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dsyev

 NAME
      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, eigenvectors
      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 des-
              troyed.

      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) DOUBLE PRECISION array, dimension (LWORK)

              On exit, if INFO = 0, WORK(1) returns the optimal
              LWORK.

      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.

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