NAG Library Routine Document

F06HMF (ZROT)

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     N – INTEGERInput

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

2:     CX($*$) – 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:     INCX – INTEGERInput

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

4:     CY($*$) – 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:     INCY – INTEGERInput

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.

6  Error Indicators and Warnings

7  Accuracy

8  Further Comments

9  Example