15 December 2024 06:52:23 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_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_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_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 06:52:23 PM