 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ zlar2v()

 subroutine zlar2v ( integer N, complex*16, dimension( * ) X, complex*16, dimension( * ) Y, complex*16, dimension( * ) Z, integer INCX, double precision, dimension( * ) C, complex*16, dimension( * ) S, integer INCC )

ZLAR2V applies a vector of plane rotations with real cosines and complex sines from both sides to a sequence of 2-by-2 symmetric/Hermitian matrices.

Purpose:
``` ZLAR2V applies a vector of complex plane rotations with real cosines
from both sides to a sequence of 2-by-2 complex Hermitian matrices,
defined by the elements of the vectors x, y and z. For i = 1,2,...,n

(       x(i)  z(i) ) :=
( conjg(z(i)) y(i) )

(  c(i) conjg(s(i)) ) (       x(i)  z(i) ) ( c(i) -conjg(s(i)) )
( -s(i)       c(i)  ) ( conjg(z(i)) y(i) ) ( s(i)        c(i)  )```
Parameters
 [in] N ``` N is INTEGER The number of plane rotations to be applied.``` [in,out] X ``` X is COMPLEX*16 array, dimension (1+(N-1)*INCX) The vector x; the elements of x are assumed to be real.``` [in,out] Y ``` Y is COMPLEX*16 array, dimension (1+(N-1)*INCX) The vector y; the elements of y are assumed to be real.``` [in,out] Z ``` Z is COMPLEX*16 array, dimension (1+(N-1)*INCX) The vector z.``` [in] INCX ``` INCX is INTEGER The increment between elements of X, Y and Z. INCX > 0.``` [in] C ``` C is DOUBLE PRECISION array, dimension (1+(N-1)*INCC) The cosines of the plane rotations.``` [in] S ``` S is COMPLEX*16 array, dimension (1+(N-1)*INCC) The sines of the plane rotations.``` [in] INCC ``` INCC is INTEGER The increment between elements of C and S. INCC > 0.```

Definition at line 110 of file zlar2v.f.

111 *
112 * -- LAPACK auxiliary routine --
113 * -- LAPACK is a software package provided by Univ. of Tennessee, --
114 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
115 *
116 * .. Scalar Arguments ..
117  INTEGER INCC, INCX, N
118 * ..
119 * .. Array Arguments ..
120  DOUBLE PRECISION C( * )
121  COMPLEX*16 S( * ), X( * ), Y( * ), Z( * )
122 * ..
123 *
124 * =====================================================================
125 *
126 * .. Local Scalars ..
127  INTEGER I, IC, IX
128  DOUBLE PRECISION CI, SII, SIR, T1I, T1R, T5, T6, XI, YI, ZII,
129  \$ ZIR
130  COMPLEX*16 SI, T2, T3, T4, ZI
131 * ..
132 * .. Intrinsic Functions ..
133  INTRINSIC dble, dcmplx, dconjg, dimag
134 * ..
135 * .. Executable Statements ..
136 *
137  ix = 1
138  ic = 1
139  DO 10 i = 1, n
140  xi = dble( x( ix ) )
141  yi = dble( y( ix ) )
142  zi = z( ix )
143  zir = dble( zi )
144  zii = dimag( zi )
145  ci = c( ic )
146  si = s( ic )
147  sir = dble( si )
148  sii = dimag( si )
149  t1r = sir*zir - sii*zii
150  t1i = sir*zii + sii*zir
151  t2 = ci*zi
152  t3 = t2 - dconjg( si )*xi
153  t4 = dconjg( t2 ) + si*yi
154  t5 = ci*xi + t1r
155  t6 = ci*yi - t1r
156  x( ix ) = ci*t5 + ( sir*dble( t4 )+sii*dimag( t4 ) )
157  y( ix ) = ci*t6 - ( sir*dble( t3 )-sii*dimag( t3 ) )
158  z( ix ) = ci*t3 + dconjg( si )*dcmplx( t6, t1i )
159  ix = ix + incx
160  ic = ic + incc
161  10 CONTINUE
162  RETURN
163 *
164 * End of ZLAR2V
165 *
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