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¶

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

# Check OS support for F2Py
from IndirectImport import is_supported_f2py_platform
if is_supported_f2py_platform():
    # 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 (last modified: 2020-03-27)