Thu Sep 13 09:51:34 2018

HYPERCUBE_INTEGRALS_TEST
  Python version: 3.6.5
  Test the HYPERCUBE_INTEGRALS library.

I4VEC_PRINT_TEST
  Python version: 3.6.5
  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: 3.6.5
  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.

I4VEC_UNIFORM_AB_TEST
  Python version: 3.6.5
  I4VEC_UNIFORM_AB computes pseudorandom values
  in an interval [A,B].

  The lower endpoint A = -100
  The upper endpoint B = 200
  The initial seed is 123456789


  The random vector:

     0     -35
     1     187
     2     149
     3      69
     4      25
     5     -81
     6     -23
     7     -67
     8     -87
     9      90
    10     -82
    11      35
    12      20
    13     127
    14     139
    15    -100
    16     170
    17       5
    18     -72
    19     -96

I4VEC_UNIFORM_AB_TEST:
  Normal end of execution.

R8MAT_PRINT_TEST
  Python version: 3.6.5
  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: 3.6.5
  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: 3.6.5
  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: 3.6.5
  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.

R8MAT_UNIFORM_01_TEST
  Python version: 3.6.5
  R8MAT_UNIFORM_01 computes a random R8MAT.

  0 <= X <= 1
  Initial seed is 123456789

  Random R8MAT:

  Col:       0             1             2             3       
  Row
      0 :    0.218418     0.0661187     0.0617272    0.00183837  
      1 :    0.956318      0.257578      0.449539      0.897504  
      2 :    0.829509      0.109957      0.401306      0.350752  
      3 :    0.561695      0.043829      0.754673     0.0945448  
      4 :    0.415307      0.633966      0.797287     0.0136169  

R8MAT_UNIFORM_01_TEST:
  Normal end of execution.

R8MAT_UNIFORM_AB_TEST
  Python version: 3.6.5
  R8MAT_UNIFORM_AB computes a random R8MAT.

  -1 <= X <= 5
  Initial seed is 123456789

  Random R8MAT:

  Col:       0             1             2             3       
  Row
      0 :     0.31051     -0.603288     -0.629637      -0.98897  
      1 :     4.73791      0.545467       1.69723       4.38502  
      2 :     3.97706     -0.340259       1.40784       1.10451  
      3 :     2.37017     -0.737026       3.52804     -0.432731  
      4 :     1.49184       2.80379       3.78372     -0.918299  

R8MAT_UNIFORM_AB_TEST:
  Normal end of execution.

HYPERCUBE01_MONOMIAL_INTEGRAL_TEST
  Python version: 3.6.5
  HYPERCUBE01_MONOMIAL_INTEGRAL returns the integral of a monomial
  over the interior of the unit hypercube in 3D.
  Compare with a Monte Carlo estimate.

  Using M = 3

  Number of sample points used is 4192

  Ex  Ey  Ez     MC-Estimate           Exact      Error

   4
   3
   0
       0.0479881            0.05       0.002
   0
   2
   3
       0.0817332       0.0833333      0.0016
   4
   4
   2
       0.0118586       0.0133333      0.0015
   0
   3
   0
        0.246879            0.25      0.0031
   4
   3
   0
       0.0479881            0.05       0.002
   4
   0
   4
       0.0375109            0.04      0.0025
   3
   4
   0
       0.0481349            0.05      0.0019
   1
   0
   4
       0.0964596             0.1      0.0035
   1
   3
   0
        0.121836           0.125      0.0032
   0
   4
   2
       0.0645985       0.0666667      0.0021
   1
   2
   2
       0.0532703       0.0555556      0.0023
   3
   0
   4
       0.0470921            0.05      0.0029
   1
   0
   1
        0.243841            0.25      0.0062
   4
   1
   4
       0.0183829            0.02      0.0016
   3
   3
   0
       0.0602641          0.0625      0.0022
   4
   4
   2
       0.0118586       0.0133333      0.0015
   0
   4
   4
         0.03867            0.04      0.0013
   1
   3
   2
       0.0395885       0.0416667      0.0021
   0
   4
   0
        0.197368             0.2      0.0026
   0
   4
   3
       0.0484177            0.05      0.0016

HYPERCUBE01_MONOMIAL_INTEGRAL_TEST:
  Normal end of execution.

HYPERCUBE01_SAMPLE_TEST
  Python version: 3.6.5
  HYPERUBE01_SAMPLE samples the unit hypercube
  in M dimensions.

  Sample points in the unit hypercube.

  Row: 
      0       
      1       
      2       

  Col
      0 :
    0.218418  
    0.956318  
    0.829509  

      1 :
    0.561695  
    0.415307  
   0.0661187  

      2 :
    0.257578  
    0.109957  
    0.043829  

      3 :
    0.633966  
   0.0617272  
    0.449539  

      4 :
    0.401306  
    0.754673  
    0.797287  

      5 :
  0.00183837  
    0.897504  
    0.350752  

      6 :
   0.0945448  
   0.0136169  
    0.859097  

      7 :
    0.840847  
    0.123104  
  0.00751236  

      8 :
    0.260303  
    0.912484  
    0.113664  

      9 :
    0.351629  
    0.822887  
    0.267132  


HYPERCUBE01_SAMPLE_TEST
  Normal end of execution.

HYPERCUBE01_VOLUME_TEST
  Python version: 3.6.5
  HYPERCUBE01_VOLUME returns the volume of the unit hypercube
  in M dimensions.

  HYPERCUBE01_VOLUME(3) = 1

HYPERCUBE01_VOLUME_TEST
  Normal end of execution.

MONOMIAL_VALUE_TEST
  Python version: 3.6.5
  Use monomial_value() to evaluate some monomials
  in dimensions 1 through 3.

  Spatial dimension M =  1
  Exponents: -1

   V(X)               X(0)

      0.111111      9.0000
         0.125      8.0000
           0.2      5.0000
      0.333333      3.0000
            -1     -1.0000

  Spatial dimension M =  2
  Exponents: -1 -2

   V(X)               X(0)      X(1)

    -0.0277778     -1.0000    6.0000
     -0.111111     -1.0000    3.0000
    0.00680272      3.0000    7.0000
       0.03125      8.0000   -2.0000
     0.0277778      9.0000    2.0000

  Spatial dimension M =  3
  Exponents: -3 -3 5

   V(X)               X(0)      X(1)      X(2)

        0.0625      8.0000   -1.0000   -2.0000
   -0.00137174      1.0000    9.0000   -1.0000
   0.000244141      2.0000    8.0000    1.0000
       1.21363      6.0000    5.0000    8.0000
      0.158766      3.0000    9.0000    5.0000

MONOMIAL_VALUE_TEST
  Normal end of execution.

HYPERCUBE_INTEGRALS_TEST:
  Normal end of execution.
Thu Sep 13 09:51:34 2018