StatisticsOfPeaksWorkspace v1¶

StatisticsOfPeaksWorkspace dialog.

Table of Contents

Summary
Properties
Description
Usage
Source

Properties ¶

Name	Direction	Type	Default	Description
InputWorkspace	Input	PeaksWorkspace	Mandatory	An input PeaksWorkspace with an instrument.
PointGroup	Input	string	-1 (Triclinic)	Which point group applies to this crystal? Allowed values: [‘-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 (Orthorombic)’, ‘23 (Cubic)’, ‘2mm (Orthorombic)’, ‘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 (Orthorombic)’, ‘mm2 (Orthorombic)’, ‘mmm (Orthorombic)’]
LatticeCentering	Input	string	Primitive	Appropriate lattice centering for the peaks. Allowed values: [‘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		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’]

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 $N_{unique}$ .

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 = 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 %d" % 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 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: Algorithms | Crystal\Peaks | DataHandling\Text