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NAME

       chegvd.f -

SYNOPSIS

   Functions/Subroutines
       subroutine chegvd (ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK, RWORK, LRWORK,
           IWORK, LIWORK, INFO)
           CHEGST

Function/Subroutine Documentation

   subroutine chegvd (integerITYPE, characterJOBZ, characterUPLO, integerN, complex, dimension(
       lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB, real, dimension( * )W,
       complex, dimension( * )WORK, integerLWORK, real, dimension( * )RWORK, integerLRWORK,
       integer, dimension( * )IWORK, integerLIWORK, integerINFO)
       CHEGST

       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.

       Parameters:
           ITYPE

                     ITYPE is 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

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

           UPLO

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

           N

                     N is INTEGER
                     The order of the matrices A and B.  N >= 0.

           A

                     A is 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

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

           B

                     B is 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

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

           W

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

           WORK

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

           LWORK

                     LWORK is 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

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

           LRWORK

                     LRWORK is 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

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

           LIWORK

                     LIWORK is 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

                     INFO is 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.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           November 2011

       Further Details:

             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.

       Contributors:
           Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

       Definition at line 249 of file chegvd.f.

Author

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