How to intersect two or more matrices? - matlab

Question

Let say I have some number of matrices with non-negative entries, N matrices for example of equal sizes MxM. For example, I have 3 matrices as follow:
A1=[2, 2, 0;
2, 2, 0;
0, 2, 0];
A2=[4, 0, 4;
4, 3, 0;
0, 0, 1];
A3=[2, 0, 0;
1, 0, 3;
3, 4, 3];
I want to find the intersection of A1, A2, and A3 in matlab. That means I want to get the follow matrix:
B=[-1, 2, 4;
-1, -1, 3;
3, -1, -1];
If the intersection of the (i, j) element of the N matrices, i.e., the elements A1(i, j), A2(i, j), A3(i, j), is at most one nonzero number then B(i,j) equals that number. Else if the intersection is at least two numbers I output -1 as I showed in the previous example.
How can I do this in matlab without loops?

Answer 1

First, concatenate to a single 3D-Matrix:
A=cat(3,A1,A2,A3)
Then count the non-zero elements, which gives the location of the -1-Elements:
L=(sum(A~=0,3)>1)
Finally, There where L=1 we want a -1, otherwise we want the single element at that location, which is the sum because the others are zero:
L*-1+(1-L).*sum(A,3)

Answer 2

I would do it something like so:
First, count up the non-zero elements at each location across all matrices:
foo = (A1 ~= 0) + (A2 ~= 0) + (A3 ~= 0);
Next, find those which have more than one non-zero element, and set them to -1 in the result:
B = zeros(3,3);
B(foo > 1) = -1;
Finally, find the non-zero elements (since in the elements we care about there is only one non-zero element, this is the same as the sum across matrices)
sumA = A1 + A2 + A3;
And add them into the result matrix
B(foo == 1) = sumA(foo == 1);