% matrix_timing checks how the time to do matrix operations scales
%   with the dimension of the matrix.  It uses the MATLAB tic and toc
%   functions to do the timing.

% Programmer: Dick Furnstahl  furnstahl.1@osu.edu
% Revision history:
%   20-May-2005 -- original version for Physics 263
close all; clear;          % this closes plots and sets variables to zero

exp_min = 2;        % the smallest matrix dimension is 10^(exp_min)
exp_max = 3;        % the largest matrix dimension is 10^(exp_max)
num_matrices = 10;  % the number of different matrices to test

% sizes is an array with the range of matrix dimensions,
%  spaced logarithmically (and rounded to integers)
sizes = round( logspace(exp_min,exp_max,num_matrices) );  
                 
% consider each matrix size in turn
for n = 1:num_matrices
   size = sizes(n);        % "size" is the dimension of the current matrix
   disp('now calculating matrix dimension: '); disp(size);  % print out 

   M = rand(size,size);    % create a size-by-size matrix with random 
                           %  entries between 0 and 1 

   % timing for taking a determinant
   tic;                    % start the stopwatch
   detM = det(M);          % do the calculation we're timing
   time_det(n) = toc;      % stop the stopwatch and save the result in 
                           %  the vector time_det
   
   % timing for taking an inverse
   tic;                    % start the stopwatch
   inverseM = inv(M);      % do the calculation we're timing
   time_inv(n) = toc;      % stop the stopwatch and save the result in 
                           %  the vector time_inv
end

figure(1);
% plot the first curve with circles ('o')
loglog(sizes,time_det,'o');
title('time for matrix operations');            % add a title
xlabel('dimension of matrix'); ylabel('time');  % add labels
hold on;

% now plot another curve with 'x' (others: '*', '+')
loglog(sizes,time_inv,'x');
legend('determinant','inverse');
hold off;