SLAED4 (3) Linux Manual Page

slaed4.f –

Synopsis

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 (integerN, integerI, real, dimension( * )D, real, dimension( * )Z, real, dimension( * )DELTA, realRHO, realDLAM, integerINFO)

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

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:

N

 N is INTEGER

 The length of all arrays.

I

 I is INTEGER

 The index of the eigenvalue to be computed. 1 <= I <= N.

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.

Z

 Z is REAL array, dimension (N)

 The components of the updating vector.

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.

RHO

 RHO is REAL

 The scalar in the symmetric updating formula.

DLAM

 DLAM is REAL

 The computed lambda_I, the I-th updated eigenvalue.

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.

Author

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