built-in and custom grain size distributions

[damulaoshi]

Dear Romain,
First of all, thank you for developing this wonderful software! It has been very helpful for my research.

I have two questions regarding the definition of grain size distributions:
(1) Regarding existing distribution types (lognormal, beta, Weibull, etc., that you defined here: https://neper.info/doc/exprskeys.html#statistical-distributions): Could you point me to where I can find the exact mathematical definitions (e.g., PDF equations) or the specific source code implementation for these? I would like to verify the formulas used.
(2) Regarding custom distributions: I read your comment in Issue #487 about providing a file with x and y values on a regular grid. However, I am still unsure about the exact format required. Could you please provide a concrete example of how the input file should be formatted (e.g., for a Gamma distribution with the following PDF (from Wikipedia) with a shape parameter α and a scale parameter θ:
)?
A small sample text file or a screenshot would be very helpful.

Thank you in advance for your help. We will, of course, acknowledge your assistance in our upcoming publication.

Have a nice day,
Best regards,
Damu

[rquey]

1. The functions are src/contrib/ut/src/ut_fct/ut_fct.c. All by normal and lognormal were contributed (and I didn't really check them), so let me know if you find something strange.
2. It's a simple data file.

Here is an example:

distrib:

0.650000000000 0.020000000000
0.750000000000 0.212000000000
0.850000000000 1.305000000000
0.950000000000 3.443000000000
1.050000000000 3.402000000000
1.150000000000 1.356000000000
1.250000000000 0.243000000000
1.350000000000 0.018000000000
1.450000000000 0.001000000000

$ neper -T -n 100 -morpho "diameq:custom(distrib),1-sphericity:lognormal(0.145,0.03)" -o d

========================    N   e   p   e   r    =======================
Info   : A software package for polycrystal generation and meshing.
Info   : Version 4.10.1
Info   : Built with: gsl|muparser|opengjk|openmp|nlopt|libscotch (full)
Info   : Running on 14 threads.
Info   : <https://neper.info>
Info   : Copyright (C) 2003-2024, and GNU GPL'd, by Romain Quey.
Info   : Loading initialization file `/home/rquey/.neperrc'...
Info   : ---------------------------------------------------------------
Info   : MODULE  -T loaded with arguments:
Info   : [ini file] (none)
Info   : [com line] -n 100 -morpho
         diameq:custom(distrib),1-sphericity:lognormal(0.145,0.03) -o d
Info   : ---------------------------------------------------------------
Info   : Reading input data...
Info   : Creating domain...
Info   : Creating tessellation...
Info   :     [i] Parsing file `distrib'...
Info   :     [i] Parsed file `distrib'.
Info   :   - Setting seeds... 100%
Info   :   - Running tessellation...
Info   :     > Initial solution: f   =2.806483114
Info   :     > Iteration  15264: fmin=0.000037901 f=0.000037901  
Info   :     > Final solution  : f   =0.000037901 (15264 iterations)
Info   :     > Reached `eps' criterion.
Info   : Generating crystal orientations...
Info   : Writing results...
Info   :     [o] Writing file `d.tess'...
Info   :     [o] Wrote file `d.tess'.
Info   : Elapsed time: 20.697 secs.
========================================================================

[damulaoshi]

Thank you for the quick reply! The lognormal distribution should generally be fine, but I will review the others since I haven't used them before. I understand the approach now, and the file for the custom-defined PDF seems quite straightforward. Thanks again!