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

On entry: the vector $z$ , as returned by f06fsf.
If $incz > 0$ , $z_{i}$ must be stored in $z (1 + (i - 1) \times incz)$ , for $i = 1, 2, \dots, n$ .

If $incz < 0$ , $z_{i}$ must be stored in $z (1 - (n - i) \times incz)$ , for $i = 1, 2, \dots, n$ .
3: $incz$ – Integer Input: On entry: the increment in the subscripts of z between successive elements of $z$ .
4: $z1$ – Real (Kind=nag_wp) Input: On entry: the scalar $ζ$ , as returned by f06fsf.
If $ζ = 0$ , $P$ is assumed to be the unit matrix and the transformation is skipped.
5: $alpha$ – Real (Kind=nag_wp) Input/Output: On entry: the original scalar $α$ .

On exit: the transformed scalar $α$ .
6: $x (*)$ – Real (Kind=nag_wp) array Input/Output: Note: the dimension of the array x must be at least $\max (1, 1 + (n - 1) \times |incx|)$ .

On entry: the original vector $x$ .
If $incx > 0$ , $x_{i}$ must be stored in $x (1 + (i - 1) \times incx)$ , for $i = 1, 2, \dots, n$ .

If $incx < 0$ , $x_{i}$ must be stored in $x (1 - (n - i) \times incx)$ , for $i = 1, 2, \dots, n$ .

On exit: the transformed vector $x$ stored in the same array elements used to supply the original vector $x$ .
7: $incx$ – Integer Input: On entry: the increment in the subscripts of x between successive elements of $x$ .

6 Error Indicators and Warnings

None.

7 Accuracy

Not applicable.

8 Parallelism and Performance

f06fuf makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.

Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.