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RedHat 9 (Linux i386) - man page for dlaed7 (redhat section l)

DLAED7(l)					)					DLAED7(l)

NAME
       DLAED7  -  compute  the	updated  eigensystem of a diagonal matrix after modification by a
       rank-one symmetric matrix

SYNOPSIS
       SUBROUTINE DLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ, INDXQ, RHO,  CUTPNT,
			  QSTORE, QPTR, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK, INFO )

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

	   DOUBLE	  PRECISION RHO

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

	   DOUBLE	  PRECISION D( * ), GIVNUM( 2, * ), Q( LDQ, * ), QSTORE( * ), WORK( * )

PURPOSE
       DLAED7 computes the updated eigensystem of a diagonal matrix after modification by a rank-
       one  symmetric  matrix.	This routine is used only for the eigenproblem which requires all
       eigenvalues and optionally eigenvectors of a dense symmetric matrix that has been  reduced
       to tridiagonal form.  DLAED1 handles the case in which all eigenvalues and eigenvectors of
       a symmetric tridiagonal matrix are desired.

	 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 DLAED8.

	     The second stage consists of calculating the updated
	     eigenvalues. This is done by finding the roots of the secular
	     equation via the routine DLAED4 (as called by DLAED9).
	     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
       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.

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

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

       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) DOUBLE PRECISION array, dimension (N)
	      On entry, the eigenvalues of the rank-1-perturbed matrix.  On exit, the eigenvalues
	      of the repaired matrix.

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

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

       INDXQ  (output) INTEGER array, dimension (N)
	      The  permutation which will reintegrate the subproblem just solved back into sorted
	      order, i.e., D( INDXQ( I = 1, N ) ) will be in ascending order.

       RHO    (input) DOUBLE PRECISION
	      The subdiagonal element used to create the rank-1 modification.

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

	      QSTORE  (input/output)  DOUBLE PRECISION array, dimension (N**2+1) Stores eigenvec-
	      tors of submatrices encountered during divide and conquer,  packed  together.  QPTR
	      points to beginning of the submatrices.

       QPTR   (input/output) INTEGER array, dimension (N+2)
	      List  of	indices pointing to beginning of submatrices stored in QSTORE. The subma-
	      trices 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 eigen-
	      block.

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

       WORK   (workspace) DOUBLE PRECISION array, dimension (3*N+QSIZ*N)

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

       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

LAPACK version 3.0			   15 June 2000 				DLAED7(l)


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