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


SYNOPSIS

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

           CHARACTER     JOBZ, UPLO

           INTEGER       INFO, LDA, LWORK, N

           REAL          A( LDA, * ), W( * ), WORK( * )


PURPOSE

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

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

               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  SSYTRD
               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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