How to vectorize vector indexing?

I want to vectorize the operation of indexing an element in a vector. That is, given a vector of vector indices, I want to pick the corresponding elements out of a matrix where each row is the vector to index.

e.g.

For a matrix

 [1  2  3  4;
  5  6  7  8;
  9 10 11 12]

and the vector of row indices

 [2 3 1]

I want to return

 [2;
  7;
  9]

Can this be done with a one-liner?

Answer 1

[Matt Fig]

Another approach:

% Data
A = [1  2  3  4;
     5  6  7  8;
     9 10 11 12];
c = [2 3 1];

%Extraction:
E = A((1:size(A,1))+(c-1)*size(A,1)).'

If size(A,1) is already known (say m=3), then the obvious simplification results...

E = A((1:m)+(c-1)*m).'

[Ken]

Thanks Matt and Paulo for your answers. Although the simplicity of the diag(a(:,c)) approach is the elegant solution I was looking for, it's far slower than Matt's linear indexing approach. It also exceeds MATLAB's maximum variable size much more easily because it creates a square matrix with dimension numel(c).

In a quick test indexing 50000 vectors, each 1000 elements long, the linear indexing approach was about 80 times faster than arrayfun. The diag method exceeded the maximum variable size.

[Matt Fig]

Notice also that this:

ROW + (COL-1)*size(A,1)

is just an in-lining of SUB2IND for 2D matrices, something every chronic MATLABer should have memorized (IMO)...

Answer 2

[Paulo Silva]

a=[1  2  3  4;
  5  6  7  8;
  9 10 11 12];

v=[2 3 1];

diag(a(1:end,v))

Another way

arrayfun(@(x,y)a(x,y),1:3,v)'