How to find a specific row in the matrix and extract it to the new matrix

Can anyone give me any suggestion how I can find the specific row (matrix= criteria) from main matrix (big matrix) and then extract to the some sub-matrices (A, B, C)

Z = [1  1  1  2
2  2  3  1
3  1  3  4
4  2  1  3
5  1  1  2
6  2  3  1
7  1  3  4
8  1  1  2
9  2  3  1
10  1  3  4
11  1  1  2
12  2  1  3
13  2  1  3
14  2  1  3
15  2  3  1
16  1  3  4
17  2  1  3
18  1  1  2
19  1  1  2
20  2  3  1
21  2  3  1
22  1  3  4
23  1  1  2
24  2  1  3
25  2  1  3
26  2  3  1
27  1  3  4]

M = [1  1  2
2  3  1
1  3  4]

[Azzi Abdelmalek]

What is your criterion

[Moe]

Criteria is the second matrix in the photo.

For example I need to find all of rows in the first matrix that according to the "A" criteria has [1 1 2]. Therefore, output should be same as third matrix:

[1  1  1  2
5  1  1  2
8  1  1  2
11  1  1  2
18  1  1  2
19  1  1  2
23  1  1  2]

Answer 1

[Andrei Bobrov]

Z = [1 1 1 2
2 2 3 1
3 1 3 4
4 2 1 3
5 1 1 2
6 2 3 1
7 1 3 4
8 1 1 2
9 2 3 1
10 1 3 4
11 1 1 2
12 2 1 3
13 2 1 3
14 2 1 3
15 2 3 1
16 1 3 4
17 2 1 3
18 1 1 2
19 1 1 2
20 2 3 1
21 2 3 1
22 1 3 4
23 1 1 2
24 2 1 3
25 2 1 3
26 2 3 1
27 1 3 4];
M = [1 1 2
2 3 1
1 3 4];

[l,i0] = ismember(Z(:,2:end),M,'rows');
zz = Z(l,:);
out = accumarray(i0(l),(1:nnz(i0))',[],@(x){sortrows(zz(x,:))});

Answer 2

[Guillaume]

Use ismember with the 'rows' option:

ismatchrow = ismember(Z(:, 2:end), M(1, :), 'rows');
A = Z(ismatchrow, :)

Or to obtain a cell array with all the submatrices:

[~, matchrow] = ismember(Z(:, 2:end), M, 'rows');
matches = cell(1, max(matchrow));
for m = 1:max(matchrow)
   matches{m} = Z(matchrow == m, :);
end
celldisp(matches)

Answer 3

[Star Strider]

This works:

[Zu, ia, ic] = unique(Z(:,2:4), 'rows');
[Lia,Locb]  = ismember(M,Zu,'rows');

for k1 = 1:size(M,1)
    R{k1} = find(Locb(k1) == ic);
end
A = Z(R{1},:);
B = Z(R{2},:);
C = Z(R{3},:);