TESTING/EIG/sget53.f(3)    Library Functions Manual    TESTING/EIG/sget53.f(3)

NAME
       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.

LAPACK                          Version 3.12.0         TESTING/EIG/sget53.f(3)