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/FTLEH.m

@@ -0,0 +1,149 @@
+tic
+clear all
+%% Choice of the mass parameter
+mu=0.1;
+
+%% Computation of Lagrangian Points
+[xl1,yl1,xl2,yl2,xl3,yl3,xl4,yl4,xl5,yl5] = Lagr(mu);
+
+%% Computation of initial total energy
+E_L1=-Omega(xl1,yl1,mu);
+E=E_L1+0.03715; % Offset as in figure 2.2 "LCS in the ER3BP"
+
+%% Initial conditions range
+x_0_min=-0.8;
+x_0_max=-0.2;
+
+vx_0_min=-2;
+vx_0_max=2;
+
+y_0=0;
+
+% Elements for grid definition
+n=200;
+
+% Dimensionless integrating time
+T=2;
+
+% Grid initializing
+[x_0,vx_0]=ndgrid(linspace(x_0_min,x_0_max,n),linspace(vx_0_min,vx_0_max,n));
+vy_0=sqrt(2*E+2*Omega(x_0,y_0,mu)-vx_0.^2);
+
+% Kinetic energy computation
+E_cin=E+Omega(x_0,y_0,mu);
+
+%% Transforming into Hamiltonian variables
+px_0=vx_0-y_0;
+py_0=vy_0+x_0;
+
+% Inizializing
+x_T=zeros(n,n);
+y_T=zeros(n,n);
+px_T=zeros(n,n);
+py_T=zeros(n,n);
+filtro=ones(n,n);
+E_T=zeros(n,n);
+a=zeros(n,n); % matrix of numbers of integration steps for each integration
+np=0; % number of integrated points
+
+fprintf(' con n = %i\n',n)
+
+%% Energy tolerance setting
+energy_tol=inf;
+
+%% Computation of the Jacobian of the system
+options=odeset('Jacobian',@cr3bp_jac);
+
+%% Parallel integration of equations of motion
+parfor i=1:n
+	for j=1:n
+		if E_cin(i,j)>0 && isreal(vy_0(i,j)) % Check for real velocity and positive Kinetic energy
+			[t,Y]=ode45(@fH,[0 T],[x_0(i,j); y_0; px_0(i,j); py_0(i,j)],options);
+            % Try to obtain the name of the solver for a following use
+%  			sol=ode45(@f,[0 T],[x_0(i,j); y_0; vx_0(i,j); vy_0(i,j)],options);
+% 			Y=sol.y';
+% 			solver=sol.solver;
+			a(i,j)=length(Y);
+            %Saving solutions
+			x_T(i,j)=Y(a(i,j),1); 
+			px_T(i,j)=Y(a(i,j),3);
+			y_T(i,j)=Y(a(i,j),2);
+			py_T(i,j)=Y(a(i,j),4);
+			%Computation of final total energy and difference with
+			%initial one
+			E_T(i,j)=EnergyH(x_T(i,j),y_T(i,j),px_T(i,j),py_T(i,j),mu);
+			delta_E=abs(E_T(i,j)-E);
+			if  delta_E > energy_tol; %Check of total energy conservation
+				fprintf(' Ouch! Wrong Integration: i,j=(%i,%i)\n E_T=%.2f \n delta_E=%.2f\n\n',i,j,E_T(i,j),delta_E);
+				filtro(i,j)=2; %Saving position of the point
+            end
+			np=np+1;
+        else
+			filtro(i,j)=0; % 1=interesting point; 0=non-sense point; 2= bad integration point		
+		end
+	end
+end
+
+t_integrazione=toc;
+fprintf('  n = %i\n',n)
+fprintf(' energy_tol = %.2f\n',energy_tol)
+fprintf('total	\t%i\n',n^2)
+fprintf('nunber	\t%i\n',np)
+fprintf('time to integrate	\t%.2f s\n',t_integr)
+
+%% Back to Lagrangian variables
+vx_T=px_T+y_T;
+vy_T=py_T-x_T;
+%% FTLE Computation
+fprintf('adesso calcolo ftle\n')
+tic
+dphi=zeros(2,2);
+ftle=zeros(n-2,n-2);
+
+for i=2:n-1
+	for j=2:n-1
+		if filtro(i,j) && ... % Check for interesting point
+				filtro(i,j-1) && ...
+				filtro(i,j+1) && ...
+				filtro(i-1,j) && ...
+				filtro(i+1,j)
+			
+			dphi(1,1)=(x_T(i-1,j)-x_T(i+1,j))/(x_0(i-1,j)-x_0(i+1,j));
+			
+			dphi(1,2)=(x_T(i,j-1)-x_T(i,j+1))/(vx_0(i,j-1)-vx_0(i,j+1));
+			
+			dphi(2,1)=(vx_T(i-1,j)-vx_T(i+1,j))/(x_0(i-1,j)-x_0(i+1,j));
+			
+			dphi(2,2)=(vx_T(i,j-1)-vx_T(i,j+1))/(vx_0(i,j-1)-vx_0(i,j+1));
+            
+			if filtro(i,j)==2 % Manual setting to visualize bad integrated points 
+				ftle(i-1,j-1)=-Inf;
+			else
+				ftle(i-1,j-1)=1/(2*T)*log(max(abs(eig(dphi'*dphi))));
+			end
+		end
+	end
+end
+
+%% Plotting results
+% figure
+% plot(t,Y)
+% figure
+% plot(Y(:,1),Y(:,2))
+% figure
+
+xx=linspace(x_0_min,x_0_max,n);
+vvx=linspace(vx_0_min,vx_0_max,n);
+[x,vx]=ndgrid(xx(2:n-1),vvx(2:n-1));
+figure
+pcolor(x,vx,ftle)
+shading flat
+
+t_ftle=toc;
+fprintf('tempo per integrare      \t%.2f s\n',t_integrazione)
+fprintf('tempo per calcolare ftle \t%.2f s\n',t_ftle)
+
+% save(['var_' num2str(n) '_' num2str(clock(4)])
+
+nome=['var_xvx_', 'ode00', '_n',num2str(n),'_e',num2str(energy_tol),'_H'];
+save(nome)