension )

template<class T >

casacore::FitGaussian< T >::FitGaussian	(	uInt	dimension,
		uInt	numgaussians
	)

Member Function Documentation

template<class T >

T casacore::FitGaussian< T >::chisquared ( )

Return the chi squared of the fit.

template<class T >

Bool casacore::FitGaussian< T >::converged ( )

Returns True if the fit (eventually) converged to a value.

template<class T >

void casacore::FitGaussian< T >::correctParameters ( Matrix< T > & parameters )

Internal function for ensuring that parameters stay within their stated domains (see Gaussian2D and Gaussian3D.)

template<class T >

uInt casacore::FitGaussian< T >::countFreeParameters ( )

private

Find the number of unmasked parameters to be fit.

template<class T >

Matrix<T> casacore::FitGaussian< T >::defaultRetryMatrix ( )

private

Sets the retry matrix to a default value.

This is done automatically if the retry matrix is not set directly.

template<class T >

const Matrix<T>& casacore::FitGaussian< T >::errors ( )

inline

Definition at line 182 of file FitGaussian.h.

References casacore::FitGaussian< T >::itsSolutionErrors.

template<class T >

void casacore::FitGaussian< T >::expandRetryMatrix ( uInt rowstoadd )

private

Add one or more rows to the retry matrix.

template<class T >

Matrix<T> casacore::FitGaussian< T >::fit	(	const Matrix< T > &	pos,
		const Vector< T > &	f,
		T	maximumRMS = `1.0`,
		uInt	maxiter = `1024`,
		T	convcriteria = `0.0001`
	)

Run the fit, using the data provided in the arguments pos and f.

The fit will retry from different initial estimates until it converges to a value with an RMS error less than maximumRMS. If this cannot be accomplished it will simply take the result that generated the best RMS.

template<class T >

Matrix<T> casacore::FitGaussian< T >::fit	(	const Matrix< T > &	pos,
		const Vector< T > &	f,
		const Vector< T > &	sigma,
		T	maximumRMS = `1.0`,
		uInt	maxiter = `1024`,
		T	convcriteria = `0.0001`
	)

template<class T >

Bool& casacore::FitGaussian< T >::mask	(	uInt	gaussian,
		uInt	parameter
	)

Mask out some parameters so that they are not modified during fitting.

template<class T >

const Bool& casacore::FitGaussian< T >::mask	(	uInt	gaussian,
		uInt	parameter
	)		const

template<class T >

uInt casacore::FitGaussian< T >::nRetryFactors ( )

inline

Return the number of retry options available.

Definition at line 162 of file FitGaussian.h.

References casacore::FitGaussian< T >::itsRetryFctr, and casacore::Matrix< T, Alloc >::nrow().

template<class T >

T casacore::FitGaussian< T >::RMS ( )

Return the RMS of the fit.

template<class T >

void casacore::FitGaussian< T >::setDimensions ( uInt dimensions )

Adjust the number of dimensions.

template<class T >

void casacore::FitGaussian< T >::setFirstEstimate ( const Matrix< T > & estimate )

Set the initial estimate (the starting point of the first fit.)

template<class T >

void casacore::FitGaussian< T >::setMaxRetries ( uInt nretries )

inline

Set the maximum number of retries.

Definition at line 147 of file FitGaussian.h.

References casacore::FitGaussian< T >::itsMaxRetries.

template<class T >

void casacore::FitGaussian< T >::setMaxTime ( Double maxtime )

inline

Set the maximum amount of time to spend (in seconds).

If time runs out during a fit the process will still complete that fit.

Definition at line 151 of file FitGaussian.h.

References casacore::FitGaussian< T >::itsMaxTime.

template<class T >

void casacore::FitGaussian< T >::setNumGaussians ( uInt numgaussians )

Adjust the number of gaussians to fit.

template<class T >

void casacore::FitGaussian< T >::setRetryFactors ( )

Set the retry factors, the values that are added/multiplied with the first estimate on subsequent attempts if the first attempt fails.

Using the function with no argument sets the retry factors to the default.

template<class T >

void casacore::FitGaussian< T >::setRetryFactors ( const Matrix< T > & retryfactors )

template<class T >

const Matrix<T>& casacore::FitGaussian< T >::solution ( )

inline

Allow access to the fit parameters from this class.

Definition at line 181 of file FitGaussian.h.

References casacore::FitGaussian< T >::itsSolutionParameters.

Member Data Documentation

template<class T >

T casacore::FitGaussian< T >::itsChisquare

private

Definition at line 203 of file FitGaussian.h.

template<class T >

uInt casacore::FitGaussian< T >::itsDimension

private

Definition at line 199 of file FitGaussian.h.

template<class T >

Matrix<T> casacore::FitGaussian< T >::itsFirstEstimate

private

Definition at line 208 of file FitGaussian.h.

template<class T >

Matrix<Bool> casacore::FitGaussian< T >::itsMask

private

Definition at line 210 of file FitGaussian.h.

template<class T >

uInt casacore::FitGaussian< T >::itsMaxRetries

private

Definition at line 201 of file FitGaussian.h.

Referenced by casacore::FitGaussian< T >::setMaxRetries().

template<class T >

Double casacore::FitGaussian< T >::itsMaxTime

private

Definition at line 202 of file FitGaussian.h.

Referenced by casacore::FitGaussian< T >::setMaxTime().

template<class T >

uInt casacore::FitGaussian< T >::itsNGaussians

private

Definition at line 200 of file FitGaussian.h.

template<class T >

Matrix<T> casacore::FitGaussian< T >::itsRetryFctr

private

Definition at line 209 of file FitGaussian.h.

Referenced by casacore::FitGaussian< T >::nRetryFactors().

template<class T >

T casacore::FitGaussian< T >::itsRMS

private

Definition at line 204 of file FitGaussian.h.

template<class T >

Matrix<T> casacore::FitGaussian< T >::itsSolutionErrors

private

The errors on the solution parameters.

Definition at line 227 of file FitGaussian.h.

Referenced by casacore::FitGaussian< T >::errors().

template<class T >

Matrix<T> casacore::FitGaussian< T >::itsSolutionParameters

private

The solutions to the fit.

Definition at line 224 of file FitGaussian.h.

Referenced by casacore::FitGaussian< T >::solution().

template<class T >

Bool casacore::FitGaussian< T >::itsSuccess

private

Definition at line 205 of file FitGaussian.h.

template<class T >

LogIO casacore::FitGaussian< T >::os

private

Definition at line 206 of file FitGaussian.h.

The documentation for this class was generated from the following file:

scimath/Fitting/FitGaussian.h

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

template<class T> class casacore::FitGaussian< T >

Review Status

Prerequisite

Etymology

Synopsis

Example

Motivation

Template Type Argument Requirements (T)

Thrown Exceptions

To Do

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class T>
class casacore::FitGaussian< T >