14-Aug-2022 11:23:01

r8col_test():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  Test r8col()

I4_LOG_10_TEST
  I4_LOG_10: whole part of log base 10,

  X, I4_LOG_10

     0             0
     1             0
     2             0
     3             0
     9             0
    10             1
    11             1
    99             1
   101             2
    -1             0
    -2             0
    -3             0
    -9             0

i4vec_indicator1_test():
  i4vec_indicator1() returns an indicator vector.

  The "indicator1" vector:

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

i4vec_print_test():
  i4vec_print() prints an I4VEC

  The I4VEC:

     1:     91
     2:     92
     3:     93
     4:     94

i4vec_transpose_print_test():
  i4vec_transpose_print() prints an integer vector
  with 5 entries to a row, and a title.

  Output from I4VEC_PRINT:

     1:      1
     2:      2
     3:      3
     4:      4
     5:      5
     6:      6
     7:      7
     8:      8
     9:      9
    10:     10
    11:     11
    12:     12

  My array:  
       1       2       3       4       5       6       7       8       9      10
      11      12

perm1_check_test():
  perm1_check() checks a permutation of 1,...,N.

  Permutation 1:
       5       2       3       4       1

  Permutation 2:
       4       1       3       0       2

PERM1_CHECK - Warning!
  Permutation is missing the value 5.

  Permutation 3:
       0       2       1       3       2

PERM1_CHECK - Warning!
  Permutation is missing the value 4.

r8col_find_test():
  r8col_find() finds a column in a table matching
  a given set of data.

  R8COL_FIND returns ICOL = 3

r8col_indicator_test():
  r8col_indicator() returns an indicator matrix.

  Indicator matrix:

  Col:       1             2             3             4       
  Row
      1 :          11            12            13            14  
      2 :          21            22            23            24  
      3 :          31            32            33            34  
      4 :          41            42            43            44  
      5 :          51            52            53            54  

R8COL_INSERT_TEST
  R8COL_INSERT inserts new columns.


  The unsorted matrix:

  Col:       1             2             3             4       
  Row
      1 :           2             4             1             3  
      2 :           6             8             5             7  
      3 :          10            12             9            11  

  The sorted matrix:

  Col:       1             2             3             4       
  Row
      1 :           1             2             3             4  
      2 :           5             6             7             8  
      3 :           9            10            11            12  

  New column:

     1:            3
     2:            7
     3:           11

  The data was already in column 3

  New column:

     1:            3
     2:            4
     3:           18

  The updated matrix:

  Col:       1             2             3             4             5       
  Row
      1 :           1             2             3             3             4  
      2 :           5             6             4             7             8  
      3 :           9            10            18            11            12  

R8COL_MAX_TEST
  For an R8COL, an array of column vectors;
  R8COL_MAX computes maximums;

  The array:

  Col:       1             2             3             4       
  Row
      1 :           1             2             3             4  
      2 :           5             6             7             8  
      3 :           9            10            11            12  

  Column maximums:

     1:            3
     2:            3
     3:            3
     4:            3

R8COL_MEAN_TEST
  For an R8COL, an array of column vectors;
  R8COL_MEAN computes means;

  The array:

  Col:       1             2             3             4       
  Row
      1 :           1             2             3             4  
      2 :           5             6             7             8  
      3 :           9            10            11            12  

  Column means:

     1:            5
     2:            6
     3:            7
     4:            8

R8COL_MIN_TEST
  For an R8COL, an array of column vectors;
  R8COL_MIN computes minimums;

  The array:

  Col:       1             2             3             4       
  Row
      1 :           1             2             3             4  
      2 :           5             6             7             8  
      3 :           9            10            11            12  

  Column minimums:

     1:            1
     2:            2
     3:            3
     4:            4

R8COL_PERMUTE_TEST
  R8COL_PERMUTE permutes an R8COL in place.

