08-Jan-2022 09:19:15

row_echelon_integer_test():
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  Test row_echelon_integer()

I4MAT_IS_INTEGER_TEST
  I4MAT_IS_INTEGER is TRUE if every entry of an I4MAT
  is an integer.

  Example 1: Obviously integer:


a =

     1     2     3
     4     5     6

  A is an integer matrix.

  Example 2: Obviously NOT integer:


a =

    1.0000    2.0000    3.0000
    4.0000    5.0000    6.5000

  A is NOT an integer matrix.

  Example 3: Not Integer, Not obvious:


a =

    1.0000    2.0000    3.0000
    4.0000    5.0000    6.0000

  A is NOT an integer matrix.

  Example 4: Not Integer, Not obvious:


a =

   1.0e+08 *

    0.0000    0.0000    3.0000
    0.0000    0.0000    0.0000

  A is NOT an integer matrix.

I4MAT_PRINT_TEST
  I4MAT_PRINT prints an I4MAT.

  The I4MAT:

  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  

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 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 reduced row echelon form 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

  IRREF form:

  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_SOLVE_BINARY_TEST:
  I4MAT_RREF_SOLVE_BINARY seeks binary solutions of
  an Integer Row-Reduced Echelon Form (IRREF) system A*x=b
  when A and b contain integer values.

  The IRREF matrix A:

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

    1:       1        0        0        0        0        0        1        0       -1        0  
    2:       0        1        0        0        0        0        0        0        1        0  
    3:       0        0        1        0        0        0        1        0       -1        0  
    4:       0        0        0        1        0        0        0        0        1        1  
    5:       0        0        0        0        1        0        0        0        0        1  
    6:       0        0        0        0        0        1       -1        0        1        0  
    7:       0        0        0        0        0        0        0        1        0       -1  
    8:       0        0        0        0        0        0        0        0        0        0  
    9:       0        0        0        0        0        0        0        0        0        0  

  The right hand side b:

     1:      0
     2:      1
     3:      0
     4:      1
     5:      1
     6:      1
     7:      0
     8:      0
     9:      0

  Binary solution vectors x:

  Col:       1        2        3        4  
  Row

    1:       0        0        1        0  
    2:       1        1        0        0  
    3:       0        0        1        0  
    4:       1        0        0        0  
    5:       1        0        1        1  
    6:       1        1        0        1  
    7:       0        0        0        1  
    8:       0        1        0        0  
    9:       0        0        1        1  
   10:       0        1        0        0  

I4MAT_RREF_SOLVE_BINARY_NZ_TEST():
  I4MAT_RREF_SOLVE_BINARY_NZ seeks binary solutions of
  an Integer Row-Reduced Echelon Form (IRREF) system A*x=b
  which have exactly NZ nonzeros.

  The IRREF matrix A:

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

    1:       1        0        0        0        0        0        1        0       -1        0  
    2:       0        1        0        0        0        0        0        0        1        0  
    3:       0        0        1        0        0        0        1        0       -1        0  
    4:       0        0        0        1        0        0        0        0        1        1  
    5:       0        0        0        0        1        0        0        0        0        1  
    6:       0        0        0        0        0        1       -1        0        1        0  
    7:       0        0        0        0        0        0        0        1        0       -1  
    8:       0        0        0        0        0        0        0        0        0        0  
    9:       0        0        0        0        0        0        0        0        0        0  

  The right hand side b:

     1:      0
     2:      1
     3:      0
     4:      1
     5:      1
     6:      1
     7:      0
     8:      0
     9:      0

  Only consider binary solutions with exactly 4 nonzeros.

  Binary solution vectors x:

  Col:       1        2        3        4  
  Row

    1:       0        1        0        0  
    2:       1        0        1        0  
    3:       0        1        0        0  
    4:       1        0        0        0  
    5:       1        1        0        1  
    6:       1        0        1        1  
    7:       0        0        0        1  
    8:       0        0        1        0  
    9:       0        1        0        1  
   10:       0        0        1        0  

I4MAT_RREF_SYSTEM_TEST
  MATLAB 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
  A*x=b, where A and b contain only integer values.

  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

  Integer solution x:

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

  Norm of A*x-b = 0

I4VEC_BINARY_NEXT_TEST
  I4VEC_BINARY_NEXT generates the next binary vector.

  000
  001
  010
  011
  100
  101
  110
  111

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 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

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 every entry of an R8VEC
  is an integer.

  Example 1: Obviously integer:


a =

     1     2     3     4     5     6

  A is an integer vector.

  Example 2: Obviously NOT integer:


a =

    1.0000    2.0000    3.0000    4.0000    5.0000    6.5000

  A is NOT an integer vector.

  Example 3: Not Integer, Not obvious:


a =

    1.0000    2.0000    3.0000    4.0000    5.0000    6.0000

  A is NOT an integer vector.

  Example 4: Not Integer, Not obvious:


a =

   1.0e+08 *

    0.0000    0.0000    3.0000    0.0000    0.0000    0.0000

  A is NOT an integer vector.

R8VEC_PRINT_TEST
  R8VEC_PRINT prints an R8VEC.

  The R8VEC:

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

R8VEC_TRANSPOSE_PRINT_TEST
  R8VEC_TRANSPOSE_PRINT prints an R8VEC "tranposed",
  that is, placing multiple entries on a line.
  The vector X:               1           2.2          -3.3          4.45         5.678
                            600        0.0078         8.123          9.45         10.03
                           11.1         12.99

row_echelon_integer_test():
  Normal end of execution.

08-Jan-2022 09:19:16