Creating an array of partial sums of certain array

Suppose I have an initial array [a1 a2 a3 a4 a5]. Then I have to create an array = [a1, a2, a3, a4, a5, a1+a2, a2+a3, a3+a4, a4+a5, a1+a2+a3, a2+a3+a4, a3+a4+a5, a1+a2+a3+a4, a2+a3+a4+a5, a1+a2+a3+a4+a5]. Array has total 5*(5+1)/2 =15 elements. How to do it?

I need to extend it to any finite (say n) no. of elements in the initial array so that the resulting array has n(n+1)/2 elements.

Thank you.

Answer 1

[Dyuman Joshi]

Here is an approach, however I am not sure how fast this will be for a large n

y=[1 2 3 4 5 6];
n=numel(y);
z=cell(1,n);
for k=1:n
    z{k}=movsum(y,k,'Endpoints','discard');
end
out=[z{:}]

out = 1×21

1 2 3 4 5 6 3 5 7 9 11 6 9 12 15 10 14 18 15 20 21

Answer 2

[John D'Errico]

For example, consider the vector (I've used syms here, so you can see that it works, and generate the correct terms. Had a been any numeric vector, it would work as well.)

n = 5;
syms a [1,n]
a

a = 

Now what happens when you multiply that vector by an array, of the form

diag(a)*tril(ones(n))

ans = 

Does that look somewhat like what you anted? Not exactly, I know. But, is it close?

So then, what would cumsum do?

cumsum(diag(a)*tril(ones(n)))

ans = 

So the list of terms that you are looking to find are in the lower half of that matrix. Can you extract them trivially? Again, we can use find and tril. Putting it all together now, we have

ind = find(tril(ones(n)));
A = cumsum(diag(a)*tril(ones(n)));
A = A(ind)

A = 

How many terms are in that result?

numel(A)

ans = 15

So now try it out.

a = 1:7; % we expect to see 28 total terms in the result.
n = numel(a);
ind = tril(ones(n)) == 1;
A = cumsum(diag(a)*tril(ones(n)));
A = A(ind)

A = 28×1

1 3 6 10 15 21 28 2 5 9

numel(A)

ans = 28

[Dyuman Joshi]

John, I think using logical indexing would be a better fit as compared to using find(), specially for larger values of n

[John D'Errico]

Yes. find was not necessary there. I am not at all sure what size arrays are involved. We were never told that information.

[Sheet]

Thank You.