slasd4()

subroutine slasd4	(	integer	n,
		integer	i,
		real, dimension( * )	d,
		real, dimension( * )	z,
		real, dimension( * )	delta,
		real	rho,
		real	sigma,
		real, dimension( * )	work,
		integer	info )

SLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by sbdsdc.

Download SLASD4 + dependencies [TGZ] [ZIP] [TXT]

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.
!> 

Parameters

[in]	N	!> N is INTEGER !> The length of all arrays. !>
[in]	I	!> I is INTEGER !> The index of the eigenvalue to be computed. 1 <= I <= N. !>
[in]	D	!> D is REAL array, dimension ( N ) !> The original eigenvalues. It is assumed that they are in !> order, 0 <= D(I) < D(J) for I < J. !>
[in]	Z	!> Z is REAL array, dimension ( N ) !> The components of the updating vector. !>
[out]	DELTA	!> DELTA is REAL 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. !>
[in]	RHO	!> RHO is REAL !> The scalar in the symmetric updating formula. !>
[out]	SIGMA	!> SIGMA is REAL !> The computed sigma_I, the I-th updated eigenvalue. !>
[out]	WORK	!> WORK is REAL 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. !>
[out]	INFO	!> INFO is 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.
!> 

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

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