Tue May 20 22:31:38 2025

simplex_integrals_test():
  python version: 3.10.12
  numpy version:  1.26.4
  Test simplex_integrals().

simplex_integrals_test01():
  Estimate monomial integrals using Monte Carlo
  over the interior of the unit simplex in M dimensions.

  Number of sample points used is 4192

  We randomly choose the exponents.

  Ex  Ey  Ez     MC-Estimate      Exact           Error

   1   1   2     0.000391098     0.000396825     5.7e-06
   4   3   4      4.0012e-08     3.96429e-08     3.7e-10
   3   1   1     0.000148277      0.00014881     5.3e-07
   2   2   1     9.85469e-05     9.92063e-05     6.6e-07
   4   0   2     0.000134435     0.000132275     2.2e-06
   0   1   3      0.00115253      0.00119048     3.8e-05
   4   1   3     3.63209e-06      3.6075e-06     2.5e-08
   3   1   0      0.00116483      0.00119048     2.6e-05
   0   2   4     0.000125292     0.000132275       7e-06
   3   1   0      0.00116483      0.00119048     2.6e-05
   0   3   2     0.000290293     0.000297619     7.3e-06
   1   4   4     1.11016e-06      1.2025e-06     9.2e-08
   4   0   4     1.42662e-05       1.443e-05     1.6e-07
   2   1   4     1.33102e-05     1.32275e-05     8.3e-08
   2   1   3     3.30797e-05     3.30688e-05     1.1e-08
   2   4   0     0.000128012     0.000132275     4.3e-06
   2   2   3     6.54163e-06     6.61376e-06     7.2e-08
   0   4   4     1.35119e-05       1.443e-05     9.2e-07
   1   4   2     1.28483e-05     1.32275e-05     3.8e-07
   2   4   1       1.306e-05     1.32275e-05     1.7e-07

simplex01_sample_test():
  simplex01_sample() samples the unit simplex in M dimensions.

  Sample points in the unit simplex.

  Row:       0             1             2       
  Col
      0 :   0.0949552     0.0764135     0.0103283  
      1 :    0.278521      0.212319     0.0095862  
      2 :    0.799997      0.019708      0.173142  
      3 :    0.529619      0.166902     0.0634232  
      4 :    0.118778      0.209452      0.367284  
      5 :    0.449058      0.175341      0.301716  
      6 :   0.0721064      0.273944     0.0510219  
      7 :    0.367957      0.162462      0.146845  
      8 :    0.294647      0.166532      0.250878  
      9 :   0.0478356       0.14378       0.26257  

simplex01_volume_test():
  simplex01_volume() returns the volume of the unit simplex
  in M dimensions.

   M   Volume

   1  1
   2  0.5
   3  0.166667
   4  0.0416667
   5  0.00833333
   6  0.00138889
   7  0.000198413
   8  2.48016e-05
   9  2.75573e-06

simplex_integrals_test():
  Normal end of execution.
Tue May 20 22:31:38 2025