I'd like to compute the Cholesky factor of the following obviously positive definite matrix of dimensions MxM:

(I + R*R^t)

where R is an upper trapezoidal matrix with dimensions MxN, and M << N. It seems this could be done more stably and efficiently without actually having to calculate R*R^t (unstable) followed by adding the diagonal of ones and then using dpotrf.

Is there anything in LAPACK that could help with this? Thanks!