Extracting multiple Sub-matrices of different sizes from Large Matrices

I have a set of 3 large matrices

A =  [
  1  3  0  0  0  0  1  1  0  345  1  1.1  0.9;
  2  2  0  0  0  0  1  1  0  345  1  1.1  0.9;
  3  2  0  0  0  0  1  1  0  345  1  1.1  0.9;
  4  1  0  0  0  0  1  1  0  345  1  1.1  0.9;
  5  1  90  30  0  0  1  1  0  345  1  1.1  0.9;
  6  1  0  0  0  0  1  1  0  345  1  1.1  0.9;
  7  1  100  35  0  0  1  1  0  345  1  1.1  0.9;
  8  1  0  0  0  0  1  1  0  345  1  1.1  0.9;
  9  1  125  50  0  0  1  1  0  345  1  1.1  0.9;];
%
B = [
  1  0  0  300  -300  1  100  1  250  10  0  0  0  0  0  0  0  0  0  0  0;
  2  163  0  300  -300  1  100  1  300  10  0  0  0  0  0  0  0  0  0  0  0;
  3  85  0  300  -300  1  100  1  270  10  0  0  0  0  0  0  0  0  0  0  0;];
C = [
  1  4  0  0.0576  0  250  250  250  0  0  1  -360  360;
  4  5  0.017  0.092  0.158  250  250  250  0  0  1  -360  360;
  5  6  0.039  0.17  0.358  150  150  150  0  0  1  -360  360;
  3  6  0  0.0586  0  300  300  300  0  0  1  -360  360;
  6  7  0.0119  0.1008  0.209  150  150  150  0  0  1  -360  360;
  7  8  0.0085  0.072  0.149  250  250  250  0  0  1  -360  360;
  8  2  0  0.0625  0  250  250  250  0  0  1  -360  360;
  8  9  0.032  0.161  0.306  250  250  250  0  0  1  -360  360;
  9  4  0.01  0.085  0.176  250  250  250  0  0  1  -360  360; ];

Part A The first and second columns of matrix C correspond to starting and target nodes of a graph respectively. I have created a graph with 9 nodes. The reference node in this case is 1. I need to determine the shortest path between 1 and each of the nodes in the graph, then determine all other nodes connected to each node by a a single edge. That is Let G be the graph, let i denote each of the nodes that is i={1, ..., 9}. For each i, create a set of nodes which includes 1) all nodes in the shortest path between node 1 and node i 2) All nodes directly connected to i but not on the shortest path from 1, that is exactly one hop away from i or Immediately adjacent to i. This is the MATLAB code I have written for this

Edges=adjacency(G);
Path = shortestpath(G,1,5);
node = graphtraverse(Edges,5,'depth',1);
seti=unique([Path node]);
Answer:
seti=[1 4 5 6]

This is for just one node (i=5). I want to do this for all 9 nodes simultaneously

Part B After creating the set seti for i={1, ...., 9} with the list of adjacent nodes and nodes on the shortest path for i. From the matrices A and B. I would like to search the first column for numbers corresponding to any of the numbers within the node set. When matching numbers are found, I would like to extract the entire row in A and B corresponding to the row in which a matching element has been found. In other words for all 9 node sets created above, I would like to create smaller 9 submatrices from the A and B large matrices.

This MATLAB code enables me extract submatrices for only node 5

[ii5,jj5] = find(squeeze(any(A(:,1) == reshape([seti],1,1,[]),2)));
A5 = accumarray(jj5,ii5,[],@(x){A(x,:)});
A5=cell2mat(A5);
Answer:
A5=[  1  3  0  0  0  0  1  1  0  345  1  1.1  0.9;
  4  1  0  0  0  0  1  1  0  345  1  1.1  0.9;
  5  1  90  30  0  0  1  1  0  345  1  1.1  0.9;
  6  1  0  0  0  0  1  1  0  345  1  1.1  0.9; ];
%Submatrix from B
[ii5a,jj5a] = find(squeeze(any(B(:,1) == reshape([seti],1,1,[]),2)));
B5 = accumarray(jj5a,ii5a,[],@(x){B(x,:)});
B5=cell2mat(B5); 
Answer: 
B5= [1   0  0  300  -300  1  100  1  250  10  0  0  0  0  0  0  
     0   0  0  0];

Part C Now I want to extract submatrices from the matrix C. I need to search the first two columns of the matrix 'C' and extract submatrices again based on the set of nodes in set i above. This time I start by searching for i from the first 2 columns of C if node i is found in either the first or second column, I extract the entire corresponding row then generate a submatrix. I again search the same two columns for the rest of the node ids in the seti, I need to extract an entire row if both the elements in the first and second column of that row are in the original set of nodes seti. I then create one submatrix from these two submatrices and remove duplicates This is how am extracting the submatrix where the first or second columns contain i.

i=5
[ii5b,jj5b] = find(squeeze(any(C(:,1:2) == reshape([5],1,1,[]),2)));
C5a = accumarray(jj5b,ii5b,[],@(x){C(x,:)});
C5a=cell2mat(C5a) 

For i=5
submatrix 1 in part c would be
C5a=[4  5  0.017  0.092  0.158  250  250  250  0  0  1  -360  360;
     5  6  0.039  0.17  0.358  150  150  150  0  0  1  -360  360;]

submatrix 2 should be C5B=[1 4 0 0.0576 0 250 250 250 0 0 1 -360 360;] Desired matrix

C5=[4  5  0.017  0.092  0.158  250  250  250  0  0  1  -360  360;
    5  6  0.039  0.17  0.358  150  150  150  0  0  1  -360  360;
    1  4  0  0.0576  0  250  250  250  0  0  1  -360  360;]

Questions How can extract submatrix 2 for part c? s in from matrix C, How can I extract a submatrix by searching the first two columns for only those rows in which both the first and second element in col 1 and 2 are in seti.

Like I mentioned earlier my examples are for only one node (i=5). I need to do this for all 9 nodes simultaneous, I would like to generate all 9 sub-matrices for each Part A Part B and Part C. As in a total of 27 matrices simultaneously.

Please advise on a good way to this?

The reason for this is I am going to be changing values in the main matrices A, B, C like 1000 times and I want these changes to propagate to the submatrices simultaneously I'd appreciate any input.

Thank you, puttogether

Answer 1

[Faiz Gouri]

You can use 'ismember' function to compare first two columns of 'C' and 'seti' and then extract rows from C where they are same.

 result = C(ismember(C(:,1:2),seti(:,1:2), 'rows'), :)

[puttogether]

Thank you, This answers the first part of the question I had.

The second part of the question is basically how to generate multiple sub matrices/vectors simultaneously. For example in Part A I would like generate 9 vectors seti where i is 1 through 9 and extract corresponding submatrices from parts B and C. Does my question make sense? Let me know if this is possible. Thanks again