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

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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)];
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
Louis Vallance
Louis Vallance on 27 Sep 2017
I have corrected my original question to reflect the correct behaviour!

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Accepted Answer

Matt J
Matt J on 27 Sep 2017
Edited: Matt J on 27 Sep 2017
St=reshape( [Sxxi;Txyi;Txzi; Txyi;Syyi;Tyzi; Txzi;Tyzi;Syyi] , 3,3,[])
Javier Fernandez
Javier Fernandez on 9 Dec 2020
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])

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More Answers (1)

Stephen on 27 Sep 2017
Edited: Stephen on 27 Sep 2017
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;

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