Help interpreting the anisotropic magnification matrix

Does anyone know how I one might go about decomposing the matrix emitted by anisotropic mag estimation into rotation, scale, skew? It’s been a long while since I’ve done lin alg, but my old notes on decomposing 2x2 transform matrices is not giving me results that make sense.


Hi @yoshiokc,

I believe the singular value decomposition can be used to decompose the anisotropic magnification matrix into a rotation, scaling (by 2 independent factors along orthogonal axes), and a subsequent rotation.

Note that before doing SVD on the anisotropic magnification matrix, you’ll have to pull it from particle dataset’s ctf/anisomag entry, reshape it into a shape of (2,2) (C-order), and then add it to the 2x2 identity matrix — this is because CryoSPARC stores the matrix with the identity subtracted off, for convenience reasons.


1 Like

oooohh, identity is subtracted? that makes more sense what I’m seeing… in the past I’ve used the QR decomposition to get these values… I was alos copying the values out of the log- did not check to confirm if the values in the log and the particles are the same

ah yes, that seems to have worked! thanks @mmclean !

1 Like