Gauss-Jordan matrix inversion

Uses the rref(A) function from Reduced row echelon form.

func gauss_jordan_invert (M) {

    var I = M.len.of {|i|
        M.len.of {|j|
            i == j ? 1 : 0
        }
    }

    var A = gather {
        ^M -> each {|i| take(M[i] + I[i]) }
    }

    rref(A).map { .last(M.len) }
}

var A = [
    [-1, -2, 3, 2],
    [-4, -1, 6, 2],
    [ 7, -8, 9, 1],
    [ 1, -2, 1, 3],
]

say gauss_jordan_invert(A).map {
    .map { "%6s" % .as_rat }.join("  ")
}.join("\n")

Output:

-21/23   17/69  13/138   19/46
-38/23   15/23    1/23   15/23
-16/23   25/69  11/138    9/46
-13/23   16/69   -2/69   13/23

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