[dmritool-discussion] Generating optimal multi-shell scheme

[Michael Dayan]

dmritool has been very useful to generate multi-shell scheme but I would
like to know more about the optimal protocol to generate such shemes:

1) Is SamplingSchemeQSpaceIMOCEstimation the most adequate function for
this purpose? What parameters to change to improve the results? I tried to
use higher "tesselate orders" than 7 (e.g. 8, 11, ...) but kept getting a
"Segmentation fault (core dumped)" error.

2) To assess the quality of the results how to interpret the statistics of
the generated scheme, in particular the minimum and maximum angle values?
Below is an example of statistics for a 2-shell scheme with 60 and 90
directions in the first and second shell.

 OrientationStatistics  imoc_60x90_shell1.txt imoc_60x90_shell2.txt
--combine
file: imoc_60x90_shell1.txt
size = 60
60 unique samples, 0 antipodal samples, 0 repeated samples.
minimal angle = 14.1538, radian=0.24703 (covering radius)
maximal angle = 14.7301, radian=0.257089
mean angle = 14.3346
std angle = 0.144217
upper bound (120 points) = 19.9391, radian=0.348003
upper bound (60 points) = 28.2194, radian=0.492521
electrostaticEnergy (order=2) = 3.05481
electrostaticEnergy (order=1) = 1.98694

file: imoc_60x90_shell2.txt
size = 90
90 unique samples, 0 antipodal samples, 0 repeated samples.
minimal angle = 11.5536, radian=0.201648 (covering radius)
maximal angle = 19.6656, radian=0.34323
mean angle = 12.3677
std angle = 1.45567
upper bound (180 points) = 16.2761, radian=0.284071
upper bound (90 points) = 23.0295, radian=0.401941
electrostaticEnergy (order=2) = 2.8735
electrostaticEnergy (order=1) = 1.92306

Combine 2 orientations
size = 150
150 unique samples, 0 antipodal samples, 0 repeated samples.
minimal angle = 8.95306, radian=0.15626 (covering radius)
maximal angle = 14.4468, radian=0.252144
mean angle = 10.2967
std angle = 1.42696
upper bound (300 points) = 12.6048, radian=0.219995
upper bound (150 points) = 17.8313, radian=0.311216
electrostaticEnergy (order=2) = 2.79829
electrostaticEnergy (order=1) = 1.89174
Spherical code cost function = 0.1903
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