PHPOffice / PhpSpreadsheet

                $this->ort[$m] -= $g;

                // Apply Householder similarity transformation

                // H = (I -u * u' / h) * H * (I -u * u') / h)

                for ($j = $m; $j < $this->n; ++$j) {

                    $f = 0.0;

                    for ($i = $high; $i >= $m; --$i) {

                        $f += $this->ort[$i] * $this->H[$i][$j];

                    }

                    $f /= $h;

                    for ($i = $m; $i <= $high; ++$i) {

                        $this->H[$i][$j] -= $f * $this->ort[$i];

                    }

                }

                for ($i = 0; $i <= $high; ++$i) {

                    $f = 0.0;

                    for ($j = $high; $j >= $m; --$j) {

                        $this->H[$i][$j] -= $f * $this->ort[$i];

                    }

                }

                for ($i = 0; $i <= $high; ++$i) {

                    $f = 0.0;

                    for ($j = $high; $j >= $m; --$j) {

                        $f += $this->ort[$j] * $this->H[$i][$j];

                    }

                    $f = $f / $h;

                    for ($j = $m; $j <= $high; ++$j) {

                        $this->H[$i][$j] -= $f * $this->ort[$j];

                    }

                }

                $this->ort[$m] = $scale * $this->ort[$m];

                $this->H[$m][$m - 1] = $scale * $g;

            }