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RedHat 9 (Linux i386) - man page for dlasd4 (redhat section l)

DLASD4(l)					)					DLASD4(l)

NAME
       DLASD4  - subroutine computes the square root of the I-th updated eigenvalue of a positive
       symmetric rank-one modification to a positive diagonal matrix whose entries are	given  as
       the  squares of the corresponding entries in the array d, and that  0 <= D(i) < D(j) for i
       < j  and that RHO > 0

SYNOPSIS
       SUBROUTINE DLASD4( N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO )

	   INTEGER	  I, INFO, N

	   DOUBLE	  PRECISION RHO, SIGMA

	   DOUBLE	  PRECISION D( * ), DELTA( * ), WORK( * ), Z( * )

PURPOSE
       This subroutine computes the square root of the I-th updated eigenvalue of a positive sym-
       metric  rank-one modification to a positive diagonal matrix whose entries are given as the
       squares of the corresponding entries in the array d, and that 0 <= D(i) < D(j) for i  <	j
       and  that  RHO > 0. This is arranged by the calling routine, and is no loss in generality.
       The rank-one modified system is thus

	      diag( D ) * diag( D ) +  RHO *  Z * Z_transpose.

       where we assume the Euclidean norm of Z is 1.

       The method consists of approximating the rational functions in  the  secular  equation  by
       simpler interpolating rational functions.

ARGUMENTS
       N      (input) INTEGER
	      The length of all arrays.

       I      (input) INTEGER
	      The index of the eigenvalue to be computed.  1 <= I <= N.

       D      (input) DOUBLE PRECISION array, dimension ( N )
	      The  original  eigenvalues.  It is assumed that they are in order, 0 <= D(I) < D(J)
	      for I < J.

       Z      (input) DOUBLE PRECISION array, dimension ( N )
	      The components of the updating vector.

       DELTA  (output) DOUBLE PRECISION array, dimension ( N )
	      If N .ne. 1, DELTA contains (D(j) - sigma_I) in its  j-th component.   If  N  =  1,
	      then  DELTA(1)  =  1.   The vector DELTA contains the information necessary to con-
	      struct the (singular) eigenvectors.

       RHO    (input) DOUBLE PRECISION
	      The scalar in the symmetric updating formula.

       SIGMA  (output) DOUBLE PRECISION
	      The computed lambda_I, the I-th updated eigenvalue.

       WORK   (workspace) DOUBLE PRECISION array, dimension ( N )
	      If N .ne. 1, WORK contains (D(j) + sigma_I) in its  j-th component.  If N = 1, then
	      WORK( 1 ) = 1.

       INFO   (output) INTEGER
	      = 0:  successful exit
	      > 0:  if INFO = 1, the updating process failed.

PARAMETERS
       Logical	variable  ORGATI (origin-at-i?) is used for distinguishing whether D(i) or D(i+1)
       is treated as the origin.

       ORGATI = .true.	  origin at i ORGATI = .false.	 origin at i+1

       Logical variable SWTCH3 (switch-for-3-poles?) is for noting if we are working  with  THREE
       poles!

       MAXIT is the maximum number of iterations allowed for each eigenvalue.

       Further Details ===============

       Based on contributions by Ren-Cang Li, Computer Science Division, University of California
       at Berkeley, USA

LAPACK version 3.0			   15 June 2000 				DLASD4(l)


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