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F06 (Blas) Chapter Introduction
f06bp:  FL   CL   CPP   AD   PY   MB 

NAG FL Interface
f06bpf (deig2)

NAG Library Manual, Mark 29
Interfaces:  FL   CL   CPP   AD   PY   MB 
NAG FL Interface Introduction
F06 (Blas) Chapter Contents
F06 (Blas) Chapter Introduction
f06bp:  FL   CL   CPP   AD   PY   MB 

▸▿ Contents

© The Numerical Algorithms Group Ltd. 2023
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1 Purpose

f06bpf returns an eigenvalue of a 2×2 real symmetric matrix.

2 Specification

Fortran Interface
Function f06bpf ( a, b, c)
Real (Kind=nag_wp) :: f06bpf
Real (Kind=nag_wp), Intent (In) :: a, b, c
C Header Interface
#include <nag.h>
double  f06bpf_ (const double *a, const double *b, const double *c)
The routine may be called by the names f06bpf or nagf_blas_deig2.

3 Description

f06bpf returns an eigenvalue of the 2×2 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 = a-c 2b .
This is the eigenvalue nearer to c if a≠c, and is equal to c-b if a=c.

4 References

None.

5 Arguments

1: a – Real (Kind=nag_wp) Input
On entry: the value a, the (1,1) element of the input matrix.
2: b – Real (Kind=nag_wp) Input
On entry: the value b, the (1,2) or (2,1) element of the input matrix.
3: c – Real (Kind=nag_wp) Input
On entry: the value c, the (2,2) element of the input matrix.

6 Error Indicators and Warnings

None.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
f06bpf is not threaded in any implementation.

9 Further Comments

None.

10 Example

None.
NAG Library Manual, Mark 29
Interfaces:  FL   CL   CPP   AD   PY   MB 
NAG FL Interface Introduction
F06 (Blas) Chapter Contents
F06 (Blas) Chapter Introduction
f06bp:  FL   CL   CPP   AD   PY   MB 
© The Numerical Algorithms Group Ltd. 2023