@epostma Hi Erik,
I did wonder about the inflection point business, and since my function is analytic I may be able to find an expression for the inflection points as function of the input parameter for the 2nd stage. I won't know for sure until I have tried, there are several of these points and I assume I need them all. Reading through your 4 posts of 2010 outlining Maple's algorithm (and thanks for that ref, btw, these are very helpful posts) I take it that handing over the points with the 2nd derivative being 0 should already speed things up... or does the algorithm choke if it gets one where the curvature does not actually change sign (i.e. not a true inflection point)? Looking at the algorithm as outlined by you it is however not clear whether the algorithm Maple uses is more efficient than the pedestrian way if the pdf changes for every point generated. It is clearly tuned towards generating many points with a fixed pdf (which probably covers >90% of all applications).
I do wonder, however, why the thing chokes if I hand it a non-normalized pdf. A part of the reason why my simple approach works ok is that I can hand it an unnormalized function. There is nothing I saw in your (Maple's) algorithm that appears dependent on the normalization of the pdf; yet the generator stalls if I hand it an (even slighly) unnormalized pdf.
Be that as it may, what I have works and is good enough for my present purpose, and I thank you for reading my post and commenting as it is good to know I am not too far off what I shold be doing.
PS: There are a number of posts that Maple employees have done highlighting features of Maple (another one is e.g. Darrin Ohashi's posts on parallel programming). I seem to discover these serendipitously. Is there a way to find all of these, and only these?