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## 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

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## NAME

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

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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