Tue Oct 19 11:53:28 2021

hypersphere_integrals_test
  Python version: 3.6.9
  Test hypersphere_integrals().

hypersphere01_area_test
  Python version: 3.6.9
  hypersphere01_area returns the volume of the unit hypersphere.

   M  Area

   1  2
   2  6.28319
   3  12.5664
   4  19.7392
   5  26.3189
   6  31.0063
   7  33.0734
   8  32.4697
   9  29.6866
  10  25.5016

hypersphere01_area_test
  Normal end of execution.

hypersphere01_monomial_integral
  Python version: 3.6.9
  hypersphere01_monomial_integral returns the integral of
  a monomial over the surface of the unit hypersphere in 3D.
  Compare with a Monte Carlo estimate.

  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

   6   0   4       0.0559704       0.0543999      0.0016
   2   8   4      0.00192842      0.00195282     2.4e-05
   8   2   6     0.000573331     0.000574358       1e-06
   4   8   2      0.00199101      0.00195282     3.8e-05
   6   2   4      0.00415946      0.00418461     2.5e-05
   2   6   0        0.201252        0.199466      0.0018
   4   4   2       0.0108708         0.01088     9.1e-06
   6   2   6      0.00139897      0.00139487     4.1e-06
   8   4   6     8.91547e-05      9.0688e-05     1.5e-06
   6   6   2      0.00140709      0.00139487     1.2e-05
   8   2   4       0.0019343      0.00195282     1.9e-05
   0   4   2         0.35886        0.359039     0.00018
   4   2   2       0.0397036       0.0398932     0.00019
   4   0   2        0.366654        0.359039      0.0076
   0   6   0         1.78102          1.7952       0.014
   8   0   8      0.00415362       0.0040205     0.00013
   6   0   0         1.79176          1.7952      0.0034
   4   2   2       0.0397036       0.0398932     0.00019
   2   2   2        0.119353         0.11968     0.00033
   0   6   0         1.78102          1.7952       0.014

hypersphere_monomial_integral_test
  Normal end of execution.

hypersphere01_sample_test
  Python version: 3.6.9
  hypersphere01_sample samples the unit hypersphere
  in M dimensions.

  Sample points on the unit hypersphere.

  Row:       0             1             2       
  Col
      0 :    -0.74123      0.652921      0.155799  
      1 :   -0.116682     -0.906777      0.405143  
      2 :   -0.410718     -0.837805     -0.359713  
      3 :    0.220145     -0.920391      0.323135  
      4 :   -0.119581     -0.374581      0.919451  
      5 :  -0.0219073      0.224492       0.97423  
      6 :    0.537532     -0.666078     -0.517108  
      7 :   -0.119723     -0.913578      0.388641  
      8 :    0.518488     -0.827302     -0.216199  
      9 :     -0.8889     -0.431324     -0.154327  

hypersphere01_sample_test
  Normal end of execution.

hypersphere_integrals_test:
  Normal end of execution.
Tue Oct 19 11:53:28 2021