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MATLAB: how to multiply a multidimensional matrix using one-dimensional vector indices without loops?

I am currently looking for an efficient way to slice up multidimensional matrices in MATLAB. For example, for example, I have a multidimensional matrix such as

A = rand(10,10,10)

I would like to get a subset of this matrix (let's call it B

) at some indices along each dimension. To do this, I have access to the index vectors along each dimension:

ind_1 = [1,4,5]
ind_2 = [1,2]
ind_3 = [1,2]

Right now I'm doing it rather inefficiently like this:

N1 = length(ind_1)
N2 = length(ind_2)
N3 = length(ind_3)

B = NaN(N1,N2,N3)

for i = 1:N1
   for j = 1:N2
     for k = 1:N3

      B(i,j,k) = A(ind_1(i),ind_2(j),ind_3(k))

     end
   end
end

I suspect there is a smarter way to do this. Ideally I am looking for a solution that is not used for loops and can be used for an arbitrary dimensional matrix N

.

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2 answers


It's actually very simple:

B = A(ind_1, ind_2, ind_3);

As you can see Matlab indices can be vectors and then the result is the Cartesian product of those vector indices. More information on Matlab indexing can be found here .



If the number of dimensions is unknown during programming, you can define the indices in the core of the cell and then expand into a comma separated list :

ind = {[1 4 5], [1 2], [1 2]};
B = A(ind{:});
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You can refer to data in matrices simply by specifying indices, as in the following example:

B = A(start:stop, :, 2);

In the example:



  • start:stop

    gets a range of data between two points
  • :

    gets all records
  • 2

    only gets one record

In your case, since all your indices are 1D, you can simply use:

C = A(x_index, y_index, z_index);
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