DSYEVD  -  compute all eigenvalues and, optionally, eigen­
       vectors of a real symmetric matrix A


SYNOPSIS

       SUBROUTINE DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK,  LWORK,
                          IWORK, LIWORK, INFO )

           CHARACTER      JOBZ, UPLO

           INTEGER        INFO, LDA, LIWORK, LWORK, N

           INTEGER        IWORK( * )

           DOUBLE         PRECISION  A( LDA, * ), W( * ), WORK( *
                          )


PURPOSE

       DSYEVD computes all eigenvalues and, optionally, eigenvec­
       tors  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  assump­
       tions  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 with­
       out guard digits, but we know of none.

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


ARGUMENTS

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

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

       N       (input) INTEGER
               The order of the matrix A.  N >= 0.

       A       (input/output) 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 con­
               tains  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

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

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

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

       LWORK   (input) 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  size  of
               the  WORK  array,  returns this value as the first
               entry of the WORK  array,  and  no  error  message
               related to LWORK is issued by XERBLA.

       IWORK   (workspace/output) INTEGER array, dimension
               (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 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 size of
               the IWORK array, returns this value as  the  first
               entry  of  the  IWORK  array, and no error message
               related to LIWORK is issued by XERBLA.

       INFO    (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille­
               gal value
               >  0:   if  INFO = i, the algorithm failed to con­
               verge; i off-diagonal elements of an  intermediate
               tridiagonal form did not converge to zero.

       Based on contributions by
          Jeff  Rutter,  Computer Science Division, University of
       California
          at Berkeley, USA
       Modified by Francoise Tisseur, University of Tennessee.


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