Creating a MATLAB vector with an overlapping pattern

Question

I have an array containing a pattern:

p = [1, 2, 2, 1];

I want to replicate the pattern but need to add the first and last elements. I'd prefer to find a better way than looping, if possible.

Meaning:

[1, 2, 2, 1]
         [1, 2, 2, 1]
[1, 2, 2, 2, 2, 2, 1]

I found something that does almost exactly what I need here: https://stackoverflow.com/a/15545970/2434277

But I can't find a way to make the overlap-addition happen. That is, it does this:

[1, 2, 2, 1, 1, 2, 2, 1]

Any ideas?

Thanks!

Quick edit: I'll need to replicate several times, but I don't know the number in advance.

Answer 1

Is it conv that you are looking for ?

> conv([1 0 0 0 1],[1 2 2 1])
 1     2     2     1     1     2     2     1

> conv([1 0 0 1],[1 2 2 1])
 1     2     2     2     2     2     1

The first argument of conv may also be a sparse matrix:

full(sparse(1,[1 5 18],1))
  1     0     0     0     1     0     0     0     0     0     0     0     0     0     0     0     0     1
conv(full(sparse(1,[1 5 18],1)),[1 2 2 1])
  1     2     2     1     1     2     2     1     0     0     0     0     0     0     0     0     0     1     2     2     1

Answer 2

Here's a way:

p = [1, 2, 2, 1];

n = length(p);
p(end + n - 1) = 0; %//pad with 0s
p(n:end) = p(n:end) + p(1:n)

Or you could do it in one line if you want:

[p, zeros(1, length(p)-1] + [zeros(1, length(p)-1, p]

But if you want a general solution for m repetitions then I suggest you use conv (as answered by user2987828) like this:

k = []; %// Leave off this line if you are certain that k won't exist yet
n = length(p);
k(1:n-1:(n-1)*m+1)=1; 
conv(k,p);