# NAG Library Routine Document

## 1Purpose

f06bhf applies a real similarity rotation to a $2$ by $2$ real symmetric matrix.

## 2Specification

Fortran Interface
 Subroutine f06bhf ( x, y, z, c, s)
 Real (Kind=nag_wp), Intent (In) :: c, s Real (Kind=nag_wp), Intent (Inout) :: x, y, z
#include nagmk26.h
 void f06bhf_ (double *x, double *y, double *z, const double *c, const double *s)

## 3Description

f06bhf applies a real similarity rotation, with parameters $c$ and $s$, to a given $2$ by $2$ real symmetric matrix; that is, it performs the operation:
 $x y y z ← c s -s c x y y z c -s s c .$
None.

## 5Arguments

1:     $\mathbf{x}$ – Real (Kind=nag_wp)Input/Output
On entry: the value $x$, the $\left(1,1\right)$ element of the input matrix.
On exit: the transformed value $x$.
2:     $\mathbf{y}$ – Real (Kind=nag_wp)Input/Output
On entry: the value $y$, the $\left(1,2\right)$ or $\left(2,1\right)$ element of the input matrix.
On exit: the transformed value $y$.
3:     $\mathbf{z}$ – Real (Kind=nag_wp)Input/Output
On entry: the value $z$, the $\left(2,2\right)$ element of the input matrix.
On exit: the transformed value $z$.
4:     $\mathbf{c}$ – Real (Kind=nag_wp)Input
On entry: the value $c$, the cosine of the rotation.
5:     $\mathbf{s}$ – Real (Kind=nag_wp)Input
On entry: the value $s$, the sine of the rotation.

None.

Not applicable.

## 8Parallelism and Performance

f06bhf is not threaded in any implementation.