Tue Oct 19 17:10:38 2021

sphere_monte_carlo_tests():
  Python version: 3.6.9
  Test sphere_monte_carlo().

i4vec_print_test
  Python version: 3.6.9
  i4vec_print prints an I4VEC.

  Here is an I4VEC:

     0      91
     1      92
     2      93
     3      94

i4vec_print_test:
  Normal end of execution.

i4vec_transpose_print_test
  Python version: 3.6.9
  i4vec_transpose_print prints an I4VEC
  with 5 entries to a row, and an optional title.

  My array:  
       1
       2
       3
       4
       5
       6
       7
       8
       9
      10

      11
      12


i4vec_transpose_print_test:
  Normal end of execution.

r8mat_print_test
  Python version: 3.6.9
  r8mat_print prints an R8MAT.

  Here is an R8MAT:

  Col: 
      0       
      1       
      2       
      3       
      4       

  Row
      0 :
          11  
          12  
          13  
          14  
          15  

      1 :
          21  
          22  
          23  
          24  
          25  

      2 :
          31  
          32  
          33  
          34  
          35  

      3 :
          41  
          42  
          43  
          44  
          45  


  Col: 
      5       

  Row
      0 :
          16  

      1 :
          26  

      2 :
          36  

      3 :
          46  


r8mat_print_test:
  Normal end of execution.

r8mat_print_some_test
  Python version: 3.6.9
  r8mat_print_some prints some of an R8MAT.

  Here is an R8MAT:

  Col: 
      3       
      4       
      5       

  Row
      0 :
          14  
          15  
          16  

      1 :
          24  
          25  
          26  

      2 :
          34  
          35  
          36  


r8mat_print_some_test:
  Normal end of execution.

r8mat_transpose_print_test
  Python version: 3.6.9
  r8mat_transpose_print prints an R8MAT.

  Here is an R8MAT, transposed:

  Row: 
      0       
      1       
      2       
      3       

  Col
      0 :
          11  
          21  
          31  
          41  

      1 :
          12  
          22  
          32  
          42  

      2 :
          13  
          23  
          33  
          43  


r8mat_transpose_print_test:
  Normal end of execution.

r8mat_transpose_print_some_test
  Python version: 3.6.9
  r8mat_transpose_print_some prints some of an R8MAT, transposed.

  R8MAT, rows 0:2, cols 3:5:

  Row: 
      0       
      1       
      2       

  Col
      3 :
          14  
          24  
          34  

      4 :
          15  
          25  
          35  

      5 :
          16  
          26  
          36  


r8mat_transpose_print_some_test:
  Normal end of execution.

r8vec_print_test
  Python version: 3.6.9
  r8vec_print prints an R8VEC.

  Here is an R8VEC:

     0:       123.456
     1:         5e-06
     2:        -1e+06
     3:       3.14159

r8vec_print_test:
  Normal end of execution.

sphere01_area_test
  Python version: 3.6.9
  sphere01_area returns the volume of the unit sphere.

  sphere01_area() =  12.5664

sphere01_area_test
  Normal end of execution.

sphere01_monomial_integral_test
  Python version: 3.6.9
  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

   0
   2
   4
        0.367012        0.359039       0.008
   2
   6
   2
       0.0179705       0.0181333     0.00016
   8
   6
   6
     2.22498e-05     2.15924e-05     6.6e-07
   2
   4
   6
      0.00433129      0.00418461     0.00015
   4
   2
   6
      0.00427276      0.00418461     8.8e-05
   0
   0
   8
         1.41206         1.39626       0.016
   0
   2
   6
        0.204166        0.199466      0.0047
   2
   2
   0
        0.828554        0.837758      0.0092
   0
   2
   2
        0.848132        0.837758        0.01
   6
   0
   8
      0.00983391      0.00976408       7e-05
   8
   4
   4
     0.000348238     0.000344615     3.6e-06
   4
   6
   8
     9.49214e-05      9.0688e-05     4.2e-06
   0
   0
   2
         4.24402         4.18879       0.055
   4
   6
   6
     0.000254856     0.000246153     8.7e-06
   8
   2
   0
        0.124358        0.126933      0.0026
   2
   6
   0
         0.19561        0.199466      0.0039
   0
   0
   4
         2.55025         2.51327       0.037
   6
   4
   4
      0.00085233     0.000836921     1.5e-05
   0
   8
   8
      0.00411073       0.0040205       9e-05
   2
   2
   0
        0.828554        0.837758      0.0092

