TESTING/EIG/cget52.f(3)    Library Functions Manual    TESTING/EIG/cget52.f(3)

NAME
       TESTING/EIG/cget52.f

SYNOPSIS
   Functions/Subroutines
       subroutine cget52 (left, n, a, lda, b, ldb, e, lde, alpha, beta, work,
           rwork, result)
           CGET52

Function/Subroutine Documentation
   subroutine cget52 (logical left, integer n, complex, dimension( lda, * ) a,
       integer lda, complex, dimension( ldb, * ) b, integer ldb, complex,
       dimension( lde, * ) e, integer lde, complex, dimension( * ) alpha,
       complex, dimension( * ) beta, complex, dimension( * ) work, real,
       dimension( * ) rwork, real, dimension( 2 ) result)
       CGET52

       Purpose:


            CGET52  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.

            CGET52 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, CGET52 does
                     nothing.  It must be at least zero.

           A

                     A is COMPLEX 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 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 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 array, dimension (N)
                     The values a(i) as described above, which, along with b(i),
                     define the generalized eigenvalues.

           BETA

                     BETA is COMPLEX array, dimension (N)
                     The values b(i) as described above, which, along with a(i),
                     define the generalized eigenvalues.

           WORK

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

           RWORK

                     RWORK is REAL array, dimension (N)

           RESULT

                     RESULT is REAL 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 159 of file cget52.f.

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

LAPACK                          Version 3.12.0         TESTING/EIG/cget52.f(3)