Wed Oct  8 09:07:36 2025

triangle01_integrals_test():
  python version: 3.10.12
  numpy version:  1.26.4
  Test triangle01_integrals().

triangle01_sample_test():
  triangle01_sample() randomly samples the unit triangle.

  Number of samples to select is N = 10

  Random points in unit triangle.

  Row:       0             1       
  Col
      0 :    0.574315      0.168518  
      1 :    0.216155      0.427428  
      2 :    0.015385      0.829596  
      3 :   0.0260846      0.857617  
      4 :   0.0051187     0.0348849  
      5 :    0.121513      0.177998  
      6 :    0.396071     0.0374706  
      7 :    0.650233      0.336196  
      8 :    0.631276      0.311678  
      9 :    0.401047      0.289897  

triangle01_monomial_integral_test01
  Python version: 3.10.12
  triangle01_monomial_integral computes the integral of
  a monomial X^I Y^J over the unit triangle.

   I   J    Integral(X^I Y^J)

   0   0             0.5

   0   1        0.166667
   1   0        0.166667

   0   2       0.0833333
   1   1       0.0416667
   2   0       0.0833333

   0   3            0.05
   1   2       0.0166667
   2   1       0.0166667
   3   0            0.05

   0   4       0.0333333
   1   3      0.00833333
   2   2      0.00555556
   3   1      0.00833333
   4   0       0.0333333

triangle01_monomial_integral_test02
  Python version: 3.10.12
  Estimate monomial integrals using Monte Carlo
  over the interior of the unit triangle in 2D.

  Number of sample points used is 4192

  We restrict this test to randomly chosen even exponents.

  Ex  Ey     MC-Estimate      Exact           Error

   0   0             0.5             0.5    0.00e+00
   0   1        0.165778        0.166667    8.88e-04
   0   2       0.0828021       0.0833333    5.31e-04
   0   3       0.0495862            0.05    4.14e-04
   0   4       0.0330443       0.0333333    2.89e-04
   1   0        0.165595        0.166667    1.07e-03
   1   1       0.0408714       0.0416667    7.95e-04
   1   2       0.0163113       0.0166667    3.55e-04
   1   3       0.0080923      0.00833333    2.41e-04
   1   4      0.00457072       0.0047619    1.91e-04
   2   0       0.0834498       0.0833333    1.16e-04
   2   1        0.016287       0.0166667    3.80e-04
   2   2      0.00542641      0.00555556    1.29e-04
   2   3      0.00231664      0.00238095    6.43e-05
   2   4      0.00114523      0.00119048    4.52e-05
   3   0       0.0506118            0.05    6.12e-04
   3   1      0.00813582      0.00833333    1.98e-04
   3   2      0.00232182      0.00238095    5.91e-05
   3   3     0.000872891     0.000892857    2.00e-05
   3   4     0.000386173     0.000396825    1.07e-05
   4   0       0.0341102       0.0333333    7.77e-04
   4   1      0.00465408       0.0047619    1.08e-04
   4   2      0.00115703      0.00119048    3.34e-05
   4   3     0.000388202     0.000396825    8.62e-06
   4   4     0.000155712      0.00015873    3.02e-06

triangle01_integrals_test():
  Normal end of execution.
Wed Oct  8 09:07:36 2025