# A complicated matrix manipulation

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J AI on 19 Jun 2020
Commented: J AI on 19 Jun 2020
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.

Stephen Cobeldick on 19 Jun 2020
Your example matrix only has five rows, so none of your example code accessing its (non-existent) sixth row will work.
J AI on 19 Jun 2020
it was a typo..i added anotther row. thanks for pointing out

Stephen Cobeldick on 19 Jun 2020
Edited: Stephen Cobeldick on 19 Jun 2020
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 on 19 Jun 2020
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)?
Stephen Cobeldick on 19 Jun 2020
'...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 on 19 Jun 2020
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