How to extract diagonal elements of multidimensional array ?

Question

shuang Yang 2023-3-23

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https://ww2.mathworks.cn/matlabcentral/answers/1934075-how-to-extract-diagonal-elements-of-multidimensional-array

评论： Mattia Marsetti 2023-3-24

采纳的回答： the cyclist

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If I have a m-order n-dimensional tensor

. How should I extract the diagonal elements

?

For example

% Generate a 3-order 4-dimensional tensor
rng('default')
A = rand(4,4,4)
A = 
A(:,:,1) =

    0.8147    0.6324    0.9575    0.9572
    0.9058    0.0975    0.9649    0.4854
    0.1270    0.2785    0.1576    0.8003
    0.9134    0.5469    0.9706    0.1419


A(:,:,2) =

    0.4218    0.6557    0.6787    0.6555
    0.9157    0.0357    0.7577    0.1712
    0.7922    0.8491    0.7431    0.7060
    0.9595    0.9340    0.3922    0.0318


A(:,:,3) =

    0.2769    0.6948    0.4387    0.1869
    0.0462    0.3171    0.3816    0.4898
    0.0971    0.9502    0.7655    0.4456
    0.8235    0.0344    0.7952    0.6463


A(:,:,4) =

    0.7094    0.6551    0.9597    0.7513
    0.7547    0.1626    0.3404    0.2551
    0.2760    0.1190    0.5853    0.5060
    0.6797    0.4984    0.2238    0.6991

The diagonal elements are A(1,1,1) = 0.8147, A(2,2,2) = 0.0357, A(3,3,3) = 0.7655 and A(4,4,4) = 0.6991.

I was hoping to have a tensor_diag function that takes a tensor A as an input parameter and returns a vector consisting of its diagonal elements.

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Stephen23 2023-3-23

编辑：Stephen23 2023-3-23

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@Mattia Marsetti: your code throws an error on the example array:

rng('default')
A = rand(4,4,4)
A = 
A(:,:,1) =

    0.8147    0.6324    0.9575    0.9572
    0.9058    0.0975    0.9649    0.4854
    0.1270    0.2785    0.1576    0.8003
    0.9134    0.5469    0.9706    0.1419


A(:,:,2) =

    0.4218    0.6557    0.6787    0.6555
    0.9157    0.0357    0.7577    0.1712
    0.7922    0.8491    0.7431    0.7060
    0.9595    0.9340    0.3922    0.0318


A(:,:,3) =

    0.2769    0.6948    0.4387    0.1869
    0.0462    0.3171    0.3816    0.4898
    0.0971    0.9502    0.7655    0.4456
    0.8235    0.0344    0.7952    0.6463


A(:,:,4) =

    0.7094    0.6551    0.9597    0.7513
    0.7547    0.1626    0.3404    0.2551
    0.2760    0.1190    0.5853    0.5060
    0.6797    0.4984    0.2238    0.6991
get_tensor(A)
Index in position 4 exceeds array bounds. Index must not exceed 1.

Error in solution>get_tensor (line 19)
    out(i)=eval(str);
function out=get_tensor(v)
size_v=size(v);
if sum(size_v == size_v(1))<numel(size_v)
    error('the input vector is not a sqare matrix');
end
N = size_v(1);
out=zeros(N,1);
for i=1:N
    str='v(';
    for s=1:N
        str=[str 'i,'];
    end
    str(end:end+1)=');';
    out(i)=eval(str);
end
end

Note that you could easily replace the evil EVAL with a cell array and a comma-separated list.

Mattia Marsetti 2023-3-24

Thanks for the hint Stephen23, I'll try that

Regards

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Answer 1

the cyclist 2023-3-23

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rng('default')
N = 4;
A = rand(N,N,N);
A(1:N^2+N+1:end)
ans = 1×4
    0.8147    0.0357    0.7655    0.6991

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shuang Yang 2023-3-23

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Thank you very much for your answer, although this is not the correct answer, but I should have guessed how to write it, the correct version of it should be like this

rng('default')
%% order = 2
N = 3;
A = rand(N,N)
A = 3×3
    0.8147    0.9134    0.2785
    0.9058    0.6324    0.5469
    0.1270    0.0975    0.9575
A(1:N+1:end)
ans = 1×3
    0.8147    0.6324    0.9575
%% order = 3
N = 4;
A = rand(N,N,N) % 
A = 
A(:,:,1) =

    0.9649    0.4854    0.9157    0.0357
    0.1576    0.8003    0.7922    0.8491
    0.9706    0.1419    0.9595    0.9340
    0.9572    0.4218    0.6557    0.6787


A(:,:,2) =

    0.7577    0.1712    0.0462    0.3171
    0.7431    0.7060    0.0971    0.9502
    0.3922    0.0318    0.8235    0.0344
    0.6555    0.2769    0.6948    0.4387


A(:,:,3) =

    0.3816    0.4898    0.7547    0.1626
    0.7655    0.4456    0.2760    0.1190
    0.7952    0.6463    0.6797    0.4984
    0.1869    0.7094    0.6551    0.9597


A(:,:,4) =

    0.3404    0.2551    0.9593    0.2575
    0.5853    0.5060    0.5472    0.8407
    0.2238    0.6991    0.1386    0.2543
    0.7513    0.8909    0.1493    0.8143
A(1:N^2+N+1:end)
ans = 1×4
    0.9649    0.7060    0.6797    0.8143
%% order = 4
N = 4;
A = rand(N,N,N,N);
A(1:N^3+N^2+N+1:end)
ans = 1×4
    0.2435    0.3692    0.0292    0.6569
A(1)
ans = 0.2435
A(2,2,2,2)
ans = 0.3692
A(3,3,3,3)
ans = 0.0292
%% order = 5
N = 7;
A = rand(N,N,N,N,N);
A(1:N^4+N^3+N^2+N+1:end)
ans = 1×7
    0.6280    0.7118    0.6596    0.5435    0.6933    0.9827    0.9083

the cyclist 2023-3-23

Ah, I read your question too quickly, and didn't make my solution general enough. Glad you found it.

Stephen23 2023-3-23

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@shuang Yang: you could generalize that:

A(1:sum(N.^(0:ndims(A)-1):end)

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Answer 2

Bruno Luong 2023-3-23

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1934075-how-to-extract-diagonal-elements-of-multidimensional-array#answer_1199495

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N = 7;
A = rand(N,N,N,N,N);
p=ndims(A);
N=length(A);
% Method 1: generalization of cyclist's answer
step = polyval(ones(1,p),N);
idx = 1:step:N^p;
A(idx)
ans = 1×7
    0.4728    0.2804    0.8097    0.9442    0.5680    0.1666    0.9129
% Method 2
c = repmat({1:N}, [1,p]);
idx = sub2ind(size(A), c{:});
A(idx)
ans = 1×7
    0.4728    0.2804    0.8097    0.9442    0.5680    0.1666    0.9129

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How to extract diagonal elements of multidimensional array ?

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How to extract diagonal elements of multidimensional array ?

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