NAG Library Routine Document

f06hmf (zrot)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of elements in $x$ and $y$.

2:     $\mathbf{cx}\left(*\right)$ – Complex (Kind=nag_wp) arrayInput/Output

Note: the dimension of the array cx must be at least $\max \left(1,1+\left(\mathbf{n}-1\right)\times \left|\mathbf{incx}\right|\right)$.

On entry: the $n$-element vector $x$.

If $\mathbf{incx}>0$, $x_{\mathit{i}}$ must be stored in $\mathbf{cx}\left(1+\left(\mathit{i}-1\right)\times \mathbf{incx}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$.

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

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:     $\mathbf{incx}$ – IntegerInput

On entry: the increment in the subscripts of cx between successive elements of $x$.

4:     $\mathbf{cy}\left(*\right)$ – Complex (Kind=nag_wp) arrayInput/Output

Note: the dimension of the array cy must be at least $\max \left(1,1+\left(\mathbf{n}-1\right)\times \left|\mathbf{incy}\right|\right)$.

On entry: the $n$-element vector $y$.

If $\mathbf{incy}>0$, $y_{\mathit{i}}$ must be stored in $\mathbf{cy}\left(1+\left(\mathit{i}-1\right)\times \mathbf{incy}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$.

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

Intermediate elements of cy are not referenced.

On exit: the transformed vector $y$.

Intermediate elements of cy are unchanged.

5:     $\mathbf{incy}$ – IntegerInput

On entry: the increment in the subscripts of cy between successive elements of $y$.

6:     $\mathbf{c}$ – Real (Kind=nag_wp)Input

On entry: the value $c$, the cosine of the rotation.

7:     $\mathbf{s}$ – Complex (Kind=nag_wp)Input

On entry: the value $s$, the sine of the rotation.

6

Error Indicators and Warnings

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example