A complicated matrix manipulation

So I have a matrix, let's say

A = [1 2;
    1 0;
    3 2;
    0 1;
    2 1;
    1 2];

[r,c] = size(A);

In general, what I would like to do is:

for i = 1:r-1
   x = A(6,1)*A(i,1) + A(6,2)*A(i,2); 
end

However, here is the issue: if A(i,1) and/or A(i,2) is zero, and let's assume just A(i,1) is 0 and A(i,2) is non-zero, then, instead I would like to do:

x = A(6,1)*A(i-1,1) + A(6,2)*A(i,2);

And in case, even A(i-1,1) is also zero, then, I would like to do:

x = A(6,1)*A(i-2,1) + A(6,2)*A(i,2);

and so on and so forth (same for A(i,2)). Note, A(1,1), A(1,2), A(6,1), A(6,2) are always non-zeros. I am trying to get my head around it, but so far no luck, although it seems it should have a simple and efficient way.

Your help is highly appreciated. Please let me know if anything seems confusing.

Thanks in advance!

[Stephen23]

Your example matrix only has five rows, so none of your example code accessing its (non-existent) sixth row will work.

[J AI]

it was a typo..i added anotther row. thanks for pointing out

Answer 1

[Stephen23]

Try this reasonably "simple and efficient way":

r = size(A,1);
x = nan(r,1);
for k = 1:r
    r1 = find(A(1:k,1),1,'last');
    r2 = find(A(1:k,2),1,'last');
    x(k) = A(6,1).*A(r1,1) + A(6,2).*A(r2,2);
end

[J AI]

works great! thanks a lot. I am accepting the answer since you have perfectly nailed it. however, I was wondering, is there a way for generalizing it for "n" number of columns of A (without having to go in a "for" loop)?

[Stephen23]

'...generalizing it for "n" number of columns of A'

C = cumsum(A(:)~=0,1); % requires that first and last rows do not contain zeros!
B = nonzeros(A);
B = reshape(B(C),size(A));
x = sum(A(6,:).*B,2)

Personally I would just use a loop, as it makes the code intent much clearer.

[J AI]

i agree for loops are clearer, but when you have a large-sized A with 10,000 columns, like i do, it is better getting the job done without a for loop. but as i said, i agree with you - in fact, i am not sure what's happening in the code you just provided so i will be figuring it out. thanks a lot man! really appreciate your help