You get bigger round-off errors when computing the difference between logarithms than when computing the logarithm of the ratio. That's why a logarithmic mean of almost equal numbers turned out very badly.
(-/@:^. ,. ^.@:%/)1e13+?2 6$0 _3.55271e_15 _3.10862e_15 1.42109e_14 1.53211e_14 3.55271e_14 3.4861e_14 _7.10543e_15 _6.10623e_15 _6.39488e_14 _6.27276e_14 3.55271e_15 3.33067e_15 Den 10:36 tirsdag den 22. april 2014 skrev Linda Alvord <lindaalv...@verizon.net>: You're right! (lousy proofreading.) I'm getting better at reading all your >"slight of hand". > >Linda > >-----Original Message----- >From: programming-boun...@forums.jsoftware.com >[mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Bo Jacoby >Sent: Tuesday, April 22, 2014 2:47 AM >To: programm...@jsoftware.com >Subject: Re: [Jprogramming] Logarithmic Mean > >Of course you ment to write that a >negative divided by a negative is always a positive. > >Den 21:55 mandag den 21. april 2014 skrev Linda Alvord ><lindaalv...@verizon.net>: > >That was a good math lesson! I couldn't believe I hadn't noticed that a >>negative divided by a negative is always a negative. You used some cleveer >>ways of simplifying the expression. I liked how you Went outside the >>parentheses or were "thinking outside the box" >> >>Linda >> >> >>-----Original Message----- >>From: programming-boun...@forums.jsoftware.com >>[mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Bo Jacoby >>Sent: Monday, April 21, 2014 7:16 AM >>To: programm...@jsoftware.com >>Subject: Re: [Jprogramming] Logarithmic Mean >> >>Hi Linda. Translating from your version to mine: >> >> 5(13 :'(|x-y)%|(^.x)-^.y')20 NB. Linda's lm3 >>10.8202 >> 5(13 :'(x-y)%(^.x)-^.y')20 NB. omitting '|' >>10.8202 >> 5*1(13 :'(x-y)%(^.x)-^.y')20%5 NB. homogeneity >>10.8202 >> 5*(13 :'(1-y)%(^.1)-^.y')20%5 NB. fix x=1 >>10.8202 >> 5*(13 :'(<:y)%^.y')20%5 NB. (x%y) = (-x)%-y >>10.8202 >> 13 :'(<:y)%^.y' NB. tacit >><: % ^. >> 5*(<:%^.)20%5 NB. check >>10.8202 >> 5(13 :'y* (<:%^.) x%y') 20 NB. linearity >>10.8202 >> 13 :'y* (<:%^.) x%y' NB. tacit >>] * [: (<: % ^.) % >> 5(] * [: (<: % ^.) %)20 NB. check >>10.8202 >> >> >> >>Den 11:17 mandag den 21. april 2014 skrev Linda Alvord >><lindaalv...@verizon.net>: >> >>I should have gone to the original website a lot sooner. >>> >>> lm3=: 13 :'(|x-y)%|(^.x)-^.y' >>> 5 lm2 20 >>>10.8202 >>> >>> lm3 >>>([: | -) % [: | ([: ^. [) - [: ^. ] >>> >>> Now this agrees with Bo's shorter version.. >>> >>>Linda >>> >>>-----Original Message----- >>>From: programming-boun...@forums.jsoftware.com >>>[mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Bo Jacoby >>>Sent: Monday, April 21, 2014 12:48 AM >>>To: programm...@jsoftware.com >>>Subject: Re: [Jprogramming] Logarithmic Mean >>> >>>Try this: >>> >>> l=. 13 : '(<:y)%^.y' >>> lm=. 13 : 'y*l x%y' f. NB. logarithmic mean >>> lm >>>] * [: (<: % ^.) % >>> 3 lm 3.000002 >>>3 >>> 3 lm 3.00002 >>>3.00001 >>> >>>Thanks. Bo. >>> >>> >>>Den 2:04 mandag den 21. april 2014 skrev Raul Miller >>><rauldmil...@gmail.com>: >>> >>>On Sun, Apr 20, 2014 at 7:08 PM, Henry Rich <henryhr...@nc.rr.com> wrote: >>>>> More exact equality isn't enough - as you can see from the example, it >>>>> calculates a mean of 2.7 when 3 is the right answer. The problem there >>>is >>>>> roundoff error I expect. >>>> >>>>I doubt the numbers I am working with would have even 10 digits of >>>>accuracy, so I'm actually not too worried. >>>> >>>>Thanks, >>>> >>>> >>>>-- >>>>Raul >>>>---------------------------------------------------------------------- >>>>For information about J forums see http://www.jsoftware.com/forums.htm > >>> >>>> >>>> >>>> >>>---------------------------------------------------------------------- >>>For information about J forums see http://www.jsoftware.com/forums.htm >> >>>---------------------------------------------------------------------- >>>For information about J forums see http://www.jsoftware.com/forums.htm >>> >>> >>> >>---------------------------------------------------------------------- >>For information about J forums see http://www.jsoftware.com/forums.htm >> >>---------------------------------------------------------------------- >>For information about J forums see http://www.jsoftware.com/forums.htm >> >> >---------------------------------------------------------------------- >For information about J forums see http://www.jsoftware.com/forums.htm > >---------------------------------------------------------------------- >For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
