Hi all, I'm currently comparing more closely the different ways of how to compute principal components, leading to some remarks or suggestions (and questions) about the respective documentation. 1) eigensym: (i) The resulting eigenvalues are ascending, and there's a relatively complicated code example about how to get them in descending order, namely: <help-now> matrix U e = eigensym(A, &U) Tmp = msortby((-e' | U)',1)' e = -Tmp[1,]' U = Tmp[2:,] # now largest to smallest eigenvalues print e U </help-now> I guess that this help predates the introduction of the mreverse() function? Because the same effect can be achieved simply by doing: <help-simple> # now largest to smallest eigenvalues e = mreverse(e) U = mreverse(U')' </help-simple> So, OK to change the help example there? Or am I missing something? (ii) The mreverse() calls in hansl take a little time. Certainly not dramatic, but if you need the descending ordering, I found that this little overhead is what makes the eigensym-based solution slightly slower than using svd(). So a follow-up question or suggestion: Why not introduce an optional boolean 3rd arg to eigensym, switching to descending order? I'm guessing that the reordering at the C level (or even BLAS?) would be noticeably faster than in hansl. 2) princomp: There's a verbal explanation of how they are computed, which I find difficult to follow. I have verified that the following computations coincide: <hansl> clear A = mnormal(30,10) matrix v = empty # to hold eigenvectors etc. # eigensym-based m = cdemean(A) eigensym(m'm, &v) pe = m * mreverse(v')' # plain princomp pp = princomp(A, cols(A), TRUE) set assert warn assert(sum(abs(pe - pp)) == 0) </hansl> I think it would be helpful to include an example like this one in the princomp help. Or maybe a variant based on the correlation matrix (default in princomp) instead of the covariance like here. OK? thanks sven