How to index one array by assigned vector in certain dimension

Question

Warren Chuo 2021-6-14

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/856035-how-to-index-one-array-by-assigned-vector-in-certain-dimension

评论： Warren Chuo 2021-6-21

采纳的回答： DGM

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Hi,

I'd like to form a new 2D array by indexing another 3D array, where the indexing is via one assigned vector.

Details like below:

Given arr_i,vec_i, want to find func_index as

arr_o = func_index(arr_i,vec_i);
%%%
arr_i1 = [111,112,113,114; ...
          121,122,123,124];
arr_i2 = [211,212,213,214; ...
          221,222,223,224];
arr_i3 = [311,312,313,314; ...
          321,322,323,324];
arr_i = cat(3,arr_i1,arr_i2,arr_i3);               
vec_i = [2,3,1,2];
arr_o = func_index(arr_i,vec_i);
%%%

With above operation, I expect arr_o will be

[211,312,113,214; ...
 221,322,123,224];

The in/out relationship of func_index is:

arr_o(1:2,1) = arr_i(1:2,1,2), since vec_i(1) == 2;
arr_o(1:2,2) = arr_i(1:2,2,3), since vec_i(2) == 3;
arr_o(1:2,3) = arr_i(1:2,3,1), since vec_i(3) == 1;
arr_o(1:2,4) = arr_i(1:2,4,2), since vec_i(4) == 2;

Keypoint here is assigned vector actually index 3D array in certain one dimension (in this case is dim_3), and result in new 2D array.

Please propose matrix operation (avoiding loop, since the real array is quite big).

Thanks!!

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Answer 1

DGM 2021-6-15

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https://ww2.mathworks.cn/matlabcentral/answers/856035-how-to-index-one-array-by-assigned-vector-in-certain-dimension#answer_724860

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There are probably multiple ways of doing this. It could probably be done with a bunch of reshaping and such, but I did it this way. I'm not sure which would be faster or less confusing.

arr_i1 = [111,112,113,114; ...
          121,122,123,124];
arr_i2 = [211,212,213,214; ...
          221,222,223,224];
arr_i3 = [311,312,313,314; ...
          321,322,323,324];
arr_i = cat(3,arr_i1,arr_i2,arr_i3);    
% [211,312,113,214;
%  221,322,123,224];
% calculate all 8 subscripts for each axis
xvec = repelem(1:4,2);
yvec = repmat(1:2,[1 4]);
zvec = repelem([2 3 1 2],2);
% convert to linear indices
idx = sub2ind(size(arr_i),yvec,xvec,zvec);
reshape(arr_i(idx),2,[])
ans = 2×4
   211   312   113   214
   221   322   123   224

Otherwise, trying to do something directly like

arr_i(:,1:4,[2 3 1 2])

Would give the intersection of the subscript ranges. Such a result would be a much larger set than intended, and the desired result would be its block diagonal.

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DGM 2021-6-15

在 MATLAB Online 中打开

If you don't have repelem, you can probably just use kron()

x = 1:4
x = 1×4
     1     2     3     4
repelem(x,2)
ans = 1×8
     1     1     2     2     3     3     4     4
kron(x,[1 1])
ans = 1×8
     1     1     2     2     3     3     4     4