%function []=prob_9_1_10()
%
% Written by:
% -- 
% John L. Weatherwax                2006-12-16
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

addpath( '../Tcodes' ); 

eArray = 10.^( [ -3 -6 -9 -12 -15 ] ); 

clc; close all; 

% Without pivoting we have:
% 
A = ones(2,2); b = 2*ones(2,1); errorA=zeros(size(b));
for ei=1:length(eArray),
  % replace the (1,1) entry in A and b with the correct values
  A(1,1) = eArray(ei); 
  b(1) = 1+eArray(ei); 
  % solve the system (without pivoting):
  x = slv(A,b);
  errorA(ei) = norm( [1,1] - x );
end

figure; loglog( eArray, errorA, 'o' ); 
xlabel( 'epsilon value' ); ylabel( 'normed errorA against truth' ); 
title( 'WITHOUT pivoting. epsilon v.s. error' ); 


% With pivoting we have:
% 
A = ones(2,2); b = 2*ones(2,1); errorA=zeros(size(b));
for ei=1:length(eArray),
  % replace the (2,1) entry in A and b with the correct values
  A(2,1) = eArray(ei); 
  b(2) = 1+eArray(ei); 
  % solve the system (without pivoting):
  x = slv(A,b);
  errorA(ei) = norm( [1,1] - x )+eps;
end

figure; loglog( eArray, errorA, 'o' ); 
xlabel( 'epsilon value' ); ylabel( 'normed errorA against truth' ); 
title( 'WITH pivoting. epsilon v.s. error' );