ESMF_DLASD4 Subroutine

subroutine ESMF_DLASD4(N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO)

\brief \b ESMF_DLASD4 \htmlonly Download ESMF_DLASD4 + dependencies [TGZ] [ZIP] [TXT] \endhtmlonly \par Purpose:

\verbatim

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. \endverbatim \param[in] N \verbatim N is INTEGER The length of all arrays. \endverbatim

\param[in] I \verbatim I is INTEGER The index of the eigenvalue to be computed. 1 <= I <= N. \endverbatim

\param[in] D \verbatim D is DOUBLE PRECISION array, dimension ( N ) The original eigenvalues. It is assumed that they are in order, 0 <= D(I) < D(J) for I < J. \endverbatim

\param[in] Z \verbatim Z is DOUBLE PRECISION array, dimension ( N ) The components of the updating vector. \endverbatim

\param[out] DELTA \verbatim DELTA is 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. \endverbatim

\param[in] RHO \verbatim RHO is DOUBLE PRECISION The scalar in the symmetric updating formula. \endverbatim

\param[out] SIGMA \verbatim SIGMA is DOUBLE PRECISION The computed sigma_I, the I-th updated eigenvalue. \endverbatim

\param[out] WORK \verbatim WORK is 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. \endverbatim

\param[out] INFO \verbatim INFO is INTEGER = 0: successful exit > 0: if INFO = 1, the updating process failed. \endverbatim \par Internal Parameters:

\verbatim 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. \endverbatim \author Univ. of Tennessee \author Univ. of California Berkeley \author Univ. of Colorado Denver \author NAG Ltd. \date November 2011 \ingroup auxOTHERauxiliary \par Contributors:

Ren-Cang Li, Computer Science Division, University of California
at Berkeley, USA

Arguments