How to Select one element from each row of a matrix A based on a column matrix B.

Hello Everyone,

I need to select one element from each row of matrix A of size 6400 X 8 based on another column matrix of size 6400 X 1.

For e.g. lets say A( 6400X8) = [ 1 0 1 0 0 0 1 1; 0 1 0 1 1 1 0 0; 1 0 1 0 0 0 1 0; 0 1 0 0 0 0 0 1; 1 0 0 1 0 0 1 1; 1 0 1 0 0 0 1 0; ...... ..... ];

and let B (6400X1) = [ 6; 7; 1; 4; 5; 8; .; .; .; ]; Now I need a matrix C which has elements from each row of matrix A based on matrix B.

                         A( 6400X8) = [ 1 0 1 0 0(0) 1 1; 
                                        0 1 0 1 1 1 (0)0;
                                       (1) 0 1 0 0 0 1 0;
                                        0 1 0 (0)0 0 0 1;
                                        1 0 0 1 (0)0 1 1;
                                        1 0 1 0 0 0 1 (0);
                                        ......;
                                        ......;
                                                         ];

Therefore C = [ 0; 0; 1; 0; 0; 0; .; .; .; .; ];

Please help me. Thanks in advance.

Answer 1

[Bård Skaflestad]

So, if I understand correctly, your vector B contains column indices (i.e., numbers between 1 and size(A,2) inclusive) such that you want to extract the elements C(i)=A(i,B(i)) for all i=1:size(A,1). Is that correct?

If so, this is a perfect case for linear indexing. Much more about this technique can be found in Steve Eddins' blog at http://blogs.mathworks.com/steve/2008/02/08/linear-indexing/. In this case I'd write something along the lines of

I = (1 : size(A, 1)) .';
J = reshape(B, [], 1);
k = sub2ind(size(A), I, J);
C = A(k);

Answer 2

[Sean de Wolski]

You could use sub2ind():

idx = sub2ind(size(A),(1:numel(B)).',B); %not tested in ML
AB = A(idx);

for more info:

doc sub2ind