slaed4()

subroutine slaed4	(	integer	N,
		integer	I,
		real, dimension( * )	D,
		real, dimension( * )	Z,
		real, dimension( * )	DELTA,
		real	RHO,
		real	DLAM,
		integer	INFO
	)

SLAED4 used by SSTEDC. Finds a single root of the secular equation.

Download SLAED4 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

 This subroutine computes the I-th updated eigenvalue of a symmetric
 rank-one modification to a diagonal matrix whose elements are
 given in the array d, and that

            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 )  +  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, 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 > 2, DELTA contains (D(j) - lambda_I) in its j-th component. If N = 1, then DELTA(1) = 1. If N = 2, see SLAED5 for detail. The vector DELTA contains the information necessary to construct the eigenvectors by SLAED3 and SLAED9.
[in]	RHO	RHO is REAL The scalar in the symmetric updating formula.
[out]	DLAM	DLAM is REAL The computed lambda_I, the I-th updated eigenvalue.
[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