CXML
        	    
LAPACK version 3.0
dlaed0(3)

PURPOSE
  DLAED0 - compute all eigenvalues and corresponding eigenvectors of a
  symmetric tridiagonal matrix using the divide and conquer method

SYNTAX
  SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, WORK,
		     IWORK, INFO )

      INTEGER	     ICOMPQ, INFO, LDQ, LDQS, N, QSIZ

      INTEGER	     IWORK( * )

      DOUBLE	     PRECISION D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, *
		     ), WORK( * )

DESCRIPTION
  DLAED0 computes all eigenvalues and corresponding eigenvectors of a
  symmetric tridiagonal matrix using the divide and conquer method.

ARGUMENTS
  ICOMPQ  (input) INTEGER
	  = 0:	Compute eigenvalues only.
	  = 1:	Compute eigenvectors of original dense symmetric matrix also.
	  On entry, Q contains the orthogonal matrix used to reduce the
	  original matrix to tridiagonal form.	= 2:  Compute eigenvalues and
	  eigenvectors of tridiagonal matrix.

  QSIZ	 (input) INTEGER
	 The dimension of the orthogonal matrix used to reduce the full
	 matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.

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

  D	 (input/output) DOUBLE PRECISION array, dimension (N)
	 On entry, the main diagonal of the tridiagonal matrix.	 On exit, its
	 eigenvalues.

  E	 (input) DOUBLE PRECISION array, dimension (N-1)
	 The off-diagonal elements of the tridiagonal matrix.  On exit, E has
	 been destroyed.

  Q	 (input/output) DOUBLE PRECISION array, dimension (LDQ, N)
	 On entry, Q must contain an N-by-N orthogonal matrix.	If ICOMPQ = 0
	 Q is not referenced.  If ICOMPQ = 1	On entry, Q is a subset of
	 the columns of the orthogonal matrix used to reduce the full matrix
	 to tridiagonal form corresponding to the subset of the full matrix
	 which is being decomposed at this time.  If ICOMPQ = 2	   On entry,
	 Q will be the identity matrix.	 On exit, Q contains the eigenvectors
	 of the tridiagonal matrix.

  LDQ	 (input) INTEGER
	 The leading dimension of the array Q.	If eigenvectors are desired,
	 then  LDQ >= max(1,N).	 In any case,  LDQ >= 1.

	 QSTORE (workspace) DOUBLE PRECISION array, dimension (LDQS, N)
	 Referenced only when ICOMPQ = 1.  Used to store parts of the
	 eigenvector matrix when the updating matrix multiplies take place.

  LDQS	 (input) INTEGER
	 The leading dimension of the array QSTORE.  If ICOMPQ = 1, then
	 LDQS >= max(1,N).  In any case,  LDQS >= 1.

  WORK	 (workspace) DOUBLE PRECISION array,
	 If ICOMPQ = 0 or 1, the dimension of WORK must be at least 1 + 3*N +
	 2*N*lg N + 2*N**2 ( lg( N ) = smallest integer k such that 2^k >= N
	 ) If ICOMPQ = 2, the dimension of WORK must be at least 4*N + N**2.

  IWORK	 (workspace) INTEGER array,
	 If ICOMPQ = 0 or 1, the dimension of IWORK must be at least 6 + 6*N
	 + 5*N*lg N.  ( lg( N ) = smallest integer k such that 2^k >= N ) If
	 ICOMPQ = 2, the dimension of IWORK must be at least 3 + 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).

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