Add low-level method to find the UB matrix given a list of peaks and the lattice parameters.

[Dennis Mikkelson]

Given a list of peak positions and the lattice parameters, find the UB matrix that best indexes the peaks, without changing any of the lattice parameters. If the lattice parameters can be adjusted to better match the data, the BestFit_UB method can be used once the peaks are indexed by the UB matrix returned by this method.

[Dennis Mikkelson]

(In [12675]) Added method to check for a valid index. Added tests for NumberIndexed() and ValidIndex() methods. refs #3205

[Dennis Mikkelson]

(In [12704]) Added method to generate list of direction vectors, uniformly distributed over the y>0 hemisphere. This will be used for finding reciprocal space plane normal directions that have specified spacing. refs #3205

[Dennis Mikkelson]

(In [12731]) Added method BestFit_Direction that will find the direction, in a list of directions, that most nearly corresponds to plane normals in reciprocal space, for a specified plane spacing. refs #3205

[Dennis Mikkelson]

(In [12755]) Changed name of earlier BestFit_Direction() to SelectDirection(), since that more accurately describes it's action of selecting the best vector from a list. Added new method BestFit_Direction() that uses QR factorization to optimize the direction and length of the plane normal to a family of planes in reciprocal space, given a list of Qxyz vectors and one of the Miller indices for those vectors. refs #3205

[Dennis Mikkelson]

(In [12768]) Added method to generate a list containing the circle of vectors that all form a specified angle with a specified axis vector. This method will be used to find the family of planes in the reciprocal lattice corresponding to a second unit cell basis vector. refs #3205

[Dennis Mikkelson]

(In [12836]) Added methods GetIndexedPeaks_1D() and GetIndexedPeaks_3D() to indexing utils. Added tests for methods: BestFit_Direction(), GetIndexedPeaks_1D() GetIndexedPeaks_3D() and SelectDirection(), so all methods now have tests. refs #3205

[Dennis Mikkelson]

(In [12842]) Added method BestFit_UB() that finds the UB matrix given lattice parameters and a list of Q vectors. Added test for this method as well. refs #3205

[Dennis Mikkelson]

While the key method for finding a UB given lattice parameters currently works, it is very sensitive to the accuracy of the lattice parameters. Further improvements to this are need so that it is more robust with real data. For example, it may help to first index peaks at lower Q then gradually extend the peaks being indexed to include higher Q peaks.

[Dennis Mikkelson]

(In [12985]) Cleaned up test code by putting code that gets a vector of Q's for testing into static method. refs #3205

[Dennis Mikkelson]

(In [12990]) Added method GetIndexedPeaks() that takes a UB matrix instead of one or three direction vectors. Added test for this method. refs #3205

[Dennis Mikkelson]

(In [12991]) Removed package specifier Kernel from Kernel::DblMatrix. For some reason this does not build on Win7, but does on Linux? refs #3205

[Dennis Mikkelson]

(In [13003]) Added method Make_c_dir() to calculate the third edge vector of a rotated unit cell, given the other two rotated edge vectors, the length of side "c" and the cell angles. refs #3205

[Dennis Mikkelson]

(In [13006]) Added method ScanFor_UB() that makes an initial scan across a large set of rotations to identify a UB that indexes the peaks. refs #3205

[Dennis Mikkelson]

(In [13037]) Added a fairly robust method Find_UB(), that first searches a huge list of possible orientations to find a UB that indexes a small subset of low magnitude Q vectors. It then does a least squares refinement on the UB, and gradually increases the number of peaks to be indexed by adding Q vectors with increasing |Q|, doing a least squares refinement at each step. The number of low |Q| peaks to be initially indexed and the distance between possible orientations are controlled by parameters. refs #3205

[Dennis Mikkelson]

(In [13050]) Find_UB() given lattice parameters now properly adds Q vectors from the sorted list, rather than from the original list. refs #3205

[Dennis Mikkelson]

In [13295]:

Fix minor error in documentation comment.
refs #3205

[Dennis Mikkelson]

In [13492]:

Removed older method for finding UB given lattice
parameters. The newer method is more robust.
refs #3205

[Dennis Mikkelson]

In [13792]:

Added option to shift list of peaks indexed to
be centered around a specified peak.
refs #3205

[Dennis Mikkelson]

In [13924]:

Added sort of list of Q's in all cases to Find_UB given
lattice parameters.
Updated test to test both cases: where default base_index
is used and where base_index specifies an actual peak.
refs #3205

[Dennis Mikkelson]

In [13925]:

Renamed the Find_UB method that took indexed peaks
to Optimize_UB, and Find_Direction to Optimize_Direction
to more accurately reflect the use of these methods.
refs #3205

[Janik Zikovsky]

Have used these (indirectly) with the FindUBUsingLatticeParameters algo.

[Stuart Campbell]

This ticket has been transferred to github issue ​4052