14 September 2021  10:27:51.016 AM

ROW_ECHELON_INTEGER_TEST
  FORTRAN90 version
  Test the ROW_ECHELON_INTEGER library.

I4_GCD_TEST
  I4_GCD computes the greatest common factor,

         I       J  I4_GCD

        36      30       6
        49      -7       7
         0      71      71
        12      12      12
        36      49       1
         1      42       1
        91      28       7

I4MAT_PRINT_TEST
  I4MAT_PRINT prints an I4MAT.
 
  The matrix:
 
  Col        1       2       3
  Row
 
    1:      11      12      13
    2:      21      22      23
    3:      31      32      33
    4:      41      42      43
    5:      51      52      53

I4MAT_PRINT_SOME_TEST
  I4MAT_PRINT_SOME prints some of an I4MAT.
 
  The I4MAT, rows 2:4, cols 1:2:
 
  Col        1       2
  Row
 
    2:      21      22
    3:      31      32
    4:      41      42

I4MAT_REF_TEST
  I4MAT_REF computes the 
  integer row echelon form (IREF) of an I4MAT.
 
  Input A:
 
  Col        1       2       3       4       5       6       7
  Row
 
    1:       1       3       0       2       6       3       1
    2:      -2      -6       0      -2      -8       3       1
    3:       3       9       0       0       6       6       2
    4:      -1      -3       0       1       0       9       3

  The pseudo-determinant =              6
 
  IREF of A:
 
  Col        1       2       3       4       5       6       7
  Row
 
    1:       1       3       0       2       6       3       1
    2:       0       0       0       2       4       9       3
    3:       0       0       0       0       0       3       1
    4:       0       0       0       0       0       0       0

I4MAT_ROW_SWAP_TEST
  I4MAT_ROW_SWAP swaps two rows of an I4MAT.
 
  Input A:
 
  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

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

I4MAT_RREF_TEST
  I4MAT_RREF computes the 
  integer row reduced echelon form (IRREF) of an I4MAT.
 
  Input A:
 
  Col        1       2       3       4       5       6       7
  Row
 
    1:       1       3       0       2       6       3       1
    2:      -2      -6       0      -2      -8       3       1
    3:       3       9       0       0       6       6       2
    4:      -1      -3       0       1       0       9       3

  The pseudo-determinant =              6
 
  IREF of A:
 
  Col        1       2       3       4       5       6       7
  Row
 
    1:       1       3       0       0       2       0       0
    2:       0       0       0       1       2       0       0
    3:       0       0       0       0       0       3       1
    4:       0       0       0       0       0       0       0

I4MAT_RREF_SYSTEM_TEST
  FORTRAN90 version.
  I4MAT_RREF_SYSTEM computes the linear system associated
  with an integer reduced row echelon form of an I4MAT.

  Look at a "wide" matrix:
 
  Input A1:
 
  Col        1       2       3       4       5       6       7
  Row
 
    1:       1       3       0       2       6       3       1
    2:      -2      -6       0      -2      -8       3       1
    3:       3       9       0       0       6       6       2
    4:      -1      -3       0       1       0       9       3

  The pseudo-determinant =    6
 
  A2, the IRREF of A1:
 
  Col        1       2       3       4       5       6       7
  Row
 
    1:       1       3       0       0       2       0       0
    2:       0       0       0       1       2       0       0
    3:       0       0       0       0       0       3       1
    4:       0       0       0       0       0       0       0
 
  B2, the right hand side:
 
         1:             1
         2:             1
         3:             1
         4:             0

  The original system is CONSISTENT.
 
  A3, the augmented IRREF:
 
  Col        1       2       3       4       5       6       7
  Row
 
    1:       1       3       0       0       2       0       0
    2:       0       1       0       0       0       0       0
    3:       0       0       1       0       0       0       0
    4:       0       0       0       1       2       0       0
    5:       0       0       0       0       1       0       0
    6:       0       0       0       0       0       3       1
    7:       0       0       0       0       0       0       1
 
  B3, the augmented RHS:
 
         1:             1
         2:             0
         3:             0
         4:             1
         5:             0
         6:             1
         7:             0
 
  Indices of degrees of freedom.
 
         1:             2
         2:             3
         3:             5
         4:             7

  Look at a "tall" matrix:
 
  Input A1:
 
  Col        1       2       3       4
  Row
 
    1:       1      -2       3      -1
    2:       3      -6       9      -3
    3:       0       0       0       0
    4:       2      -2       0       1
    5:       6      -8       6       0
    6:       3       3       6       9
    7:       1       1       2       3

  The pseudo-determinant =   32
 
  A2, the IRREF of A1:
 
  Col        1       2       3       4
  Row
 
    1:      16       0       0      29
    2:       0      16       0      21
    3:       0       0      16      -1
    4:       0       0       0       0
    5:       0       0       0       0
    6:       0       0       0       0
    7:       0       0       0       0
 
  B2, the right hand side:
 
         1:             1
         2:             1
         3:             1
         4:             1
         5:             1
         6:             1
         7:             1

  The original system is INCONSISTENT.
 
