F06HMF (ZROT) (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F06HMF (ZROT)

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

 Contents

    1  Purpose
    7  Accuracy
    10  Example

1  Purpose

F06HMF (ZROT) applies a plane rotation with a real cosine and complex sine to two complex vectors.

2  Specification

SUBROUTINE F06HMF ( N, CX, INCX, CY, INCY, C, S)
INTEGER  N, INCX, INCY
REAL (KIND=nag_wp)  C
COMPLEX (KIND=nag_wp)  CX(*), CY(*), S
The routine may be called by its LAPACK name zrot.

3  Description

F06HMF (ZROT) applies a plane rotation, where the cosine is real and the sine is complex, to two n-element complex vectors x and y:
xT yT c s -s- c xT yT .  

4  References

None.

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 max1, 1+N-1 ×INCX .
On entry: the n-element vector x.
If INCX>0, xi must be stored in CX1+i-1×INCX, for i=1,2,,N.
If INCX<0, xi must be stored in CX1-N-i×INCX, for i=1,2,,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 max1, 1+N-1 ×INCY .
On entry: the n-element vector y.
If INCY>0, yi must be stored in CY1+i-1×INCY, for i=1,2,,N.
If INCY<0, yi must be stored in CY1-N-i×INCY, for i=1,2,,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

None.

7  Accuracy

Not applicable.

8  Parallelism and Performance

Not applicable.

9  Further Comments

None.

10  Example

None.

F06HMF (ZROT) (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2015