Create a 3D matrix from multiple 1D vectors without FOR loop

Question

fsgeek 2017-9-27

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/358536-create-a-3d-matrix-from-multiple-1d-vectors-without-for-loop

评论： Javier Fernandez 2020-12-9

采纳的回答： Matt J

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Hello everyone,

I would like to construct a three-dimensional 3x3xL matrix from a series of one-dimensional vectors.

So far I achieve this with the following code:

St = zeros(3.0, 3.0, L);
for i = 1:L
    St(:, :, i) = [Sxxi(i), Txyi(i), Txzi(i);...
    Txyi(i), Syyi(i), Tyzi(i);...
    Txzi(i), Tyzi(i), Szzi(i)];
end

Where each of the six tensor components is a vector of size 1xL. I find this code to be quite silly and unnecessarily slow.

I'm wondering if there's a way to concatenate the six components into the 3x3xL matrix without using a FOR loop? At fist glance it looks like this might be achievable with CAT() but I'm not sure how this would work.

The parameter L is arbitrary so I'm trying to develop a solution which works for any length.

Thanks in advance,

Louis Vallance

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KSSV 2017-9-27

But the loop you showed, will give you a 2D matrix..not 3D.

fsgeek 2017-9-27

I have corrected my original question to reflect the correct behaviour!

Thanks,

Louis

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Answer 1

Matt J 2017-9-27

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https://ww2.mathworks.cn/matlabcentral/answers/358536-create-a-3d-matrix-from-multiple-1d-vectors-without-for-loop#answer_283333

编辑：Matt J 2017-9-27

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St=reshape( [Sxxi;Txyi;Txzi; Txyi;Syyi;Tyzi; Txzi;Tyzi;Syyi] , 3,3,[])

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fsgeek 2017-9-27

This method works perfectly. I feel embarrassed that I didn't see it earlier!

Thanks,

Louis

Javier Fernandez 2020-12-9

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Sorry for reviving old threads, but I would like to point out that the given solution

St=reshape( [Sxxi;Txyi;Txzi; Txyi;Syyi;Tyzi; Txzi;Tyzi;Syyi] , 3,3,[])

is not fully correct because it actually gives the transpose of the expected result. In this case it makes no difference because the input tensor is symmetric and thus, it actually works.

The correct solution for non-symmetric matrices would need to account for that transpose by using permute as:

St=permute( reshape(   [Sxxi;Txyi;Txzi; Txyi;Syyi;Tyzi; Txzi;Tyzi;Syyi]  , 3,3,[]) , [2,1,3])

Javier

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Answer 2

Stephen23 2017-9-27

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/358536-create-a-3d-matrix-from-multiple-1d-vectors-without-for-loop#answer_283334

编辑：Stephen23 2017-9-27

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St = zeros(3,3,L);
St(1,1,:) = Sxxi;
St(1,2,:) = Txyi;
St(1,3,:) = Txzi;
St(2,1,:) = Txyi;
St(2,2,:) = Syyi;
St(2,3,:) = Tyzi;
St(3,1,:) = Txzi;
St(3,2,:) = Tyzi;
St(3,3,:) = Szzi;