# 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

Univ. of Colorado Denver

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