Element-wise array replication in Matlab
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.
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.
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
a = [1 2 3]; N = 3; b = reshape(repmat(a,N,1), 1, )
>> n=3; >> a(floor((0:size(a,2)*n-1)/n)+1) ans = 1 1 1 2 2 2 3 3 3
Some exotic alternatives. Admittedly more funny than useful:
Assign the (first) result of meshgrid to a vector:
b = NaN(1,numel(a)*n); %// pre-shape result b(:) = meshgrid(a,1:n);
Build a matrix that multiplied by a gives the result:
b = a * fliplr(sortrows(repmat(eye(numel(a)),n,1))).';
Use ind2sub to generate the indices:
[~, ind] = ind2sub([n 1],1:numel(a)*n); b = a(ind);
If you have the image processing toolbox, there is another alternative:
N = 3; imresize(a, [1 N*numel(a)],'nearest')
% 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));