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dlasd4 examples
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Man Page Details
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NAME
       DLASD4  -  compute  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 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. 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 construct 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.

  Internal 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

