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https://github.com/KevinMidboe/linguist.git
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Added matlab code samples.
All of these code samples currently are mis-identified in my repositories. I'm donating them to the cause.
This commit is contained in:
Michele Mastropietro
178
samples/Matlab/FTLE_reg.m
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178
samples/Matlab/FTLE_reg.m
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tic
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clear all
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%% Elements for grid definition
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n=100;
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%% Dimensionless integrating time
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T=2;
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%% Choice of the mass parameter
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mu=0.1;
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%% Computation of Lagrangian Points
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[xl1,yl1,xl2,yl2,xl3,yl3,xl4,yl4,xl5,yl5] = Lagr(mu);
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%% Computation of initial total energy
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E_L1=-Omega(xl1,yl1,mu);
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C_L1=-2*E_L1; % C_L1 = 3.6869532299 from Szebehely
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E=E_L1+0.03715; % Offset as in figure 2.2 "LCS in the ER3BP"
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%% Initial conditions range
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x_0_min=-0.8;
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x_0_max=-0.2;
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vx_0_min=-2;
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vx_0_max=2;
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y_0=0;
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% Grid initializing
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[x_0,vx_0]=ndgrid(linspace(x_0_min,x_0_max,n),linspace(vx_0_min,vx_0_max,n));
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vy_0=sqrt(2*E+2.*Omega(x_0,y_0,mu)-vx_0.^2);
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% Kinetic energy computation
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E_cin=E+Omega(x_0,y_0,mu);
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% Inizializing
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x_T=zeros(n,n);
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y_T=zeros(n,n);
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vx_T=zeros(n,n);
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vy_T=zeros(n,n);
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filtro=ones(n,n);
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E_T=zeros(n,n);
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delta_E=zeros(n,n);
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a=zeros(n,n); % matrix of numbers of integration steps for each integration
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np=0; % number of integrated points
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fprintf('integro con n = %i\n',n)
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%% Energy tolerance setting
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energy_tol=0.1;
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%% Setting the options for the integrator
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RelTol=1e-12;AbsTol=1e-12; % From Short
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% RelTol=1e-13;AbsTol=1e-22; % From JD James Mireles
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% RelTol=3e-14;AbsTol=1e-16; % HIGH accuracy from Ross
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options=odeset('AbsTol',AbsTol,'RelTol',RelTol);
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%% Parallel integration of equations of motion
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h=waitbar(0,'','Name','Integration in progress, please wait!');
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S=zeros(n,n);
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r1=zeros(n,n);
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r2=zeros(n,n);
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g=zeros(n,n);
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for i=1:n
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waitbar(i/n,h,sprintf('Computing i=%i',i));
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parfor j=1:n
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r1(i,j)=sqrt((x_0(i,j)+mu).^2+y_0.^2);
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r2(i,j)=sqrt((x_0(i,j)-1+mu).^2+y_0.^2);
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g(i,j)=((1-mu)./(r1(i,j).^3)+mu./(r2(i,j).^3));
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if E_cin(i,j)>0 && isreal(vy_0(i,j)) % Check for real velocity and positive Kinetic energy
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S(i,j)=g(i,j)*T;
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[s,Y]=ode45(@f_reg,[0 S(i,j)],[x_0(i,j); y_0; vx_0(i,j); vy_0(i,j)],options,mu);
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a(i,j)=length(Y);
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% if s(a(i,j)) < 2
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% filtro(i,j)=3;
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% end
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% Saving solutions
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x_T(i,j)=Y(a(i,j),1);
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vx_T(i,j)=Y(a(i,j),3);
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y_T(i,j)=Y(a(i,j),2);
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vy_T(i,j)=Y(a(i,j),4);
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% Computation of final total energy and difference with
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% initial one
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E_T(i,j)=Energy(x_T(i,j),y_T(i,j),vx_T(i,j),vy_T(i,j),mu);
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delta_E(i,j)=abs(E_T(i,j)-E);
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if delta_E(i,j) > energy_tol; % Check of total energy conservation
