QR & RQ Factorization

from the documentation (here is a page that shows it though). To use this version, import rq like this:

from scipy.linalg import rq

Alternatively, you can use the more common QR factorization and with some modifications write your own RQ function. 

from scipy.linalg import qr

def rq(A): 
 Q,R = qr(flipud(A).T)
 R = flipud(R.T)
 Q = Q.T 
 return R[:,::-1],Q[::-1,:]

RQ factorization is not unique. The sign of the diagonal elements can vary. In computer vision we need them to be positive to correspond to focal length and other positive parameters. To get a consistent result with positive diagonal you can apply a transform that changes the sign. Try this on a camera matrix like this:

# factor first 3*3 part of P
K,R = rq(P[:,:3])

# make diagonal of K positive
T = diag(sign(diag(K)))

K = dot(K,T)
R = dot(T,R) #T is its own inverse

The RQ decomposition transforms a matrix A into the product of an upper triangular matrix R (also known as right-triangular) and an orthogonal matrix Q. The only difference from QR decomposition is the order of these matrices.

QR decomposition is Gram–Schmidt orthogonalization of columns of A, started from the first column.

RQ decomposition is Gram–Schmidt orthogonalization of rows of A, started from the last row.