% Name: 

% main function for Exercise 1
clear all
close all
format compact

% Test the two functions matVec and invMatVec
  R = triu(rand(5))+ eye(5); %generate random 5 x 5 triangular matrix R
  x = rand(5,1);              %generate random 5 x 1 vector x
  
          %calculate solution of Rx with matVec
          %calculate solution of Rx with *
          %compare the two solutions
          
          %calculate solution of R^{-1}x with invMatVec
          %calculate solution of R^{-1}x with \
          %compare the two solutions
  

          
% Time measurements
N= 2.^[1:12]; %take 2^[1:10] for old PC's

% Rx
b1 = matVec(R,x);
timeMV = zeros(size(N,2),1);
for k = 1:size(N,2)
  n = N(k)
              % create Random n x n upper triangular matrix R
              % create random n x 1 vector x
  tic
              % calculate solution b = Rx
  timeMV(k) = toc;
end


% R^{-1}x
b1 = invMatVec(R,x);
timeIMV = zeros(size(N,2),1);
for k = 1:size(N,2)
  n = N(k)
              % create Random n x n upper triangular matrix R
              % create random n x 1 vector x
  tic
              % calculate solution b = R^{-1}x
  timeIMV(k) = toc;
end


% Create loglog Plot for the times
loglog(N,timeMV,'d-')
hold on
loglog(N,timeIMV,'ro-')
legend('MatVec','InvMatVec','location','SouthEast')
xlabel('N')
ylabel('time [s]')
xlim([1,5000])