21 January 2017 08:43:08 AM

SIMPLEX_GRID_TEST:
  C version
  Test the SIMPLEX_GRID library.

TEST01:
  SIMPLEX_GRID_SIZE counts the points in a regular grid
  with N+1 points on a side, in an M-dimensional simplex.

        M: 0     1     2     3     4     5
    N:
    0:     1     1     1     1     1     1
    1:     1     2     3     4     5     6
    2:     1     3     6    10    15    21
    3:     1     4    10    20    35    56
    4:     1     5    15    35    70   126
    5:     1     6    21    56   126   252
    6:     1     7    28    84   210   462
    7:     1     8    36   120   330   792
    8:     1     9    45   165   495  1287
    9:     1    10    55   220   715  2002
   10:     1    11    66   286  1001  3003

TEST02:
  SIMPLEX_GRID_INDEX_NEXT lists, one by one, the indices
  of a simplex grid that uses N+1 points on a side,
  in an M-dimensional simplex.

   #:  1  2  3  (*)

   0:  0  0  0 (  3)
   1:  0  0  1 (  2)
   2:  0  0  2 (  1)
   3:  0  0  3 (  0)
   4:  0  1  0 (  2)
   5:  0  1  1 (  1)
   6:  0  1  2 (  0)
   7:  0  2  0 (  1)
   8:  0  2  1 (  0)
   9:  0  3  0 (  0)
  10:  1  0  0 (  2)
  11:  1  0  1 (  1)
  12:  1  0  2 (  0)
  13:  1  1  0 (  1)
  14:  1  1  1 (  0)
  15:  1  2  0 (  0)
  16:  2  0  0 (  1)
  17:  2  0  1 (  0)
  18:  2  1  0 (  0)
  19:  3  0  0 (  0)

TEST03:
  SIMPLEX_GRID_INDEX_SAMPLE returns a randomly selected
  index of a simplex grid that uses N+1 points on a side,
  in an M-dimensional simplex.

   #:  1  2  3  (*)

   1:  0  1  1 (  1)
   2:  1  0  2 (  0)
   3:  0  1  2 (  0)
   4:  1  0  2 (  0)
   5:  3  0  0 (  0)
   6:  0  1  0 (  2)
   7:  0  0  3 (  0)
   8:  0  0  3 (  0)
   9:  2  0  0 (  1)
  10:  0  1  1 (  1)
  11:  0  0  0 (  3)
  12:  1  0  2 (  0)
  13:  2  1  0 (  0)
  14:  1  1  1 (  0)
  15:  2  0  0 (  1)
  16:  1  0  0 (  2)
  17:  0  0  2 (  1)
  18:  1  2  0 (  0)
  19:  1  0  0 (  2)
  20:  0  2  0 (  1)

TEST04:
  SIMPLEX_GRID_INDEX_TO_POINT returns the physical point
  corresponding to a grid index of a simplex grid that
  that uses N+1 points on a side,
  in an M-dimensional simplex.

  Simplex vertices:

  Row:        0             1     
  Col

    0:              20               0
    1:              30              40
    2:              10              20

  Choosing random simplex indices to convert:
   #:  1  2  3     X        Y

   1:  1  4  0     28.0000   32.0000
   2:  0  0  5     10.0000   20.0000
   3:  1  2  2     20.0000   24.0000
   4:  3  2  0     24.0000   16.0000
   5:  0  5  0     30.0000   40.0000
   6:  0  1  4     14.0000   24.0000
   7:  2  1  2     18.0000   16.0000
   8:  4  1  0     22.0000    8.0000
   9:  1  4  0     28.0000   32.0000
  10:  1  2  2     20.0000   24.0000

TEST05:
  SIMPLEX_GRID_INDEX_ALL returns all the indices
  of a simplex grid that uses N+1 points on a side,
  in an M-dimensional simplex.

  Transposed Simplex Grid Index Matrix:

  Row:      0       1       2       3  
  Col

    0:      0       0       0       3  
    1:      0       0       1       2  
    2:      0       0       2       1  
    3:      0       0       3       0  
    4:      0       1       0       2  
    5:      0       1       1       1  
    6:      0       1       2       0  
    7:      0       2       0       1  
    8:      0       2       1       0  
    9:      0       3       0       0  
   10:      1       0       0       2  
   11:      1       0       1       1  
   12:      1       0       2       0  
   13:      1       1       0       1  
   14:      1       1       1       0  
   15:      1       2       0       0  
   16:      2       0       0       1  
   17:      2       0       1       0  
   18:      2       1       0       0  
   19:      3       0       0       0