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CLAED7(l)			       )			     CLAED7(l)

NAME
       CLAED7  -  compute  the	updated eigensystem of a diagonal matrix after
       modification by a rank-one symmetric matrix

SYNOPSIS
       SUBROUTINE CLAED7( N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D,  Q,  LDQ,
			  RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIV‐
			  COL, GIVNUM, WORK, RWORK, IWORK, INFO )

	   INTEGER	  CURLVL, CURPBM, CUTPNT, INFO, LDQ, N, QSIZ, TLVLS

	   REAL		  RHO

	   INTEGER	  GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), IWORK( * ),
			  PERM( * ), PRMPTR( * ), QPTR( * )

	   REAL		  D( * ), GIVNUM( 2, * ), QSTORE( * ), RWORK( * )

	   COMPLEX	  Q( LDQ, * ), WORK( * )

PURPOSE
       CLAED7 computes the updated eigensystem of a diagonal matrix after mod‐
       ification by a rank-one symmetric matrix. This routine is used only for
       the  eigenproblem  which requires all eigenvalues and optionally eigen‐
       vectors of a dense or banded Hermitian matrix that has been reduced  to
       tridiagonal form.

	 T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out)

	 where Z = Q'u, u is a vector of length N with ones in the
	 CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.

	  The eigenvectors of the original matrix are stored in Q, and the
	  eigenvalues are in D.	 The algorithm consists of three stages:

	     The first stage consists of deflating the size of the problem
	     when there are multiple eigenvalues or if there is a zero in
	     the Z vector.  For each such occurence the dimension of the
	     secular equation problem is reduced by one.  This stage is
	     performed by the routine SLAED2.

	     The second stage consists of calculating the updated
	     eigenvalues. This is done by finding the roots of the secular
	     equation via the routine SLAED4 (as called by SLAED3).
	     This routine also calculates the eigenvectors of the current
	     problem.

	     The final stage consists of computing the updated eigenvectors
	     directly using the updated eigenvalues.  The eigenvectors for
	     the current problem are multiplied with the eigenvectors from
	     the overall problem.

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

	      CUTPNT  (input) INTEGER Contains the location of the last eigen‐
	      value in the leading sub-matrix.	min(1,N) <= CUTPNT <= N.

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

       TLVLS  (input) INTEGER
	      The  total  number  of  merging levels in the overall divide and
	      conquer tree.

	      CURLVL (input) INTEGER The current level in  the	overall	 merge
	      routine, 0 <= curlvl <= tlvls.

	      CURPBM  (input) INTEGER The current problem in the current level
	      in the overall merge routine (counting from upper left to	 lower
	      right).

       D      (input/output) REAL array, dimension (N)
	      On  entry,  the  eigenvalues of the rank-1-perturbed matrix.  On
	      exit, the eigenvalues of the repaired matrix.

       Q      (input/output) COMPLEX array, dimension (LDQ,N)
	      On entry, the eigenvectors of the rank-1-perturbed  matrix.   On
	      exit, the eigenvectors of the repaired tridiagonal matrix.

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

       RHO    (input) REAL
	      Contains the subdiagonal element used to create the rank-1 modi‐
	      fication.

       INDXQ  (output) INTEGER array, dimension (N)
	      This contains the permutation which will	reintegrate  the  sub‐
	      problem just solved back into sorted order, ie. D( INDXQ( I = 1,
	      N ) ) will be in ascending order.

       IWORK  (workspace) INTEGER array, dimension (4*N)

       RWORK  (workspace) REAL array,
	      dimension (3*N+2*QSIZ*N)

       WORK   (workspace) COMPLEX array, dimension (QSIZ*N)

	      QSTORE (input/output)  REAL  array,  dimension  (N**2+1)	Stores
	      eigenvectors  of	submatrices encountered during divide and con‐
	      quer, packed together. QPTR points to beginning of the submatri‐
	      ces.

       QPTR   (input/output) INTEGER array, dimension (N+2)
	      List  of	indices pointing to beginning of submatrices stored in
	      QSTORE. The submatrices are numbered starting at the bottom left
	      of the divide and conquer tree, from left to right and bottom to
	      top.

	      PRMPTR (input) INTEGER array, dimension (N lg N) Contains a list
	      of  pointers  which indicate where in PERM a level's permutation
	      is stored.  PRMPTR(i+1) - PRMPTR(i) indicates the	 size  of  the
	      permutation and also the size of the full, non-deflated problem.

       PERM   (input) INTEGER array, dimension (N lg N)
	      Contains	the  permutations  (from  deflation and sorting) to be
	      applied to each eigenblock.

	      GIVPTR (input) INTEGER array, dimension (N lg N) Contains a list
	      of  pointers  which  indicate  where  in GIVCOL a level's Givens
	      rotations are stored.  GIVPTR(i+1)  -  GIVPTR(i)	indicates  the
	      number of Givens rotations.

	      GIVCOL (input) INTEGER array, dimension (2, N lg N) Each pair of
	      numbers indicates a pair of columns to take place	 in  a	Givens
	      rotation.

	      GIVNUM  (input)  REAL  array,  dimension (2, N lg N) Each number
	      indicates the S value to be used	in  the	 corresponding	Givens
	      rotation.

       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

LAPACK version 3.0		 15 June 2000			     CLAED7(l)
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