egg|nomz|egg changed the topic of #kspacademia to: https://gist.github.com/pdn4kd/164b9b85435d87afbec0c3a7e69d3e6d | Dogs are cats. Spiders are cat interferometers. | Космизм сегодня! | Document well, for tomorrow you may get mauled by a ネコバス. | <UmbralRaptor> egg|nomz|egg: generally if your eyes are dewing over, that's not the weather. | <ferram4> I shall beat my problems to death with an engineer.
<egg>
bofh: double-double
<egg>
bofh: fugue theme
<bofh>
egg: gotcha, and I'll ask for the latter.
<bofh>
few mins.
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<egg>
!wpn hillexed
* Qboid
gives hillexed a quill
<hillexed>
with this quill I will pierce the pages
<hillexed>
not the best idea in retrospect now there's a giant hole in my paper whoops
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<egg>
hmmm why are the tests taking an eternity to link
<egg>
did i break the linker
<egg>
meow
* UmbralRaptor
meows at egg's linker
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<egg>
AAAAAAAAAAAAA phl wrote LegendrePolynomial recursively
<bofh>
(I like that one blogpost of Ryg's where he does fancy templating for Legendre & Chebyshev and then it turns out it's simpler and faster to just do the nonrecursive way for any n and it's still faster)
<kmath>
<eggleroy> (T(s?j|[xšr])|(Ts?c|C)h|Č|Ç|C[sz]?)[eê]b[îiıyư](s[jz]|sch?|[sc]h|[šșşsx])[ëéeo](ff?|[vwp]) ⏎ ⏎ Consistency: there is a… https://t.co/aR9v3paUYM
<bofh>
:P
<iximeow>
!meow
* Qboid
meows at
<egg>
bofh: to clarify: that computes the coefficients, and the actual evaluation is run time and fast. But it's eggsponential to compute the coefficients that way obviously...
<kmath>
<✔Alex_Parker> Of course they choose the middle of the night to stare intently up the chimney. When ELSE would you do that. https://t.co/FeXOouc4GH
<egg>
bofh: the article says "which is immediate from the recursion formula"
<egg>
but it has binomial coefficients with non-integer arguments :-p
<bofh>
yeah WTF that formula is just wrong.
<bofh>
(also is in *no way* "immediate from the recursion formula", tho I can kinda see where that binomial corfficient comes from... interpret it as poch(0.5*(n+k-1),k)/k!)
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<bofh>
(it is still the wrong formula and why is it on the page... it's not in Abramowitz&Stegun *or* Gradshteyn&Ryzhik either).
<egg>
bofh: aside from being wrong it is much better than the one above when you want to compute the coefficients, it doesn't overflow as much
<egg>
bofh: okay so if it's neither in the american nor in the russian tables, is it in some french tables?
<bofh>
yeah, like I'm trying to derive the correct one (I believe it'll be the same modulo sign errors) right now then edit some sense into that wikipedia article. >_>
<bofh>
which *are* the major French numerical tables? I know they exist...
<egg>
bofh: hmm, here the signs seem to be right actually
<egg>
(as in phl checked them in mathematica and the formulae give the same as LegendreP)
<bofh>
Hrm, is it differing conventions, then? Should lookup how LegendreP is defined...
<egg>
bofh: that's the penultimate equation on the wikipedia article too
<bofh>
yep.
<bofh>
(weird that wolfram takes it as the definition, which seems utterly backwards to me???)
<bofh>
(standard way I've seen Legendre polys derived is Gram-Schmidt on { 1, x, x^2, ... }, alternately using the 3-term recurrence derivable from Legendre's DE).
<egg>
whitequark: any news from коти or her kitten?
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<bofh>
egg: yeah aren't those just geopotential coefficients?
