DSTEDC (3lapack)

compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method

SYNOPSIS

  SUBROUTINE DSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO
                     )

      CHARACTER      COMPZ

      INTEGER        INFO, LDZ, LIWORK, LWORK, N

      INTEGER        IWORK( * )

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

PURPOSE

  DSTEDC computes all eigenvalues and, optionally, eigenvectors of a
  symmetric tridiagonal matrix using the divide and conquer method.  The
  eigenvectors of a full or band real symmetric matrix can also be found if
  DSYTRD or DSPTRD or DSBTRD has been used to reduce this matrix to
  tridiagonal form.

  This code 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.  See DLAED3
  for details.

ARGUMENTS

  COMPZ   (input) CHARACTER*1
          = 'N':  Compute eigenvalues only.
          = 'I':  Compute eigenvectors of tridiagonal matrix also.
          = 'V':  Compute eigenvectors of original dense symmetric matrix
          also.  On entry, Z contains the orthogonal matrix used to reduce
          the original matrix to tridiagonal form.

  N       (input) INTEGER
          The dimension of the symmetric tridiagonal matrix.  N >= 0.

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

  E       (input/output) DOUBLE PRECISION array, dimension (N-1)
          On entry, the subdiagonal elements of the tridiagonal matrix.  On
          exit, E has been destroyed.

  Z       (input/output) DOUBLE PRECISION array, dimension (LDZ,N)
          On entry, if COMPZ = 'V', then Z contains the orthogonal matrix
          used in the reduction to tridiagonal form.  On exit, if INFO = 0,
          then if COMPZ = 'V', Z contains the orthonormal eigenvectors of the
          original symmetric matrix, and if COMPZ = 'I', Z contains the
          orthonormal eigenvectors of the symmetric tridiagonal matrix.  If
          COMPZ = 'N', then Z is not referenced.

  LDZ     (input) INTEGER
          The leading dimension of the array Z.  LDZ >= 1.  If eigenvectors
          are desired, then 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 COMPZ = 'N' or N <= 1 then
          LWORK must be at least 1.  If COMPZ = 'V' and N > 1 then LWORK must
          be at least ( 1 + 3*N + 2*N*lg N + 3*N**2 ), where lg( N ) =
          smallest integer k such that 2**k >= N.  If COMPZ = 'I' and N > 1
          then LWORK must be at least ( 1 + 3*N + 2*N*lg N + 2*N**2 ).

  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 COMPZ = 'N' or N <= 1 then
          LIWORK must be at least 1.  If COMPZ = 'V' and N > 1 then LIWORK
          must be at least ( 6 + 6*N + 5*N*lg N ).  If COMPZ = 'I' 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:  The algorithm failed to compute an eigenvalue while working
          on the submatrix lying in rows and columns INFO/(N+1) through
          mod(INFO,N+1).