6.3

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FindPeaksMD v1

../_images/FindPeaksMD-v1_dlg.png

FindPeaksMD dialog.

Summary

Find peaks in reciprocal space in a MDEventWorkspace or a MDHistoWorkspace.

Properties

Name Direction Type Default Description
InputWorkspace Input IMDWorkspace Mandatory An input MDEventWorkspace or MDHistoWorkspace with at least 3 dimensions.
PeakDistanceThreshold Input number 0.1 Threshold distance for rejecting peaks that are found to be too close from each other. This should be some multiple of the radius of a peak. Default: 0.1.
MaxPeaks Input number 500 Maximum number of peaks to find. Default: 500.
PeakFindingStrategy Input string VolumeNormalization Strategy for finding peaks in an MD workspace.1. VolumeNormalization: This is the default strategy. It will sort all boxes in the workspace by deacresing order of signal density (total weighted event sum divided by box volume). 2.NumberOfEventsNormalization: This option is only valid for MDEventWorkspaces. It will use the total weighted event sum dividedby the number of events. This can improve peak finding for histogram-basedraw data which has been converted to an EventWorkspace. The threshold forpeak finding can be controlled by the SingalThresholdFactor property which shouldbe larger than 1. Note that this approach does not work for event-based raw data. Allowed values: [‘VolumeNormalization’, ‘NumberOfEventsNormalization’]
DensityThresholdFactor Input number 10 The overall signal density of the workspace will be multiplied by this factor to get a threshold signal density below which boxes are NOT considered to be peaks. See the help. Default: 10.0
SignalThresholdFactor Input number 1.5 The overal signal value (not density!) normalized by the number of events is compared to the specified signal threshold. Boxes which are below this threshold are NOT considered to be peaks.This property is enabled when the PeakFindingStrategy has been set to NumberOfEventsNormalization. The value of boxes which contain peaks will be above 1. See the below for more information. Default: 1.50
CalculateGoniometerForCW Input boolean False This will calculate the goniometer rotation (around y-axis only) for a constant wavelength. This only works for Q sample workspaces.
Wavelength Input number Optional Wavelength to use when calculating goniometer angle. If notset will use the wavelength parameter on the instrument.
InnerGoniometer Input boolean False Whether the goniometer to be calculated is the most inner (phi) or most outer (omega)
FlipX Input boolean False Used when calculating goniometer angle if the q_lab x value should be negative, hence the detector of the other side (right) of the beam
OutputType Input string Automatic Type of Peak in OutputWorkspace. Allowed values: [‘Automatic’, ‘Peak’, ‘LeanElasticPeak’]
OutputWorkspace Output IPeaksWorkspace Mandatory An output PeaksWorkspace with the peaks’ found positions.
AppendPeaks Input boolean False If checked, then append the peaks in the output workspace if it exists. If unchecked, the output workspace is replaced (Default).
EdgePixels Input number 0 Remove peaks that are at pixels this close to edge.

Description

This algorithm is used to find single-crystal peaks in a multi-dimensional workspace (MDEventWorkspace or MDHistoWorkspace). It looks for high signal density areas, and is based on an algorithm designed by Dennis Mikkelson for ISAW.

The algorithm proceeds in this way:

  • Sorts all the boxes in the workspace by decreasing order of signal density (total weighted event sum divided by box volume).
    • It will skip any boxes with a density below a threshold. The threshold is \(TotalSignal / TotalVolume * DensityThresholdFactor\).
  • The centroid of the strongest box is considered a peak.
  • The centroid of the next strongest box is calculated.
    • We look through all the peaks that have already been found. If the box is too close to an existing peak, it is rejected. This distance is PeakDistanceThreshold.
  • This is repeated until we find up to MaxPeaks peaks.

Each peak created is placed in the output PeaksWorkspace or LeanElasticPeaksWorkspace (depending on the OutputType option), which can be a new workspace or replace the old one. If OutputType is the default Automatic then the output type will be PeakWorkspace unless the input workspace doesn’t contain an experiment info in which case it will default to LeanElasticPeaksWorkspace.

This algorithm works on a MDHistoWorkspace resulting from the BinMD v1 algorithm also. It works in the same way, except that the center of each bin is used since the centroid is not accessible. It may give better results on Workspace2D’s that were converted to MDWorkspaces.

For data which has originally been based on histogram-type data and that has been converted to event-based data it might be beneficial to select the NumberOfEventNormalization for the PeakFindingStrategy property instead of the VolumeNormalization which is the default. This will disable the DensityThresholdFactor property and enable the SignalThresholdFactor property. The algorithmic steps remain the same as above but instead of using the signal density as the sorting quantity the signal count (total weighted event sum divided by the number of events) is used. If the events are weighted this will result in boxes with signal counts larger than one for peaks and for the majority of background counts the signal count will be 1. Hence it is possible to discriminate between peaks and background. Note that the NumberOfEventNormalization selection of the PeakFindingStrategy property does not make sense for all scenarios and infact might not produce useful results for your particular case.

