MATLAB: extract values from 3d matrix at given row and column indcies using sub2ind 3d

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I have 3d matrix A that has my data. At multiple locations defined by row and column indcies as shown by matrix row_col_idx I want to extract all data along the third dimension as shown below:

A = cat(3,[1:3;4:6], [7:9;10:12],[13:15;16:18],[19:21;22:24])  %matrix(2,3,4) 
row_col_idx=[1 1;1 2; 2 3]; 

idx = sub2ind(size(A(:,:,1)), row_col_idx(:,1),row_col_idx(:,2));
out=nan(size(A,3),size(row_col_idx,1));
for k=1:size(A,3) 
    temp=A(:,:,k);
    out(k,:)=temp(idx);          
end
out

The output of this code is as follows:

A(:,:,1) =

     1     2     3
     4     5     6


A(:,:,2) =

     7     8     9
    10    11    12


A(:,:,3) =

    13    14    15
    16    17    18


A(:,:,4) =

    19    20    21
    22    23    24


out =

     1     2     6
     7     8    12
    13    14    18
    19    20    24

The output is as expected. However, the actual A and row_col_idx are huge, so this code is computationally expensive. Is there away to vertorize this code to avoid the loop and the temp matrix?

vectorization matlab arrays
2 Answers

This can be vectorized using linear indexing and implicit expansion:

out = A( row_col_idx(:,1) + ...
        (row_col_idx(:,2)-1)*size(A,1) + ...
        (0:size(A,1)*size(A,2):numel(A)-1) ).';

The above builds an indexing matrix as large as the output. If this is unacceptable due to memory limiations, it can be avoided by reshaping A:

sz = size(A); % store size A
A = reshape(A, [], sz(3)); % collapse first two dimensions
out = A(row_col_idx(:,1) + (row_col_idx(:,2)-1)*sz(1),:).'; % linear indexing along
% first two dims of A
A = reshape(A, sz); % reshape back A, if needed
user_25869220

A more efficient method is using the entries of the row_col_idx vector for selecting the elements from A. I have compared the two methods for a large matrix, and as you can see the calculation is much faster. For the A given in the question, it gives the same output

A = rand([2,3,10000000]);
row_col_idx=[1 1;1 2; 2 3];

idx = sub2ind(size(A(:,:,1)), row_col_idx(:,1),row_col_idx(:,2));
out=nan(size(A,3),size(row_col_idx,1));
tic;
for k=1:size(A,3)
    temp=A(:,:,k);
    out(k,:)=temp(idx);
end
time1 = toc;

%% More efficient method:
out2 = nan(size(A,3),size(row_col_idx,1));
tic;
for jj = 1:size(row_col_idx,1)
    out2(:,jj) = [A(row_col_idx(jj,1),row_col_idx(jj,2),:)];
end
time2 = toc;

fprintf('Time calculation 1: %d\n',time1);
fprintf('Time calculation 2: %d\n',time2);

Gives as output:

Time calculation 1: 1.954714e+01
Time calculation 2: 2.998120e-01
user_91895740
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