  A (Unpermuted):

  Col:       1             2             3             4             5       
  Row
      1 :          11            12            13            14            15  
      2 :          21            22            23            24            25  
      3 :          31            32            33            34            35  

  The (column) permutation vector:

     1:      2
     2:      4
     3:      5
     4:      1
     5:      3

  A (Permuted):

  Col:       1             2             3             4             5       
  Row
      1 :          12            14            15            11            13  
      2 :          22            24            25            21            23  
      3 :          32            34            35            31            33  

R8COL_PRINT_TEST
  R8COL_PRINT prints an R8COL.

  The R8COL matrix of columns:

  Col:       1             2             3             4       
  Row
      1 :          11            12            13            14  
      2 :          21            22            23            24  
      3 :          31            32            33            34  
      4 :          41            42            43            44  
      5 :          51            52            53            54  
      6 :          61            62            63            64  

R8COL_PRINT_SOME_TEST
  R8COL_PRINT_SOME prints some of an R8COL.

  The R8COL, rows 2:4, cols 1:2:

  Col:       1             2       
  Row
      2 :          21            22  
      3 :          31            32  
      4 :          41            42  

R8COL_SORT_HEAP_A_TEST
  R8COL_SORT_HEAP_A ascending heap sorts a table of
  columns.

  The unsorted matrix:

  Col:       1             2             3             4       
  Row
      1 :           2             4             1             3  
      2 :           6             8             5             7  
      3 :          10            12             9            11  

  The sorted matrix:

  Col:       1             2             3             4       
  Row
      1 :           1             2             3             4  
      2 :           5             6             7             8  
      3 :           9            10            11            12  

  New column:

     1:            3
     2:            7
     3:           11

  The data was already in column 3

  New column:

     1:            3
     2:            4
     3:           18

  The updated matrix:

  Col:       1             2             3             4             5       
  Row
      1 :           1             2             3             3             4  
      2 :           5             6             4             7             8  
      3 :           9            10            18            11            12  

R8COL_SORT_HEAP_INDEX_A_TEST
  R8COL_SORT_HEAP_INDEX_A computes an index vector which
  ascending heap sorts an R8COL.

  The unsorted R8COL (transposed):

  Row:       1             2             3       
  Col
    1:           2           6          10
    2:           4           8          12
    3:           1           5           9
    4:           3           7          11
    5:           2           6           0
    6:           3           4          18
    7:           0           0           0
    8:           0           6          10
    9:           2           6          10
   10:           3           7          11
   11:           2           0          10
   12:           2           6          10
   13:           1           5           9
   14:           1           5         9.1
   15:           1         5.1           9

  The (implicitly) sorted R8COL (transposed)

     2:      4.000000    8.000000   12.000000
     3:      1.000000    5.000000    9.000000
     4:      3.000000    7.000000   11.000000
     5:      2.000000    6.000000    0.000000
     6:      3.000000    4.000000   18.000000
     7:      0.000000    0.000000    0.000000
     8:      0.000000    6.000000   10.000000
     9:      2.000000    6.000000   10.000000
    10:      3.000000    7.000000   11.000000
    11:      2.000000    0.000000   10.000000
    12:      2.000000    6.000000   10.000000
    13:      1.000000    5.000000    9.000000
    14:      1.000000    5.000000    9.100000
    15:      1.000000    5.100000    9.000000
     1:      2.000000    6.000000   10.000000

R8COL_SORT_QUICK_A_TEST
  R8COL_SORT_QUICK_A sorts a table of columns.


  The unsorted matrix:

  Col:       1             2             3             4             5       
  Row
      1 :     8.14724       9.13376       2.78498       9.64889       9.57167  
      2 :     9.05792       6.32359       5.46882       1.57613       4.85376  
      3 :     1.26987      0.975404       9.57507       9.70593        8.0028  

  Col:       6             7             8             9            10       
  Row
      1 :     1.41886       7.92207      0.357117       6.78735       3.92227  
      2 :     4.21761       9.59492       8.49129        7.5774       6.55478  
      3 :     9.15736       6.55741       9.33993       7.43132       1.71187  

  The sorted matrix:

