F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF06BEF

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

F06BEF generates a real Jacobi plane rotation.

## 2  Specification

 SUBROUTINE F06BEF ( JOB, X, Y, Z, C, S)
 REAL (KIND=nag_wp) X, Y, Z, C, S CHARACTER(1) JOB

## 3  Description

F06BEF generates a real Jacobi plane rotation with parameters $c$ and $s$, which diagonalizes a given $2$ by $2$ real symmetric matrix:
 $c s -s c x y y z c -s s c = a 0 0 b .$
None.

## 5  Parameters

1:     JOB – CHARACTER(1)Input
On entry: specifies the property which determines the precise form of the rotation.
${\mathbf{JOB}}=\text{'B'}$
$c\ge 1/\sqrt{2}$.
${\mathbf{JOB}}=\text{'S'}$
$0\le c\le 1/\sqrt{2}$.
${\mathbf{JOB}}=\text{'M'}$
$\left|a\right|\ge \left|b\right|$.
Constraint: ${\mathbf{JOB}}=\text{'B'}$, $\text{'S'}$ or $\text{'M'}$.
2:     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 value $a$.
3:     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 value $t$, the tangent of the rotation.
4:     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 value $b$.
5:     C – REAL (KIND=nag_wp)Output
On exit: the value $c$, the cosine of the rotation.
6:     S – REAL (KIND=nag_wp)Output
On exit: the value $s$, the sine of the rotation.

None.

Not applicable.