---
name: "dget53.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/dget53.f"
---

# dget53.f(3)

## NAME

TESTING/EIG/dget53.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dget53** (a, lda, b, ldb, scale, wr, wi, result, info)\
 **DGET53**

## Function/Subroutine Documentation

### subroutine dget53 (double precision, dimension( lda, \* ) a, integer lda, double precision, dimension( ldb, \* ) b, integer ldb, double precision scale, double precision wr, double precision wi, double precision result, integer info)

**DGET53**

**Purpose:**

```
!>
!> DGET53  checks the generalized eigenvalues computed by DLAG2.
!>
!> 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  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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION
!>          The  s in the formula  s A - w B .  It is
!>          assumed to be non-negative.
!>
```

*WR*

```
!>          WR is DOUBLE PRECISION
!>          The real part of the eigenvalue  w  in the formula
!>          s A - w B .
!>
```

*WI*

```
!>          WI is DOUBLE PRECISION
!>          The imaginary part of the eigenvalue  w  in the formula
!>          s A - w B .
!>
```

*RESULT*

```
!>          RESULT is DOUBLE PRECISION
!>          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 .
!>          =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

Univ. of Colorado Denver

NAG Ltd.

Definition at line **125** of file **dget53.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.