select 150 representative orientations from 2000 groups of Euler angles

[HanyuXu666]

Dear all:

Hello everyone, I have some problem with selecting representative orientations. I have a .txt contains 2000 groups of Euler angles, and I want to pick 150 of them to represent the texture. Here's my current code:

% Step 1: Load the Euler angles from Ref-A.txt
eulers = readmatrix('OQAA.txt'); % Replace with your filename

% Extract columns for phi1, PHI, and phi2
phi1 = eulers(:,1); % First column
PHI = eulers(:,2); % Second column
phi2 = eulers(:,3); % Third column

% Step 2: Create orientation objects
CS = crystalSymmetry('cubic');
SS = specimenSymmetry('cubic');

% Create orientation objects
ori = orientation.byEuler(phi1 * degree, PHI * degree, phi2 * degree, CS, SS);

% Step 3: Calculate the Orientation Distribution Function (ODF)
odf = calcDensity(ori);

% Step 4: Sample orientations from the ODF
numSamples = 150; % Desired number of representative orientations
allSampledOri = discreteSample(odf, numSamples); % Sample orientations

% Step 5: Extract Euler angles from the sampled orientations
repEuler = allSampledOri.Euler; % Matrix with [phi1, PHI, phi2] in degrees

% Step 6: Save the representative orientations to a file
writematrix(repEuler, 'representative_euler_angles_OQAA.txt', 'Delimiter', ' ');

After running the code, I got 150 groups of Euler angles. I then plotted the pole figure:

This is the pole figure of my original 2000 groups Euler angles:

These two figures are quite different. So could some body please help me to check my code?
Thanks in advance!!

Best Regards,
Hanyu

[zmichels]

A few quick thoughts:

1. Looks like the same texture to me in both plots -- how is the result different from what you expected?
2. You only selected 150 points, which is not a very robust population from which to infer statistics.
3. Have you tried changing the call to discreteSample() to use 'withoutReplacement'? I'm not sure if it would get you a result you like more, but should be different than the default. However, the difference might be difficult to discern with only 150 selected from 2000 (less than 1% of the original population).

Perhaps it is helpful to hear that IMO nothing appears to be malfunctioning with discreteSample or your procedure -- the result is exactly what I would expect.

BTW, for what reason do you want to limit the selection so drastically (esp if trying to make density contour plots, which benefit from a larger sample size)?

Let us know how goes!

Zach

[HanyuXu666]

Dear Zach,

Thank you so much for your prompt reply, I really appreciate it!!!

1.In my opinion, these 150 groups are too concentrated, and the Euler angle values ​​in representative_euler_angles_OQAA.txt cannot be found in OQAA.txt. In other words, this code selects orientations not directly from the original 2000 groups.

I try the following code:
allSampledOri = discreteSample(odf, numSamples,'withoutReplacement')
almost nothing different in comparison to my previous results

The reason why I only select 150 groups: I use DAMASK to do 2D damage simulation, which has a limit on the number of grains, and simulating the damage evolution of 2000 grains is very difficult, but 100 to 200 grains is relatively easy and time-saving.

Best Regards,
Hanyu

[zmichels]

FWIW, I don't think you'll ever get a distribution from 150 orientations that has a similar diffuse appearance as the full 2000 — the full dataset has the same maxima but is less pronounced due to the scatter present in numerous orientations. If you plot just the points of your 150-orientation selection... does it reveal any of the distribution/scatter you see in the full dataset? Or are all the points inside the contours you plotted? Does providing more parameters for the ODF calculation help or change anything?

Z

[zmichels]

What if... you initially randomly sample the ODF with many more points using discreteSample(), which may yield more of the character. Then, from that set, randomly select 150.
At first thought, I don't see why it should provide anything different... but perhaps extracting the final group from a randomized index instead of just discreteSample() will perform slightly differently. I don't know though.

[zmichels]

If you plot the points instead of the contours... do you see a distribution with more diffuse shape (more variation in the distribution extent without the contours maybe)?

[zmichels]

I have some unexpected bandwidth today to play along, if that might help. Are you able (and willing) to share the original txt file or orientation info/data by some means?

Cheers,
Zach

[zmichels]

Here's what I tried with some mtex-supplied example data. It seemed to work more as-expected in this application than in yours. I used version 5.11.2. My approach was to load some data (which starts out with >4,000 orientations in this case)... and then proceed on two parallel paths... one in which I made an ODF from all the initial data, and a second, in which I randomly selected (using discreteSample) 2000 orientations from the orientation set from which to make the ODF (in order to start with something closer to your case). Then from each ODF I discreteSampled 150 orientations. In both cases, the plots retain much of the initial distribution's character (unlike in your result). So... I don't know if this helps, but here it is.

