CXML
        	    
LAPACK version 3.0
dlaed9(3)

PURPOSE
  DLAED9 - find the roots of the secular equation, as defined by the values
  in D, Z, and RHO, between KSTART and KSTOP

SYNTAX
  SUBROUTINE DLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, S, LDS,
		     INFO )

      INTEGER	     INFO, K, KSTART, KSTOP, LDQ, LDS, N

      DOUBLE	     PRECISION RHO

      DOUBLE	     PRECISION D( * ), DLAMDA( * ), Q( LDQ, * ), S( LDS, * ),
		     W( * )

DESCRIPTION
  DLAED9 finds the roots of the secular equation, as defined by the values in
  D, Z, and RHO, between KSTART and KSTOP. It makes the appropriate calls to
  DLAED4 and then stores the new matrix of eigenvectors for use in
  calculating the next level of Z vectors.

ARGUMENTS
  K	  (input) INTEGER
	  The number of terms in the rational function to be solved by
	  DLAED4.  K >= 0.

  KSTART  (input) INTEGER
	  KSTOP	  (input) INTEGER The updated eigenvalues Lambda(I), KSTART
	  <= I <= KSTOP are to be computed.  1 <= KSTART <= KSTOP <= K.

  N	  (input) INTEGER
	  The number of rows and columns in the Q matrix.  N >= K (delation
	  may result in N > K).

  D	  (output) DOUBLE PRECISION array, dimension (N)
	  D(I) contains the updated eigenvalues for KSTART <= I <= KSTOP.

  Q	  (workspace) DOUBLE PRECISION array, dimension (LDQ,N)

  LDQ	  (input) INTEGER
	  The leading dimension of the array Q.	 LDQ >= max( 1, N ).

  RHO	  (input) DOUBLE PRECISION
	  The value of the parameter in the rank one update equation.  RHO >=
	  0 required.

  DLAMDA  (input) DOUBLE PRECISION array, dimension (K)
	  The first K elements of this array contain the old roots of the
	  deflated updating problem.  These are the poles of the secular
	  equation.

  W	  (input) DOUBLE PRECISION array, dimension (K)
	  The first K elements of this array contain the components of the
	  deflation-adjusted updating vector.

  S	  (output) DOUBLE PRECISION array, dimension (LDS, K)
	  Will contain the eigenvectors of the repaired matrix which will be
	  stored for subsequent Z vector calculation and multiplied by the
	  previously accumulated eigenvectors to update the system.

  LDS	  (input) INTEGER
	  The leading dimension of S.  LDS >= max( 1, K ).

  INFO	  (output) INTEGER
	  = 0:	successful exit.
	  < 0:	if INFO = -i, the i-th argument had an illegal value.
	  > 0:	if INFO = 1, an eigenvalue did not converge

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