Loops aren't slow. You generally only need to remove them if there are native functions that accept array inputs, which happens to be the case here:
%generate random data
n=4;
x=rand(n,200);
y=rand(n,200);
%your corrected code
i=1;
Min=ones(1,200);
while i<=200%why aren't you using a for-loop here?
min_y = min(y(:,i));
pos_y = find(y(:,i)==min_y);
phi0s = x(pos_y ,i);
Min(1,i) = phi0s;
i=i+1;
end
%vectorized
[~,idx]=min(y,[],1);
ind=sub2ind(size(x),idx,1:size(y,2));
Min2=x(ind);
isequal(Min2,Min)
