bsxfun:
Apply element-by-element binary operation to two arrays withsingleton expansion enabled.
repmat:
Replicate and tile an array.
Overview:
There are two approaches to apply element-by-element binary operation to two arrays with singleton expansion enabled, using bsxfun directly or applying repmat first and then make binary operation.
Example:
>> a=rand(3,2)
a =
0.8721 0.3843
0.9016 0.0373
0.9518 0.9271
>> b=zeros(3,1)
b =
0
0
0
>> bsxfun(@minus,a,b)% operation with singleton expansion enabled
ans =
0.8721 0.3843
0.9016 0.0373
0.9518 0.9271
>> a-b % operation with singleton expansion disabled
Error using -
Matrix dimensions must agree.
>> a-repmat(b,1,2)
ans =
0.8721 0.3843
0.9016 0.0373
0.9518 0.9271
Speed test:
Below is a speed test of the two approaches. Please find code at Appendix 1.
As shown in the graph, bsxfun is almost twice faster than repeat.
Why bsxfun is faster:
There are two reasons why bsxfun is faster than the other approach:
1. bsxfun avoids explicit allocation of memory and actual replication of the array;
2. bsxfun is one of the multi-threaded Matlab functions.
FurthermZ http://www.2cto.com/kf/ware/vc/" target="_blank" class="keylink">vcmUuLi48L3N0cm9uZz48YnI+CklzIGl0IGEgZ29vZCBpZGVhIHRvIHJlcGxhY2Ugbm9ybWFsICh2YXJzIGluIHNhbWUgZGltZW5zaW9uKSBlbGVtZW50LWJ5LWVsZW1lbnQgb3BlcmF0aW9uIHdpdGggYnN4ZnVuPzxicj4KPHA+QmVsb3cgaXMgdGhlIHJlc3VsdCBvZiBteSB0ZXN0LiBQbGVhc2UgZmluZCB0ZXN0IGNvZGUgaW4gQXBwZW5kaXggMi48L3A+CjxwPjxicj4KPC9wPgo8cD48aW1nIHNyYz0="https://www.cppentry.com/upload_files/article/76/1_nocpm__.png" alt="\">
As shown in the graph, there is no need to replace normal element-by-element operation with bsxfun.
Appendix 1.
Comparison of bsxfun and repmat.
clear;
n = 300;
k = 1;
a = ones(10,1);
repmat_result = zeros(n,1);
bsxf_result = zeros(n,1);
num_repeat = 100;
tt = zeros(num_repeat,1);
for i = 1:n;
r = rand(1,i*k);
for it = 1:num_repeat;
tic,
x = bsxfun(@plus,a,r);
tt(it) = toc;
end;
bsxf_result(i) = mean(tt) / n;
for it = 1:num_repeat;
tic,
y = repmat(a,1,i*k)+repmat(r,10,1);
tt(it) = toc;
end;
repmat_result(i) = mean(tt) / n;
end
plot(bsxf_result,"-r')
hold on
plot(repmat_result,'-b')
legend('bsxfun','repmat') xlabel('Complexity') ylabel('Speed')
title('Speed test of element-by-element binary operation')
Appendix 2. Comparison of normal binary operation and bsxfun.
clear;
n = 300;
k = 1;
repmat_result = zeros(n,1);
bsxf_result = zeros(n,1);
num_repeat = 100;
tt = zeros(num_repeat,1);
for i = 1:n;
r = rand(k,i*k);
for it = 1:num_repeat;
tic,
x = bsxfun(@plus,r,r);
tt(it) = toc;
end;
bsxf_result(i) = mean(tt) / n;
for it = 1:num_repeat;
tic,
y = r+r;
tt(it) = toc;
end;
repmat_result(i) = mean(tt) / n;
end
plot(bsxf_result,'-r')
hold on
plot(repmat_result,'-b')
legend('bsxfun','+')
xlabel('Complexity') ylabel('Speed')
title('Speed test of element-by-element binary operation')