zstedc(3F)

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

SYNOPSIS
     SUBROUTINE ZSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, LRWORK,
                        IWORK, LIWORK, INFO )

         CHARACTER      COMPZ

         INTEGER        INFO, LDZ, LIWORK, LRWORK, LWORK, N

         INTEGER        IWORK( * )

         DOUBLE         PRECISION D( * ), E( * ), RWORK( * )

         COMPLEX*16     WORK( * ), Z( LDZ, * )

PURPOSE
     ZSTEDC computes all eigenvalues and, optionally, eigenvectors of a
     symmetric tridiagonal matrix using the divide and conquer method.  The
     eigenvectors of a full or band complex Hermitian matrix can also be found
     if ZHETRD or ZHPTRD or ZHBTRD 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 Hermitian matrix also.
             On entry, Z contains the unitary 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) COMPLEX*16 array, dimension (LDZ,N)
             On entry, if COMPZ = 'V', then Z contains the unitary 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 Hermitian 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) COMPLEX*16 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 'I', or N <=
             1, LWORK must be at least 1.  If COMPZ = 'V' and N > 1, LWORK
             must be at least N*N.

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

     LRWORK  (input) INTEGER
             The dimension of the array RWORK.  If COMPZ = 'N' or N <= 1,
             LRWORK must be at least 1.  If COMPZ = 'V' and N > 1, LRWORK 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, LRWORK must be at least 1 + 3*N + 2*N*lg N + 3*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,
             LIWORK must be at least 1.  If COMPZ = 'V' or N > 1,  LIWORK must
             be at least 6 + 6*N + 5*N*lg N.  If COMPZ = 'I' or N > 1,  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).