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BayesQuasi v1

Summary

This algorithm runs the Fortran QLines programs which fits a Delta function of amplitude 0 and Lorentzians of amplitude A(j) and HWHM W(j) where j=1,2,3. The whole function is then convolved with the resolution function.

Properties

Name	Direction	Type	Default	Description
Program	Input	string	QL	The type of program to run (either QL or QSe). Allowed values: [‘QL’, ‘QSe’]
SampleWorkspace	Input	MatrixWorkspace	Mandatory	Name of the Sample input Workspace
ResolutionWorkspace	Input	MatrixWorkspace	Mandatory	Name of the resolution input Workspace
ResNormWorkspace	Input	WorkspaceGroup		Name of the ResNorm input Workspace
MinRange	Input	number	-0.2	The start of the fit range. Default=-0.2
MaxRange	Input	number	0.2	The end of the fit range. Default=0.2
SampleBins	Input	number	1	The number of sample bins
ResolutionBins	Input	number	1	The number of resolution bins
Elastic	Input	boolean	True	Fit option for using the elastic peak
Background	Input	string	Flat	Fit option for the type of background. Allowed values: [‘Sloping’, ‘Flat’, ‘Zero’]
FixedWidth	Input	boolean	True	Fit option for using FixedWidth
UseResNorm	Input	boolean	False	fit option for using ResNorm
WidthFile	Input	string		The name of the fixedWidth file
Loop	Input	boolean	True	Switch Sequential fit On/Off
OutputWorkspaceFit	Output	WorkspaceGroup	Mandatory	The name of the fit output workspaces
OutputWorkspaceResult	Output	MatrixWorkspace	Mandatory	The name of the result output workspaces
OutputWorkspaceProb	Output	MatrixWorkspace		The name of the probability output workspaces

Description

This algorithm can only be run on windows due to f2py support and the underlying fortran code

The model that is being fitted is that of a delta-function (elastic component) of amplitude A(0) and Lorentzians of amplitude A(j) and HWHM W(j) where j=1,2,3. The whole function is then convolved with the resolution function. The -function and Lorentzians are intrinsically normalised to unity so that the amplitudes represent their integrated areas.

For a Lorentzian, the Fourier transform does the conversion: \(1/(x^{2}+\delta^{2}) \Leftrightarrow exp[-2\pi(\delta k)]\). If x is identified with energy E and \(2\pi k\) with \(t/\hbar\) where t is time then: \(1/[E^{2}+(\hbar / \tau)^{2}] \Leftrightarrow exp[-t/\tau]\) and \(\sigma\) is identified with \(\hbar / \tau.\) The program estimates the quasielastic components of each of the groups of spectra and requires the resolution file and optionally the normalisation file created by ResNorm.

For a Stretched Exponential, the choice of several Lorentzians is replaced with a single function with the shape : \(\psi\beta(x) \Leftrightarrow exp[-2\pi(\sigma k)\beta]\). This, in the energy to time FT transformation, is \(\psi\beta(E) \Leftrightarrow exp[-(t/\tau)\beta]\). So \(\sigma\) is identified with \((2\pi)\beta\hbar/\tau\). The model that is fitted is that of an elastic component and the stretched exponential and the program gives the best estimate for the \(\beta\) parameter and the width for each group of spectra.

Usage

Example - BayesQuasi

# Load in test data
sampleWs = Load('irs26176_graphite002_red.nxs')
resWs = Load('irs26173_graphite002_red.nxs')

# Run BayesQuasi algorithm
fit_ws, result_ws, prob_ws = BayesQuasi(Program='QL', SampleWorkspace=sampleWs, ResolutionWorkspace=resWs,
                                    MinRange=-0.547607, MaxRange=0.543216, SampleBins=1, ResolutionBins=1,
                                    Elastic=False, Background='Sloping', FixedWidth=False, UseResNorm=False,
                                    WidthFile='', Loop=True)

Categories: AlgorithmIndex | Workflow\MIDAS

Source

Python: BayesQuasi.py