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# FindUBUsingFFT v1¶

## Summary¶

Calculate the UB matrix from a peaks workspace, given min(a,b,c) and max(a,b,c).

## Properties¶

Name

Direction

Type

Default

Description

PeaksWorkspace

InOut

IPeaksWorkspace

Mandatory

Input Peaks Workspace

MinD

Input

number

Mandatory

Lower Bound on Lattice Parameters a, b, c

MaxD

Input

number

Mandatory

Upper Bound on Lattice Parameters a, b, c

Tolerance

Input

number

0.15

Indexing Tolerance (0.15)

Iterations

Input

number

4

Iterations to refine UB (4)

DegreesPerStep

Input

number

1.5

The resolution of the search through possible orientations is specified by this parameter. One to two degrees per step is usually adequate.

## Description¶

Given a set of peaks, and given a range of possible a,b,c values, this algorithm will attempt to find a UB matrix, corresponding to the Niggli reduced cell, that fits the data. The algorithm projects the peaks on many possible direction vectors and calculates a Fast Fourier Transform of the projections to identify regular patterns in the collection of peaks. Based on the calcuated FFTs, a list of directions corresponding to possible real space unit cell edge vectors is formed. The directions and lengths of the vectors in this list are optimized (using a least squares approach) to index the maximum number of peaks, after which the list is sorted in order of increasing length and duplicate vectors are removed from the list.

The algorithm then chooses three of the remaining vectors with the shortest lengths that are linearly independent, form a unit cell with at least a minimum volume and for which the corresponding UB matrix indexes at least 80% of the maximum number of indexed using any set of three vectors chosen from the list.

A UB matrix is formed using these three vectors and the resulting UB matrix is again optimized using a least squares method. Finally, starting from this matrix, a matrix corresponding to the Niggli reduced cell is calculated and returned as the UB matrix. If the specified peaks are accurate and belong to a single crystal, this method should produce the UB matrix corresponding to the Niggli reduced cell. However, other software will usually be needed to adjust this UB to match a desired conventional cell. While this algorithm will occasionally work for as few as four peaks, it works quite consistently with at least ten peaks, and in general works best with a larger number of peaks.

## Usage¶

Example:

ws=LoadIsawPeaks("TOPAZ_3007.peaks")
print("After LoadIsawPeaks does the workspace have an orientedLattice: %s" % ws.sample().hasOrientedLattice())

FindUBUsingFFT(ws,MinD=8.0,MaxD=13.0)
print("After FindUBUsingFFT does the workspace have an orientedLattice: %s" % ws.sample().hasOrientedLattice())

print(ws.sample().getOrientedLattice().getUB())


Output:

After LoadIsawPeaks does the workspace have an orientedLattice: False
After FindUBUsingFFT does the workspace have an orientedLattice: True
[[ 0.01223576  0.00480107  0.08604016]
[-0.11654506  0.00178069 -0.00458823]
[-0.02737294 -0.08973552 -0.02525994]]


Categories: AlgorithmIndex | Crystal\UBMatrix