CXML
        	    
LAPACK version 3.0
zstedc(3)

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

SYNTAX
  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, * )

DESCRIPTION
  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 INFO = 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.

	  If LWORK = -1, then a workspace query is assumed; the routine only
	  calculates the optimal size of the WORK array, returns this value
	  as the first entry of the WORK array, and no error message related
	  to LWORK is issued by XERBLA.

  RWORK	  (workspace/output) DOUBLE PRECISION array,
	  dimension (LRWORK) On exit, if INFO = 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 + 4*N + 2*N**2 .

	  If LRWORK = -1, then a workspace query is assumed; the routine only
	  calculates the optimal size of the RWORK array, returns this value
	  as the first entry of the RWORK array, and no error message related
	  to LRWORK is issued by XERBLA.

  IWORK	  (workspace/output) INTEGER array, dimension (LIWORK)
	  On exit, if INFO = 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 3 + 5*N .

	  If LIWORK = -1, then a workspace query is assumed; the routine only
	  calculates the optimal size of the IWORK array, returns this value
	  as the first entry of the IWORK array, and no error message related
	  to LIWORK is issued by XERBLA.

  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).

FURTHER DETAILS
  Based on contributions by
     Jeff Rutter, Computer Science Division, University of California
     at Berkeley, USA