mirror of
https://github.com/KevinMidboe/linguist.git
synced 2025-10-29 17:50:22 +00:00
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
|
|
tic
|
|
% initialize integration time T, f(x,t), discretization size n ----------------
|
|
T = 20;
|
|
f_x_t = inline('[v(2);-sin(v(1))]','t','v');
|
|
grid_min = -3.4;
|
|
grid_max = 3.4;
|
|
grid_width = grid_max-grid_min;
|
|
n = 35;
|
|
grid_spacing = grid_min:(grid_width/(n-1)):grid_max;
|
|
advected_x=zeros(n,n);
|
|
advected_y=zeros(n,n);
|
|
% integrate all initial points for t in [0,T] --------------------------------
|
|
for i = 1:n
|
|
for j = 1:n
|
|
[t,x] = ode45(f_x_t,[0,T],[grid_spacing(i),grid_spacing(j)]);
|
|
% store advected positions as they would appear in (x,y) coords ------
|
|
advected_x(n-j+1,i) = x(length(x(:,1)),1);
|
|
advected_y(n-j+1,i) = x(length(x(:,2)),2);
|
|
end
|
|
end
|
|
sigma=zeros(n,n);
|
|
% at each point in interior of grid, store FTLE ------------------------------
|
|
for i = 2:n-1
|
|
for j = 2:n-1
|
|
% compute Jacobian phi -----------------------------------------------
|
|
phi(1,1) = (advected_x(i,j+1)-advected_x(i,j-1))/(2*grid_width/(n-1));
|
|
phi(1,2) = (advected_x(i-1,j)-advected_x(i+1,j))/(2*grid_width/(n-1));
|
|
phi(2,1) = (advected_y(i,j+1)-advected_y(i,j-1))/(2*grid_width/(n-1));
|
|
phi(2,2) = (advected_y(i-1,j)-advected_y(i+1,j))/(2*grid_width/(n-1));
|
|
% find max eigenvalue of phi'*phi ------------------------------------
|
|
lambda_max = max(abs(eig(phi'*phi)));
|
|
% store FTLE ---------------------------------------------------------
|
|
sigma(i,j) = log(lambda_max)/abs(T);
|
|
end
|
|
end
|
|
toc
|
|
%% plot FTLE field ------------------------------------------------------------
|
|
figure
|
|
contourf(grid_spacing,grid_spacing,sigma);
|
|
colorbar('location','EastOutside'); |