Calculate Goniometer For Constant Wavelength

The CalculateGoniometerForCW option allows you to keep only one instrument definition from a set of merged MD workspaces. It only works for a constant wavelength source and only for Q sample workspaces. It also assumes the goniometer rotation is around the y-axis only.

You can specify if the goniometer to calculated is omega or phi, outer or inner respectively, by setting the option InnerGoniometer. The existing goniometer on the workspace will then be taken into account correctly.

The goniometer (\(G\)) is calculated from \(\textbf{Q}_{sample}\) for a given wavelength (\(\lambda\)) by:

First calculate the \(\textbf{Q}_{lab}\) using \(\textbf{Q}_{sample}\) and \(\lambda\).

\[k = \frac{2 \pi}{\lambda}\]
\[\begin{split}G \textbf{Q}_{sample} = \textbf{Q}_{lab} = \left(\begin{array}{c} -k\sin(\theta)\cos(\phi) \\ -k\sin(\theta)\sin(\phi) \\ k (1-\cos(\theta)) \end{array}\right) (1)\end{split}\]
\[|\textbf{Q}_{sample}|^2 = |\textbf{Q}_{lab}|^2 = 2 k^2 (1-\cos(\theta))\]

\(\therefore\)

\[\theta = \cos^{-1}(1-\frac{|\textbf{Q}_{sample}|^2}{2k^2})\]
\[\phi = \sin^{-1}(-\frac{\textbf{Q}_{sample}^y}{k \sin(\theta)})\]

where \(\theta\) is from 0 to \(\pi\) and \(\phi\) is from \(-\pi/2\) to \(\pi/2\). This means that it will assume your detector position is on the left of the beam even it it’s not, unless the option FlipX is set to True then the \(\textbf{Q}_{lab}^x = -\textbf{Q}_{lab}^x\).

Now you have \(\theta\), \(\phi\) and k you can get \(\textbf{Q}_{lab}\) using (1).

We need to now solve \(G \textbf{Q}_{sample} = \textbf{Q}_{lab}\). For a rotation around y-axis only we want to find \(\psi\) for:

\[\begin{split}G = \begin{bmatrix} \cos(\psi) & 0 & \sin(\psi) \\ 0 & 1 & 0 \\ -\sin(\psi) & 0 & \cos(\psi) \end{bmatrix} (2)\end{split}\]

which gives two equations

\[\cos(\psi)\textbf{Q}_{sample}^x+\sin(\psi)\textbf{Q}_{sample}^z = \textbf{Q}_{lab}^x\]
\[-\sin(\psi)\textbf{Q}_{sample}^x+\cos(\psi)\textbf{Q}_{sample}^z = \textbf{Q}_{lab}^z\]

make

\[\begin{split}A = \begin{bmatrix} \textbf{Q}_{sample}^x & \textbf{Q}_{sample}^z \\ \textbf{Q}_{sample}^z & -\textbf{Q}_{sample}^x \end{bmatrix}\end{split}\]
\[\begin{split}B = \begin{bmatrix} \textbf{Q}_{lab}^x \\ \textbf{Q}_{lab}^z \end{bmatrix}\end{split}\]

Then we need to solve \(A X = B\) for \(X\) where

\[\begin{split}X = \begin{bmatrix} \cos{\psi} \\ \sin{\psi} \end{bmatrix} = A^{-1} B\end{split}\]

then

\[\psi = \tan^{-1}\left(\frac{\sin{\psi}}{\cos{\psi}}\right)\]

Put \(\psi\) into (2) and you have the goniometer for that peak.

Usage

Example - IntegratePeaks:

The code iteslef works but disabled from doc tests as takes too long to complete. User should provide its own event nexus file instead of TOPAZ_3132_event.nxs used within this example. The original TOPAZ_3132_event.nxs file is available in Mantid system tests repository.

