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.

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.

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