Lorentzian1D v1

../_images/Lorentzian1D-v1_dlg.png

Lorentzian1D dialog.

Table of Contents

Summary

== Deprecation notice == Instead of using this algorithm to fit a Lorentzian please use the Fit algorithm where the Function parameter of this algorithm is used to specified the fitting function, including selecting a Lorentzian.

Properties

Name Direction Type Default Description
InputWorkspace Input MatrixWorkspace Mandatory Name of the input Workspace
WorkspaceIndex Input number 0 The Workspace to fit, uses the workspace numbering of the spectra (default 0)
StartX Input number Optional A value of x in, or on the low x boundary of, the first bin to include in the fit (default lowest value of x)
EndX Input number Optional A value in, or on the high x boundary of, the last bin the fitting range (default the highest value of x)
BG0 InOut number 0 Constant background value (default 0)
BG1 InOut number 0 Linear background modelling parameter (default 0)
Height InOut number 0 height of peak (not the height may be refined to a negative value to fit a dipped curve)
PeakCentre InOut number 0 Centre of peak (default 0)
HWHM InOut number 1 half-width at half-maximum (default 1)
Fix Input string   A list of comma separated parameter names which should be fixed in the fit
MaxIterations Input number 500 Stop after this number of iterations if a good fit is not found
OutputStatus Output string    
OutputChi2overDoF Output number    
Output Input string   If not empty OutputParameters TableWorksace and OutputWorkspace will be created.

Description

Takes a histogram in a 2D workspace and fit it to a Lorentzian function, i.e. to the function:

\mbox{BG0}+\mbox{BG1}*x+\mbox{Height}* \left( \frac{\mbox{HWHM}^2}{(x-\mbox{PeakCentre})^2+\mbox{HWHM}^2} \right)

where

  • BG0 - constant background value
  • BG1 - constant background value
  • Height - height of peak (at maximum)
  • PeakCentre - centre of peak
  • HWHM - half-width at half-maximum

Note that the FWHM (Full Width Half Maximum) equals two times HWHM, and the integral over the Lorentzian equals \mbox{Height} * \pi * \mbox{HWHM} (ignoring the linear background). In the literature you may also often see the notation \gamma = HWHM.

The figure below illustrate this symmetric peakshape function fitted to a TOF peak:

LorentzianWithConstBackground.png

LorentzianWithConstBackground.png

Categories: Algorithms | Optimization\FitAlgorithms

Source

C++ source: Lorentzian1D.cpp

C++ header: Lorentzian1D.h