Package edu.cnu.mdi.splot.fit

Class LorentzianFitter

java.lang.Object

edu.cnu.mdi.splot.fit.ALeastSquaresFitter

edu.cnu.mdi.splot.fit.LorentzianFitter

All Implemented Interfaces:

IFitStringGetter, IFitter

public final class LorentzianFitter
extends ALeastSquaresFitter

Nonlinear least-squares fitter for a Lorentzian (Cauchy / Breit-Wigner) peak with a constant baseline:

 y(x) = A * (Γ/2)² / [(x - x&sub0;)² + (Γ/2)²] + B
 

Normalisation

The parameter A is the peak height above baseline (i.e. y(x₀) = A + B), not the area. This matches the Gaussian fitter convention used elsewhere in splot, making it easy to switch between the two.

Parameter ordering

• params[0] = A — peak height above baseline
• params[1] = x₀ — peak center
• params[2] = Γ — full-width at half-maximum (FWHM); enforced >= DEFAULT_MIN_GAMMA
• params[3] = B — baseline offset

Relationship to Gaussian

A Lorentzian has heavier tails than a Gaussian of the same FWHM. For a Gaussian, FWHM = 2√(2 ln 2)·σ ≈ 2.355·σ. Both models have the same peak-height parameter A and baseline B, so they can be compared directly.

Typical applications

Resonance peaks in nuclear/particle physics (Breit-Wigner), spectral line shapes in atomic spectroscopy, quality-factor measurements in mechanical or electrical resonators, natural line widths.

Author:

heddle

Field Summary

Fields

Modifier and Type	Field	Description
static final double	DEFAULT_MIN_GAMMA	Minimum FWHM to avoid divide-by-zero in the Jacobian.
static final int	IDX_A	Index of peak-height parameter A.
static final int	IDX_B	Index of baseline parameter B.
static final int	IDX_G	Index of FWHM parameter Γ.
static final int	IDX_X0	Index of peak-center parameter x₀.
static final String[]	PARAM_NAMES	Display names used in legend strings and fit summaries.

Fields inherited from class edu.cnu.mdi.splot.fit.ALeastSquaresFitter

CAPSIG, checker, covarianceThreshold, initialGuesser, maxEvaluations, maxIterations, MU, OMEGA, optimizer, PHI, SMALLSIG, SUB0, SUB1, SUB2, subArray, SUBN, SUP0, SUP1, SUP2, SUPN

Constructor Summary

Constructors

Constructor	Description
LorentzianFitter()	Creates a fitter with the default Levenberg-Marquardt optimizer.
LorentzianFitter(org.apache.commons.math3.fitting.leastsquares.LeastSquaresOptimizer optimizer)	Creates a fitter with a custom optimizer.

Method Summary

Modifier and Type	Method	Description
Evaluator	asEvaluator(FitResult fit)	Returns an Evaluator that computes A * (Γ/2)² / [(x − x₀)² + (Γ/2)²] + B.
protected double[]	defaultInitialGuess(double[] x, double[] y, double[] weights)	Default initial guess used if the caller does not provide an explicit override.
protected org.apache.commons.math3.fitting.leastsquares.ParameterValidator	defaultValidator()	Default validator/bounds policy (optional).
String	functionForm()
protected int	getParameterCount()
IFitStringGetter	getStringGetter()	Get the descriptive string getter for this fitter.
protected org.apache.commons.math3.fitting.leastsquares.MultivariateJacobianFunction	model(double[] x)	Build the model + analytic (or numeric) Jacobian for this fitter, given x values.
String	modelName()
String	parameterName(int index)	Return the display name of a fitted parameter.

Methods inherited from class edu.cnu.mdi.splot.fit.ALeastSquaresFitter

buildFitResult, clampingValidator, fit, fit, fit, getChecker, getCovarianceThreshold, getMaxEvaluations, getMaxIterations, safeCovariances, validateWeights, validateXY, weightsFromSigmaY

Methods inherited from class java.lang.Object

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

Field Details

IDX_A

public static final int IDX_A

Index of peak-height parameter A.

