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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 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.

