sget53.f - Man Page

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

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.