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# clar2v

```
NAME
CLAR2V - apply a vector of complex plane rotations with real
cosines from both sides to a sequence of 2-by-2 complex Her-
mitian matrices,

SYNOPSIS
SUBROUTINE CLAR2V( N, X, Y, Z, INCX, C, S, INCC )

INTEGER        INCC, INCX, N

REAL           C( * )

COMPLEX        S( * ), X( * ), Y( * ), Z( * )

PURPOSE
CLAR2V applies a vector of complex plane rotations with real
cosines from both sides to a sequence of 2-by-2 complex Her-
mitian 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)  )

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

X       (input/output) COMPLEX array, dimension (1+(N-
1)*INCX)
The vector x; the elements of x are assumed to be
real.

Y       (input/output) COMPLEX array, dimension (1+(N-
1)*INCX)
The vector y; the elements of y are assumed to be
real.

Z       (input/output) COMPLEX array, dimension (1+(N-
1)*INCX)
The vector z.

INCX    (input) INTEGER
The increment between elements of X, Y and Z. INCX >
0.

C       (input) REAL array, dimension (1+(N-1)*INCC)

The cosines of the plane rotations.

S       (input) COMPLEX array, dimension (1+(N-1)*INCC)
The sines of the plane rotations.

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