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/gpu_RKF45_FILE.m

@@ -0,0 +1,156 @@
+tic
+clear
+%% Range definition
+n=200;
+
+mu=0.1;
+[xl1,yl1,xl2,yl2,xl3,yl3,xl4,yl4,xl5,yl5]=Lagr(mu);
+C_L1=2*Omega(xl1,yl1,mu);
+E_0=-C_L1/2+0.03715;
+Y_0=0;
+
+nx=n;
+x_0_min=-0.8;
+x_0_max=-0.15;
+x_0=linspace(x_0_min, x_0_max, nx);
+dx=(x_0_max-x_0_min)/(nx-1);
+
+nvx=n;
+vx_0_min=-2;
+vx_0_max=2;
+vx_0=linspace(vx_0_min, vx_0_max, nvx);
+dvx=(vx_0_max-vx_0_min)/(nvx-1);
+
+ny=3;
+dy=(dx+dvx)/2;
+y_0=[Y_0-dy Y_0 Y_0+dy];
+
+
+
+ne=3;
+de=dy;
+e_0=[E_0-de E_0 E_0+de];
+
+%% Definition of arrays of initial conditions
+
+%In this approach, only useful pints are stored and integrated
+
+m=1;
+% x=zeros(1,nx*ny*nvx*ne);
+% y=zeros(1,nx*ny*nvx*ne);
+% vx=zeros(1,nx*ny*nvx*ne);
+% e=zeros(1,nx*ny*nvx*ne);
+% vy=zeros(1,nx*ny*nvx*ne);
+filter=zeros(nx,3,nvx,3);
+
+for i=1:nx
+	for j=1:ny
+		for k=1:nvx
+			for l=1:ne
+				v_y=-sqrt(2*Omega(x_0(i),y_0(j),mu)+2*e_0(l)-vx_0(k)^2);
+				if ~((j~=2) && (l~=2)) && isreal(v_y)
+					x(m)=x_0(i);
+					y(m)=y_0(j);
+					vx(m)=vx_0(k);
+					e(m)=e_0(l);
+					vy(m)=v_y;
+					filter(i,j,k,l)=1;
+					m=m+1;
+				end
+			end
+		end
+	end
+end
+
+%% Selection of useful points
+
+%% Data transfer to GPU
+x_gpu=gpuArray(x);
+y_gpu=gpuArray(y);
+vx_gpu=gpuArray(vx);
+vy_gpu=gpuArray(vy);
+
+%% Integration on GPU
+N=1;
+t0=0;
+
+[x_f,y_f,vx_f,vy_f]=arrayfun(@RKF45_FILE_gpu,t0,N,x_gpu,y_gpu,vx_gpu,vy_gpu,mu);
+
+%% Data back to CPU and GPU memory cleaning
+clear x_gpu y_gpu vx_gpu vy_gpu
+x_T=gather(x_f);
+clear x_f
+y_T=gather(y_f);
+clear y_f
+vx_T=gather(vx_f);
+clear vx_f
+vy_T=gather(vy_f);
+clear vy_f
+
+%% Construction of matrix for FTLE computation
+
+X_T=zeros(nx,ny,nvx,ne);
+Y_T=zeros(nx,ny,nvx,ne);
+VX_T=zeros(nx,ny,nvx,ne);
+VY_T=zeros(nx,ny,nvx,ne);
+E_T=zeros(nx,ny,nvx,ne);
+m=1;
+for i=1:nx
+    for j=1:ny
+        for k=1:nvx
+            for l=1:ne
+                if filter(i,j,k,l)==1
+                    X_T(i,j,k,l)=x_T(m);
+                    Y_T(i,j,k,l)=y_T(m);
+                    VX_T(i,j,k,l)=vx_T(m);
+                    VY_T(i,j,k,l)=vy_T(m);
+                    E_T(i,j,k,l)=0.5*(VX_T(i,j,k,l)^2+VY_T(i,j,k,l)^2)-Omega(X_T(i,j,k,l),Y_T(i,j,k,l),mu);
+                    m=m+1;
+                end
+            end
+        end
+    end
+end
+
+%% Compute filter for FTLE
+filter_ftle=filter;
+for i=2:(nx-1)
+	for j=2:(ny-1)
+		for k=2:(nvx-1)
+			for l=2:(ne-1)
+				if filter(i,j,k,l)==0 || filter (i,j,k,l)==3
+					filter_ftle(i,j,k,l)=0;
+					
+					filter_ftle(i+1,j,k,l)=0;
+					filter_ftle(i-1,j,k,l)=0;
+					
+					filter_ftle(i,j+1,k,l)=0;
+					filter_ftle(i,j-1,k,l)=0;
+					
+					filter_ftle(i,j,k+1,l)=0;
+					filter_ftle(i,j,k-1,l)=0;
+					
+					filter_ftle(i,j,k,l+1)=0;
+					filter_ftle(i,j,k,l-1)=0;
+				end
+			end
+			
+		end
+	end
+end
+%% FTLE computation
+
+[ftle, dphi]=Compute_FILE_gpu( X_T, Y_T, VX_T, E_T, dx, dy, dvx, de, N, filter_ftle);
+
+%% Plot results
+figure
+FTLE=squeeze(ftle(:,2,:,2));
+FTLE(1,:)=[];
+% FTLE(2,:)=[];
+FTLE(:,1)=[];
+% FTLE(:,2)=[];
+x_0(1)=[];
+vx_0(1)=[];
+pcolor(x_0, vx_0, FTLE')
+shading flat
+toc