dlasd4 man page on Scientific

Man page or keyword search:  
man Server   26626 pages
apropos Keyword Search (all sections)
Output format
Scientific logo
[printable version]

DLASD4(1)	    LAPACK auxiliary routine (version 3.2)	     DLASD4(1)

NAME
       DLASD4  - subroutine compute the square root of the I-th updated eigen‐
       value of a positive symmetric rank-one modification to a positive diag‐
       onal 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 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 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 sec‐
       ular 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 compo‐
	      nent.  If N = 1, then DELTA(1) = 1.  The vector  DELTA  contains
	      the  information necessary to construct the (singular) eigenvec‐
	      tors.

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

       SIGMA  (output) DOUBLE PRECISION
	      The computed sigma_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	compo‐
	      nent.  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 auxiliary routine (versioNovember 2008			     DLASD4(1)
[top]

List of man pages available for Scientific

Copyright (c) for man pages and the logo by the respective OS vendor.

For those who want to learn more, the polarhome community provides shell access and support.

[legal] [privacy] [GNU] [policy] [cookies] [netiquette] [sponsors] [FAQ]
Tweet
Polarhome, production since 1999.
Member of Polarhome portal.
Based on Fawad Halim's script.
....................................................................
Vote for polarhome
Free Shell Accounts :: the biggest list on the net