# NAG Library Routine Document

## 1Purpose

f06bpf returns an eigenvalue of a $2$ by $2$ real symmetric matrix.

## 2Specification

Fortran Interface
 Function f06bpf ( a, b, c)
 Real (Kind=nag_wp) :: f06bpf Real (Kind=nag_wp), Intent (In) :: a, b, c
#include nagmk26.h
 double f06bpf_ (const double *a, const double *b, const double *c)

## 3Description

f06bpf returns an eigenvalue of the $2$ by $2$ real symmetric matrix
 $a b b c ,$
via the function name. The result is intended for use as a shift in symmetric eigenvalue routines.
The eigenvalue is computed as
 $c - b f + sign⁡f × 1+f2 ,$
where $f=\frac{a-c}{2b}$.
This is the eigenvalue nearer to $c$ if $a\ne c$, and is equal to $c-b$ if $a=c$.

None.

## 5Arguments

1:     $\mathbf{a}$ – Real (Kind=nag_wp)Input
On entry: the value $a$, the $\left(1,1\right)$ element of the input matrix.
2:     $\mathbf{b}$ – Real (Kind=nag_wp)Input
On entry: the value $b$, the $\left(1,2\right)$ or $\left(2,1\right)$ element of the input matrix.
3:     $\mathbf{c}$ – Real (Kind=nag_wp)Input
On entry: the value $c$, the $\left(2,2\right)$ element of the input matrix.

None.

Not applicable.

## 8Parallelism and Performance

f06bpf is not threaded in any implementation.