Table 1 shows the average CPU timings for the coordinate-wise algorithm, and the LARS procedure [Efron et al., 2004]. All algorithms are implemented as R language functions. The coordinate-wise algorithm does all of its numerical work in Fortran, while LARS (written by Efron and Hastie) does much of its work in R, calling Fortran routines for some matrix operations. However comparisons in [Friedman et al., 2007] showed that LARS was actually faster than a version coded entirely in Fortran. Comparisons between different programs are always tricky: in particular the LARS procedure computes the entire path of solutions, while the coordinate-wise procedure solves the problem for a set of pre-defined points along the solution path. In the orthogonal case, LARS takes min(N, p) steps: hence to make things roughly comparable, we called the latter two algorithms to solve a total of min(N, p) problems along the path. Table 1 shows timings in seconds averaged over three runs. We see that glmnet is considerably faster than LARS; the covariance-updating version of the algorithm is a little faster than the naive version when
