15 December 2024 06:20:00 PM

rref2_test():
  C version
  Test rref(), which analyzes matrices using the
  reduced row echelon form (RREF)

is_rref_test():
  is_rref() reports if a matrix is in reduced row echelon format.

  Matrix A0:

  Col:          0             1             2             3             4     
  Row

    0:               1               0               0               9               4
    1:               0               0               1               0               8
    2:               0               0               0               0               0
    3:               0               0               0               1               0
  is_rref(A0) = 0

  Matrix A1:

  Col:          0             1             2             3             4     
  Row

    0:               1               0               0               9               4
    1:               0               0               0               1               0
    2:               0               0               1               0               8
    3:               0               0               0               1               0
  is_rref(A1) = 0

  Matrix A2:

  Col:          0             1             2             3             4     
  Row

    0:               1               0               0               9               4
    1:               0               1               0               2               8
    2:               0               0               3               0               0
    3:               0               0               0               0               0
  is_rref(A2) = 0

  Matrix A3:

  Col:          0             1             2             3             4     
  Row

    0:               1               0               3               9               4
    1:               0               1               0               2               8
    2:               0               0               1               0               0
    3:               0               0               0               0               0
  is_rref(A3) = 0

  Matrix A4:

  Col:          0             1             2             3             4     
  Row

    0:               1               0               3               0               4
    1:               0               1               2               0               8
    2:               0               0               0               1               0
    3:               0               0               0               0               0
  is_rref(A4) = 1

rref_compute_test():
  rref_compute() is a user-written code to compute the
  reduced row echelon form (RREF) of a matrix.

  Matrix A:

  Col:          0             1             2             3             4     
  Row

    0:               1               3               0               2               6
    1:              -2              -6               0              -2              -8
    2:               3               9               0               0               6
    3:              -1              -3               0               1               0

  Col:          5             6     
  Row

    0:               3               1
    1:               3               1
    2:               6               2
    3:               9               3

  rref_compute(A):

  Col:          0             1             2             3             4     
  Row

    0:               1               3               0               0               2
    1:               0               0               0               1               2
    2:               0               0               0               0               0
    3:               0               0               0               0               0

  Col:          5             6     
  Row

    0:               0               0
    1:               0     2.77556e-17
    2:               1        0.333333
    3:               0               0

  Column indices

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

rref_columns_test():
  rref_columns() uses the reduced row echelon form (RREF)
  of a matrix to find the linearly independent columns.

  Matrix A:

  Col:          0             1             2             3     
  Row

    0:               1               2               3               1
    1:               2               4               9               3
    2:               3               6               0               0
    3:               4               8               0               2
    4:               5              10               6               6
    5:               6              12               6               3
    6:               7              14               2               1

  Number of independent columns is 3

  Independent column indices

       0:        0
       1:        2
       2:        3

  Independent columns:

  Col:          0             1             2     
  Row

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

rref_determinant_test():
  rref_determinant() uses the reduced row echelon form 
  of a square matrix to compute the determinant.

  matrix A:

  Col:          0             1             2             3     
  Row

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

  Estimated determinant of A = 1

rref_inverse_test():
  rref_inverse() uses the reduced row echelon form
  of a square matrix to compute its inverse.

  matrix A:

  Col:          0             1             2             3     
  Row

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

  Estimated inverse A_inv:

  Col:          0             1             2             3     
  Row

    0:              68             -41             -17              10
    1:             -41              25              10              -6
    2:             -17              10               5              -3
    3:              10              -6              -3               2

  Product A_inv * A:

  Col:          0             1             2             3     
  Row

    0:               1     5.68434e-14    -2.84217e-14     5.68434e-14
    1:               0               1     7.10543e-15               0
    2:    -7.10543e-15    -3.19744e-14               1    -7.10543e-15
    3:     5.32907e-15     1.95399e-14     7.10543e-15               1

rref_rank_test():
  rref_rank() uses the reduced row echelon form
  of a matrix to estimate its rank.

  matrix A:

  Col:          0             1             2             3             4     
  Row

    0:               1               3               0               2               6
    1:              -2              -6               0              -2              -8
    2:               3               9               0               0               6
    3:              -1              -3               0               1               0

  Col:          5             6     
  Row

    0:               3               1
    1:               3               1
    2:               6               2
    3:               9               3

  A has rank 3

rref_solve_test():
  rref_solve() uses the reduced row echelon form
  of a square matrix to solve a linear system.

  matrix A:

  Col:          0             1             2             3     
  Row

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

  Right hand side b:

  Col:          0     
  Row

    0:              57
    1:              79
    2:              88
    3:              86

  Estimated solution:

  Col:          0     
  Row

    0:               1
    1:               2
    2:               3
    3:               4

  Product A * x:

  Col:          0     
  Row

    0:              57
    1:              79
    2:              88
    3:              86

rref2_test():
  Normal end of execution.

15 December 2024 06:20:00 PM