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Massive time required for pdist

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Hello,
I am using the Matlab function pdist to calculate the distance between two points. However, I noticed that the function needs a lot of time, despite it is using all four cores. I build this example to demonstrate the massive time comsumption. If I calculate the distance between two points with my own code, it is much faster. The example calculates the distance between a thousand points.
clear
close all
clc
tic
j=1;
X = rand(1000,2);
Y = rand(1000,2);
fprintf('Time for array creation: ');
toc
tic
for i = 1:1:size(Y,1)
for k = 1:1:size(X,1)
A(j,1) =sqrt((Y(i,1)-X(k,1))^2 + (Y(i,2)-X(k,2))^2);
j = j+1;
end
end
fprintf('Time for own distance calculation: ');
toc
j = 1;
tic
for i = 1:1:size(Y,1)
for k = 1:1:size(X,1)
P = [Y(i,1),Y(i,2);X(k,1),X(k,2)];
B(j,1) = pdist(P,'euclidean');
j = j+1;
end
end
fprintf('Time for distance calculation using Matlab function pdist: ');
toc
Output:
Time for array creation: Elapsed time is 0.000386 seconds.
Time for own distance calculation: Elapsed time is 0.251026 seconds.
Time for distance calculation using Matlab function pdist: Elapsed time is 10.776532 seconds.
You can clearly see, that the Matlab function pdist takes over 10 seconds longer.
My question is: Why? What else is this function doing?
Would be nice to know.
Thank you very much
Kind regards,
Sebastian

Accepted Answer

Chunru
Chunru on 4 Oct 2021
Edited: Chunru on 4 Oct 2021
%tic
X = rand(1000,2);
Y = rand(1000,2);
% fprintf('Time for array creation: ');
%toc
%% Version 1
tic
j=1;
for i = 1:1:size(Y,1)
for k = 1:1:size(X,1)
A(j,1) =sqrt((Y(i,1)-X(k,1))^2 + (Y(i,2)-X(k,2))^2);
j = j+1;
end
end
size(A)
ans = 1×2
1000000 1
t = toc;
fprintf('Time for own distance calculation: %.6f\n', t);
Time for own distance calculation: 0.307268
%% Version 1.1
% Pre-allocate A
tic
j=1;
A = inf(size(X,1)*size(Y,1), 1);
for i = 1:1:size(Y,1)
for k = 1:1:size(X,1)
A(j,1) =sqrt((Y(i,1)-X(k,1))^2 + (Y(i,2)-X(k,2))^2);
j = j+1;
end
end
size(A)
ans = 1×2
1000000 1
t = toc;
fprintf('Time for own distance calculation with preallocation: %.6f\n', t);
Time for own distance calculation with preallocation: 0.112437
%% Version 2
tic
j=1;
for i = 1:1:size(Y,1)
for k = 1:1:size(X,1)
P = [Y(i,1),Y(i,2);X(k,1),X(k,2)];
B(j,1) = pdist(P,'euclidean'); % one pair
j = j+1;
end
end
size(B)
ans = 1×2
1000000 1
t = toc;
fprintf('Time for distance calculation using Matlab function pdist: %.6f\n', t);
Time for distance calculation using Matlab function pdist: 15.181589
%% Version 2.1
% Pre-allocate B before hand
tic
j=1;
B = inf(size(X,1)*size(Y,1), 1);
for i = 1:1:size(Y,1)
for k = 1:1:size(X,1)
P = [Y(i,1),Y(i,2);X(k,1),X(k,2)];
B(j,1) = pdist(P,'euclidean');
j = j+1;
end
end
size(B)
ans = 1×2
1000000 1
t = toc;
fprintf('Time for distance calculation using Matlab function pdist: %.6f\n', t);
Time for distance calculation using Matlab function pdist: 12.980660
%% Version 3
% pdist of many points (this compute distance x2-x1, x3-x1, ... x1000-x1,
% y1-x1, ..., y10001; x3-x2, ..., x1000-x2, ..., y1000-x2 etc
% doc pdist
tic
p = pdist([X; Y]); % dist
size(p)
ans = 1×2
1 1999000
t = toc;
fprintf('Time for distance calculation using Matlab function pdist (many points): %.6f\n', t);
Time for distance calculation using Matlab function pdist (many points): 0.016222
  1 Comment
Sebastian Stumpf
Sebastian Stumpf on 6 Oct 2021
Thank you for your detailed answer. It looks like I didn't use the function very efficently.
Kind regards

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