dget53.f - Man Page

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

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 '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 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 'scale factor' 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 '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 dget53.f.