Please mention the dimensions of Ui. "300 points" does not clarify both dimensions of a matrix. It helps to help you, if you post some working input data.
I do not see the purpose of:
for k=1:m
dmin1 = min(sqrt((u(1,1) - Ni(k,1))^2 + (u(1,2) - Ni(k,2))^2));
end
The argument of min() is a scalar. Then the result is in every case:
dmin1 = sqrt((u(1,1) - Ni(m,1))^2 + (u(1,2) - Ni(m,2))^2);
The same happens for dmin2 and LocalMax. Let me guess, that instead of the loops you want:
dmin1 = min(sqrt((u(1,1) - Ni(:,1)).^2 + (u(1,2) - Ni(:,2)).^2));
Letting an array shrink iteratively needs a lot of ressource: Ui(1,:)=[] . If you do this on a [500'000 x 3] array, this allocates 3 TB or RAM successively. Ni and Pi are growing iteratively, which suffers from the same problem. I cannot run your code and due to the useless for-loops I assume, it does not work correctly at all, but the speed can be improved by changing:
Ni=[100 100 100];
Pi=[100 100 100];
to
nUi = size(Ui, 1);
Ni = zeros(nUi, 3); % Pre-allocation with maximum size
Pi = zeros(nUi, 3);
Ni(1, :) = [100 100 100];
Pi(1, :) = [100 100 100];
and
u=Ui(1,:);
to
u=Ui(i,:);
This is a strange construction:
for i=1:length(Ui)
...
Ui(1,:)=[];
if isempty(Ui)
break;
end
end
The FOR loop gets its limits when it is entered the first time. So the shrinking Ui does not change the limit. Then this would be better:
current = 1;
while current <= nUi
u = Ui(currentm :);
...
% Replace Ui(1,:)=[]; by:
current = current + 1;
end
