Is there a way to speed up concatenation in MATLAB?

问题

I want to concatenate along the third dimension

z = cat(3,A,B,C);

Many many times. I if I was doing that along the second dimension then

z = [A,B,C];

Would be faster than

z = cat(2,A,B,C);

Can a similar thing be done along the third dimension or is there any other way to speed this up?

回答1:

There are some indexing options to get a slightly better performance than cat(3,...).

Both solutions use U(30,30,3)=0; instead of zeros(30,30,3) to preallocate, but it is unsave as it will result in a subscript dimension missmatch when U is already a variable of a larger size.

The first option is to assign the different slices individually.

%fast but unsafe preallocation
U(30,30,3)=0;
%robust alternative:
%U=zeros(30,30,3)
U(:,:,3)=C;
U(:,:,1)=A;
U(:,:,2)=B;

The second option is to use linear indexing. For z1 = cat(3,A,B,C); and z2=[A;B;C] it is true that z1(:)==z2(:)

%fast but unsafe preallocation
U(30,30,3)=0;
%robust alternative:
%U=zeros(30,30,3)
U(:)=[A,B,C];

I benchmarked the solutions, comparing it to cat(3,A,B,C) and [A,B,C]. The linear indexing solution is only slightly slower than [A,B,C].

0.392289 s for 2D CAT
0.476525 s for Assign slices
0.588346 s for cat(3...)
0.392703 s for linear indexing

Code for benchmarking:

N=30;
A=randn(N,N);
B=randn(N,N);
C=randn(N,N);
T=containers.Map;
cycles=10^5;
tic;
for i=1:cycles
    W=[A;B;C];
    X=W+1;
end
T('2D CAT')=toc;
tic;
for i=1:cycles
    W=cat(3,A,B,C);
    X=W+1;
end
T('cat(3...)')=toc;
U=zeros(N,N,3);
tic;
for i=1:cycles
    U(N,N,3)=0;
    U(:,:,3)=C;
    U(:,:,1)=A;
    U(:,:,2)=B;
    V=U+1;
end
T('Assign slices')=toc;
tic;
for i=1:cycles
    U(N,N,3)=0;
    U(:)=[A,B,C];
    V=U+1;
end
T('linear indexing')=toc;


for X=T.keys
    fprintf('%f s for %s\n',T(X{1}),X{1})
end

来源：https://stackoverflow.com/questions/33761451/is-there-a-way-to-speed-up-concatenation-in-matlab

标签

matlab

optimization

matrix

concatenation