Hi Ed, I've added https://github.com/PDLPorters/pdl/issues/518 to hold comments on benchmarking PDL. I'll take a run at it when the weather gets warmer (it's still cold in the PC room 8-} ), but I've linked to my previous experience in case anyone else wants to have a go. But be warned - benchmarking tickles the obsessive part of your brain something fierce.
cheers, Boyd On Tue, 7 Jan 2025 at 20:16, Ed . <ej...@hotmail.com> wrote: > Hi Luis and all, > > Two points: > > - I've been looking at how Julia does loop fusion, in order to steal > ideas; these are now starting to form more concretely, which I think is > good! But I also looked up how it does on performance, and learned of a > thread where they discussed a benchmark: > https://discourse.julialang.org/t/programming-language-benchmark-2/108429 - > I'd like us to have a benchmark in that for PDL, does anyone feel like > having a go? Boyd? > - I've now added a Ufunc::diffcentred (based on Luis's rotate algorithm), > and Ufunc::partial; the latter adjusts Luis's work to take an ndarray as > first param so it can be a method, and takes instruction on which method to > use (centred (default), forward, backward). I'm about to add a PCHIP option > too, currently only using > https://metacpan.org/pod/PDL::Primitive#pchip_chim, but it would be > possible to use pchip_chic which offers more control of boundary > conditions. Feedback welcome. > > Best regards, > Ed > > ------------------------------ > *From:* Luis Mochan <moc...@icf.unam.mx> > *Sent:* 21 November 2024 15:55 > *To:* Ed . <ej...@hotmail.com> > *Cc:* Boyd Duffee <boyd.duf...@gmail.com>; pdl-devel < > pdl-devel@lists.sourceforge.net>; perldl < > pdl-gene...@lists.sourceforge.net> > *Subject:* Re: [Pdl-devel] curl of vector > > On Thu, Nov 21, 2024 at 03:09:37PM +0000, Ed . wrote: > > Hi Luis, > > > > Thank you for both the code and the explanation! I was aware of the > limitations of diffover for this (including its name - just "diff" caused > clashes with Text::Diff in a downstream module). I'm proposing to rename > "diffover" to "numdiff" (for numerical differentiation) in the next version > of PDL, any objections? > > However, it just takes the differences between consecutive values. I > would call it firstdiff, as there are also second, third, > etc. diffs. These are analogous, but not equal, to the corresponding > (first, second, etc.) derivatives one find in calculus, and may be > used to build approximate derivatives, as in the examples. > > > I considered using diff2 in my quickly-written prototype, but chose > > diffover so as not to shrink the dim by 1. > > There are other PDL methods that allow the user to specify what to do > with the boundaries. Maybe the same should be done here. In my > solution the boundary could be kept if the function is periodic, but > otherwise, it should be thrown away. Another alternative is to add > values beyond the boundary: repeating the boundary value would > correspond to a 0 value for the derivative at the boundary. One could > also add f_{n+1}=2f_{n}-f_{n-1}, which would correspond to a null > curvature at the boundary. Or the easiest, which is to trim down the > derivative at the boundary by droping the last element for forward > differences, the first for backward differences and both for centered > differences. > > > I am also keen to capture the 3 functions you've made, probably with > > "partial" going into Ufunc, and gaining an options param that has > > "difference" of either "forward", "backward", or "centred", or > > "shrink" using diff2. "div" and "curl" would then "just" be examples > > in the docs. Does anyone see any difficulties with this? Boyd, I don't > > feel this would clash with an Advent posting in any important way, but > > I'm very pleased to hear your thoughts if you disagree :-) > > Would be useful. > > Notice that I assumed the function was defined on a regular grid. If > not, more elaborate schemes would be needed to estimate the centered > derivative. > > Another alternative for finding derivative, which may be useful in > some cases, is to make a Fourier transform of the data, multiply it by > i()*(wavevector) and then transform back. > > Best regards, > Luis > > > > > > Best regards, > > Ed > > > > > -- > > o > W. Luis Mochán, | tel:(52)(777)329-1734 /<(*) > Instituto de Ciencias Físicas, UNAM | fax:(52)(777)317-5388 `>/ /\ > Av. Universidad s/n CP 62210 | (*)/\/ \ > Cuernavaca, Morelos, México | moc...@fis.unam.mx /\_/\__/ > GPG: 791EB9EB, C949 3F81 6D9B 1191 9A16 C2DF 5F0A C52B 791E B9EB >
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