 LAPACK  3.9.0 LAPACK: Linear Algebra PACKage

## ◆ clar2v()

 subroutine clar2v ( integer N, complex, dimension( * ) X, complex, dimension( * ) Y, complex, dimension( * ) Z, integer INCX, real, dimension( * ) C, complex, dimension( * ) S, integer INCC )

CLAR2V 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:
``` CLAR2V 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 array, dimension (1+(N-1)*INCX) The vector x; the elements of x are assumed to be real.``` [in,out] Y ``` Y is COMPLEX array, dimension (1+(N-1)*INCX) The vector y; the elements of y are assumed to be real.``` [in,out] Z ``` Z is COMPLEX 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 REAL array, dimension (1+(N-1)*INCC) The cosines of the plane rotations.``` [in] S ``` S is COMPLEX 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.```
Date
December 2016

Definition at line 113 of file clar2v.f.

113 *
114 * -- LAPACK auxiliary routine (version 3.7.0) --
115 * -- LAPACK is a software package provided by Univ. of Tennessee, --
116 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
117 * December 2016
118 *
119 * .. Scalar Arguments ..
120  INTEGER INCC, INCX, N
121 * ..
122 * .. Array Arguments ..
123  REAL C( * )
124  COMPLEX S( * ), X( * ), Y( * ), Z( * )
125 * ..
126 *
127 * =====================================================================
128 *
129 * .. Local Scalars ..
130  INTEGER I, IC, IX
131  REAL CI, SII, SIR, T1I, T1R, T5, T6, XI, YI, ZII,
132  \$ ZIR
133  COMPLEX SI, T2, T3, T4, ZI
134 * ..
135 * .. Intrinsic Functions ..
136  INTRINSIC aimag, cmplx, conjg, real
137 * ..
138 * .. Executable Statements ..
139 *
140  ix = 1
141  ic = 1
142  DO 10 i = 1, n
143  xi = real( x( ix ) )
144  yi = real( y( ix ) )
145  zi = z( ix )
146  zir = real( zi )
147  zii = aimag( zi )
148  ci = c( ic )
149  si = s( ic )
150  sir = real( si )
151  sii = aimag( si )
152  t1r = sir*zir - sii*zii
153  t1i = sir*zii + sii*zir
154  t2 = ci*zi
155  t3 = t2 - conjg( si )*xi
156  t4 = conjg( t2 ) + si*yi
157  t5 = ci*xi + t1r
158  t6 = ci*yi - t1r
159  x( ix ) = ci*t5 + ( sir*real( t4 )+sii*aimag( t4 ) )
160  y( ix ) = ci*t6 - ( sir*real( t3 )-sii*aimag( t3 ) )
161  z( ix ) = ci*t3 + conjg( si )*cmplx( t6, t1i )
162  ix = ix + incx
163  ic = ic + incc
164  10 CONTINUE
165  RETURN
166 *
167 * End of CLAR2V
168 *
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