% MACM 316 - Week 3
% Computation Time demo
% Description: Finds the mean computation time for Gaussian Elimination on a
% random matrix
% Instructor: Ben Adcock
%

clear

Ntr=200; % Number of trials
N=200; % Matrix size
stepsize = 5;
%meanvector = zeros((N/stepsize),1);
meanvector = zeros(N,1);
xvector = 1:1:N;

%times=zeros(Ntr,1); % Vector of timing data for Ntr trials
%times = zeros(N/stepsize,1);
for i=1:N %keep incrementing for different N with set stepsize
    times = zeros(Ntr,1);
    for j=1:Ntr

        % Form a random matrix A and right-hand side b (normally distributed)
        A=randn(N,N);
        b=randn(N,1);

        % Apply backslash and calculate time taken
        tic;
        x=A\b;
        times(j)=toc;

    end
    meantimes = mean(times);
    meanvector(i) = meantimes
end

N;
%mean_time=mean(times);
plot(xvector,meanvector,'r+')
%loglog(xvector,meanvector,'r+')
title(['Mean time vs Matrix Size'])
xlabel(['Matrix size'])
ylabel(['Mean time'])
hold on
%scatter(xvector,meanvector)
%lsline
%hold on
hold on
%f = polyfit(xvector',meanvector,1)
%plot(xvector,f)
%x1 = [1:1:N]
%y1 = polyval(f,x1)
%loglog(x1,y1)
%hold on