4.2

StatisticsOfPeaksWorkspace v1

../_images/StatisticsOfPeaksWorkspace-v1_dlg.png

StatisticsOfPeaksWorkspace dialog.

Summary

Statistics of a PeaksWorkspace.

Properties

Name Direction Type Default Description
InputWorkspace Input PeaksWorkspace Mandatory An input PeaksWorkspace with an instrument.
PointGroup Input string -1 Which point group applies to this crystal? Allowed values: [‘-1’, ‘-3’, ‘-3 r’, ‘-31m’, ‘-3m’, ‘-3m r’, ‘-3m1’, ‘-4’, ‘-42m’, ‘-43m’, ‘-4m2’, ‘-6’, ‘-62m’, ‘-6m2’, ‘1’, ‘112’, ‘112/m’, ‘11m’, ‘2’, ‘2/m’, ‘222’, ‘23’, ‘2mm’, ‘3’, ‘3 r’, ‘312’, ‘31m’, ‘32’, ‘32 r’, ‘321’, ‘3m’, ‘3m r’, ‘3m1’, ‘4’, ‘4/m’, ‘4/mmm’, ‘422’, ‘432’, ‘4mm’, ‘6’, ‘6/m’, ‘6/mmm’, ‘622’, ‘6mm’, ‘m’, ‘m-3’, ‘m-3m’, ‘m2m’, ‘mm2’, ‘mmm’, ‘-1 (Triclinic)’, ‘-3 (Trigonal - Hexagonal)’, ‘-3 r (Trigonal - Rhombohedral)’, ‘-31m (Trigonal - Hexagonal)’, ‘-3m (Trigonal - Hexagonal)’, ‘-3m r (Trigonal - Rhombohedral)’, ‘-3m1 (Trigonal - Hexagonal)’, ‘-4 (Tetragonal)’, ‘-42m (Tetragonal)’, ‘-43m (Cubic)’, ‘-4m2 (Tetragonal)’, ‘-6 (Hexagonal)’, ‘-62m (Hexagonal)’, ‘-6m2 (Hexagonal)’, ‘1 (Triclinic)’, ‘112 (Monoclinic, unique axis c)’, ‘112/m (Monoclinic, unique axis c)’, ‘11m (Monoclinic, unique axis c)’, ‘2 (Monoclinic, unique axis b)’, ‘2/m (Monoclinic, unique axis b)’, ‘222 (Orthorhombic)’, ‘23 (Cubic)’, ‘2mm (Orthorhombic)’, ‘3 (Trigonal - Hexagonal)’, ‘3 r (Trigonal - Rhombohedral)’, ‘312 (Trigonal - Hexagonal)’, ‘31m (Trigonal - Hexagonal)’, ‘32 (Trigonal - Hexagonal)’, ‘32 r (Trigonal - Rhombohedral)’, ‘321 (Trigonal - Hexagonal)’, ‘3m (Trigonal - Hexagonal)’, ‘3m r (Trigonal - Rhombohedral)’, ‘3m1 (Trigonal - Hexagonal)’, ‘4 (Tetragonal)’, ‘4/m (Tetragonal)’, ‘4/mmm (Tetragonal)’, ‘422 (Tetragonal)’, ‘432 (Cubic)’, ‘4mm (Tetragonal)’, ‘6 (Hexagonal)’, ‘6/m (Hexagonal)’, ‘6/mmm (Hexagonal)’, ‘622 (Hexagonal)’, ‘6mm (Hexagonal)’, ‘m (Monoclinic, unique axis b)’, ‘m-3 (Cubic)’, ‘m-3m (Cubic)’, ‘m2m (Orthorhombic)’, ‘mm2 (Orthorhombic)’, ‘mmm (Orthorhombic)’, ‘222 (Orthorombic)’, ‘mm2 (Orthorombic)’, ‘2mm (Orthorombic)’, ‘m2m (Orthorombic)’, ‘mmm (Orthorombic)’]
LatticeCentering Input string P Appropriate lattice centering for the peaks. Allowed values: [‘P’, ‘C’, ‘A’, ‘B’, ‘I’, ‘F’, ‘Robv’, ‘Rrev’, ‘H’, ‘Primitive’, ‘C-face centred’, ‘A-face centred’, ‘B-face centred’, ‘Body centred’, ‘All-face centred’, ‘Rhombohedrally centred, obverse’, ‘Rhombohedrally centred, reverse’, ‘Hexagonally centred, reverse’]
OutputWorkspace Output PeaksWorkspace Mandatory Output PeaksWorkspace
StatisticsTable Output TableWorkspace StatisticsTable An output table workspace for the statistics of the peaks.
SortBy Input string ResolutionShell Sort the peaks by resolution shell in d-Spacing(default), bank, run number, or only overall statistics. Allowed values: [‘ResolutionShell’, ‘Bank’, ‘RunNumber’, ‘Overall’]
EquivalentIntensities Input string Mean Replace intensities by mean(default), or median. Allowed values: [‘Mean’, ‘Median’]
SigmaCritical Input number 3 Removes peaks whose intensity deviates more than SigmaCritical from the mean (or median).
EquivalentsWorkspace Output MatrixWorkspace EquivalentIntensities Output Equivalent Intensities
WeightedZScore Input boolean False Use weighted ZScore if true. If false, standard ZScore (default).

