How to find the row numbers for the pairwise entries from one matrices to another?

I am trying to compare two matrices of length 2xn and 2xm for n>m. For example consider n=19,m=16. Then we have the following two vectors, nodes (2x19) and old_nodes (2x16).

%Nodes					Old_nodes	
0	        0				0	        0
0	        0.333333333			0	        0.333333333
0      	0.666666667			0	        0.666666667
0	        1			        0	        1
0.333333333	0			        0.333333333	0
0.333333333	0.333333333			0.333333333	0.333333333
0.333333333	0.666666667			0.333333333	0.666666667
0.333333333	1				0.333333333	1
0.666666667	1				0.666666667	0
1	        0.666666667			0.666666667	0.333333333
1	        1				0.666666667	0.666666667
1	        0.166666667			0.666666667	1
0.666666667	0				1	        0
1	        0				1	        0.333333333
0.833333333	0.166666667			1	        0.666666667
0.666666667	0.666666667			1               0
0.666666667	0.333333333					
1	        0.333333333					
0.833333333	0.333333333					
		

From here I am then trying to find out which rows in nodes are in old_nodes, there should be 16 of them. However, my attempt does not yield any effective results. I have tried the following, by taking four elements that i know are in old_nodes (rows: 6 7 10 11)

j=0
r=0
old_free=[6 7 10 11]
rows=zeros(length(old_free),1);
for i=1:length(e)
    %     i
    for jj=1:length(old_free)
        [row,~]=find(nodes(i,1)==old_nodes(old_free(jj),1) & nodes(i,2)==old_nodes(old_free(jj),2))
        if isempty(row)
            r=r+1
        else
            j=j+1
            rows(j)=row;
        end
    end
end

Essentially what i would like is a column with the indices of the coordinates from nodes which match the indices of the entries for old_nodes, which will all be unique pairs:

e.g.

1  4
5  8
11 3

If anyone can be of help, I'd greatly appreciate it.

Answer 1

[Mehdi Ben Slama]

Hi, it looks to me that the function 'ismember' does what you want. Specifically:

ismember(nodes, old_nodes, 'rows')

In this case, you're interested not only in whether the rows of 'nodes' are contained in 'old_nodes', but also their location in 'old_nodes'. You can obtain both in this manner:

[ LIA, LOCB ] = ismember(nodes, old_nodes, 'rows')

LIA is a vector with values 1 or 0 depending on whether the row of A is a member of B.

LOCB is a vector containing the location (row index) in B when a row in A is a member of B, 0 otherwise.

You should be able to get what you need by fiddling around with LOCB to get it into your desired format!

PS: do check the help section on 'ismember', it's probably more exhaustive