dstevd(3F)

NAME
     DSTEVD - compute all eigenvalues and, optionally, eigenvectors of a real
     symmetric tridiagonal matrix

SYNOPSIS
     SUBROUTINE DSTEVD( JOBZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK,
                        INFO )

         CHARACTER      JOBZ

         INTEGER        INFO, LDZ, LIWORK, LWORK, N

         INTEGER        IWORK( * )

         DOUBLE         PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )

PURPOSE
     DSTEVD computes all eigenvalues and, optionally, eigenvectors of a real
     symmetric tridiagonal matrix. 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.


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

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

     D       (input/output) DOUBLE PRECISION array, dimension (N)
             On entry, the n diagonal elements of the tridiagonal matrix A.
             On exit, if INFO = 0, the eigenvalues in ascending order.

     E       (input/output) DOUBLE PRECISION array, dimension (N)
             On entry, the (n-1) subdiagonal elements of the tridiagonal
             matrix A, stored in elements 1 to N-1 of E; E(N) need not be set,
             but is used by the routine.  On exit, the contents of E are
             destroyed.

     Z       (output) DOUBLE PRECISION array, dimension (LDZ, N)
             If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
             eigenvectors of the matrix A, with the i-th column of Z holding
             the eigenvector associated with D(i).  If JOBZ = 'N', then Z is
             not referenced.
     LDZ     (input) INTEGER
             The leading dimension of the array Z.  LDZ >= 1, and if JOBZ =
             'V', LDZ >= max(1,N).

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

     LWORK   (input) INTEGER
             The dimension of the array WORK.  If JOBZ  = 'N' or N <= 1 then
             LWORK must be at least 1.  If JOBZ  = 'V' and N > 1 then LWORK
             must be at least ( 1 + 3*N + 2*N*lg N + 2*N**2 ), where lg( N ) =
             smallest integer k such that 2**k >= N.

     IWORK   (workspace/output) INTEGER array, dimension (LIWORK)
             On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.

     LIWORK  (input) INTEGER
             The dimension of the array IWORK.  If JOBZ  = 'N' or N <= 1 then
             LIWORK must be at least 1.  If JOBZ  = 'V' and N > 1 then LIWORK
             must be at least 2+5*N.

     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 E did not converge to zero.