Using rdivide for multidimensional matrices

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;

Answer 1

[Matt J]

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.

Answer 2

[Bruno Luong]

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), []);

Answer 3

[Matt J]

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;