 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ 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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