Using rdivide for multidimensional matrices

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deathtime
deathtime 2023-9-12
编辑： Bruno Luong 2023-9-13
I have a 5 by 10 by 3 force matrix:
F = rand(5, 10, 3);
The first dimension represents grid points on a mesh (5 mesh points).
The second dimension represents different conditions (10 different conditions).
The third dimension represents 3D components of force (3 components: x, y and z respectively).
I also have a basis vector matrix which I plan to use for a transformation:
basisVectorMat = [0.9659 -0.2588 0; 0 0 -1; 0.2588 0.9659 0];
I would like to transform all the x, y and z force components of F for 3 mesh points (1st, 3rd and 5th) points for 3 different conditions (the 2nd, 4th and 7th elements of the condition dimension). This is a reverse transformation, so the operation to carry out would be F_transformed = F * inv(basisVectorMat), or as I have been advised by Matlab help: F_transformed = F / basisVectorMat.
In order to make it clear, if I just had a single array representing the force [FX, FY, FZ] (so just a single mesh point and condition), this is how I would carry out the operation:
F = rand(1, 3);
F_transformed = F / basisVectorMat
How would I do the operation for the initial matrix defined with multiple mesh points and conditions, for the aforementioned indices, in a vectorized fashion.
My guess would have been to do something like the following:
F = rand(5, 10, 3);
F_transformed = F;
F_transformed([1 3 4], [2 4 7], :) = F([1 3 4], [2 4 7], :) / basisVectorMat;

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采纳的回答

Matt J
Matt J 2023-9-12
编辑：Matt J 2023-9-12
One way:
Fp=permute( F([1,3,5],[2,4,7],:), [1,3,2]);
Fp_transformed= pagerdivide( Fp , basisVectorMat);
F_transformed([1 3 4], [2 4 7], :) =ipermute(Fp_transformed, [1,3,2]);
Of course, it would be better had you not chosen to have the x,y,z components spread along the 3rd dimension. Then there would be no need to permute, which is expensive.

更多回答（2 个）

Bruno Luong
Bruno Luong 2023-9-12
编辑：Bruno Luong 2023-9-13
Put the first extraction of two subindices as a multi-row matrix, do the algebra calculation then put it back.
F = rand(5, 10, 3);
pntidx = [1 3 4];
condidx = [2 4 7];
F_transformed = F;
X = reshape(F_transformed(pntidx,condidx,:),[], size(F,3));
Y = X/basisVectorMat;
F_transformed(pntidx,condidx,:) = reshape(Y, length(pntidx),length(condidx), []);
Matt J
Matt J 2023-9-12
编辑：Matt J 2023-9-12
Using the KronProd class, downloadable from here,
https://www.mathworks.com/matlabcentral/fileexchange/25969-efficient-object-oriented-kronecker-product-manipulation?s_tid=srchtitle
you could do,
B=KronProd({1,basisVectorMat},[1,1,2],[3,3,nan]);
F_transformed([1 3 4], [2 4 7], :) = F([1 3 4], [2 4 7], :) / B;

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