  Col:       1             2             3             4             5       
  Row
      1 :    0.357117       1.41886       2.78498       3.92227       6.78735  
      2 :     8.49129       4.21761       5.46882       6.55478        7.5774  
      3 :     9.33993       9.15736       9.57507       1.71187       7.43132  

  Col:       6             7             8             9            10       
  Row
      1 :     7.92207       8.14724       9.13376       9.57167       9.64889  
      2 :     9.59492       9.05792       6.32359       4.85376       1.57613  
      3 :     6.55741       1.26987      0.975404        8.0028       9.70593  

R8COL_SORTED_TOL_UNIQUE_TEST
  R8COL_SORTED_TOL_UNIQUE returns tolerably unique columns
  in a sorted R8COL.


  The unsorted R8COL (transposed):

  Row:       1             2             3       
  Col
    1:         1.9           0          10
    2:           2           6          10
    3:           4           8          12
    4:           1           5           9
    5:           3           7          11
    6:           2           6           0
    7:           2           0        10.1
    8:           2         0.1          10
    9:           3           4          18
   10:         1.9           8          10
   11:           0           0           0
   12:           0           6          10
   13:         2.1           0          10
   14:           2           6          10
   15:           3           7          11
   16:           2           0          10
   17:           2           0          10
   18:           2           6          10
   19:           1           5           9
   20:           2           0        10.1
   21:           1           5         9.1
   22:           1         5.1           9

  The sorted R8COL (transposed):

  Row:       1             2             3       
  Col
    1:           0           0           0
    2:           0           6          10
    3:           1           5           9
    4:           1           5           9
    5:           1           5         9.1
    6:           1         5.1           9
    7:         1.9           0          10
    8:         1.9           8          10
    9:           2           0          10
   10:           2           0          10
   11:           2           0        10.1
   12:           2           0        10.1
   13:           2         0.1          10
   14:           2           6           0
   15:           2           6          10
   16:           2           6          10
   17:           2           6          10
   18:         2.1           0          10
   19:           3           4          18
   20:           3           7          11
   21:           3           7          11
   22:           4           8          12

  Equality tolerance set to 2.500000e-01

  Number of tolerably unique columns is 10

  The tolerably unique sorted R8COL (transposed):

  Row:       1             2             3       
  Col
    1:           0           0           0
    2:           0           6          10
    3:           1           5           9
    4:         1.9           0          10
    5:         1.9           8          10
    6:           2           6           0
    7:           2           6          10
    8:           3           4          18
    9:           3           7          11
   10:           4           8          12

R8COL_SORTED_TOL_UNIQUE_COUNT_TEST
  R8COL_SORTED_TOL_UNIQUE_COUNT counts tolerably unique
  columns in a sorted R8COL.


  The unsorted R8COL (transposed):

  Row:       1             2             3       
  Col
    1:         1.9           0          10
    2:           2           6          10
    3:           4           8          12
    4:           1           5           9
    5:           3           7          11
    6:           2           6           0
    7:           2           0        10.1
    8:           2         0.1          10
    9:           3           4          18
   10:         1.9           8          10
   11:           0           0           0
   12:           0           6          10
   13:         2.1           0          10
   14:           2           6          10
   15:           3           7          11
   16:           2           0          10
   17:           2           0          10
   18:           2           6          10
   19:           1           5           9
   20:           2           0        10.1
   21:           1           5         9.1
   22:           1         5.1           9

  The sorted R8COL (transposed):

  Row:       1             2             3       
  Col
    1:           0           0           0
    2:           0           6          10
    3:           1           5           9
    4:           1           5           9
    5:           1           5         9.1
    6:           1         5.1           9
    7:         1.9           0          10
    8:         1.9           8          10
    9:           2           0          10
   10:           2           0          10
   11:           2           0        10.1
   12:           2           0        10.1
   13:           2         0.1          10
   14:           2           6           0
   15:           2           6          10
   16:           2           6          10
   17:           2           6          10
   18:         2.1           0          10
   19:           3           4          18
   20:           3           7          11
   21:           3           7          11
   22:           4           8          12

  Equality tolerance set to 2.500000e-01

  Number of tolerably unique columns is 10

R8COL_SORTED_TOL_UNDEX_TEST
  R8COL_SORTED_TOL_UNDEX produces index vectors which 
  create a sorted list of the tolerably unique columns of 
  a sorted R8COL and a map from the original R8COL to the 
  (implicit) R8COL of sorted tolerably unique elements.

