% Copyright (c) 2001-2009 by Ales Cerny

%************************************************************************%
% chapter11sect9c.m - supplementary program to                            %
% Ales Cerny (2009) Mathematical Techniques in Finance (2nd ed.)         % 
% Princeton University Press http://press.princeton.edu/titles/9079.html %
%************************************************************************%
    
% This code is provided 'as-is', without any express or implied warranty.  
% 
% Permission is granted to anyone to use this code for any purpose, 
% subject to the following restrictions:
% 
% 1. The origin of this code must not be misrepresented; you must not
%    claim that you wrote the original code.
% 2. Modified code versions must be plainly marked as such, and must not 
%    be misrepresented as being the original code.
% 3. This notice may not be removed from any source distribution.

% NOTICE TO STUDENTS: To avoid accusations of plagiarism, if you use this 
% code or its modifications in assessed work you should prepend it with a 
% note stating: 
%   "This is the original/modified version of the code chapter11sect9c.m by 
%    Ales Cerny (2009), Mathematical Techniques in Finance (2nd ed.),  
%    Princeton University Press. The original version is available from 
%    http://www.martingales.info/mtfweb2".
% A similar acknowledgement should appear prominently inside your written 
% report.

clear;
clc;

data= [-0.02918     0.06140    -0.00259722;
        0.08962    -0.1523      0.01854934;
        0.15155     0.10073     0.13588459; 
       -0.12491    -0.09442    -0.11532253; 
       -0.04639     0.01230    -0.02901336; 
        0.05284     0.03451     0.04719985;
        0.03719     0.03337     0.03586913; 
       -0.00900     0.10135     0.02323722; 
       -0.18073    -0.09395    -0.15441354; 
        0.05896    -0.00299     0.04056263]; 

sigY=data'* data;
[Q,R] = qr(data,0);
idx = rank(R); 
disp(' ');
disp('         covariance matrix sigY             ');
disp(' ');
disp(sigY);
disp(' ');
disp(' ');
disp('lower triangular matrix from QR decomposition of data');
disp(' ');
disp(R(1:idx,:)');
disp(' ');
disp(' ');
disp('                  R * R''                      ');
disp(' ');
disp(R'*R);
disp(' ');