ZGET52  does an eigenvector check for the generalized eigenvalue


 problem.


 The basic test for right eigenvectors is:


                           | b(i) A E(i) -  a(i) B E(i) |


         RESULT(1) = max   -------------------------------


                      i    n ulp max( |b(i) A|, |a(i) B| )


 using the 1-norm.  Here, a(i)/b(i) = w is the i-th generalized


 eigenvalue of A - w B, or, equivalently, b(i)/a(i) = m is the i-th


 generalized eigenvalue of m A - B.


                         H   H  _      _


 For left eigenvectors, A , B , a, and b  are used.


 ZGET52 also tests the normalization of E.  Each eigenvector is


 supposed to be normalized so that the maximum 'absolute value'


 of its elements is 1, where in this case, 'absolute value'


 of a complex value x is  |Re(x)| + |Im(x)| ; let us call this


 maximum 'absolute value' norm of a vector v  M(v).


 If a(i)=b(i)=0, then the eigenvector is set to be the jth coordinate


 vector. The normalization test is:


         RESULT(2) =      max       | M(v(i)) - 1 | / ( n ulp )


                    eigenvectors v(i)

LEFT

          LEFT is LOGICAL


          =.TRUE.:  The eigenvectors in the columns of E are assumed


                    to be *left* eigenvectors.


          =.FALSE.: The eigenvectors in the columns of E are assumed


                    to be *right* eigenvectors.

N

          N is INTEGER


          The size of the matrices.  If it is zero, ZGET52 does


          nothing.  It must be at least zero.

A

          A is COMPLEX*16 array, dimension (LDA, N)


          The matrix A.

LDA

          LDA is INTEGER


          The leading dimension of A.  It must be at least 1


          and at least N.

B

          B is COMPLEX*16 array, dimension (LDB, N)


          The matrix B.

LDB

          LDB is INTEGER


          The leading dimension of B.  It must be at least 1


          and at least N.

E

          E is COMPLEX*16 array, dimension (LDE, N)


          The matrix of eigenvectors.  It must be O( 1 ).

LDE

          LDE is INTEGER


          The leading dimension of E.  It must be at least 1 and at


          least N.

ALPHA

          ALPHA is COMPLEX*16 array, dimension (N)


          The values a(i) as described above, which, along with b(i),


          define the generalized eigenvalues.

BETA

          BETA is COMPLEX*16 array, dimension (N)


          The values b(i) as described above, which, along with a(i),


          define the generalized eigenvalues.

WORK

          WORK is COMPLEX*16 array, dimension (N**2)

RWORK

          RWORK is DOUBLE PRECISION array, dimension (N)

RESULT

          RESULT is DOUBLE PRECISION array, dimension (2)


          The values computed by the test described above.  If A E or


          B E is likely to overflow, then RESULT(1:2) is set to


          10 / ulp.

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