Element-wise array replication in Matlab

Question

Let's say I have a one-dimensional array:

a = [1, 2, 3];

Is there a built-in Matlab function that takes an array and an integer n and replicates each element of the array n times?

For example calling replicate(a, 3) should return [1,1,1,2,2,2,3,3,3].

Note that this is not at all the same as repmat. I can certainly implement replicate by doing repmat on each element and concatenating the result, but I am wondering if there is a built in function that is more efficient.

Mesenchyme

Answer 1

As of R2015a, there is a built-in and documented function to do this, repelem:

repelem Replicate elements of an array.
    W = repelem(V,N), with vector V and scalar N, creates a vector W where each element of V is repeated N times.

The second argument can also be a vector of the same length as V to specify the number of replications for each element. For 2D replication:

B = repelem(A,N1,N2)

No need for kron or other tricks anymore!

UPDATE: For a performance comparison with other speedy methods, please see the Q&A Repeat copies of array elements: Run-length decoding in MATLAB.

Sassoon

How did you know this before R2015a was out?! – Negativism

@LuisMendo Pre-release. I love reading release notes almost as much as accumarray. :). But I immediately deleted my answer an then undeleted it on release day so as not to break the terms of the pre-release. – Sassoon

Answer 2

I'm a fan of the KRON function:

>> a = 1:3;
>> N = 3;
>> b = kron(a,ones(1,N))

b =

    1     1     1     2     2     2     3     3     3

You can also look at this related question (which dealt with replicating elements of 2-D matrices) to see some of the other solutions involving matrix indexing. Here's one such solution (inspired by Edric's answer):

>> b = a(ceil((1:N*numel(a))/N))

b =

    1     1     1     2     2     2     3     3     3

Sabu

what a nice solution, but what about if N be a matrix of frequency of elements of a, means that each element of N is correspond with one element of a? – Alunite

@ghedas: That's addressed here, if you hadn't yet seen it. – Sabu

Answer 3

a = [1 2 3];
N = 3;

b = reshape(repmat(a,N,1), 1, [])

Positivism

unlike kron, this solution is purely memory management, and does not drag multiplication into it. – Burrell

Answer 4

>> n=3;
>> a(floor((0:size(a,2)*n-1)/n)+1)

ans =

     1     1     1     2     2     2     3     3     3

Jyoti

Answer 5

Some exotic alternatives. Admittedly more funny than useful:

1. Assign the (first) result of meshgrid to a vector:

   b = NaN(1,numel(a)*n); %// pre-shape result
   b(:) = meshgrid(a,1:n);
   

2. Build a matrix that multiplied by a gives the result:

   b = a * fliplr(sortrows(repmat(eye(numel(a)),n,1))).';
   

3. Use ind2sub to generate the indices:

   [~, ind] = ind2sub([n 1],1:numel(a)*n);
   b = a(ind);
   

Negativism

Answer 6

If you have the image processing toolbox, there is another alternative:

N = 3;
imresize(a, [1 N*numel(a)],'nearest')

Circumvent

Actually, your code is wrong. It should be imresize(a, [1 N*numel(a)],'nearest'), with an N, not a 2. When you correct this, your solution is actually about 3 times slower than the KRON solution (and 5 times slower than the indexing solution a(ceil((1:N*numel(a))/N))). – Sabu

Answer 7

% To get b = [1 1 1 2 2 2 3 3 3]
N = 3;
a = [1 2 3];
temp_a = a(ones(N,1),:);
b = reshape(temp_a,1,numel(temp_a));

% To get b = [1 2 3 1 2 3 1 2 3]
N = 3;
a = [1 2 3];
temp_a = a(ones(N,1),:);
b = reshape(temp_a',1,numel(temp_a));

Maximalist