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#.. testcode:: exFindPeaksMD


def print_tableWS(pTWS,nRows):
    ''' Method to print part of the table workspace '''
    tab_names=pTWS.keys()
    row = ""
    for name in tab_names:
        if len(name)>8:
           name= name[:8]
        row += "| {:8} ".format(name)
    print(row + "|")

    for i in range(nRows):
        row = ""
        for name in tab_names:
              col = pTWS.column(name);
              data2pr=col[i]
              if type(data2pr) is float:
                  row += "| {:8.1f} ".format(data2pr)
              else:
                  row += "| {:8} ".format(str(data2pr))
        print(row + "|")

# load test workspace
Load(Filename=r'TOPAZ_3132_event.nxs',OutputWorkspace='TOPAZ_3132_event',LoadMonitors='1')

# build peak workspace necessary for IntegrateEllipsoids algorithm to work
ConvertToMD(InputWorkspace='TOPAZ_3132_event',QDimensions='Q3D',dEAnalysisMode='Elastic',Q3DFrames='Q_sample',LorentzCorrection='1',OutputWorkspace='TOPAZ_3132_md',\
MinValues='-25,-25,-25',MaxValues='25,25,25',SplitInto='2',SplitThreshold='50',MaxRecursionDepth='13',MinRecursionDepth='7')
peaks=FindPeaksMD(InputWorkspace='TOPAZ_3132_md',PeakDistanceThreshold='0.37680',MaxPeaks='50',DensityThresholdFactor='100',OutputWorkspace='TOPAZ_3132_peaks')

# print 10 rows of table workspace
print_tableWS(peaks,10)

Output:

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#.. testoutput:: exFindPeaksMD

| RunNumbe | DetID    | h        | k        | l        | Waveleng | Energy   | TOF      | DSpacing | Intens   | SigInt   | BinCount | BankName | Row      | Col      | QLab     | QSample  | PeakNumb |
| 3132     | 1124984  |      0.0 |      0.0 |      0.0 |      3.1 |      8.5 |  14482.3 |      2.0 |      0.0 |      0.0 |   1668.0 | bank17   |    120.0 |     42.0 | [1.57771,1.21779,2.37854] | [2.99396,0.815958,0.00317344] | 1        |
| 3132     | 1156753  |      0.0 |      0.0 |      0.0 |      2.1 |     18.8 |   9725.7 |      1.3 |      0.0 |      0.0 |   1060.0 | bank17   |    145.0 |    166.0 | [2.48964,1.45725,3.88666] | [4.52618,1.71025,0.129461] | 2        |
| 3132     | 1141777  |      0.0 |      0.0 |      0.0 |      1.7 |     28.1 |   7963.2 |      1.0 |      0.0 |      0.0 |     96.0 | bank17   |     17.0 |    108.0 | [2.60836,2.31423,4.86391] | [5.69122,1.79492,-0.452799] | 3        |
| 3132     | 1125241  |      0.0 |      0.0 |      0.0 |      1.6 |     33.9 |   7252.2 |      1.0 |      0.0 |      0.0 |     83.0 | bank17   |    121.0 |     43.0 | [3.15504,2.42573,4.75121] | [5.97829,1.63473,0.0118744] | 4        |
| 3132     | 1170598  |      0.0 |      0.0 |      0.0 |      1.5 |     34.1 |   7224.6 |      0.9 |      0.0 |      0.0 |     73.0 | bank17   |    166.0 |    220.0 | [3.43363,1.70178,5.39301] | [6.07726,2.59962,0.281759] | 5        |
| 3132     | 1214951  |      0.0 |      0.0 |      0.0 |      1.9 |     22.8 |   8839.5 |      1.7 |      0.0 |      0.0 |    719.0 | bank18   |    231.0 |    137.0 | [2.73683,1.43808,2.11574] | [3.5786,0.470838,1.00329] | 6        |
| 3132     | 1207827  |      0.0 |      0.0 |      0.0 |      1.7 |     27.9 |   7991.7 |      1.3 |      0.0 |      0.0 |    447.0 | bank18   |     19.0 |    110.0 | [2.80324,2.29519,3.09134] | [4.71517,0.554412,0.37714] | 7        |
| 3132     | 1232949  |      0.0 |      0.0 |      0.0 |      1.2 |     53.3 |   5782.1 |      0.9 |      0.0 |      0.0 |     45.0 | bank18   |     53.0 |    208.0 | [4.29033,2.63319,4.46168] | [6.52658,1.27985,1.00646] | 8        |
| 3132     | 1189484  |      0.0 |      0.0 |      0.0 |      1.1 |     63.4 |   5299.3 |      1.0 |      0.0 |      0.0 |     31.0 | bank18   |    108.0 |     38.0 | [4.02414,3.39659,3.83664] | [6.4679,0.298896,0.726133] | 9        |
| 3132     | 1218337  |      0.0 |      0.0 |      0.0 |      1.0 |     79.8 |   4724.1 |      0.8 |      0.0 |      0.0 |     15.0 | bank18   |     33.0 |    151.0 | [4.96622,3.61607,5.32554] | [7.99244,1.19363,0.892655] | 10       |

Categories: AlgorithmIndex | Optimization\PeakFinding | MDAlgorithms\Peaks

Source

C++ header: FindPeaksMD.h

C++ source: FindPeaksMD.cpp