How can I sum the rows of a matrix at a fixed distance between each other?

Hi, I have a vector A (m*p)x1 and I want to create a vector B px1 where B(i)=sum_{n=0}^{m-1}A(i+p*n), e.g.

m=3;
p=4;
A=[12;11;10;9;8;7;6;5;4;3;2;1];
B=[A(1)+A(5)+A(9);A(2)+A(6)+A(10);A(3)+A(7)+A(11);A(4)+A(8)+A(12)];

I can't use loops.

Answer 1

[Sean de Wolski]

Use reshape and sum along a specific dimension:

m=3;
p=4;
A=[12;11;10;9;8;7;6;5;4;3;2;1];
B=[A(1)+A(5)+A(9);A(2)+A(6)+A(10);A(3)+A(7)+A(11);A(4)+A(8)+A(12)];
C=sum(reshape(A,p,m),2);

assert(isequal(B,C));

Answer 2

[Wayne King]

 A = reshape(A,4,3);
 sum(A,2)