SO3FunCBF.discreteSample

A method of SO3FunCBF.

a random sample of n orientations drawn from an orientation density, of directions from a density on the sphere, of numbers from a density on an interval, or n random members of a list

Syntax

ori = discreteSample(odf, n)

ori = discreteSample(odf, n, resolution=2*degree)

v = discreteSample(sF, n)

x = discreteSample(lambda x: np.exp(-x), n, range=(0, 5))

ori = discreteSample(ori, n, withoutReplacement=True)

ebsd = discreteSample(ebsd, n)

Description

How the sample is drawn depends on what is sampled:

• a density on SO(3) or the sphere: grid nodes drawn with probability proportional to the values, each moved by a random rotation of up to 1.5 times the grid resolution and turned by a random element of each symmetry group. A finer resolution gives a more exact sample.
• a radial function (unimodalODF, calcDensity): exactly, a centre by its weight, the angle by the distribution of the kernel and a uniform axis; a sum of radial functions term by term.
• a Bingham distribution: exactly, by rejection.
• any other callable of numbers (a def, a lambda, a NumPy ufunc such as np.exp, an S1Fun): its values at 10000 points of the range.
• a list, a map, grains or boundary segments: n of its members, with replacement unless withoutReplacement=True, which returns all members when n exceeds their number; an empty list gives none without replacement and is refused otherwise.

MATLAB’s ‘compact’ sampling and the indices of the members drawn from a list are not provided.

Input

Keywords

Output

Example

Draw a reproducible orientation sample from a model texture, then compare its pole positions with the model pole density. No experimental data are needed.

import numpy as np
import matplotlib.pyplot as plt
from mtex import (crystalFrame, orientation, unimodalODF, degree, discreteSample,
                  Miller, plotPF, mtexColorbar)

cs = crystalFrame('m-3m')
centre = orientation.byEuler(25*degree, 35*degree, 45*degree, cs)
odf = unimodalODF(centre, halfwidth=12*degree)
sample = discreteSample(odf, 300, rng=np.random.default_rng(9))
print('Sample size:', sample.size)
print('Median angle to centre (degrees):', round(float(np.median(sample.angle(centre))/degree), 2))
h = Miller(1, 0, 0, cs)
plotPF(odf, h, antipodal=True, resolution=5*degree)
mtexColorbar(title='Model pole density (mrd)')
plotPF(sample, h, antipodal=True, markerSize=3)
plt.show()

The first figure is the model density; the second contains sampled orientation poles. The seed makes this draw reproducible. Sampling from a density differs from selecting members of an existing list, where withoutReplacement=True prevents selecting the same member twice.

Sample size: 300
Median angle to centre (degrees): 15.23
  I'm plotting 208 random orientations out of 300 given orientations
  You can specify the number of points by the option "points".
  The option "all" ensures that all data are plotted

See also

SO3Fun.calcComponents, calcDensity, RandomSampling, S2FunSampling

MATLAB’s SO3FunCBF.discreteSample

@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}