sphere01_monomial_integral_test
  Normal end of execution.

sphere01_monte_carlo_test
  Use sphere01_sample to estimate integrals over 
  the surface of the unit sphere.

         N        1              X^2             Y^2
             Z^2             X^4           X^2Y^2           Z^4

         1
       12.566371
        7.161284
        4.178211
        1.226876
        4.081050
        2.381066
        0.119782

         2
       12.566371
        8.448666
        3.988140
        0.129565
        5.754080
        2.616296
        0.002389

         4
       12.566371
        1.867551
        6.360111
        4.338709
        0.509519
        1.183588
        2.736324

         8
       12.566371
        2.060910
        3.355648
        7.149812
        0.814697
        0.668027
        5.495903

        16
       12.566371
        3.408256
        5.530310
        3.627805
        1.576063
        1.119217
        1.785104

        32
       12.566371
        4.217100
        4.207281
        4.141989
        2.461332
        0.912744
        2.380183

        64
       12.566371
        4.204504
        4.083083
        4.278784
        2.438576
        0.814067
        2.414674

       128
       12.566371
        4.631872
        3.805924
        4.128575
        2.829701
        0.853364
        2.456211

       256
       12.566371
        4.192838
        4.044400
        4.329133
        2.566649
        0.782253
        2.638958

       512
       12.566371
        4.069067
        4.222999
        4.274305
        2.432634
        0.795822
        2.592655

      1024
       12.566371
        4.269650
        3.998881
        4.297840
        2.577979
        0.805429
        2.581159

      2048
       12.566371
        4.252752
        4.188047
        4.125572
        2.561073
        0.848714
        2.456583

      4096
       12.566371
        4.158192
        4.201363
        4.206816
        2.474718
        0.827885
        2.519128

      8192
       12.566371
        4.218089
        4.175543
        4.172739
        2.546873
        0.822713
        2.512544

     16384
       12.566371
        4.224760
        4.199765
        4.141846
        2.538058
        0.844623
        2.468182

     32768
       12.566371
        4.222085
        4.163837
        4.180448
        2.540099
        0.839612
        2.502344

     65536
       12.566371
        4.202796
        4.181339
        4.182235
        2.521027
        0.838849
        2.509632


     Exact
       12.566371
        4.188790
        4.188790
        4.188790
        2.513274
        0.837758
        2.513274


sphere01_sample_test
  Python version: 3.6.9
  sphere01_sample samples the unit sphere.

  Sample points on the unit sphere.

  Row: 
      0       
      1       
      2       

  Col
      0 :
    -0.92934  
    0.359464  
   0.0843386  

      1 :
   -0.800564  
   -0.490641  
    0.344048  

      2 :
   -0.514984  
   -0.309428  
    0.799403  

      3 :
  -0.0522509  
   -0.866019  
   -0.497274  

      4 :
   -0.647325  
   -0.349892  
     0.67716  

      5 :
   -0.542996  
    0.765072  
    0.346152  

      6 :
   -0.697059  
    0.139594  
    0.703294  

      7 :
    0.529343  
    0.371151  
   -0.762917  

      8 :
   -0.539307  
   -0.317651  
   -0.779901  

      9 :
    0.109222  
   -0.781219  
    0.614627  


sphere01_sample_test
  Normal end of execution.

sphere_monte_carlo_tests():
  Normal end of execution.
Tue Oct 19 17:10:40 2021