% example data
mtexdata forsterite
sampleName = 'odfSampling';

%% initial pole-figure plot of orientations
phase = 'olivine'
o = ebsd(phase).orientations;
cs = o.CS;
h = [Miller(1,0,0,'direction',cs),Miller(0,1,0,'direction',cs),Miller(0,0,1,'direction',cs)];

% fig 1
figure
plotPDF(o,h,'antipodal','lower','points','all', 'MarkerFaceColor','k', 'MarkerEdgeColor', 'none', 'MarkerSize', 2)
annotation('textbox',[0.005,0.95,0.12,0.06],'String',sprintf('n = %i',length(o)),'FitBoxToText','on','EdgeColor','none')
saveas(gcf, sprintf('%s_%s_initialOrsPts_PoleFigure.png',sampleName,phase))

% fig 2
figure
plotPDF(o,h,'antipodal','lower','contourf','halfwidth',10*degree, 'colorrange','equal')
cb = mtexColorbar('Title','M.U.D.');
mtexColorMap(LaboTeXColorMap)
annotation('textbox',[0.005,0.95,0.12,0.06],'String',sprintf('n = %i',length(o)),'FitBoxToText','on','EdgeColor','none')
saveas(gcf, sprintf('%s_%s_initialOrsContour_PoleFigure.png',sampleName,phase))

% fig 3
figure
plotPDF(o,h,'antipodal','lower','smooth','halfwidth',10*degree, 'colorrange','equal')
hold on
plotPDF(o,h,'antipodal','lower','points','all', 'MarkerFaceColor','k', 'MarkerEdgeColor', 'none', 'MarkerSize', 1)
cb = mtexColorbar('Title','M.U.D.');
mtexColorMap(LaboTeXColorMap)
annotation('textbox',[0.005,0.95,0.12,0.06],'String',sprintf('n = %i',length(o)),'FitBoxToText','on','EdgeColor','none')
saveas(gcf, sprintf('%s_%s_initialOrsSmoothPtsCombo_PoleFigure.png',sampleName,phase))

%% Lets randomly slet 2000 orientations to get to similar starting point
o2k = discreteSample(o,2000);

figure
plotPDF(o2k,h,'antipodal','lower','points','all', 'MarkerFaceColor','k', 'MarkerEdgeColor', 'none', 'MarkerSize', 2)
annotation('textbox',[0.005,0.95,0.12,0.06],'String',sprintf('n = %i',length(o2k)),'FitBoxToText','on','EdgeColor','none')
saveas(gcf, sprintf('%s_%s_o2k_OrsPts.png',sampleName,phase))

figure
plotPDF(o2k,h,'antipodal','lower','contourf','halfwidth',10*degree, 'colorrange','equal')
cb = mtexColorbar('Title','M.U.D.');
mtexColorMap(LaboTeXColorMap)
annotation('textbox',[0.005,0.95,0.12,0.06],'String',sprintf('n = %i',length(o)),'FitBoxToText','on','EdgeColor','none')
saveas(gcf, sprintf('%s_%s_o2k_OrsContour.png',sampleName,phase))

%% Compute ODFs
odf = calcDensity(o);
odf2k = calcDensity(o2k);

%% Plot the ODF
figure
plotPDF(odf,h,'antipodal','lower','contourf','halfwidth', 10*degree, 'colorrange','equal')
cb = mtexColorbar('Title','M.U.D.');
mtexColorMap(LaboTeXColorMap)
saveas(gcf, sprintf('%s_%s_ODF_PoleFigure.png',sampleName,phase))


figure
plotPDF(odf2k,h,'antipodal','lower','contourf','halfwidth', 10*degree, 'colorrange','equal')
cb = mtexColorbar('Title','M.U.D.');
mtexColorMap(LaboTeXColorMap)
saveas(gcf, sprintf('%s_%s_ODF2k_PoleFigure.png',sampleName,phase))

%% discreteSample 150 ors from the ODFs
oFromODF = discreteSample(odf, 150)
oFromODF2k = discreteSample(odf2k, 150)

%% plots of odf-sampled points
figure
plotPDF(oFromODF,h,'antipodal','lower','contourf', 'halfwidth', 10*degree, 'colorrange','equal')
cb = mtexColorbar('Title','M.U.D.');
mtexColorMap(LaboTeXColorMap)
saveas(gcf, sprintf('%s_%s_orsFromODFContour_PoleFigure.png',sampleName,phase))


figure
plotPDF(oFromODF2k,h,'antipodal','lower','contourf', 'halfwidth', 10*degree, 'colorrange','equal')
cb = mtexColorbar('Title','M.U.D.');
mtexColorMap(LaboTeXColorMap)
saveas(gcf, sprintf('%s_%s_orsFromODF2kContour_PoleFigure.png',sampleName,phase))

Initial imported data:
points:

contours:

combo:

ODF (all initial):

2,000 randomly selected from initial set:
points:

contours:

odf from the 2k ors:

ODF-sampled orientations (n = 150)
from full ODF:

from 2k-ors-based ODF:

[zmichels]

I just recognized now a major flaw in my approach attempting to replicate your situation... I used all the points from the map rather than one-point per grain (so bigger grains have more points). I can try later a similar approach after extracting those from a larger dataset (will need more grains to get 2000).