Reduced row echelon form

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}"
    for row in array {
        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 ''
}

Output:

Original Matrix
     1     2    -1    -4
     2     3    -1   -11
    -2     0    -3    22

Reduced Row Echelon Form Matrix
     1     0     0    -8
     0     1     0     1
     0     0     1    -2


Original Matrix
     3     0    -3     1
   1/2   3/2    -3    -2
   1/5   4/5  -8/5  3/10

Reduced Row Echelon Form Matrix
     1     0     0 -41/2
     0     1     0 -217/6
     0     0     1 -125/6


Original Matrix
     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

Reduced Row Echelon Form Matrix
     1     2     0     0     3     4
     0     0     1     0     0    -1
     0     0     0     1     0     0
     0     0     0     0     0     0
     0     0     0     0     0     0