  A3, the augmented IRREF:
 
  Col        1       2       3       4
  Row
 
    1:      16       0       0      29
    2:       0      16       0      21
    3:       0       0      16      -1
    4:       0       0       0       1
 
  B3, the augmented RHS:
 
         1:             1
         2:             1
         3:             1
         4:             0
 
  Indices of degrees of freedom.
 
         1:             4

I4MAT_U_SOLVE_TEST
  I4MAT_U_SOLVE solves an upper triangular system.
 
  Input matrix A:
 
  Col        1       2       3       4
  Row
 
    1:       1       2       4       7
    2:       0       3       5       8
    3:       0       0       6       9
    4:       0       0       0      10
 
  Right hand side b:
 
         1:            45
         2:            53
         3:            54
         4:            40
 
  Computed solution x:
 
         1:    1.0000000    
         2:    2.0000000    
         3:    3.0000000    
         4:    4.0000000    

  Norm of A*x-b =    0.00000    

I4VEC_BINARY_NEXT_TEST
  I4VEC_BINARY_NEXT generates the next binary vector.

           0           0           0
           0           0           1
           0           1           0
           0           1           1
           1           0           0
           1           0           1
           1           1           0
           1           1           1

I4VEC_IDENTITY_ROW_TEST
  I4VEC_IDENTITY_ROW returns a row of the identity matrix.

 0: 0 0 0 0 0
 1: 1 0 0 0 0
 2: 0 1 0 0 0
 3: 0 0 1 0 0
 4: 0 0 0 1 0
 5: 0 0 0 0 1
 6: 0 0 0 0 0

I4VEC_IS_BINARY_TEST
  I4VEC_IS_BINARY is TRUE if an I4VEC only contains
  0 or 1 entries.

 
  X:
           0           0           0
  X is binary.

 
  X:
           1           0           1
  X is binary.

 
  X:
           0           2           1
  X is NOT binary.

I4VEC_PRINT_TEST
  I4VEC_PRINT prints an I4VEC
 
  The I4VEC:
 
         1:            91
         2:            92
         3:            93
         4:            94

I4VEC_RED_TEST
  I4VEC_RED divides out any common factors in the
  entries of an I4VEC.
 
  Apply I4VEC_RED to each row of this matrix:
 
  Col        1       2       3
  Row
 
    1:      12      88       9
    2:       4       8     192
    3:     -12      88      94
    4:      30      18      42
    5:       0       4       8
 
  Reduced matrix:
 
  Col        1       2       3
  Row
 
    1:      12      88       9
    2:       1       2      48
    3:      -6      44      47
    4:       5       3       7
    5:       0       1       2

I4VEC_TRANSPOSE_PRINT_TEST
  I4VEC_TRANSPOSE_PRINT prints an I4VEC
  with 5 entries to a row, and an optional 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

  Call I4VEC_TRANSPOSE_PRINT with a short title:
 
  My array:
           1           2           3           4           5
           6           7           8           9          10
          11          12

KSUB_NEXT4_TEST
  KSUB_NEXT4 generates K subsets of an N set.
  N =        5
  K=         3

  Rank    Subset

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

R8VEC_IS_INTEGER_TEST
  R8VEC_IS_INTEGER is TRUE if an R8VEC only contains
  integer entries.

  Example 1: Obviously integer:


  X:     1.00000       2.00000       3.00000       4.00000       5.00000    
         6.00000    
  X is integer.

  Obviously NOT integer:


  X:     1.00000       2.00000       3.00000       4.00000       5.00000    
         6.50000    
  X is NOT integer.

  Example 3: Not Integer, Not obvious:


  X:     1.00000       2.00000       3.00000       4.00000       5.00000    
         6.00000    
  X is NOT integer.

  Example 4: Not Integer, Not obvious:


  X:     1.00000       2.00000      0.300000E+09   4.00000       5.00000    
         6.00000    
  X is NOT integer.

R8VEC_PRINT_TEST
  R8VEC_PRINT prints an R8VEC.
 
  The R8VEC:
 
         1:    123.45600    
         2:   0.50000000E-05
         3:   -1000000.0    
         4:    3.1415927    

R8VEC_TRANSPOSE_PRINT_TEST
  R8VEC_TRANSPOSE_PRINT prints an R8VEC "tranposed",
  that is, placing multiple entries on a line.
  The vector X:     1.10000       2.02000       30.3300       444.440     -0.500000E-02
                    6.66667      0.777778E+07   8.00000       99.0000       10.0000    
                    11.0000       12.0000    

ROW_ECHELON_INTEGER_TEST
  Normal end of execution.

14 September 2021  10:27:51.017 AM