Description

Statistics of the Peaks Workspaces are calculated for all peaks and by default for resolution shell(d-Spacing). There is a SortBy option to change this to by orientation (RunNumber) or by Anger camera (bank) or only do all peaks. This algorithm calls SortHKL v1, so more details are in the documentation for that algorithm.

After removing invalid peaks with I \leq 0, \sigma \leq 0 and h=k=l=0, the peaks are assigned to their respective unique reflection so that each theoretically present reflection may have n observations (n can be zero). The number of unique reflections which have at least one observation can be labeled N_{unique}.

Currently the satellite peaks are removed so only peaks with m=n=p=0 are used in the statistics. In the future, this algorithm will also calculate statistics for these peaks.

The intensities of peaks in each reflection are checked for outliers, which are removed. Outliers in this context are peaks with an intensity that deviates more than 3\sigma_{hkl} from the mean of the reflection, where \sigma_{hkl} is the standard deviation of the peak intensities.

Formulas for the statistics columns are:

N_{unique}

dSpacing_{min}

dSpacing_{max}

Multiplicity = \frac{N_{observed}}{N_{unique}}

\langle \frac{I}{\sigma_I} \rangle

In the following, all sums over hkl extend only over unique reflections with more than one observation! Output is percentages.

R_{merge} = 100 * \frac{\sum_{hkl} \sum_{j} \vert I_{hkl,j}-\langle I_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}I_{hkl,j}} where \langle I_{hkl}\rangle is the average of j multiple measurements of the n equivalent reflections.

R_{pim} = 100 * \frac{\sum_{hkl} \sqrt \frac{1}{n-1} \sum_{j=1}^{n} \vert I_{hkl,j}-\langle I_{hkl}\rangle\vert}{\sum_{hkl} \sum_{j}I_{hkl,j}}

Completeness = 100 * \frac{N_{unique}}{N_{theoretical}}

Usage

Example - an example of running StatisticsOfPeaksWorkspace with PointGroup option.

# Load example peak data and find cell
peaks = LoadIsawPeaks(Filename=r'Peaks5637.integrate')

FindUBUsingFFT(peaks, MinD=0.25, MaxD=10, Tolerance=0.2)
SelectCellWithForm(peaks, FormNumber=9, Apply=True, Tolerance=0.15)
OptimizeLatticeForCellType(peaks,
                           CellType='Hexagonal', Apply=True, Tolerance=0.2)

# Run the SortHKL algorithm
sorted, statistics_table, equivI = StatisticsOfPeaksWorkspace(peaks, PointGroup='-3m1 (Trigonal - Hexagonal)',
                                                      LatticeCentering='Rhombohedrally centred, obverse',
                                                      SortBy='Overall')

statistics = statistics_table.row(0)

peak = sorted.getPeak(0)
print("HKL of first peak in table {} {} {}".format(peak.getH(),peak.getK(),peak.getL()))
print("Multiplicity = %.2f" % statistics['Multiplicity'])
print("Resolution Min = %.2f" % statistics['Resolution Min'])
print("Resolution Max = %.2f" % statistics['Resolution Max'])
print("No. of Unique Reflections = %i" % statistics['No. of Unique Reflections'])
print("Mean ((I)/sd(I)) = %.2f" % statistics['Mean ((I)/sd(I))'])
print("Rmerge = %.2f" % statistics['Rmerge'])
print("Rpim = %.2f" % statistics['Rpim'])

Output:

HKL of first peak in table -10.0 5.0 42.0
Multiplicity = 1.21
Resolution Min = 0.21
Resolution Max = 2.08
No. of Unique Reflections = 337
Mean ((I)/sd(I)) = 27.51
Rmerge = 10.08
Rpim = 10.08

Categories: AlgorithmIndex | Crystal\Peaks | DataHandling\Text

Source

C++ source: StatisticsOfPeaksWorkspace.cpp (last modified: 2019-06-04)

C++ header: StatisticsOfPeaksWorkspace.h (last modified: 2018-10-05)