slaed4.f man 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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Referenced By

slaed4(3) is an alias of slaed4.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK