# Extracting multiple Sub-matrices of different sizes from Large Matrices

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puttogether on 13 Aug 2017
Commented: puttogether on 16 Aug 2017
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
Path = shortestpath(G,1,5);
node = graphtraverse(Edges,5,'depth',1);
seti=unique([Path node]);
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);
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);
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(,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

Faiz Gouri on 16 Aug 2017
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'), :)
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puttogether on 16 Aug 2017
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