# interp2 returns NaN when given points are within mesh boundaries

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Rohan Kotecha on 31 Dec 2022
Edited: Torsten on 31 Dec 2022
I'm writing a scrip to execute gradient descent on a function. I'm generating 150 random starting points, within the bounds of the mesh, to execute the algorithm with. However, when I run this, at some point I get a NaN - I'm pretty sure this comes from interp2. Since all the starting points I generate are within the x,y boundaries, I am very confused as to why. What do you think?
Here's the script:
fun = @(x) cos(x(1)/2)*cos(x(2)) + x(2)/10 - x(1)/5;
sol = fmincon(fun,[0,0],[],[],[],[],[-9,-8],[9,8])
fun(sol)
% Define x and y range
x = -9:0.2:9;
y = -8:0.2:8;
% Compute z values
[X, Y] = meshgrid(x, y);
%Z = comp_z(X, Y);
Z = cos(X/2).*cos(Y) + (Y/10) - (X/5);
% Plot z using imagesc
imagesc(x,y,Z);
%Set the colormap to "hot"
colormap hot;
% Add axis labels and a title
xlabel('x');
ylabel('y');
zlabel('z(x,y)');
title('z(x,y) = cos(x/2)cos(y) + (y/10) - (x/5)');
hold on;
for i = 1:150
disp(i);
% Set starting points and parameters for gradient descent
x0_1 = -8 + (rand*16);
y0_1 = -7 + (rand*14);
gamma = 0.2;
epsilon = 0.002;
% Perform gradient descent starting at (x0_1, y0_1)
descent_matrix = gradient_descent(x, y, Z, x0_1, y0_1, gamma, epsilon);
% Plot end points of gradient decents
line(descent_matrix(end,1), descent_matrix(end,2),'Marker','o','MarkerEdgeColor','cyan')
end
And here's the function:
function [descent_matrix] = gradient_descent(x, y, z, x0, y0, alpha, epsilon)
% Compute z at starting point using cubic interpolation
z0 = interp2(x, y, z, x0, y0, '*cubic');
% Compute gradient at starting point using cubic interpolation
gradz0 = [interp2(x, y, dzdx, x0, y0, 'cubic'), interp2(x, y, dzdy, x0, y0, 'cubic')];
% Store starting point in positions matrix
descent_matrix = [x0, y0, z0];
% Initialize steps counter
steps = 0;
% Perform gradient descent until step size is sufficiently small
while true
% Update x position
x0 = x0 - alpha .* gradz0(1);
% Update y position
y0 = y0 - alpha .* gradz0(2);
zi = interp2(x, y, z, x0, y0, 'cubic');
% Compute gradient at starting point using cubic interpolation
gradz0 = [interp2(x, y, dzdx, x0, y0, 'cubic'), interp2(x, y, dzdy, x0, y0, 'cubic')];
% Store starting point in positions matrix
descent_matrix = [descent_matrix; x0, y0, zi];
% Increment steps counter
steps = steps + 1;
% Check if step size is sufficiently small
if sqrt((x0 - descent_matrix(end-1,1)).^2 + (y0 - descent_matrix(end-1,2)).^2) < epsilon
% Exit loop
break;
end
end
end
Torsten on 31 Dec 2022
Edited: Torsten on 31 Dec 2022
Looking at this update
x0 = x0 - alpha .* gradz0(1);
% Update y position
y0 = y0 - alpha .* gradz0(2);
I wonder how you guarantee that x0 and y0 remain in the initial bounds
x = -9:0.2:9;
y = -8:0.2:8;
And I ask myself why you apply gradient descent on a matrix of values for z and not on the function z(x,y) itself.

Naeimeh N on 31 Dec 2022
Edited: Naeimeh N on 31 Dec 2022
1- If all the the starting points you are generating are within the range of the x and y arrays, then make sure that you have sufficient data points in the x, y, and z arrays to accurately interpolate the values.
2- Another possible issue could be that the gradient descent algorithm is getting stuck at a local minimum. You may want to try adjusting the step size (alpha) or the convergence criteria (epsilon) to see if this helps.

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