6 October 2025   6:45:32.312 PM

sphere_integrals_test():
  Fortran90 version
  Test sphere_integrals().

TEST01
  Estimate monomial integrals using Monte Carlo
  over the surface of the unit sphere in 3D.

  Number of sample points used is   4192

  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

   2   4   8    0.197807E-02    0.195282E-02    0.25E-04
   0   0   6     1.77356         1.79520        0.22E-01
   2   2   0    0.840032        0.837758        0.23E-02
   2   4   2    0.402471E-01    0.398932E-01    0.35E-03
   4   6   6    0.248680E-03    0.246153E-03    0.25E-05
   2   4   8    0.197807E-02    0.195282E-02    0.25E-04
   6   8   8    0.662710E-05    0.657160E-05    0.55E-07
   6   2   8    0.540826E-03    0.574358E-03    0.34E-04
   4   0   4    0.115690        0.119680        0.40E-02
   2   0   4    0.354514        0.359039        0.45E-02
   8   0   8    0.384634E-02    0.402050E-02    0.17E-03
   2   6   2    0.185011E-01    0.181333E-01    0.37E-03
   4   0   2    0.348451        0.359039        0.11E-01
   0   2   0     4.15773         4.18879        0.31E-01
   0   8   4    0.293053E-01    0.292922E-01    0.13E-04
   4   8   4    0.350729E-03    0.344615E-03    0.61E-05
   4   0   0     2.60472         2.51327        0.91E-01
   2   2   0    0.840032        0.837758        0.23E-02
   4   2   4    0.103830E-01    0.108800E-01    0.50E-03
   6   0   4    0.518433E-01    0.543999E-01    0.26E-02

sphere_integrals_test():
  Normal end of execution.

 6 October 2025   6:45:32.313 PM