# sget53.f - Man Page

TESTING/EIG/sget53.f

## Synopsis

### Functions/Subroutines

subroutine sget53 (a, lda, b, ldb, scale, wr, wi, result, info)
SGET53

## Function/Subroutine Documentation

### subroutine sget53 (real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real scale, real wr, real wi, real result, integer info)

SGET53

Purpose:

``` SGET53  checks the generalized eigenvalues computed by SLAG2.

The basic test for an eigenvalue is:

| det( s A - w B ) |
RESULT =  ---------------------------------------------------
ulp max( s norm(A), |w| norm(B) )*norm( s A - w B )

Two 'safety checks' are performed:

(1)  ulp*max( s*norm(A), |w|*norm(B) )  must be at least
safe_minimum.  This insures that the test performed is
not essentially  det(0*A + 0*B)=0.

(2)  s*norm(A) + |w|*norm(B) must be less than 1/safe_minimum.
This insures that  s*A - w*B  will not overflow.

If these tests are not passed, then  s  and  w  are scaled and
tested anyway, if this is possible.```
Parameters

A

```          A is REAL array, dimension (LDA, 2)
The 2x2 matrix A.```

LDA

```          LDA is INTEGER
The leading dimension of A.  It must be at least 2.```

B

```          B is REAL array, dimension (LDB, N)
The 2x2 upper-triangular matrix B.```

LDB

```          LDB is INTEGER
The leading dimension of B.  It must be at least 2.```

SCALE

```          SCALE is REAL
The 'scale factor' s in the formula  s A - w B .  It is
assumed to be non-negative.```

WR

```          WR is REAL
The real part of the eigenvalue  w  in the formula
s A - w B .```

WI

```          WI is REAL
The imaginary part of the eigenvalue  w  in the formula
s A - w B .```

RESULT

```          RESULT is REAL
If INFO is 2 or less, the value computed by the test
described above.
If INFO=3, this will just be 1/ulp.```

INFO

```          INFO is INTEGER
=0:  The input data pass the 'safety checks'.
=1:  s*norm(A) + |w|*norm(B) > 1/safe_minimum.
=2:  ulp*max( s*norm(A), |w|*norm(B) ) < safe_minimum
=3:  same as INFO=2, but  s  and  w  could not be scaled so
as to compute the test.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 125 of file sget53.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sget53(3) is an alias of sget53.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK