SSTEVD (3lapack)

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

SYNOPSIS

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

      CHARACTER      JOBZ

      INTEGER        INFO, LDZ, LIWORK, LWORK, N

      INTEGER        IWORK( * )

      REAL           D( * ), E( * ), WORK( * ), Z( LDZ, * )

PURPOSE

  SSTEVD 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) REAL 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) REAL 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) REAL 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) REAL 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.