pick elements from a 3d array, based on an indexing matrix

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Bernhard
Bernhard 2021-1-26
评论： Stephen23 2021-1-27
I have a 3d array A with nr rows, nc columns, and np pages, and an nr x nc indexing matrix I with integer elements between 1 and np. I want to create a matrix B with elements picked from A, where for each position (r,c) the element is picked from the page of A given by the value of I at that position.
A straightforward way to do this would be the double loop:
B = zeros(nr,nc);
for r = 1:nr
for c = 1:nc
p = I(r,c);
B(r,c) = A(r,c,p);
end
end
Is there a way to accelerate this by vectorization for large arrays?

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Stephen23
Stephen23 2021-1-26
编辑：Stephen23 2021-1-26
Ran in:
https://www.mathworks.com/help/matlab/ref/sub2ind.html
% fake data:
nr = 5;
nc = 7;
np = 3;
A = randi(9,nr,nc,np);
I = randi(np,nr,nc)
I = 5×7
1 1 2 1 2 2 3 1 3 3 2 3 3 1 1 2 3 2 3 1 1 2 2 2 1 3 2 2 1 1 2 3 3 1 1
% your looped approach:
B = zeros(nr,nc);
for r = 1:nr
for c = 1:nc
p = I(r,c);
B(r,c) = A(r,c,p);
end
end
B
B = 5×7
7 1 6 2 3 7 6 6 4 3 1 5 5 4 4 1 3 2 2 2 6 4 3 8 2 1 7 9 9 9 6 2 5 1 6
% SUB2IND approach:
[xr,xc] = ndgrid(1:nr,1:nc);
X = sub2ind(size(A),xr,xc,I);
C = A(X)
C = 5×7
7 1 6 2 3 7 6 6 4 3 1 5 5 4 4 1 3 2 2 2 6 4 3 8 2 1 7 9 9 9 6 2 5 1 6
  2 个评论
Bernhard
Bernhard 2021-1-26
Thank you, Stephen, that is a nice gimmick. It took about 60% of the time needed for the looped approach.
Bernhard
Stephen23
Stephen23 2021-1-27
@Bernhard: if the speed of this operation is very critical to your algorithm, then take a look inside the sub2ind file. The sub2ind function is generic, for any number of dimensions, but with a little effort you can write your own version that is hardcoded for the number of dimensions of your data and that does not require ndgrid beforehand. Whether it is worth the effort depends on your situation.

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