Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  computes  all  the eigenvalues, and optionally, the eigenvectors of a complex
       generalized   Hermitian-definite   eigenproblem,    of    the    form    A*x=(lambda)*B*x,
       A*Bx=(lambda)*x, or B*A*x=(lambda)*x

SYNOPSIS

       SUBROUTINE CHEGVD( ITYPE,  JOBZ,  UPLO,  N, A, LDA, B, LDB, W, WORK, LWORK, RWORK, LRWORK,
                          IWORK, LIWORK, INFO )

           CHARACTER      JOBZ, UPLO

           INTEGER        INFO, ITYPE, LDA, LDB, LIWORK, LRWORK, LWORK, N

           INTEGER        IWORK( * )

           REAL           RWORK( * ), W( * )

           COMPLEX        A( LDA, * ), B( LDB, * ), WORK( * )

PURPOSE

       CHEGVD computes all the  eigenvalues,  and  optionally,  the  eigenvectors  of  a  complex
       generalized    Hermitian-definite    eigenproblem,    of    the   form   A*x=(lambda)*B*x,
       A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.  Here A and
        B are assumed to be Hermitian and B is also positive definite.
        If eigenvectors are desired, it uses a divide and conquer algorithm.
        The divide and conquer algorithm makes very mild assumptions about
        floating point arithmetic. It will work on machines with a guard
        digit in add/subtract, or on those binary machines without guard
        digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
        Cray-2. It could conceivably fail on hexadecimal or decimal machines
        without guard digits, but we know of none.

ARGUMENTS

        ITYPE   (input) INTEGER
                Specifies the problem type to be solved:
                = 1:  A*x = (lambda)*B*x
                = 2:  A*B*x = (lambda)*x
                = 3:  B*A*x = (lambda)*x

        JOBZ    (input) CHARACTER*1
                = 'N':  Compute eigenvalues only;
                = 'V':  Compute eigenvalues and eigenvectors.

        UPLO    (input) CHARACTER*1
                = 'U':  Upper triangles of A and B are stored;
                = 'L':  Lower triangles of A and B are stored.

        N       (input) INTEGER
                The order of the matrices A and B.  N >= 0.

        A       (input/output) COMPLEX array, dimension (LDA, N)
                On entry, the Hermitian matrix A.  If UPLO = 'U', the
                leading N-by-N upper triangular part of A contains the
                upper triangular part of the matrix A.  If UPLO = 'L',
                the leading N-by-N lower triangular part of A contains
                the lower triangular part of the matrix A.
                On exit, if JOBZ = 'V', then if INFO = 0, A contains the
                matrix Z of eigenvectors.  The eigenvectors are normalized
                as follows:
                if ITYPE = 1 or 2, Z**H*B*Z = I;
                if ITYPE = 3, Z**H*inv(B)*Z = I.
                If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
                or the lower triangle (if UPLO='L') of A, including the
                diagonal, is destroyed.

        LDA     (input) INTEGER
                The leading dimension of the array A.  LDA >= max(1,N).

        B       (input/output) COMPLEX array, dimension (LDB, N)
                On entry, the Hermitian matrix B.  If UPLO = 'U', the
                leading N-by-N upper triangular part of B contains the
                upper triangular part of the matrix B.  If UPLO = 'L',
                the leading N-by-N lower triangular part of B contains
                the lower triangular part of the matrix B.
                On exit, if INFO <= N, the part of B containing the matrix is
                overwritten by the triangular factor U or L from the Cholesky
                factorization B = U**H*U or B = L*L**H.

        LDB     (input) INTEGER
                The leading dimension of the array B.  LDB >= max(1,N).

        W       (output) REAL array, dimension (N)
                If INFO = 0, the eigenvalues in ascending order.

        WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
                On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

        LWORK   (input) INTEGER
                The length of the array WORK.
                If N <= 1,                LWORK >= 1.
                If JOBZ  = 'N' and N > 1, LWORK >= N + 1.
                If JOBZ  = 'V' and N > 1, LWORK >= 2*N + N**2.
                If LWORK = -1, then a workspace query is assumed; the routine
                only calculates the optimal sizes of the WORK, RWORK and
                IWORK arrays, returns these values as the first entries of
                the WORK, RWORK and IWORK arrays, and no error message
                related to LWORK or LRWORK or LIWORK is issued by XERBLA.

        RWORK   (workspace/output) REAL array, dimension (MAX(1,LRWORK))
                On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

        LRWORK  (input) INTEGER
                The dimension of the array RWORK.
                If N <= 1,                LRWORK >= 1.
                If JOBZ  = 'N' and N > 1, LRWORK >= N.
                If JOBZ  = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
                If LRWORK = -1, then a workspace query is assumed; the
                routine only calculates the optimal sizes of the WORK, RWORK
                and IWORK arrays, returns these values as the first entries
                of the WORK, RWORK and IWORK arrays, and no error message
                related to LWORK or LRWORK or LIWORK is issued by XERBLA.

        IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
                On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

        LIWORK  (input) INTEGER
                The dimension of the array IWORK.
                If N <= 1,                LIWORK >= 1.
                If JOBZ  = 'N' and N > 1, LIWORK >= 1.
                If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N.
                If LIWORK = -1, then a workspace query is assumed; the
                routine only calculates the optimal sizes of the WORK, RWORK
                and IWORK arrays, returns these values as the first entries
                of the WORK, RWORK and IWORK arrays, and no error message
                related to LWORK or LRWORK or LIWORK is issued by XERBLA.

        INFO    (output) INTEGER
                = 0:  successful exit
                < 0:  if INFO = -i, the i-th argument had an illegal value
                > 0:  CPOTRF or CHEEVD returned an error code:
                <= N:  if INFO = i and JOBZ = 'N', then the algorithm
                failed to converge; i off-diagonal elements of an
                intermediate tridiagonal form did not converge to
                zero;
                if INFO = i and JOBZ = 'V', then the algorithm
                failed to compute an eigenvalue while working on
                the submatrix lying in rows and columns INFO/(N+1)
                through mod(INFO,N+1);
                > N:   if INFO = N + i, for 1 <= i <= N, then the leading
                minor of order i of B is not positive definite.
                The factorization of B could not be completed and
                no eigenvalues or eigenvectors were computed.

FURTHER DETAILS

        Based on contributions by
           Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
        Modified so that no backsubstitution is performed if CHEEVD fails to
        converge (NEIG in old code could be greater than N causing out of
        bounds reference to A - reported by Ralf Meyer).  Also corrected the
        description of INFO and the test on ITYPE. Sven, 16 Feb 05.

 LAPACK driver routine (version 3.3.1)      April 2011                            CHEGVD(3lapack)