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RedHat 9 (Linux i386) - man page for dlaed1 (redhat section l)

DLAED1(l)					)					DLAED1(l)

NAME
       DLAED1  -  compute  the	updated  eigensystem of a diagonal matrix after modification by a
       rank-one symmetric matrix

SYNOPSIS
       SUBROUTINE DLAED1( N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, INFO )

	   INTEGER	  CUTPNT, INFO, LDQ, N

	   DOUBLE	  PRECISION RHO

	   INTEGER	  INDXQ( * ), IWORK( * )

	   DOUBLE	  PRECISION D( * ), Q( LDQ, * ), WORK( * )

PURPOSE
       DLAED1 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 eigenvectors of a tridiagonal matrix.  DLAED7 handles the  case	in  which
       eigenvalues  only  or  eigenvalues  and eigenvectors of a full symmetric matrix (which was
       reduced to tridiagonal form) 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 DLAED2.

	     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 DLAED3).
	     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.

       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  (input/output) INTEGER array, dimension (N)
	      On entry, the permutation which separately sorts the  two  subproblems  in  D  into
	      ascending  order.   On exit, the permutation which will reintegrate the subproblems
	      back into sorted order, i.e. D( INDXQ( I = 1, N ) ) will be in ascending order.

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

	      CUTPNT (input) INTEGER The location of the last  eigenvalue  in  the  leading  sub-
	      matrix.  min(1,N) <= CUTPNT <= N/2.

       WORK   (workspace) DOUBLE PRECISION array, dimension (4*N + N**2)

       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
       Modified by Francoise Tisseur, University of Tennessee.

LAPACK version 3.0			   15 June 2000 				DLAED1(l)


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