[Gretl-devel] about the eigensym() and princomp() help

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