FitGaussian.h

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.

Member Description

FitGaussian()
FitGaussian(uInt dimension)
FitGaussian(uInt dimension, uInt numgaussians)

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

void setDimensions(uInt dimensions)

Adjust the number of dimensions

void setNumGaussians(uInt numgaussians)

Adjust the number of gaussians to fit

void setFirstEstimate(const Matrix<T>& estimate)

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

void setMaxRetries(uInt nretries)

Set the maximum number of retries.

void setMaxTime(Double maxtime)

Set the maximum amount of time to spend (in seconds). If time runs out during a fit the process will still complete that fit.

void setRetryFactors()
void setRetryFactors(const Matrix<T>& retryfactors)

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.

uInt nRetryFactors()

Return the number of retry options available

Bool &mask(uInt gaussian, uInt parameter)

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

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. 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.

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)

void correctParameters(Matrix<T>& parameters)

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

T chisquared()

Return the chi squared of the fit

T RMS()

Return the RMS of the fit

Bool converged()

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

Matrix<T> defaultRetryMatrix()

masks parameters not to change in fitting

Sets the retry matrix to a default value. This is done automatically if the retry matrix is not set directly.

void expandRetryMatrix(uInt rowstoadd)

Add one or more rows to the retry matrix.

uInt countFreeParameters()

Find the number of unmasked parameters to be fit