StatisticsOfPeaksWorkspace v1¶

Summary¶

Statistics of a PeaksWorkspace.

Properties¶

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++ header: StatisticsOfPeaksWorkspace.h (last modified: 2021-03-31)

C++ source: StatisticsOfPeaksWorkspace.cpp (last modified: 2021-03-31)