f06fjf is designed for use in the safe computation of the Euclidean norm of a real vector, without unnecessary overflow or destructive underflow. An initial call to f06fjf (with

ξ = 1

and

α = 0

) may be followed by further calls to f06fjf and finally a call to f06bmf to complete the computation. Multiple calls of f06fjf may be needed if the elements of the vector cannot all be accessed in a single array x.

4 References

None.

5 Arguments

1: $n$ – Integer Input: On entry: $n$ , the number of elements in $x$ .
2: $x (*)$ – Real (Kind=nag_wp) array Input: Note: the dimension of the array x must be at least $\max (1, 1 + (n - 1) \times incx)$ .

On entry: the $n$ -element vector $x$ . $x_{i}$ must be stored in $x (1 + (i - 1) \times incx)$ , for $i = 1, 2, \dots, n$ .
Intermediate elements of x are not referenced.
3: $incx$ – Integer Input: On entry: the increment in the subscripts of x between successive elements of $x$ .

Constraint: $incx > 0$ .
4: $scal$ – Real (Kind=nag_wp) Input/Output: On entry: the scaling factor $α$ . On the first call to f06fjf $scal = 0.0$ .

Constraint: $scal \geq 0.0$ .

On exit: the updated scaling factor $\tilde{α} = \max_{i} (α, | x_{i} |)$ .
5: $sumsq$ – Real (Kind=nag_wp) Input/Output: On entry: the scaled sum of squares $ξ$ . On the first call to f06fjf $sumsq = 1.0$ .

Constraint: $sumsq \geq 1.0$ .

On exit: the updated scaled sum of squares $\tilde{ξ}$ , satisfying: $1 \leq \tilde{ξ} \leq ξ + n$ .