Filtering the common rows between two matrices

I have two matrices A and B. Matrix A consists of 3 columns and matrix B consists of 4 columns.

A = [1 2 3; 4 5 6; 7 8 9];

B = [1 2 3 90; 3 1 2 88; 4 5 6 17; 6 5 4 19; 7 8 9 12; 15 18 22 20];

And I want to filter the common rows between matrix A and B according to each row of A and store the common rows of matrix B in a cell. This cell consists of multiple arrays equal to the number of the rows of matrix A.

The expected result should be something like that:

matching_cell{1} = [1 2 3 90; 3 1 2 88];

matching_cell{2} = [4 5 6 17; 6 5 4 19];

matching_cell{3} = [7 8 9 12];

Note: I do not want to use neasted for loop with ismember as the matrices dimensions are large and it will take a lot of time to run.

Thanks.

[Dyuman Joshi]

Try this -

A = [1 2 3; 4 5 6; 7 8 9];
B = [1 2 3 90; 3 1 2 88; 4 5 6 17; 6 5 4 19; 7 8 9 12; 15 18 22 20];


%sort each row ascendigly
C = sort(B,2)

C = 6×4

1 2 3 90 1 2 3 88 4 5 6 17 4 5 6 19 7 8 9 12 15 18 20 22

%Compare rows
[idx1,idx2]=ismember(C(:,1:size(A,2)), A, 'rows');

%Split into cell arrays according to the groups
out = splitapply(@(x) {x}, B(idx1,:), idx2(idx1))

out = 3×1 cell array
    {2×4 double}
    {2×4 double}
    {[7 8 9 12]}

out{1}

ans = 2×4

1 2 3 90 3 1 2 88

Assumptions made -

> Rows in A are already sorted ascendingly

> B (and thus C) has atleast the same amount of columns as A

[Stephen23]

Note that SPLITAPPLY will fail if any row of A does not exist in B (or produce a shorter output array):

A = [1 2 3; 0 0 0; 4 5 6];
B = [1 2 3 90; 3 1 2 88; 4 5 6 17; 6 5 4 19; 7 8 9 12; 15 18 22 20];
C = sort(B,2);
[idx1,idx2]=ismember(C(:,1:size(A,2)), A, 'rows');
out = splitapply(@(x) {x}, B(idx1,:), idx2(idx1))

Error using splitapply
For N groups, every integer between 1 and N must occur at least once in the vector of group numbers.

[Dyuman Joshi]

Yes, Thank you for pointing it out, I am aware of the requirement of spliapply() as stated in the error message.

As of now, I can't seem think of a solution that would work for all cases, so I am moving my answer to a comment, and accepting your answer as it provides a robust solution.

Answer 1

[Stephen23]

A = [1,2,3; 4,5,6; 7,8,9]

A = 3×3

1 2 3 4 5 6 7 8 9

B = [1,2,3,90; 3,1,2,88; 4,5,6,17; 6,5,4,19; 7,8,9,12; 15,18,22,20]

B = 6×4

1 2 3 90 3 1 2 88 4 5 6 17 6 5 4 19 7 8 9 12 15 18 22 20

[X,Y] = ismember(sort(B(:,1:3),2),A,'rows');
F = @(n)B(n==Y,:);
C = arrayfun(F,1:size(A,1),'uni',0)

C = 1×3 cell array
    {2×4 double}    {2×4 double}    {[7 8 9 12]}

C{:}

ans = 2×4

1 2 3 90 3 1 2 88

ans = 2×4

4 5 6 17 6 5 4 19

ans = 1×4

7 8 9 12

This will produce a consistent 1*size(A,1) output cell array, even if there are rows that do not match.