4.2

MuonMaxent v1

../_images/MuonMaxent-v1_dlg.png

MuonMaxent dialog.

Properties

Name Direction Type Default Description
InputWorkspace Input Workspace Mandatory Raw muon workspace to process
InputPhaseTable Input TableWorkspace   Phase table (initial guess)
InputDeadTimeTable Input TableWorkspace   Dead time table (initial)
GroupTable Input TableWorkspace   Group Table
GroupWorkspace Input Workspace   Group Workspace
FirstGoodTime Input number 0.1 First good data time
LastGoodTime Input number 33 Last good data time
Npts Input number Mandatory Number of frequency points to fit (should be power of 2). Allowed values: [‘256’, ‘512’, ‘1024’, ‘2048’, ‘4096’, ‘8192’, ‘16384’, ‘32768’, ‘65536’, ‘131072’, ‘262144’, ‘524288’, ‘1048576’]
MaxField Input number 1000 Maximum field for spectrum
FixPhases Input boolean False Fix phases to initial values
FitDeadTime Input boolean True Fit deadtimes
DoublePulse Input boolean False Double pulse data
OuterIterations Input number 10 Number of loops to optimise phase, amplitudes, backgrounds and dead times
InnerIterations Input number 10 Number of loops to optimise the spectrum
DefaultLevel Input number 0.1 Default Level
Factor InOut number 1.04 Used to control the value chi-squared converge to
OutputWorkspace Output Workspace Mandatory Output Spectrum (combined) versus field
OutputPhaseTable Output TableWorkspace   Output phase table (optional)
OutputDeadTimeTable Output TableWorkspace   Output dead time table (optional)
ReconstructedSpectra Output Workspace   Reconstructed time spectra (optional)
PhaseConvergenceTable Output Workspace   Convergence of phases (optional)

Description

This algorithm calculates a single frequency spectrum from the time domain spectra recorded by multiple groups/detectors.

If a group contains zero counts (i.e. the detectors are dead) then they are excluded from the frequency calculation. In the outputs these groups record the phase and asymmetry as zero and 999 respectively.

The time domain data D_k(t), where t is time and k is the spectrum number, has associated errors E_k(t). If the number of points chosen is greater than the number of time domain data points then extra points are added with infinite errors. The time domain data prior to FirstGoodTime also have their errors set to infinity. The algorithm will produce the frequency spectra f(\omega) and this is assumed to be real and positive. The upper limit of the frequency spectra is determined by MaxField. The maximum frequency, \omega_\mathrm{max} can be less than the Nyquist limit \frac{\pi}{\delta T} if the instrumental frequency response function for \omega>\omega_\mathrm{max} is approximatley zero. The initial estimate of the frequency spectrum is flat.

The algorithm calculates an estimate of each time domain spectra, g_k(t) by the equation

g_k(t)=(1+A_k \Re(\mathrm{IFFT}(f(\omega) R(\omega))\exp(-j\phi_k) ) ),

where \Re(z) is the real part of z, \mathrm{IFFT} is the inverse fast Fourier transform (as defined by numpy), \phi_k is the phase and A_k is the asymmetry of the of the k^\mathrm{th} spectrum. The asymmetry is normalised such that \sum_k A_k = 1. The instrumental frequency response function, R(\omega), is is in general complex (due to a non-symmetric pulse shape) and is the same for all spectra. The values of the phases and asymmetries are fitted in the outer loop of the algorithm.

The \chi^2 value is calculated via the equation

\chi^2 = F\frac{\sum_{k,t} (D_k(t)-g_k(t))^2 }{E_k(t)^2},

where F is the Factor and is of order 1.0 (but can be adjusted by the user at the start of the algorithm for a better fit). The entropy is given by

S = - \sum_\omega f(\omega) \log\left(\frac{f(\omega)}{A}\right),

where A is the DefaultLevel; it is a parameter of the entropy function. It has a number of names in the literature, one of which is default-value since the maximum entropy solution with no data is f(\omega)=A for all \omega. The algorithm maximises S-\chi^2 and it is seen from the definition of Factor above that this algorithm property acts a Lagrange multiplier, i.e. controlling the value \chi^2 converges to.

Usage

# load data
Load(Filename='MUSR00022725.nxs', OutputWorkspace='MUSR00022725')
# estimate phases
CalMuonDetectorPhases(InputWorkspace='MUSR00022725', FirstGoodData=0.10000000000000001, LastGoodData=16, DetectorTable='phases', DataFitted='fitted', ForwardSpectra='9-16,57-64', BackwardSpectra='25-32,41-48')
MuonMaxent(InputWorkspace='MUSR00022725', InputPhaseTable='phases', Npts='16384', OuterIterations='9', InnerIterations='12', DefaultLevel=0.11, Factor=1.03, OutputWorkspace='freq', OutputPhaseTable='phasesOut', ReconstructedSpectra='time')
# get data
freq = AnalysisDataService.retrieve("freq")
print('frequency values {:.3f} {:.3f} {:.3f} {:.3f} {:.3f}'.format(freq.readY(0)[5], freq.readY(0)[690],freq.readY(0)[700], freq.readY(0)[710],freq.readY(0)[900]))

Output

frequency values 0.110 0.789 0.871 0.821 0.105

Categories: AlgorithmIndex | Muon | Arithmetic\FFT

Source

Python: MuonMaxent.py (last modified: 2019-06-26)