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# Repeat and shift array elementwise

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Kai on 17 Oct 2018
Commented: Kai on 17 Oct 2018
Hey, I have some problem about dealing with arrays. I think it is best explained with some example, so let's say I'm given the vectors
a = [1,3,7,12];
t = [3,1,2,5];
Now what I want to do is to create a new array ashift. In this array the elements a(i) should appear repeatedly t(i) times and then these repetitions should be shifted by 0:t(i)-1 (elementwise). Hence the result should be
ashift = [1,2,3,3,7,8,12,13,14,15,16];
So for example, we have a(4)=12 and t(4)=5, so ashift contains the entries a(4)+0:t(4)-1 = [12,13,14,15,16].
I have looked around and at least found a solution for the "elementwise repitition", but without shifting, in another thread. So this would be:
a = [1,3,7,12];
t = [3,1,2,5];
b = cumsum(t);
c = zeros(1,b(end));
c(b - t + 1) = 1;
arepeat = a(cumsum(c))
arepeat =
1 1 1 3 7 7 12 12 12 12 12
So now if I could create the array
shift = [0,1,2,0,0,1,0,1,2,3,4];
which basically contains these 0:t(i)-4 pieces, then I could say
ashift = arepeat + ashift;
and it would be done. In order to create the array shift, I could use a for loop
shift = [];
for i = 1:length(t)
shift = [shift,0:t(i)-1];
end
This code seems to work, but I don't really like creating the array shift subsequently (I'm sure Matlab will tell me to preallocate). Even if I figured out how to preallocate in here, this for loop still seems inefficient and not very elegant to me.
Any help and idea is appreciated!
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### Accepted Answer

Matt J on 17 Oct 2018
Edited: Matt J on 17 Oct 2018
b=cumsum(t);
adelta=[0,ones(1, b(end)-1 )];
adelta(b(1:end-1)+1)=-t(1:end-1)+1;
ashift=repelem(a,t) + cumsum(adelta)
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Kai on 17 Oct 2018
Amazing, so simple! Thanks a lot! :)

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