slaed4.f File Reference

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Functions/Subroutines
subroutine	slaed4 (N, I, D, Z, DELTA, RHO, DLAM, INFO)
	SLAED4 used by sstedc. Finds a single root of the secular equation.

---

Function/Subroutine Documentation

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 .GT. 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.

Date:

September 2012

Contributors:

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

Definition at line 146 of file slaed4.f.

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