DSYEV - compute all eigenvalues and, optionally, eigenvec­
       tors of a real symmetric matrix A


SYNOPSIS

       SUBROUTINE DSYEV( JOBZ, UPLO, N, A, LDA, W,  WORK,  LWORK,
                         INFO )

           CHARACTER     JOBZ, UPLO

           INTEGER       INFO, LDA, LWORK, N

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


PURPOSE

       DSYEV computes all eigenvalues and, optionally,  eigenvec­
       tors of a real symmetric matrix A.


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
               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     (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   (input) INTEGER
               The   length   of   the   array  WORK.   LWORK  >=
               max(1,3*N-1).  For optimal  efficiency,  LWORK  >=
               (NB+2)*N,  where  NB  is  the blocksize for DSYTRD
               returned by ILAENV.

               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.

       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.


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