Repeat and shift array elementwise

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!

Answer 1

[Matt J]

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)

[Kai]

Amazing, so simple! Thanks a lot! :)