gauss_jordan←{⎕IO ⎕ML←0 1               ⍝ Gauss-Jordan elimination.

    elim←{                              ⍝ elimination of row/col ⍺
        p←⍺+{⍵⍳⌈/⍵}|⍺↓⍵[;⍺]             ⍝ index of pivot row
        swap←⊖@⍺ p⊢⍵                    ⍝ ⍺th and pth rows exchanged
        mat←swap[⍺;⍺]÷⍨@⍺⊢swap          ⍝ col diagonal reduced to 1
        mat-(mat[;⍺]×⍺≠⍳≢⍵)∘.×mat[⍺;]   ⍝ col off-diagonals reduced to 0
    }

    0::⎕SIGNAL ⎕EN                      ⍝ pass back error to caller

    ⍺←=/↑⍳⍴⍵                            ⍝ id matrix for monadic case

    (⍴⍺)⍴(0 1×⍴⍵)↓↑elim/(⌽⍳⌊/⍴⍵),⊂⍵,⍺   ⍝ elimination/ ··· 2 1 0 (⍵,⍺)
}

code_colours

test script

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