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/double_gyre.m

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+clear all
+tic
+% initialize integration time T, f(x,t), discretization size n ----------------
+T = 8;
+x_min=0;
+x_max=2;
+y_min=0;
+y_max=1;
+n=50; % how many points per one measure unit (both in x and in y)
+ds=1/(n-1);
+x_res=(x_max-x_min)*n;
+y_res=(y_max-y_min)*n;
+grid_x=linspace(x_min,x_max,x_res);
+grid_y=linspace(y_min,y_max,y_res);
+
+advected_x=zeros(x_res,y_res);
+advected_y=zeros(x_res,y_res);
+% integrate all initial points for t in [0,T] --------------------------------
+parfor i = 1:x_res
+	for j = 1:y_res
+		[t,X] = ode45(@dg,[0,T],[grid_x(i),grid_y(j)]);
+		% store advected positions as they would appear in (x,y) coords ------
+		advected_x(i,j) = X(length(X(:,1)),1);
+		advected_y(i,j) = X(length(X(:,2)),2);
+	end
+end
+%% Compute FTLE
+sigma=zeros(x_res,y_res);
+% at each point in interior of grid, store FTLE ------------------------------
+for i = 2:x_res-1
+	for j = 2:y_res-1
+		% compute Jacobian phi -----------------------------------------------
+		phi(1,1) = (advected_x(i+1,j)-advected_x(i-1,j))/(2*ds);
+		phi(1,2) = (advected_x(i,j-1)-advected_x(i,j+1))/(2*ds);
+		phi(2,1) = (advected_y(i+1,j)-advected_y(i-1,j))/(2*ds);
+		phi(2,2) = (advected_y(i,j-1)-advected_y(i,j+1))/(2*ds);
+		% find max eigenvalue of phi'*phi ------------------------------------
+		lambda_max = max(abs(eig(phi'*phi)));
+		% store FTLE ---------------------------------------------------------
+		sigma(i,j) = log(lambda_max)/abs(2*T);
+	end
+end
+toc
+%% plot FTLE field ------------------------------------------------------------
+figure
+contourf(grid_x,grid_y,sigma');
+colorbar('location','EastOutside');
+axis equal
+shading flat