# How to vectorize vector indexing?

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Ken on 16 Apr 2011
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?

Matt Fig on 16 Apr 2011
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 on 16 Apr 2011
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 on 16 Apr 2011
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)...

Paulo Silva on 16 Apr 2011
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)'

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