Successive Refinement Demo

mtexdata dubna
odf_naive = calcODF(pf);

calcError(pf,odf_naive)

pf = PoleFigure (y↑→x)
  crystal symmetry : Quartz (321, X||a*, Y||b, Z||c*)
 
  h = (02-21), r = 72 x 19 points
  h = (10-10), r = 72 x 19 points
  h = (10-11)(01-11), r = 72 x 19 points
  h = (10-12), r = 72 x 19 points
  h = (11-20), r = 72 x 19 points
  h = (11-21), r = 72 x 19 points
  h = (11-22), r = 72 x 19 points
ans =
    0.4439    0.3836    0.2585    0.3508    0.3407    0.4099    0.3669

odf_naive.plot(pf.allH)

odf_iter = calcODFIterative(pf,'nothinning');

calcError(pf,odf_iter)

ans =
    0.3207    0.1989    0.2120    0.2095    0.1741    0.2811    0.2902

odf_iter.plot(pf.allH)

calcError(odf_iter,odf_naive,'l1')

ans =
    0.2428

plot(calcPoleFigure(pf,odf_naive-odf_iter))
%plotDiff(odf_naive,odf_iter)

cs = crystalSymmetry('cubic');
ss = specimenSymmetry;

q = rotation.byEuler(10*degree,10*degree,10*degree,'ABG');
q2 = rotation.byEuler(10*degree,30*degree,10*degree,'ABG');

odf_true = .6*unimodalODF(q,cs,ss,'halfwidth',5*degree) + ...
            .4*unimodalODF(q2,cs,ss,'halfwidth',4*degree);

h = [ ...
  Miller(1,1,1,cs), ...
  Miller(1,0,0,cs), ...
  Miller(1,1,0,cs), ...
  ];

figure, odf_true.plotPDF(h)

r = equispacedS2Grid('resolution',15*degree,'maxtheta',80*degree);

figure
plot(r,'markersize',12)

r = equispacedS2Grid('resolution',15*degree,'maxtheta',80*degree);
r = repcell(r,size(h));
pf_measured = [];
pf_simulated = [];
pf_sim_h = {};
% number of refinement steps
nsteps = 5;

for k=1:nsteps

  % perform for every Pole Figure a measurement
  pf_simulated = calcPoleFigure(odf_true,h,r,'silent');

  % merge the new measurements with old ones
  pf_measured = union(pf_simulated,pf_measured);
  plot(pf_measured,'silent')
  drawnow

  fprintf('- at resolution : %f\n', mean(cellfun(@(r) r.resolution, pf_measured.allR))/degree);

  if k < nsteps
    % odf modeling
    odf_recalc = calcODF(pf_measured,'zeroRange','silent');

    % in order to minimize the modeling error
    pf_recalcerror  = calcErrorPF(pf_measured,odf_recalc,'l1','silent');

    % we could initialized initial weights with previous estimation
    odf_recalcerror = calcODF(pf_recalcerror,'silent');

    % the error we don't know actually
    fprintf('  error true -- estimated odf   : %f\n', calcError(odf_true,odf_recalc,'silent'))

    % refine the grid for every polefigure
    for l=1:length(h)
      r_old = pf_measured{l}.r;
      [newS2G, r_new] = refine( r_old(:) );

      % selection of points of interest, naive criterion
      pf_sim_h = calcPoleFigure(odf_recalc, h(l),  r_new,'silent');
      th = quantile(pf_sim_h.intensities,0.75);
      r{l} = pf_sim_h.r(pf_sim_h.intensities > th);
    end
  end
end

- at resolution : 14.545455
  error true -- estimated odf   : 0.941439
- at resolution : 13.009430
  error true -- estimated odf   : 0.405335
- at resolution : 9.506983
  error true -- estimated odf   : 0.236237
- at resolution : 6.738829
  error true -- estimated odf   : 0.303526
- at resolution : 3.753827

pf_measured
plot(pf_measured,'silent');

pf_measured = PoleFigure (y↑→x)
  crystal symmetry : m-3m
 
  h = (111), r = 367 x 1 points
  h = (100), r = 367 x 1 points
  h = (110), r = 367 x 1 points

odf_recalc = calcODF(pf_measured,'zeroRange','resolution',2.5*degree);
fprintf('  error true -- estimated odf   : %f\n', calcError(odf_true,odf_recalc))

error true -- estimated odf   : 0.400117

odf_recalc_iterative = calcODFIterative(pf_measured,'halfwidth',2.5*degree);
fprintf('  error true -- iter. est. odf  : %f\n', calcError(odf_true,odf_recalc_iterative))

error true -- iter. est. odf  : 0.114767

calcError(odf_recalc,odf_recalc_iterative,'l1')

ans =
    0.3167