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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: generates a vector of complex plane rotations with real cosines, determined by elements of the complex vectors x and y

```NAME
LAPACK-3  -  generates  a  vector  of complex plane rotations with real
cosines, determined by elements of the complex vectors x and y

SYNOPSIS
SUBROUTINE ZLARGV( N, X, INCX, Y, INCY, C, INCC )

INTEGER        INCC, INCX, INCY, N

DOUBLE         PRECISION C( * )

COMPLEX*16     X( * ), Y( * )

PURPOSE
ZLARGV generates a vector of complex plane rotations with real cosines,
determined by elements of the complex vectors x and y.
For i = 1,2,...,n
(        c(i)   s(i) ) ( x(i) ) = ( r(i) )
( -conjg(s(i))  c(i) ) ( y(i) ) = (   0  )
where c(i)**2 + ABS(s(i))**2 = 1
The following conventions are used (these are the same as in ZLARTG,
but differ from the BLAS1 routine ZROTG):
If y(i)=0, then c(i)=1 and s(i)=0.
If x(i)=0, then c(i)=0 and s(i) is chosen so that r(i) is real.

ARGUMENTS
N       (input) INTEGER
The number of plane rotations to be generated.

X       (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCX)
On entry, the vector x.
On exit, x(i) is overwritten by r(i), for i = 1,...,n.

INCX    (input) INTEGER
The increment between elements of X. INCX > 0.

Y       (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCY)
On entry, the vector y.
On exit, the sines of the plane rotations.

INCY    (input) INTEGER
The increment between elements of Y. INCY > 0.

C       (output) DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
The cosines of the plane rotations.

INCC    (input) INTEGER
The increment between elements of C. INCC > 0.

FURTHER DETAILS
6-6-96 - Modified with a new algorithm by W. Kahan and J. Demmel
This version has a few statements commented out for thread safety
(machine parameters are computed on each entry). 10 feb 03, SJH.

LAPACK auxiliary routine (versionMarch 2011                       LAPACK-3(3)
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