TESTING/EIG/zget52.f(3)    Library Functions Manual    TESTING/EIG/zget52.f(3)

NAME
       TESTING/EIG/zget52.f

SYNOPSIS
   Functions/Subroutines
       subroutine zget52 (left, n, a, lda, b, ldb, e, lde, alpha, beta, work,
           rwork, result)
           ZGET52

Function/Subroutine Documentation
   subroutine zget52 (logical left, integer n, complex*16, dimension( lda, * )
       a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb,
       complex*16, dimension( lde, * ) e, integer lde, complex*16, dimension(
       * ) alpha, complex*16, dimension( * ) beta, complex*16, dimension( * )
       work, double precision, dimension( * ) rwork, double precision,
       dimension( 2 ) result)
       ZGET52

       Purpose:


            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)

       Parameters
           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.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Definition at line 160 of file zget52.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0         TESTING/EIG/zget52.f(3)