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fprintf(' Ouch! Wrong Integration: i,j=(%i,%i)\n E_T=%.2f \n delta_E=%f\n\n',i,j,E_T(i,j),delta_E(i,j));
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filtro(i,j)=2; % Saving position of the point
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end
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np=np+1;
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else
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filtro(i,j)=0; % 1 = interesting point; 0 = non-sense point; 2 = bad integration point
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end
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end
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end
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close(h);
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t_integrazione=toc;
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%%
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filtro_1=filtro;
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for i=2:n-1
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for j=2:n-1
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if filtro(i,j)==2 || filtro (i,j)==3
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filtro_1(i,j)=2;
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filtro_1(i+1,j)=2;
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filtro_1(i-1,j)=2;
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filtro_1(i,j+1)=2;
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filtro_1(i,j-1)=2;
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end
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end
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end
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fprintf('integato con n = %i\n',n)
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fprintf('integato con energy_tol = %f\n',energy_tol)
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fprintf('numero punti totali \t%i\n',n^2)
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fprintf('numero punti integrati \t%i\n',np)
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fprintf('tempo per integrare \t%.2f s\n',t_integrazione)
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%% FTLE Computation
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fprintf('adesso calcolo ftle\n')
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tic
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dphi=zeros(2,2);
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ftle=zeros(n-2,n-2);
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ftle_norm=zeros(n-2,n-2);
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ds_x=(x_0_max-x_0_min)/(n-1);
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ds_vx=(vx_0_max-vx_0_min)/(n-1);
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for i=2:n-1
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for j=2:n-1
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if filtro_1(i,j) && ... % Check for interesting point
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filtro_1(i,j-1) && ...
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filtro_1(i,j+1) && ...
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filtro_1(i-1,j) && ...
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filtro_1(i+1,j)
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% La direzione dello spostamento la decide il denominatore
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% TODO spiegarsi teoricamente come mai la matrice pu<EFBFBD>
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% essere ridotta a 2x2
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dphi(1,1)=(x_T(i+1,j)-x_T(i-1,j))/(2*ds_x); %(x_0(i-1,j)-x_0(i+1,j));
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dphi(1,2)=(x_T(i,j+1)-x_T(i,j-1))/(2*ds_vx); %(vx_0(i,j-1)-vx_0(i,j+1));
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dphi(2,1)=(vx_T(i+1,j)-vx_T(i-1,j))/(2*ds_x); %(x_0(i-1,j)-x_0(i+1,j));
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dphi(2,2)=(vx_T(i,j+1)-vx_T(i,j-1))/(2*ds_vx); %(vx_0(i,j-1)-vx_0(i,j+1));
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if filtro_1(i,j)==2 % Manual setting to visualize bad integrated points
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ftle(i-1,j-1)=0;
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else
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ftle(i-1,j-1)=(1/abs(T))*log(max(sqrt(abs(eig(dphi*dphi')))));
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ftle_norm(i-1,j-1)=(1/abs(T))*log(norm(dphi));
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end
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end
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end
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end
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%% Plotting results
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% figure
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% plot(t,Y)
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% figure
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% plot(Y(:,1),Y(:,2))
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% figure
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xx=linspace(x_0_min,x_0_max,n);
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vvx=linspace(vx_0_min,vx_0_max,n);
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[x,vx]=ndgrid(xx(2:n-1),vvx(2:n-1));
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figure
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pcolor(x,vx,ftle)
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shading flat
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t_ftle=toc;
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fprintf('tempo per integrare \t%.2f s\n',t_integrazione)
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fprintf('tempo per calcolare ftle \t%.2f s\n',t_ftle)
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% ora=fstringf %TODO
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% save(['var_' num2str(n) '_' num2str(clock(4)])
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nome=['var_xvx_', 'ode00', '_n',num2str(n)];
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save(nome)
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