MathPHP\LinearAlgebra\Matrix::rref PHP Method

    public function rref() : Matrix
    {
        if (isset($this->rref)) {
            return $this->rref;
        }
        $m = $this->m;
        $n = $this->n;
        $R = MatrixFactory::create($this->A);
        $swaps = 0;
        $∏scaling_factor = 1;
        $lead = 0;
        for ($r = 0; $r < $m; $r++) {
            if ($lead >= $n) {
                break;
            }
            $i = $r;
            while ($R[$i][$lead] == 0) {
                $i++;
                if ($i == $m) {
                    $i = $r;
                    $lead++;
                    if ($lead == $n) {
                        break 2;
                        // done; break out of outer loop and return.
                    }
                }
            }
            // Swap rows i and r
            if ($i !== $r) {
                $R = $R->rowInterchange($i, $r);
                $swaps++;
            }
            // Divide row $r by R[r][lead]
            $lv = $R[$r][$lead];
            $R = $R->rowDivide($r, $lv);
            if ($lv != 0) {
                $∏scaling_factor *= 1 / $lv;
            }
            // Subtract row r * R[r][lead] from row i
            for ($i = 0; $i < $m; $i++) {
                if ($i != $r) {
                    $R = $R->rowSubtract($r, $i, $R[$i][$lead]);
                }
            }
            $lead++;
        }
        $this->rref = $R;
        $this->rref_swaps = $swaps;
        $this->rref_∏scaling_factor = $∏scaling_factor;
        return $R;
    }