F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF06CHF

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

## 1  Purpose

F06CHF applies a complex similarity rotation having real cosine and complex sine to a $2$ by $2$ complex Hermitian matrix.

## 2  Specification

 SUBROUTINE F06CHF ( X, Y, Z, C, S)
 REAL (KIND=nag_wp) C COMPLEX (KIND=nag_wp) X, Y, Z, S

## 3  Description

F06CHF applies a complex similarity rotation, with parameters $c$ (real) and $s$ (complex), to a given $2$ by $2$ complex Hermitian matrix; that is, it performs the operation:
 $x y y- z ← c s- -s c x y y- z c -s- s c ,$
where $x$ and $z$ are real.
The parameter X and Z which hold $x$ and $z$ are declared complex for convenience when using the routine to operate on submatrices of larger Hermitian matrices.
Note that:
 $z y- y x ← c w- -w c z y- y x c -w- w c ,$
where $w=-\stackrel{-}{s}$, so to use F06CHF when $y$ is the $\left(2,1\right)$ element of the matrix, you can make the call
```CALL F06CHF(Z, Y, X, C, -CONJG(S))
```

None.

## 5  Parameters

1:     X – COMPLEX (KIND=nag_wp)Input/Output
On entry: the value $x$, the $\left(1,1\right)$ element of the input matrix. The imaginary part of X need not be set; it is assumed to be zero.
On exit: the transformed value $x$. The imaginary part of X is set to zero.
2:     Y – COMPLEX (KIND=nag_wp)Input/Output
On entry: the value $y$, the $\left(1,2\right)$ element of the input matrix.
On exit: the transformed value $y$.
3:     Z – COMPLEX (KIND=nag_wp)Input/Output
On entry: the value $z$, the $\left(2,2\right)$ element of the input matrix. The imaginary part of Z need not be set; it is assumed to be zero.
On exit: the transformed value $z$. The imaginary part of Z is set to zero.
4:     C – REAL (KIND=nag_wp)Input
On entry: the value $c$, the cosine of the rotation.
5:     S – COMPLEX (KIND=nag_wp)Input
On entry: the value $s$, the sine of the rotation.

None.

Not applicable.