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global, local and pointwise maxima of functions on SO(3)

Syntax

[v,pos] = max(SO3F) % the position where the maximum is atained
[v,pos] = max(SO3F,'numLocal',5) % the 5 largest local maxima
SO3F = max(SO3F, c) % maximum of a rotational functions and a constant
SO3F = max(SO3F1, SO3F2) % maximum of two rotational functions
SO3F = max(SO3F1, SO3F2, 'bandwidth', bw) % specify the new bandwidth
% compute the maximum of a multivariate function along dim
SO3F = max(SO3Fmulti,[],dim)

Input

SO3F, SO3F1, SO3F2 SO3Fun
SO3Fmulti a multivariate SO3Fun
c double

Output

v double
pos rotation / orientation

Options

kmax number of iterations
numLocal number of peaks to return
startingNodes rotation / orientation
tolerance minimum distance between two peaks
resolution minimum step size
maxStepSize maximm step size

Example

%find the local maxima of the <SantaFe.html SantaFe> ODF
[value,ori] = max(SantaFe)
plotPDF(SantaFe,Miller(0,0,1,ori.CS))
annotate(ori)
value =
    5.0192
 
ori = orientation (m-3m → xyz (222))
 
  Bunge Euler angles in degree
     phi1     Phi    phi2
  153.394 47.5633 244.002

See also

SO3Fun.min SO3Fun.max SO3Fun.calcComponents