Apply function on several matrices without for loop

Hi all,

I have hundred 3x3 rotation matrices stored in a 100x9 matrix. I would like to compute the corresponding rotation vectors using the Rodrigues convention. The desired output would be a 100x3 matrix.

Currently, I have written a function with a for loop that reads the 9 parameters of each rotation matrix line by line and fills in the corresponding rotation vector line by line.

function [rot_vectors] = rotationMatricesToVectors(rot_matrices) 

nb_rotations = size(rot_matrices,1);
rot_vectors = zeros(nb_rotations,3);

for i = 1:nb_rotations
    R = [...
        rot_matrices(i,1) rot_matrices(i,2) rot_matrices(i,3);
        rot_matrices(i,4) rot_matrices(i,5) rot_matrices(i,6);
        rot_matrices(i,7) rot_matrices(i,8) rot_matrices(i,9)];
    rot_vectors(i,:) = rotationMatrixToVector(R);
end

end

I was wondering if there is a more elegant way to write this function, in particular to avoid the for loop.

Thank you!

Guillaume

[Matt J]

Slightly better:

   Rstack=reshape(rot_matrices.',3,3,[]);

 for i = 1:nb_rotations
    rot_vectors(i,:) = rotationMatrixToVector(Rstack(:,:,i));
 end

However, for further optimization, you need to show us what rotationMatrixToVector() is doing.

[Guillaume]

@Matt, you're missing a final transpose/permute due to the unconventional linear indexing used. Either:

Rstack = permute(reshape(rot_matrices.',3,3,[]), [2 1 3]);

or

rot_vectors(i,:) = rotationMatrixToVector(Rstack(:,:,i).');

@Guillaume, matlab indexing is such that indices go down column first. It would be better if you respected that convention and thus stored your matrices in the order

[(i,1)   (i,4)   (i,7)
 (i,2)   (i,5)   (i,8)
 (i,3)   (i,6)   (i,9)]

This would significantly speed up the processing. At the moment, your code (or Matt's) does a lot of transposing. That's a slow operation as matlab needs to completely rewrite a new matrix. Storing your rotation matrices as above and actually storing them as a 9x100 would mean that only reshape operations are needed. These are near instantaneous.

-- Another Guillaume --

[Matt J]

@Guillaume2,

Good point, although I don't think the transposition should matter, ultimately. The rotation axes are the same both for a rotation matrix R and its transpose.

[Guillaume]

Hi Matt, Guillaume,

Thanks for the comments! As you suggested, I am going to change the indexing (column by column instead of row by row).

rotationMatrixToVector is actually a built-in function:

https://fr.mathworks.com/help/vision/ref/rotationmatrixtovector.html

Answer 1

[Matt J]

I doubt this will be faster than a for loop, but it does get rid of it.

function [rot_vectors] = rotationMatricesToVectors(rot_matrices) 

    nb_rotations = size(rot_matrices,1);

   Rstack=reshape(rot_matrices.',3,3,[]);

   K=kron(speye(nb_rotations),ones(3));

   K(K>0)=Rstack(:);

    [v,~]=eigs(K,1);

   rot_vectors=reshape(v,3,[]).';