  The unsorted R8COL (transposed):

  Row:       1             2             3       
  Col
    1:         1.9           0          10
    2:           2           6          10
    3:           4           8          12
    4:           1           5           9
    5:           3           7          11
    6:           2           6           0
    7:           2           0        10.1
    8:           2         0.1          10
    9:           3           4          18
   10:         1.9           8          10
   11:           0           0           0
   12:           0           6          10
   13:         2.1           0          10
   14:           2           6          10
   15:           3           7          11
   16:           2           0          10
   17:           2           0          10
   18:           2           6          10
   19:           1           5           9
   20:           2           0        10.1
   21:           1           5         9.1
   22:           1         5.1           9

  The sorted R8COL (transposed):

  Row:       1             2             3       
  Col
    1:           0           0           0
    2:           0           6          10
    3:           1           5           9
    4:           1           5           9
    5:           1           5         9.1
    6:           1         5.1           9
    7:         1.9           0          10
    8:         1.9           8          10
    9:           2           0          10
   10:           2           0          10
   11:           2           0        10.1
   12:           2           0        10.1
   13:           2         0.1          10
   14:           2           6           0
   15:           2           6          10
   16:           2           6          10
   17:           2           6          10
   18:         2.1           0          10
   19:           3           4          18
   20:           3           7          11
   21:           3           7          11
   22:           4           8          12

  Tolerance for equality is 2.500000e-01
  Number of unique entries in X is 10

  XDNU points to the representative for each item.
  UNDX selects the representatives..

     1     1     1
     2     2     2
     3     3     3
     4     3     7
     5     3     8
     6     3    14
     7     4    15
     8     5    19
     9     4    20
    10     4    22
    11     4
    12     4
    13     4
    14     6
    15     7
    16     7
    17     7
    18     4
    19     8
    20     9
    21     9
    22    10

  The tolerably unique R8COL (transposed):

  Row:       1             2             3       
  Col
    1:           0           0           0
    2:           0           6          10
    3:           1           5           9
    4:         1.9           0          10
    5:         1.9           8          10
    6:           2           6           0
    7:           2           6          10
    8:           3           4          18
    9:           3           7          11
   10:           4           8          12

R8COL_SORTR_A_TEST
  R8COL_SORTR_A is given an array, and reorders
  it so that a particular column is sorted.

  Here, the special column is 2

  Unsorted array:

  Col:       1             2             3       
  Row
      1 :     7.06046       4.38744       2.76025  
      2 :    0.318328       3.81558       6.79703  
      3 :     2.76923       7.65517       6.55098  
      4 :    0.461714         7.952       1.62612  
      5 :    0.971318       1.86873       1.18998  
      6 :     8.23458       4.89764       4.98364  
      7 :     6.94829       4.45586       9.59744  
      8 :     3.17099       6.46313       3.40386  
      9 :     9.50222       7.09365       5.85268  
     10 :    0.344461       7.54687       2.23812  

  Sorted array:

  Col:       1             2             3       
  Row
      1 :    0.971318       1.86873       1.18998  
      2 :    0.318328       3.81558       6.79703  
      3 :     7.06046       4.38744       2.76025  
      4 :     6.94829       4.45586       9.59744  
      5 :     8.23458       4.89764       4.98364  
      6 :     3.17099       6.46313       3.40386  
      7 :     9.50222       7.09365       5.85268  
      8 :    0.344461       7.54687       2.23812  
      9 :     2.76923       7.65517       6.55098  
     10 :    0.461714         7.952       1.62612  

