MathPHP\LinearAlgebra\Matrix::pivotize PHP Method

    protected function pivotize() : Matrix
    {
        $n = $this->n;
        $P = MatrixFactory::identity($n);
        $A = $this->A;
        // Set initial column max to diagonal element Aᵢᵢ
        for ($i = 0; $i < $n; $i++) {
            $max = $A[$i][$i];
            $row = $i;
            // Check for column element below Aᵢᵢ that is bigger
            for ($j = $i; $j < $n; $j++) {
                if ($A[$j][$i] > $max) {
                    $max = $A[$j][$i];
                    $row = $j;
                }
            }
            // Swap rows if a larger column element below Aᵢᵢ was found
            if ($i != $row) {
                $P = $P->rowInterchange($i, $row);
            }
        }
        return $P;
    }