General Binomial Matrix Manipulation

Let's say I have a matrix of the form:

Starting from this matrix, I would like to calculate a new matrix, in a time efficient way:

The algorithm, which I am looking for, should also work for a matrix of the form:

Does someone know how this algorithm could look like?

Best

Alex

[Akira Agata]

Assuming Astart is n-by-2 array, straight-forward way to calculate Aend would be:

Aend = [Astart(:,1).^2 Astart(:,1).*Astart(:,2) Astart(:,2).*Astart(:,1) Astart(:,2).^2];

But it's not clear for me what Aend looks like when Astart is n-by-m array.

Could you explain more detail on this?

[Alexander Pakakis]

of course, I can explain more!

Let's say I have:

then I would like to calculate this matrix:

I think, you will understand the system when see this table:

Answer 1

[Matt J]

[m,n]=size(Astart);

B=reshape(Astart,m,1,n).*Astart;

Aend=reshape(B,m,[]);

[Alexander Pakakis]

works perfectly!

Thank you Matt!

Answer 2

[Andrei Bobrov]

Aend = reshape(Abegin.*permute(Abegin,[1,3,2]),size(Abegin,1),[]);

[Alexander Pakakis]

works perfectly!

Thank you Andrei!