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CLAED7(1)		 LAPACK routine (version 3.2)		     CLAED7(1)

NAME
       CLAED7  -  computes  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 permu‐
	      tation 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 rota‐
	      tions.  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 corre‐
	      sponding 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 routine (version 3.2)	 November 2008			     CLAED7(1)
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