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.