Talk:2435: Geothmetic Meandian

Oh, this one's good. Just checked in (no, I wasn't hovering over the refresh button, my first visit today!) and one glance had me in paroxysms of laughter. But how to explain it? Gonna have to think about that. 141.101.98.96 01:12, 11 March 2021 (UTC)

I made a really bad spreadsheet to understand better how it works: https://docs.google.com/spreadsheets/d/1fqmHwDmirJrsKPdf94PutFDw31DMAYxNeR7jef1jneE/edit?usp=sharing

Someone fix my awful transcript edits please. --Char Latte49 (talk) 02:31, 11 March 2021 (UTC)

Seeing the Python added to the Explanation, try this Perl (typed straight here, so not tested)...

## Your prefered variations of "#!/usr/bin/perl", "use strict;" and "use warnings;" here! ##
sub F { my (@vals)=@_; my $invVals=1/int(@vals);
 my ($geo,$arith,$med)=(1); # Only defining $geo, so first *= works correctly!
 while (@vals) { my($lo,$hi)=(shift @vals,pop @vals); # $hi may be undef - this is intended!
  $arith+=$lo; $geo*=$lo; unless (defined $hi) {  $med =  $lo;     last }
  $arith+=$hi; $geo*=$hi; unless (@vals)       { ($med)=F($lo,$hi)      }
 }
 return ($arith*$invVals, $geo**$invVals, $med);
}
sub GMDN { my (@vals)=sort @_; my $lim=10**(-5); # Adjust $lim to taste...
  return "Error: No vals!" unless  @vals; # Catch!
  return $vals[0]          unless ($vals[$#vals]-$vals[0]) > $lim;
  return GMDM(F(@vals));
}
my @test=(1,1,2,3,5);
print "Values:              @test\nGeothmetic Meandian: ".GMDN(@test)."\n";

...debugged in my head, so probably fatally flawed but easily fixed/adapted anyway. 141.101.99.109 03:04, 11 March 2021 (UTC)

Why so complicated?

perl -e 'use strict; use warnings; sub F { my ($s,$p) = (0,1); my @srt = sort {$a<=>$b} @_; for (@_) { $s += $_; $p *= $_; } return ($s/@_,$p**(1/@_),$srt[$#_/2]); } sub Gmdn { print join(", ",@_=F(@_)),"\n" for 0..20; return @_; } print join(", ",Gmdn(1,1,2,3,5)),"\n";'

(With interim results) SCNR -- Xorg (talk) 03:18, 11 March 2021 (UTC)

I can read your version (and I see you do explicit {$a<=>$b}, which indeed may be necessary in mine for real use, along with additional sanity checks, I will check later) but I wanted to make mine neat, and slightly tricksy in implementation, but still not quite so entirely obfuscated to the more uninitiated. TIMTOWTDI, etc, so I like your (almost) bare-bones version too. ;)

(Is 20 cycles enough to converge in sufficiently extreme cases? Won't give "Too deep" error, though, even if it takes at least that long. There's a definite risk that mine might, as written.) 141.101.99.229 03:45, 11 March 2021 (UTC)

Given the lack of precision in Randall's example usage, I think 20 cycles ought to be enough for everyone ;-P. I'm trying to prove that the interval's size has to shrink by somewhat close to a factor of 1/2 every cycle, but it's tricky and it's late. If I can assume a factor of 1/2 in the long run, 64 iterations should pin down a 64-bit float.

I actually didn't try to obfuscate, I was just too lazy to type more ;-). Otherwise I might have left out the "return"s and passing parameters at all. -- Xorg (talk) 04:21, 11 March 2021 (UTC)

Side-thought: is GMDN (nowhere near as logical an ETLA contraction of the title term as, say, 'GMMD' or 'GTMD') actually an oblique reference to the GNDNs as popularised/coined by Trek canon? Worth a citation/Trivia? 162.158.158.97 04:12, 11 March 2021 (UTC)