R8COL_SUM_TEST
  For an R8COL, an array of column vectors;
  R8COL_SUM computes sums;

  The array:

  Col:       1             2             3             4       
  Row
      1 :           1             2             3             4  
      2 :           5             6             7             8  
      3 :           9            10            11            12  

  The column sums:

     1:           15
     2:           18
     3:           21
     4:           24

R8COL_SWAP_TEST
  For an R8COL, an array of column vectors;
  R8COL_SWAP swaps two columns;

  The array:

  Col:       1             2             3             4       
  Row
      1 :          11            12            13            14  
      2 :          21            22            23            24  
      3 :          31            32            33            34  

  Swap columns 1 and 3

  The updated matrix:

  Col:       1             2             3             4       
  Row
      1 :          13            12            11            14  
      2 :          23            22            21            24  
      3 :          33            32            31            34  

R8COL_TO_R8VEC_TEST
  R8COL_TO_R8VEC converts an array of columns to a vector.


  The array of columns:

  Col:       1             2             3             4       
  Row
      1 :          11            12            13            14  
      2 :          21            22            23            24  
      3 :          31            32            33            34  

  The resulting vector of columns:

     1:           11
     2:           21
     3:           31
     4:           12
     5:           22
     6:           32
     7:           13
     8:           23
     9:           33
    10:           14
    11:           24
    12:           34

R8COL_TOL_UNDEX_TEST
  R8COL_TOL_UNDEX produces index vectors which
  create a sorted list of the tolerably unique columns
  of an (unsorted) R8COL, 
  and a map from the original R8COL to the (implicit) 
  R8COL of sorted unique elements.

  The unsorted R8COL (transposed):

  Row:       1             2             3       
  Col
    1:         1.9           0          10
    2:           2           6          10
    3:           4           8          12
    4:           1           5           9
    5:           3           7          11
    6:           2           6           0
    7:           2           0        10.1
    8:           2         0.1          10
    9:           3           4          18
   10:         1.9           8          10
   11:           0           0           0
   12:           0           6          10
   13:         2.1           0          10
   14:           2           6          10
   15:           3           7          11
   16:           2           0          10
   17:           2           0          10
   18:           2           6          10
   19:           1           5           9
   20:           2           0        10.1
   21:           1           5         9.1
   22:           1         5.1           9

  Tolerance for equality = 0.250000

  Number of unique entries in X is 10

  XDNU points to the representative for each item.
  UNDX selects the representatives..

     1     6     2
     2     1     3
     3     2     4
     4     3     5
     5     4     6
     6     5     7
     7     6     9
     8     6    10
     9     7    11
    10     8    12
    11     9
    12    10
    13     6
    14     1
    15     4
    16     6
    17     6
    18     1
    19     3
    20     6
    21     3
    22     3

  The Unique R8COL (transposed):

  Row:       1             2             3       
  Col
    1:           2           6          10
    2:           4           8          12
    3:           1           5           9
    4:           3           7          11
    5:           2           6           0
    6:           2           0        10.1
    7:           3           4          18
    8:         1.9           8          10
    9:           0           0           0
   10:           0           6          10

R8COL_TRANSPOSE_PRINT_TEST
  R8COL_TRANSPOSE_PRINT prints an R8COL,
  transposed.

  Matrix row order M =    7
  Matrix column order N = 12

  The transposed matrix A:

  Row:       1             2             3             4             5       
  Col
    1:         101         201         301         401         501
    2:         102         202         302         402         502
    3:         103         203         303         403         503
    4:         104         204         304         404         504
    5:         105         205         305         405         505
    6:         106         206         306         406         506
    7:         107         207         307         407         507
    8:         108         208         308         408         508
    9:         109         209         309         409         509
   10:         110         210         310         410         510
   11:         111         211         311         411         511
   12:         112         212         312         412         512

  Row:       6             7       
  Col
    1:         601         701
    2:         602         702
    3:         603         703
    4:         604         704
    5:         605         705
    6:         606         706
    7:         607         707
    8:         608         708
    9:         609         709
   10:         610         710
   11:         611         711
   12:         612         712

R8COL_UNDEX_TEST
  R8COL_UNDEX produces index vectors which create a sorted
  list of the unique columns of an (unsorted) R8COL, 
  and a map from the original R8COL to the (implicit) 
  R8COL of sorted unique elements.

