sget53()

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

[in]	A	A is REAL array, dimension (LDA, 2) The 2x2 matrix A.
[in]	LDA	LDA is INTEGER The leading dimension of A. It must be at least 2.
[in]	B	B is REAL array, dimension (LDB, N) The 2x2 upper-triangular matrix B.
[in]	LDB	LDB is INTEGER The leading dimension of B. It must be at least 2.
[in]	SCALE	SCALE is REAL The "scale factor" s in the formula s A - w B . It is assumed to be non-negative.
[in]	WR	WR is REAL The real part of the eigenvalue w in the formula s A - w B .
[in]	WI	WI is REAL The imaginary part of the eigenvalue w in the formula s A - w B .
[out]	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.
[out]	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.