Integer, Intent (In)	::	n, incx, incy
Real (Kind=nag_wp), Intent (In)	::	c
Complex (Kind=nag_wp), Intent (In)	::	s
Complex (Kind=nag_wp), Intent (Inout)	::	cx(), cy()

C Header Interface

#include <nag.h>

void	f06hmf_ (const Integer n, Complex cx[], const Integer incx, Complex cy[], const Integer incy, const double c, const Complex *s)

The routine may be called by the names f06hmf, nagf_blas_zrot or its LAPACK name zrot.

3 Description

f06hmf applies a plane rotation, where the cosine is real and the sine is complex, to two

n

-element complex vectors

x

and

y

(\begin{array}{r} x^{T} \\ y^{T} \end{array}) \leftarrow (\begin{array}{r} c & s \\ - \bar{s} & c \end{array}) (\begin{array}{r} x^{T} \\ y^{T} \end{array}) .

4 References

None.

5 Arguments

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

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

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

Intermediate elements of cx are not referenced.

On exit: the transformed vector $x$ stored in the array elements used to supply the original vector $x$ .
Intermediate elements of cx are unchanged.
3: $incx$ – Integer Input: On entry: the increment in the subscripts of cx between successive elements of $x$ .
4: $cy (*)$ – Complex (Kind=nag_wp) array Input/Output: Note: the dimension of the array cy must be at least $\max (1, 1 + (n - 1) \times | incy |)$ .

On entry: the $n$ -element vector $y$ .
If $incy > 0$ , $y_{i}$ must be stored in $cy (1 + (i - 1) \times incy)$ , for $i = 1, 2, \dots, n$ .

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

Intermediate elements of cy are not referenced.

On exit: the transformed vector $y$ .
Intermediate elements of cy are unchanged.
5: $incy$ – Integer Input: On entry: the increment in the subscripts of cy between successive elements of $y$ .
6: $c$ – Real (Kind=nag_wp) Input: On entry: the value $c$ , the cosine of the rotation.
7: $s$ – Complex (Kind=nag_wp) Input: On entry: the value $s$ , the sine of the rotation.