Comparing only nonzero elements - matlab

Question

The specific task I'm trying to achieve is hard to describe, so here's an example: given A and x
A = [1 2;
3 0;
3 5;
4 0];
x = [1 2 3];
I want the algorithm to output
output: [1 2]
meaning that all of the nonzero elements in rows 1 and 2 in A are in x.
I have done this using cell arrays and loops; however, A and x are very large and my approach is not at all efficient. Also, I can't seem to figure out how to rework ismember to give me what I want. What is the fastest/least memory intensive method?
EDIT: Apologies, my original example was too simplistic. It is corrected now.

Answer 1

The first answer is good, but I would recommend to not using arrayfun. There are more eloquent ways to do what you ask. Use ismember combined with all, then index into the matrix A when you're done. Basically, your problem is to determine if a row has all of the values found in x and ignoring the zero values. In this case, we can find all of the values in the matrix A that are actually zero, then use this to augment our result.
Using A as the first input and x as the second input will return a matrix of the same size as A that tells you whether an element in A is found in x. If you want to check if all elements in the matrix A for a row can be found in x, check if all elements in a row is 1. On top of this, find all of the elements that are zero, then with the output of ismember set these to 1. This can be done with using a logical OR. After, you can use all and check each row independently by using the output of ismember as the first input into all and setting the second argument to 2. This would then return all of the rows in the matrix A where any column is found in x ignoring any values that are zero for a row in A which is what you're looking for:
A = [1 2; 3 0; 4 0];
x = [1 2 3];
mask = ismember(A, x);
ind = all(mask | A == 0, 2);
I'm also in favour of one-liners. We can consolidate this into one line of code:
ind = all(ismember(A, x) | A == 0, 2);
Even shorter is to simply invert A. All zero elements become true and false otherwise:
ind = all(ismember(A, x) | ~A, 2);
ind would thus be:
>> ind
ind =
3×1 logical array
1
1
0
Since you want the actual row indices, you can just use find on top of this:
>> find(ind)
ans =
1
2
To verify, let's use your second example in your comments:
>> A = [1 2;3 5;4 0];
>> x = [1 2 3];
>> ind = all(ismember(A, x) | ~A, 2)
ind =
3×1 logical array
1
0
0
>> find(ind)
ans =
1

Answer 2

I think the best way to rework ismember is to make sure there are no "no members" by just checking for the nonzero elements in A.
arrayfun can do the work in a fast way. It uses the most efficient parallel computing for your specific machine. The following line should return the correct output:
find(arrayfun(#(a) sum(~ismember(A(a,A(a,:)>0),x)),1:size(A,1))==0)
Is this what you were looking for?
However, if your problem is related to memory, then you may have to break the arrayfun operation into pieces (1:floor(size(A,1)/2), floor(size(A,1)/2):size(A,1) or smaller chunks), since MATLAB puts a bunch of workers to do the task, and may use all your available RAM memory...