Hello everyone!
I would like to know if there is any way to compute eigenvectors for a given matrix via VEX.
There is a VEX function called eigenvalues but as its name suggests it only calculates eigenvalues, not eigenvectors!
Any help would greatly be appreciated!

Is this too hard really?

Not really a VEX solution, but a solution anyway; if you have python modules configured and numpy installed you could store 3x3 matrices on points and feed those into a python SOP. Then iterate over those points and use the numpy / linear algebra functions to convert into eigenvalues and eigenvectors that you then write back to those points.

I basically just implemented the explanation on this page [web.physics.utah.edu] in a python SOP. The matrix here is a 3x3 matrix stored in the 'covariance' attribute.



Here are two other sources that helped me out;
https://www.visiondummy.com/2014/04/geometric-interpretation-covariance-matrix/ [www.visiondummy.com]
https://houdinigubbins.wordpress.com/2017/06/07/covariance-matrix/ [houdinigubbins.wordpress.com]

Thanks a lot, man!
I'm just curious to know why SideFX doesn't add the eigenvector function to VEX!

N-G
Thanks a lot, man!
I'm just curious to know why SideFX doesn't add the eigenvector function to VEX!

VEX have svddecomp (singular value decomposition). I posted an example of it here:
https://www.sidefx.com/forum/topic/84345/#post-364636 [www.sidefx.com]

This is one of the topics I plan to cover in Pragmatic VEX: Volume 2.

animatrix_

N-G
Thanks a lot, man!
I'm just curious to know why SideFX doesn't add the eigenvector function to VEX!

VEX have svddecomp (singular value decomposition). I posted an example of it here:
https://www.sidefx.com/forum/topic/84345/#post-364636 [www.sidefx.com]

This is one of the topics I plan to cover in Pragmatic VEX: Volume 2.

Thanks a lot, dear @animatrix.
I am in doubt if SVD decomposition can yield eigenvectors of a matrix, instead, it gives eigenvectors for matrix times transpose of the matrix!

N-G

animatrix_

N-G
Thanks a lot, man!
I'm just curious to know why SideFX doesn't add the eigenvector function to VEX!

VEX have svddecomp (singular value decomposition). I posted an example of it here:
https://www.sidefx.com/forum/topic/84345/#post-364636 [www.sidefx.com]

This is one of the topics I plan to cover in Pragmatic VEX: Volume 2.

Thanks a lot, dear @animatrix.
I am in doubt if SVD decomposition can yield eigenvectors of a matrix, instead, it gives eigenvectors for matrix times transpose of the matrix!

Sorry I didn't see your reply but for the record:

If your matrix is symmetric, you can use diagonalizesymmetric which computes the eigenvalue decomposition of a symmetric matrix: which is guaranteed to have a real spectrum. VEX doesn't have eigenvalue decompositions for general matrices since they would require complex numbers.

There is also eigenvalues VEX function that predates diagonalizesymmetric:
https://www.sidefx.com/docs/houdini/vex/functions/eigenvalues.html [www.sidefx.com]

There is an RFE to support non-symmetric matrices for eigenvalue decomposition: #132742. So feel free to bump that up if you want to see it in a future version of Houdini.

Thanks a lot, dear Animatrix.