MATLAB: Always NaNs in the script

MATLABnan

Hi, in my code, in the third loop, somehow the variable:
 z_i_meshgrid
always have half of it fill with NaNs, can anyone explain this plz? why doesnt this happen in the first few loops.
Many thanks,
 x_0=1;
y_0=6;
gamma=0.2;
tau=0.0002;
x_grid=-9:0.2:9;
y_grid=-8:0.2:8;
[X, Y] = meshgrid(x_grid,y_grid);
z_meshgrid=cos(X/2).*cos(Y) + Y/10 - X/5;
%%
interpolation_accuracy=5;
[x_meshgrid,y_meshgrid]=meshgrid(x_grid,y_grid);
x_i_location=find(x_grid==x_0);
y_i_location=find(y_grid==y_0);
z_0=z_meshgrid(y_i_location,x_i_location);
clear x_grid y_grid;
[gradient_x_grid,gradient_y_grid] = gradient(z_meshgrid);
gradient_zx_0 = gradient_x_grid(y_i_location,x_i_location)
gradient_zy_0 = gradient_y_grid(y_i_location,x_i_location)
cnt=1;
A=[x_0,y_0,z_0];
threshold = tau+1;
while threshold > tau
    
    
    % calculation of (x_i,y_i)
    x_i = x_0 - gamma*gradient_zx_0;
    y_i = y_0 - gamma*gradient_zy_0;
    
    % Interpolation around the point of (x_i,y_i)
    x_i_grid=linspace(x_0,(2*x_i-x_0),interpolation_accuracy);
    y_i_grid=linspace(y_0,(2*y_i-y_0),interpolation_accuracy);
    
    [x_i_meshgrid, y_i_meshgrid] = meshgrid(x_i_grid,y_i_grid);
    
    z_i_meshgrid = interp2(x_meshgrid,y_meshgrid,z_meshgrid,...
        x_i_meshgrid,y_i_meshgrid,'cubic');
    
    if cnt==1
        x_i_location = sum(size(x_i_grid)/2);
        y_i_location = sum(size(y_i_grid)/2);
    end
    
    z_i=z_i_meshgrid( y_i_location , x_i_location );
    
    %output
    cnt=cnt+1
    A(cnt,:)=[x_i,y_i,z_i];
    
    %new gradient
    gradient_x_grid = interp2(x_meshgrid,y_meshgrid,gradient_x_grid, ...
        x_i_meshgrid,y_i_meshgrid);
    gradient_x_i=gradient_x_grid( y_i_location , x_i_location )
    
    gradient_y_grid = interp2(x_meshgrid,y_meshgrid,gradient_y_grid, ...
        x_i_meshgrid,y_i_meshgrid);
    gradient_y_i=gradient_y_grid( y_i_location , x_i_location )
    
    
    
    threshold = sqrt( (x_i-x_0)^2+(y_i-y_0)^2 );
    if cnt== 3
        break
    end
    x_0=x_i;
    y_0=y_i;
    x_meshgrid=x_i_meshgrid;
    y_meshgrid=y_i_meshgrid;
    z_meshgrid=z_i_meshgrid;
 
end
A

Best Answer

Because you are interpolating at locations outside the boundaries defined by x_grid,y_grid. The locations where you interpolate, defined by x_i_grid, y_i_grid, vary from iteration to iteration and will not necessarily lie inside x_grid,y_grid for any apparent reason.
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