Tue May 20 22:32:17 2025

sphere_integrals_test():
  python version: 3.10.12
  numpy version:  1.26.4
  Test sphere_integrals().

sphere01_area_test
  sphere01_area returns the volume of the unit sphere.

  sphere01_area() =  12.5664

sphere01_monomial_integral_test():
  sphere01_monomial_integral() returns the integral of a monomial
  over the surface of the unit sphere in 3D.
  Compare with a Monte Carlo estimate.

  If any exponent is odd, the integral is zero.
  We will restrict this test to randomly chosen even exponents.

  Ex  Ey  Ez     MC-Estimate           Exact      Error

   4
   0
   2
        0.359518        0.359039     0.00048
   6
   2
   6
      0.00138839      0.00139487     6.5e-06
   2
   2
   2
        0.120018         0.11968     0.00034
   0
   8
   6
       0.0100457      0.00976408     0.00028
   0
   2
   8
        0.127062        0.126933     0.00013
   6
   4
   4
      0.00084301     0.000836921     6.1e-06
   6
   6
   2
      0.00143889      0.00139487     4.4e-05
   6
   0
   0
         1.77011          1.7952       0.025
   4
   4
   4
      0.00251079      0.00251076     3.1e-08
   2
   8
   6
     0.000578197     0.000574358     3.8e-06
   8
   2
   6
     0.000576384     0.000574358       2e-06
   8
   8
   0
      0.00412498       0.0040205      0.0001
   0
   2
   4
        0.360757        0.359039      0.0017
   2
   0
   2
        0.838489        0.837758     0.00073
   6
   4
   8
     8.85463e-05      9.0688e-05     2.1e-06
   4
   0
   0
         2.49149         2.51327       0.022
   4
   4
   2
       0.0110575         0.01088     0.00018
   2
   8
   8
     0.000212172     0.000211605     5.7e-07
   8
   0
   6
      0.00982956      0.00976408     6.5e-05
   2
   2
   6
       0.0179001       0.0181333     0.00023

sphere01_sample_test():
  sphere01_sample() samples the unit sphere.

  Sample points on the unit sphere.

  Row:       0             1             2       
  Col
      0 :    0.166273      0.768657      0.617673  
      1 :   -0.410064      0.143154      0.900752  
      2 :   -0.664351      0.276444     -0.694419  
      3 :   -0.899853      -0.41905      0.121085  
      4 :  -0.0557608      0.667695      0.742344  
      5 :    0.114788      0.258014      0.959298  
      6 :    -0.96162     -0.221474      0.161976  
      7 :    0.497158      0.504521     -0.705898  
      8 :     0.13524      0.900354       0.41361  
      9 :   -0.260911     -0.793175      0.550271  

sphere_integrals_test():
  Normal end of execution.
Tue May 20 22:32:17 2025