How to resolve the algorithm Reduced row echelon form step by step in the Sidef programming language

Published on 12 May 2024 09:40 PM

How to resolve the algorithm Reduced row echelon form step by step in the Sidef programming language

Table of Contents

Problem Statement

Show how to compute the reduced row echelon form (a.k.a. row canonical form) of a matrix. The matrix can be stored in any datatype that is convenient (for most languages, this will probably be a two-dimensional array). Built-in functions or this pseudocode (from Wikipedia) may be used: For testing purposes, the RREF of this matrix: is:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Reduced row echelon form step by step in the Sidef programming language

Source code in the sidef programming language

func rref (M) {
    var (j, rows, cols) = (0, M.len, M[0].len)
 
    for r in (^rows) {
        j < cols || return M
 
        var i = r
        while (!M[i][j]) {
            ++i == rows || next
            i = r
            ++j == cols && return M
        }
 
        M[i, r] = M[r, i] if (r != i)
        M[r] = (M[r] »/» M[r][j])
 
        for n in (^rows) {
            next if (n == r)
            M[n] = (M[n] »-« (M[r] »*» M[n][j]))
        }
        ++j
    }
 
    return M
}

func say_it (message, array) {
    say "\n#{message}";
    array.each { |row|
        say row.map { |n| " %5s" % n.as_rat }.join
    }
}

var M = [
    [ # base test case
      [  1,  2,  -1,  -4 ],
      [  2,  3,  -1, -11 ],
      [ -2,  0,  -3,  22 ],
    ],
    [ # mix of number styles
      [  3,   0,  -3,    1 ],
      [ .5, 3/2,  -3,   -2 ],
      [ .2, 4/5,  -1.6, .3 ],
    ],
    [ # degenerate case
      [ 1,  2,  3,  4,  3,  1],
      [ 2,  4,  6,  2,  6,  2],
      [ 3,  6, 18,  9,  9, -6],
      [ 4,  8, 12, 10, 12,  4],
      [ 5, 10, 24, 11, 15, -4],
    ],
];

M.each { |matrix|
    say_it('Original Matrix', matrix);
    say_it('Reduced Row Echelon Form Matrix', rref(matrix));
    say '';
}


  

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