# Is it possible numerical problem ?

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AI-CHI Chang on 7 Mar 2023
Commented: Askic V on 7 Mar 2023
I'm sorry to post long code here. But I just can't find the problem...
I tried to boost my code efficiency by removing for loop, but it came out two different results from them...
I check the first point's variable d_d, d_n, w_d, w_n in first loop. All them are the same but became different in variable sum_den 61.330229160510050 and 61.330229160510020.....That's so weired. Is it possible the numerical errors?
The input of the former one is 3D points location, neighbors for each point (num_pt*num_neighbor*3), and normal vector for each points.
for i = 1:num_pt
p_nn(i,:,:) = p(knn(i,2:end),:);
end
function [p] = BilateralFilter(p,p_nn,normal)
min_z = min(p(:,3));
maxdepth = max(p(:,3)) - min_z;
sigma_n = 0.5;
sigma_d = 0.01 + 0.5*(p(:,3) - min_z)/maxdepth;
p_permute = permute(p, [1 3 2]);
n_permute = permute(normal, [1 3 2]);
d_d = sqrt(sum((p_permute - p_nn).^2,3));
d_n = abs(sum((p_nn - p_permute).*n_permute,3));
w_d = exp(-d_d.^2./2./sigma_d.^2);
w_n = exp(-d_n.^2./2./sigma_n.^2);
residual = sum((p_nn - p_permute).*n_permute,3);
sum_num = sum(w_d.*w_n.*residaul,2);
sum_den = sum(w_d.*w_n,2);
del_p = sum_num./sum_den;
p = p + del_p.*normal;
The latter one is 3D points location, index of neighbors for each point (num_pt*num_neighbor), and normal vector for each points.
function [p] = BilateralFilter(p,knn,normal)
num_pt = size(p,1);
del_p = zeros(num_pt,1);
min_z = min(p(:,3));
maxdepth = max(p(:,3)) - min_z;
for i = 1:num_pt
idx_nn = knn(i,2:end);
p_nn = p(idx_nn,:);
sigma_n = 0.5;
sigma_d = 0.01 + 0.5*(p(i,3)-min_z)/maxdepth;
d_d = abs(sqrt(sum((p(i,:)-p_nn).*(p(i,:)-p_nn),2)));
d_n = abs(sum((p_nn-p(i,:)).*normal(i,:),2));
w_d = exp(-d_d.^2./2./sigma_d^2);
w_n = exp(-d_n.^2./2./sigma_n^2);
residual = sum((p_nn-p(i,:)).*normal(i,:),2);
sum_num = sum(w_d.*w_n.*residaul);
sum_den = sum(w_d.*w_n);
del_p(i) = sum_num/sum_den;
end
p = p + del_p.*normal;

Askic V on 7 Mar 2023
This is called a round-off error caused by floating point arithmetic.
https://pythonnumericalmethods.berkeley.edu/notebooks/chapter09.03-Roundoff-Errors.html
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Askic V on 7 Mar 2023
https://www.mathworks.com/help/symbolic/vpa.html?searchHighlight=vpa&s_tid=srchtitle_vpa_1