2 pull requests: Add median & mode to MTEX; Improve export_crc

[AzdiarGazder]

Hi Maintainers,

There are 2 pull requests here:

Pull request 1: This is based on MTEX issue number: https://github.com/mtex-toolbox/mtex/issues/265. Ralf subsequently designated this as a future "feature request". In addition to mean, I've added the calculations for median and mode for all MTEX classes and objects. Before merging, please do re-check it for completeness and errors. Fingers crossed, everything works ok! :)

Pull request 2: This increases the versatility of the export_crc fucntion. Users can now export_crc ebsd maps in .cpr and .crc format from any input map. In case of hexagonal grids, prior conversion of map data to square grids is required before invoking the function.

Warm regards, Azdi

[AzdiarGazder]

Hi Rüdiger,

Due to pre-existing dependencies, I have aimed to make minimal changes to the original "mean" scripts from which the median and mode scripts are derived. But thank you for pointing out the issue with the median and mode calculations for the orientation case. I made changes to both median and mode scripts within @quaternion and @orientation. They have been uploaded for you to review.

If we now run your script:

cs = crystalSymmetry('432');
o = orientation.byEuler([1 0 0 0; 0 1 0 0; 0 1 1 1]',cs);
angle(o,o.median)

The output is as follows:

o = orientation (432 → xyz)
  size: 4 x 1

  Bunge Euler angles in degree
     phi1     Phi    phi2
  57.2958       0       0
   130.08 44.9216  310.08
  57.2958       0       0
  57.2958       0       0

ans =

    0.0000
    0.8750
    0.0000
    0.0000

The median function in @quaternion has 2 options:

• use MATLAB's in-built median function, or
• use the custom median function that selects an element in the input list by have remarked it out for now. In the former case, the default behaviour is that when a clear median value in the input list does not exist, it returns an in-between value. The latter case is remarked for now. If you'd like to run it, please remark the line above the section and un-remark the section itself. You can compare both outputs with the commands:

  figure; plot(o), hold all, plot(o.median)
  figure; plot(o), hold all, plot(o.median('noSymmetry'))

  In this instance, the in-built returns a somewhat better "middle" value.

Similarly, the mode function in @quaternion also has 2 options:

• use MATLAB's in-built mode function, or
• use the custom mode function that selects an element in the input list by have remarked it out for now. The former case is remarked for now. If you'd like to run it, please unremark the line above the section and remark the section itself. The latter case is active. You can compare both outputs with the commands:

  figure; plot(o), hold all, plot(o.mode)
  figure; plot(o), hold all, plot(o.mode('noSymmetry'))

  In this instance, the custom script returns a somewhat better "most repeated" value.

Given the above, my solutions are not perfect. While doing this, I've also had a bit of an question I've asked myself - given that we are working with orientations, maybe it is not an arithmetic median that should be sought but a geometric median like the Weiszfeld algorithm? Here is an example on MATLAB file exchange.

I am now a fair bit confused! :) I would be very grateful for some help and clarity on the way forward in this regard.

Thank you for this! Looking forward to hearing from you.

Warm regards, Azdi

[AzdiarGazder]

Hi @kilir,

Based on your feedback, I am currently re-working the median and mode calculations. However, this will take me some time to work out.

In the meantime, if the export_crc function gets the maintainers' green light, I'd be grateful if that part could be pulled. Following that, please close this pull request. I'll make another pull request for the median and mode aspects at a later date.

Thank you for this! :)

Warm regards, Azdi

[kilir]

Hi Azdi, I think a key issue with e.g. a spherical median or a median orientation is that those are not so easily defined. The geometric median you suggest assumes an euclidean space (hence might work on the embedding) but for something like orientation space, I think it's more tricky. For the S2 case, e.g. there's a suggstion for a spherical median ( Fisher, 1985) however just for special cases such as unimodal distributions, but nothing universal as far as I could find.

Cheers, Rüdiger