Hi, I came across the situation where a relatively large symmetric but singular matrix was given (quite a few eigenvalues very close to zero) which I had to "invert". Understandably, gretl's invpd didn't like the input. So I used ginv instead, but it then turned out the result was not "sufficiently" symmetric; for example gretl's own qform function complained about the alleged non-symmetry. So I'm wondering whether hansl/gretl might benefit from a specialized ginv function for symmetric input. Below is a proposal in hansl based on standard algebra. Perhaps we even discussed something similar before? thanks sven <hansl> function matrix ginvsym(const matrix m, scalar thresh[0::1e-10]) # symmetry is only implicitly checked by eigensym matrix evecs matrix evals = eigensym(m, &evecs) if min(evals) > thresh print "Warning: generalized inv not required" matrix out = invpd(m) # (or alternatively:) # out = (evecs .* (1 / evals')) * evecs' else r = rows(m) matrix ev = selifc(evecs, evals' .> thresh) matrix out = ev .* (1 / evals[r - cols(ev) + 1: r]') * ev' endif return out end function M = mnormal(40,20) MM = M*M' matrix GMM = ginvsym(MM) # check symmetry: eval max(abs(GMM - GMM')) # check g-inverse property: eval max(abs(MM - MM*GMM*MM)) </hansl>