zget52.f3

!>
!> 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 
!> of its elements is 1, where in this case, 
!> of a complex value x is  |Re(x)| + |Im(x)| ; let us call this
!> maximum  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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