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 (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.  

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:

December 2016

Contributors:

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

Definition at line 147 of file slaed4.f.

Author

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Referenced By

The man page slaed4(3) is an alias of slaed4.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK