MATLAB: Pick elements from a 3d array, based on an indexing matrix

"array picking"

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?

Best Answer

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
Related Question