[Octave-bug-tracker] [bug #44004] eig and eigs routine

[Sebastian Glane]

URL:
  <http://savannah.gnu.org/bugs/?44004>

                 Summary: eig and eigs routine
                 Project: GNU Octave
            Submitted by: sebastian_g
            Submitted on: Wed 14 Jan 2015 06:06:42 PM GMT
                Category: Octave Function
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Inaccurate Result
                  Status: None
             Assigned to: None
         Originator Name: 
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: 3.8.1
        Operating System: GNU/Linux

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Details:

The code below demonstrates a large difference in the computed eigenvalues of
the eig- and eigs-routine. eigs will find complex pairs whereas eig finds real
ones.

It gets much better if you replace 'sm' by 'sr'. Execute the script a few
times and observe that somehow large difference occure. This seems unreliable
to me.

By the way, if you choose 'sr' and p=3, you will get the error

sigma = "sr" requires complex or unsymmetric problem



% solves Eigenvalue Problem
%   -y''= lambda^2 y on the interval (a,b)
%
% with mixed boundary conditions
%   -- dirichlet boundary condition y(a)=0
%   -- robin boundary condition   y'(b)=y(b)
clear all;
close all;
p=6;
%% number of points
n=2^p;
%% grid space
h=1/2^p;
%% numbers of eigenvalues to find
kmax=8;
%% assemble symmetric 2nd finite difference matrix
Lh=-gallery('tridiag',n,1,-2,1)./(h^2);
%% apply robin boundary in last line
Lh(n,:)=0.0;
Lh(n,n-1)=-2/h^2;
Lh(n,n)=-1/h^2*(2*h-2);
%% use eig to get all eigenvalues
[~,LambdaEig]=eig(Lh);
LambdaEig=sort(diag(LambdaEig));
lambdaEig=LambdaEig(1:kmax);
%% use eigs routine to get 1st kmax eigenvalues of smallest magnitude
[~,LambdaEigs,fl]=eigs(Lh,kmax,'sm');
lambdaEigs=sort(diag(LambdaEigs))(1:kmax);
%% compute difference of 1st kmax eigenvalues of smallest magnitude
err=abs(lambdaEig-lambdaEigs)






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