See Also:

• Constant Field Values

IDX_X0

public static final int IDX_X0

Index of peak-center parameter x₀.

See Also:

• Constant Field Values

IDX_G

public static final int IDX_G

Index of FWHM parameter Γ.

See Also:

• Constant Field Values

IDX_B

public static final int IDX_B

Index of baseline parameter B.

See Also:

• Constant Field Values

PARAM_NAMES

public static final String[] PARAM_NAMES

Display names used in legend strings and fit summaries.

DEFAULT_MIN_GAMMA

public static final double DEFAULT_MIN_GAMMA

Minimum FWHM to avoid divide-by-zero in the Jacobian.

See Also:

• Constant Field Values

Constructor Details

LorentzianFitter

public LorentzianFitter()

Creates a fitter with the default Levenberg-Marquardt optimizer.

LorentzianFitter

public LorentzianFitter(org.apache.commons.math3.fitting.leastsquares.LeastSquaresOptimizer optimizer)

Creates a fitter with a custom optimizer.

Parameters:

optimizer - the least-squares optimizer to use (non-null)

Method Details

getParameterCount

protected int getParameterCount()

Specified by:

getParameterCount in class ALeastSquaresFitter

Returns:

number of parameters for this fitter.

model

protected org.apache.commons.math3.fitting.leastsquares.MultivariateJacobianFunction model(double[] x)

Description copied from class: ALeastSquaresFitter

Build the model + analytic (or numeric) Jacobian for this fitter, given x values.

Specified by:

model in class ALeastSquaresFitter

Parameters:

x - x data (length n)

Returns:

a MultivariateJacobianFunction compatible with Commons Math least-squares

defaultInitialGuess

protected double[] defaultInitialGuess(double[] x,
 double[] y,
 double[] weights)

Description copied from class: ALeastSquaresFitter

Default initial guess used if the caller does not provide an explicit override. The default implementation delegates to the ALeastSquaresFitter.initialGuesser.

Subclasses may override if they have a better model-specific guess.

Overrides:

defaultInitialGuess in class ALeastSquaresFitter

Parameters:

x - x data

y - y data

weights - optional weights (may be null)

Returns:

initial parameter vector of length ALeastSquaresFitter.getParameterCount()

defaultValidator

protected org.apache.commons.math3.fitting.leastsquares.ParameterValidator defaultValidator()

Description copied from class: ALeastSquaresFitter

Default validator/bounds policy (optional).

Return null for "no validation". For simple bound constraints, consider using ALeastSquaresFitter.clampingValidator(double[], double[]).

Overrides:

defaultValidator in class ALeastSquaresFitter

Returns:

a parameter validator or null

asEvaluator

public Evaluator asEvaluator(FitResult fit)

Returns an Evaluator that computes A * (Γ/2)² / [(x − x₀)² + (Γ/2)²] + B.

Specified by:

asEvaluator in class ALeastSquaresFitter

Parameters:

fit - fit result from a previous call to ALeastSquaresFitter.fit(double[], double[])

Returns:

evaluator for the fitted Lorentzian

Throws:

NullPointerException - if fit is null

IllegalArgumentException - if the result has the wrong parameter count

modelName

public String modelName()

Returns:

model name suitable for a legend or report

functionForm

public String functionForm()

Returns:

mathematical function form suitable for display

parameterName

public String parameterName(int index)

Description copied from interface: IFitStringGetter

Return the display name of a fitted parameter.

Parameters:

index - zero-based parameter index

Returns:

parameter name

getStringGetter

public IFitStringGetter getStringGetter()

Description copied from class: ALeastSquaresFitter

Get the descriptive string getter for this fitter.

Specified by:

getStringGetter in class ALeastSquaresFitter

Returns:

the string getter