% Matlab code LanczosDemo.m
% For "Applied Numerical Linear Algebra", Chapter 7
% Written by James Demmel, Jun 6, 1997
%
% This program sets up the data for the plots of the
% Lanczos algorithm in Chapter 7
%
% e contains the eigenvalues, in decreasing order
clear e;
clear A;
e = [
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%
% A is a 1000x1000 diagonal sparse matrix with e as eigenvalues
%
A = spdiags(e,0,1000,1000);
%
% q is the starting vector for Lanczos (unnormalized)
%
q = ones(1000,1);
q(999) = 1e-5;
%
% m is the number of Lanczos steps to take
%
m = 99;
%
% The following paramters control the printing
%
% mm1,mm2 = indices of extreme eigenvalues for which to plot error
% and error bounds
mm1 = 1;
mm2 = 4;
%
% mine, maxe = range in which to plot eigenvalues
mine = -4;
maxe = 4;
%
% steplabel = array of values at which to draw vertical lines in plots
steplabel = (10:10:150);
%
% recomp = 1 to perform algorithm from scratch
% = 0 just to redisplay data, with possibly different
% mine, maxe, mm1, mm2, steplabel
recomp = 1;
%
% whichbound = 2 to plot all errors and error bounds
% = 1 to plot local error and error bounds
% = 0 to plot error bounds only
whichbound = 2;
%
% displayselection = 1 to display details of which Ritz vectors
% are selected, as Lanczos runs
% = 0 not to display details
displayselection = 0;