  The R8COL (transposed):

  Row:       1             2             3       
  Col
    1:         1.9           0          10
    2:           2           6          10
    3:           4           8          12
    4:           1           5           9
    5:           3           7          11
    6:           2           6           0
    7:           2           0        10.1
    8:           2         0.1          10
    9:           3           4          18
   10:         1.9           8          10
   11:           0           0           0
   12:           0           6          10
   13:         2.1           0          10
   14:           2           6          10
   15:           3           7          11
   16:           2           0          10
   17:           2           0          10
   18:           2           6          10
   19:           1           5           9
   20:           2           0        10.1
   21:           1           5         9.1
   22:           1         5.1           9

  Number of unique entries in X is 16

  XDNU points to the representative for each item.
  UNDX selects the representatives..

     1    21     2
     2     1     3
     3     2     4
     4     3     5
     5     4     6
     6     5     7
     7     6     8
     8     7     9
     9     8    10
    10     9    11
    11    10    12
    12    11    13
    13    12    14
    14    13    15
    15    14    16
    16    15    18
    17    15
    18    16
    19    17
    20    18
    21    19
    22    20

  The Unique R8COL (transposed):

  Row:       1             2             3       
  Col
    1:           2           6          10
    2:           4           8          12
    3:           1           5           9
    4:           3           7          11
    5:           2           6           0
    6:           2           0        10.1
    7:           2         0.1          10
    8:           3           4          18
    9:         1.9           8          10
   10:           0           0           0
   11:           0           6          10
   12:         2.1           0          10
   13:           2           6          10
   14:           3           7          11
   15:           2           0          10
   16:           2           6          10

R8COL_UNIFORM_AB_TEST
  R8COL_UNIFORM_AB sets an R8COL to random values in [A,B].

  The random matrix:

  Col:       1             2             3             4       
  Row
      1 :     8.01014       9.67433       8.72574       4.79987  
      2 :     4.04076       6.37772       4.03426       3.57276  
      3 :     6.04766         3.109       8.51428       4.00867  
      4 :     7.59261       3.19435        3.9482       6.92836  
      5 :     9.12723       4.06007       9.43411       5.78631  

R8COL_UNIQUE_COUNT_TEST
  For an R8COL;
  R8COL_UNIQUE_COUNT counts unique columns.


  The R8COL (transposed):

  Row:       1             2             3       
  Col
    1:           2           6          10
    2:           4           8          12
    3:           1           5           9
    4:           3           7          11
    5:           2           6           0
    6:           3           4          18
    7:           0           0           0
    8:           0           6          10
    9:           2           6          10
   10:           3           7          11
   11:           2           0          10
   12:           2           6          10
   13:           1           5           9
   14:           1           5         9.1
   15:           1         5.1           9

  Number of unique columns is 11

R8COL_VARIANCE_TEST
  For an R8COL, an array of column vectors;
  R8COL_VARIANCE computes variances;

  The array:

  Col:       1             2             3             4       
  Row
      1 :           1             2             3             4  
      2 :           5             6             7             8  
      3 :           9            10            11            12  

  Column variances:

     1:           16
     2:           16
     3:           16
     4:           16

R8VEC_PRINT_TEST
  R8VEC_PRINT prints an R8VEC.

  The R8VEC:

     1:      123.456
     2:        5e-06
     3:       -1e+06
     4:      3.14159

SORT_HEAP_EXTERNAL_TEST
  SORT_HEAP_EXTERNAL sorts objects externally.

  Unsorted array:

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

  Sorted array:

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

r8col_test()
  Normal end of execution.

14-Aug-2022 11:23:01