NAME

       dsyevd.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dsyevd (JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, LIWORK, INFO)
            DSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors
           for SY matrices

Function/Subroutine Documentation

   subroutine dsyevd (characterJOBZ, characterUPLO, integerN, double precision, dimension( lda, *
       )A, integerLDA, double precision, dimension( * )W, double precision, dimension( * )WORK,
       integerLWORK, integer, dimension( * )IWORK, integerLIWORK, integerINFO)
        DSYEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for
       SY matrices

       Purpose:

            DSYEVD computes all eigenvalues and, optionally, eigenvectors of a
            real symmetric matrix A. 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.

            Because of large use of BLAS of level 3, DSYEVD needs N**2 more
            workspace than DSYEVX.

       Parameters:
           JOBZ

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

           UPLO

                     UPLO is CHARACTER*1
                     = 'U':  Upper triangle of A is stored;
                     = 'L':  Lower triangle of A is stored.

           N

                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           A

                     A is DOUBLE PRECISION array, dimension (LDA, N)
                     On entry, the symmetric 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
                     orthonormal eigenvectors of the matrix A.
                     If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
                     or the upper triangle (if UPLO='U') of A, including the
                     diagonal, is destroyed.

           LDA

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

           W

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

           WORK

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

           LWORK

                     LWORK is INTEGER
                     The dimension of the array WORK.
                     If N <= 1,               LWORK must be at least 1.
                     If JOBZ = 'N' and N > 1, LWORK must be at least 2*N+1.
                     If JOBZ = 'V' and N > 1, LWORK must be at least
                                                           1 + 6*N + 2*N**2.

                     If LWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal sizes of the WORK and IWORK
                     arrays, returns these values as the first entries of the WORK
                     and IWORK arrays, and no error message related to LWORK 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 must be at least 1.
                     If JOBZ  = 'N' and N > 1, LIWORK must be at least 1.
                     If JOBZ  = 'V' and N > 1, LIWORK must be at least 3 + 5*N.

                     If LIWORK = -1, then a workspace query is assumed; the
                     routine only calculates the optimal sizes of the WORK and
                     IWORK arrays, returns these values as the first entries of
                     the WORK and IWORK arrays, and no error message related to
                     LWORK 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:  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).

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       Contributors:
           Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
            Modified by Francoise Tisseur, University of Tennessee
            Modified description of INFO. Sven, 16 Feb 05.

       Definition at line 185 of file dsyevd.f.

Author

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