<egg>
bofh: yes
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<egg>
bofh: but you have Pnm which is a Legendre polynomial of the z coordinate of the normalized displacement from the geocentre, and you have cos and sin mλ which are Чeбышёв polynomials of the x and y coordinates normalized in the ITRS xy plane
<Qboid>
egg meant to say: bofh: but you have Pnm which is a associated Legendre notapolynomial of the z coordinate of the normalized displacement from the geocentre, and you have cos and sin mλ which are Чeбышёв polynomials of the x and y coordinates normalized in the ITRS xy plane
<bofh>
wait, how are cos(mλ)/sin(mλ) Чeбышёв polynomials??? I'm still not seeing it.
<egg>
bofh: Чₘ(cos λ) = cos mλ
<egg>
bofh: should the polynomials of the second kind be called Ш...
<bofh>
Yes, they should. Also OKAY FINE I keep forgetting Чn(cos(x)) satisifies that relation b/c it's pretty much always nicer to work with cos(nx) instead.
<egg>
to get from (r cos φ cos λ, r cos φ sin λ, r sin φ) to λ?
<bofh>
also ooh, fixed estrin for the n=0 case
<bofh>
OHH starting from cartesian & working in spherical?
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<egg>
bofh: yeah, gravity models are always in spherical coords
<egg>
bofh: and they probably wouldn't look very nice if you eggspressed them in cartesian
<bofh>
Well, yes.
<bofh>
You *generally* want to work within spherical if possible.
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<egg>
bofh: well, you probably don't want to do your integration in spherical coords if you value your sanity
<egg>
bofh: therefore, Чебышёв!
<bofh>
wait, why *not*? I've done it before, it's possible to do it numerically stably. But I suppose Чебышёв is a lot easier, yeah.
<egg>
bofh: so, uh, we do everything barycentric, because whole-solar system
<UmbralRaptop>
Converting a coordinate problem into a spelling problem?
<egg>
bofh: so doing the integration in geocentric spherical coords, um
<egg>
bofh: even if you were interested only in near-earth stuff, third-body effects in geocentric coordinates seem like a pain
<bofh>
okay, yes, that sounds like a horror.
<egg>
bofh: also if you are at the level where you're interested only in near-earth stuff you probably want it accurate, in which case you'll notice that the Earth doesn't rotate about the ITRS z axis
<bofh>
wait, ICRS *doesn't* contain precession of thd equinoxes et al in its frame?
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<Qboid>
5d 0h 0m 0s left to event #28: 3e&Azerspace 2/Intelsat 38, VA243 [at 2018-09-07 21:56:00]. Say '!kountdown 28' for details
<egg>
bofh: ... its point is to be inertial
<egg>
the ICRF is built on quasars for that reason
<egg>
bofh: frames based on a dynamical equator are terrible for dynamics, because then *everyone* gets to enjoy the precession in the equations of motion
<bofh>
...RIGHT, you specifically want to avoid that. right. >_>
<bofh>
Yeah okay that's basically the exact same derivation I ran thru, except you then reduced the Gamma functions of half-integer argument to double factorials (which is a good idea fwiw).
<egg>
bofh: well yeah especially if you're going to compute them at compile time :-p
<egg>
bofh: although the final eggspression can be simplified, there's an (n-k-1)!!/(n-k)!
<egg>
bofh: and simplifying that probably helps further with overflows
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<bofh>
Yeah, true. And it does.
<bofh>
(I did something similar for Laguerre Polynomials awhile back)
<bofh>
'lo SnoopJeDi
<bofh>
(tho I don't compute *those* at compile time, heh. not that I *could* even, that codebase is Fortran90).
<egg>
!wpn SnoopJeDi
* Qboid
gives SnoopJeDi a segmented ctenophore
<SnoopJeDi>
hullo bofh, egg
<SnoopJeDi>
bofh, I *just* realized what I enjoy about your nick. On top of BOFH, it's delightfully close to "boffin"
<egg>
bofh: could probably get some more mileage out of double than int64 at least with factorials, factorials overflow 64 bits before they have 53 bits of binary mantissa
<bofh>
egg: yes, this is very much the case. (still the case for double factorials of odd numbers, tho those grow less quickly).