Taking alternatively elements of two vectors and compose them in Matlab

Question

Could you help me to write down a very fast algorithm in Matlab that does the following: I have 2 vectors, A of dimension nx1 and B of dimension nx1. I want to construct C of dimension 2nx1 such that

C(1)=A(1), C(2)=B(1), C(3)=A(2), C(4)=B(2), C(5)=A(3), C(6)=B(3), ...

I though about

C=[];
for j=1:n
    C=[C; [A(j) B(j)]'];
end

Do you know something faster and more efficient?

Example:

n=9
A=[1 3 5 7 9 11 13 15 17]';
B=[2 4 6 8 10 12 14 16 18]';
C=[1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18]';

Didn't you want a *fast* answer? I have added a benchmark showing relative performance. — Suever, Jun 01 '16 at 17:13

Suever · Answer 1 · 2016-06-01T17:33:14.100

Typically you will want to avoid appending data to an array within a loop like you have written it as this has to re-allocate memory every time through the loop as you expand the variable.

The easiest thing to do would be to convert them both to row vectors using (:).', concatenate them along the first dimension, and then flatten to a column vector using reshape. Because of MATLAB's column-major ordering, this will automatically inter-leave the values of A and B to create C.

C = reshape(cat(1, A(:).', B(:).'), [], 1)

Benchmark

As far as whether this is faster than indexing (@ThP's answer), here is a brief test to benchmark the two.

sizes = round(linspace(100, 10000, 100));

times1 = zeros(size(sizes));
times2 = zeros(size(sizes));

for k = 1:numel(sizes)
    A = rand(sizes(k), 1);
    B = rand(sizes(k), 1);

    times1(k) = timeit(@()combine1(A,B));
    times2(k) = timeit(@()combine2(A,B));
end

figure
plot(sizes, times1)
hold on
plot(sizes, times2)
legend('cat + reshape', 'Indexing')

function C = combine1(A, B)
    C = reshape(cat(1, A(:).', B(:).'), [], 1);
end

function C = combine2(A,B)
    C = zeros(2*numel(A),1);
    C(1:2:end) = A;
    C(2:2:end) = B;
end

Nice. It would be interesting to compare using `C(2*n,1)=0` as suggested by Luis Mendo — ThP, Jun 01 '16 at 17:18
@ThP I compared it. Hardly any difference.http://i.imgur.com/1DqE2gc.png — Suever, Jun 01 '16 at 17:19
It is just micro optimization, but the following is slightly faster ` C = [A(:).'; B(:).']; C = C(:);` The guess is that it is just a function call (since the different is about constant relative to "cat + reshape"), but if the problem consists of many function calls it may be significant. — patrik, Jun 02 '16 at 08:06

score 3 · Accepted Answer · edited Jun 01 '16 at 17:06

3

In matlab, index operations are generally faster than for-loops.
What I would do is first construct a 2nx1 matrix and then use indexing to assign the values:

C = zeros(2*n,1);
C(1:2:end) = A;
C(2:2:end) = B;

edited Jun 01 '16 at 17:06

Suever

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answered Jun 01 '16 at 17:02

ThP

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Initiallizing `c` with `c(2*n,1) = 0` is even faster (although admittedly hackish) – Luis Mendo Jun 01 '16 at 17:02
Interesting... didn't know that. – ThP Jun 01 '16 at 17:04
See [this answer](http://stackoverflow.com/a/14195309/2586922) and the linked post @ThP – Luis Mendo Jun 01 '16 at 17:09
@LuisMendo It seems that this may not be the case anymore with the new execution engine in 2015b – Suever Jun 01 '16 at 17:23

Taking alternatively elements of two vectors and compose them in Matlab

2 Answers2

Benchmark