Added matlab code samples.

All of these code samples currently are mis-identified in my repositories. I'm
donating them to the cause.

samples/Matlab/example.m

@@ -0,0 +1,41 @@
+clear all
+tic
+% initialize integration time T, f(x,t), discretization size n ----------------
+T = 20;
+f_x_t = inline('[v(2);-sin(v(1))]','t','v');
+grid_min = -3.4;
+grid_max = 3.4;
+grid_width = grid_max-grid_min;
+n = 35;
+grid_spacing = grid_min:(grid_width/(n-1)):grid_max;
+advected_x=zeros(n,n);
+advected_y=zeros(n,n);
+% integrate all initial points for t in [0,T] --------------------------------
+for i = 1:n
+	for j = 1:n
+		[t,x] = ode45(f_x_t,[0,T],[grid_spacing(i),grid_spacing(j)]);
+		% store advected positions as they would appear in (x,y) coords ------
+		advected_x(n-j+1,i) = x(length(x(:,1)),1);
+		advected_y(n-j+1,i) = x(length(x(:,2)),2);
+	end
+end
+sigma=zeros(n,n);
+% at each point in interior of grid, store FTLE ------------------------------
+for i = 2:n-1
+	for j = 2:n-1
+		% compute Jacobian phi -----------------------------------------------
+		phi(1,1) = (advected_x(i,j+1)-advected_x(i,j-1))/(2*grid_width/(n-1));
+		phi(1,2) = (advected_x(i-1,j)-advected_x(i+1,j))/(2*grid_width/(n-1));
+		phi(2,1) = (advected_y(i,j+1)-advected_y(i,j-1))/(2*grid_width/(n-1));
+		phi(2,2) = (advected_y(i-1,j)-advected_y(i+1,j))/(2*grid_width/(n-1));
+		% find max eigenvalue of phi'*phi ------------------------------------
+		lambda_max = max(abs(eig(phi'*phi)));
+		% store FTLE ---------------------------------------------------------
+		sigma(i,j) = log(lambda_max)/abs(T);
+	end
+end
+toc
+%% plot FTLE field ------------------------------------------------------------
+figure
+contourf(grid_spacing,grid_spacing,sigma);
+colorbar('location','EastOutside');