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c85255c5af
All of these code samples currently are mis-identified in my repositories. I'm donating them to the cause.
41 lines
1.5 KiB
Matlab
41 lines
1.5 KiB
Matlab
clear all
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tic
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% initialize integration time T, f(x,t), discretization size n ----------------
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T = 20;
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f_x_t = inline('[v(2);-sin(v(1))]','t','v');
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grid_min = -3.4;
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grid_max = 3.4;
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grid_width = grid_max-grid_min;
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n = 35;
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grid_spacing = grid_min:(grid_width/(n-1)):grid_max;
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advected_x=zeros(n,n);
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advected_y=zeros(n,n);
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% integrate all initial points for t in [0,T] --------------------------------
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for i = 1:n
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for j = 1:n
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[t,x] = ode45(f_x_t,[0,T],[grid_spacing(i),grid_spacing(j)]);
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% store advected positions as they would appear in (x,y) coords ------
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advected_x(n-j+1,i) = x(length(x(:,1)),1);
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advected_y(n-j+1,i) = x(length(x(:,2)),2);
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end
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end
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sigma=zeros(n,n);
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% at each point in interior of grid, store FTLE ------------------------------
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for i = 2:n-1
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for j = 2:n-1
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% compute Jacobian phi -----------------------------------------------
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phi(1,1) = (advected_x(i,j+1)-advected_x(i,j-1))/(2*grid_width/(n-1));
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phi(1,2) = (advected_x(i-1,j)-advected_x(i+1,j))/(2*grid_width/(n-1));
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phi(2,1) = (advected_y(i,j+1)-advected_y(i,j-1))/(2*grid_width/(n-1));
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phi(2,2) = (advected_y(i-1,j)-advected_y(i+1,j))/(2*grid_width/(n-1));
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% find max eigenvalue of phi'*phi ------------------------------------
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lambda_max = max(abs(eig(phi'*phi)));
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% store FTLE ---------------------------------------------------------
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sigma(i,j) = log(lambda_max)/abs(T);
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end
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end
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toc
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%% plot FTLE field ------------------------------------------------------------
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figure
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contourf(grid_spacing,grid_spacing,sigma);
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colorbar('location','EastOutside'); |