In J602 it looks ugly: ^@o. j. -: i.4 1 6.12323e_17j1 _1j1.22465e_16 _1.83697e_16j_1
while this looks nice: (_1^+:&(%~i.))4 1 0j1 _1 0j_1 >________________________________ > Fra: Roger Hui <[email protected]> >Til: [email protected] >Sendt: 16:59 onsdag den 18. juli 2012 >Emne: Re: [Jprogramming] jwiki/Essays/FFT > > ^@o. j. -: i.4 >1 0j1 _1 0j_1 > ^@o. j. 2e9 + -: i.4 >1 0j1 _1 0j_1 > >Works in J7.01 and described in .../release/eulersp.htm > > > >Bo Jacoby <[email protected]> wrote: > >> yes, J is powerful! >> >> (i.,._1^+:&(%~i.))4 NB. indexes and roots of unity >> >> 0 1 >> 1 0j1 >> 2 _1 >> 3 0j_1 >> >> >> (_1^+:&(%~i.))4 NB. roots of unity >> 1 0j1 _1 0j_1 >> >> >> - Bo >> >> >> >> >________________________________ >> > Fra: Linda Alvord <[email protected]> >> >Til: [email protected] >> >Sendt: 7:51 onsdag den 18. juli 2012 >> >Emne: Re: [Jprogramming] jwiki/Essays/FFT >> > >> >I can't believe what a relief this is: >> > >> > iroots >> >[: ,. _1 ^ [: +: i. % ] >> > >> > iroots ttem >> >3 : 0 >> >r0=. i. y >> >q0=. +: r0 % y >> >,. (_1) ^ q0 >> >) >> > irootse=: 13 :',.(_1)^+:(i.y)%y' >> > >> > irootse >> >[: ,. _1 ^ [: +: i. % ] >> > >> >Linda >> > >> > >> >-----Original Message----- >> >From: [email protected] >> >[mailto:[email protected]] On Behalf Of Linda >> Alvord >> >Sent: Wednesday, July 18, 2012 1:38 AM >> >To: [email protected] >> >Subject: Re: [Jprogramming] jwiki/Essays/FFT >> > >> >Or maybe imaginary roots: >> > >> > Iroots=: 13 :',._1^+:(i.y)%y' >> > iroots >> >[: ,. _1 ^ [: +: i. % ] >> > >> > iroots 3 >> > 1 >> >_0.5j0.866025 >> >_0.5j_0.866025 >> > >> > >> >Linda >> > >> >-----Original Message----- >> >From: [email protected] >> >[mailto:[email protected]] On Behalf Of Bo Jacoby >> >Sent: Wednesday, July 18, 2012 1:09 AM >> >To: [email protected] >> >Subject: Re: [Jprogramming] jwiki/Essays/FFT >> > >> ><[email protected]> wrote: "My roots-of-unity verb was designed to get >> >higher accuracy than simpler approaches." >> > >> >The verb >> > PoU=:_1^+: NB. Power of Unity >> > >> >is not contaminated by transcendental numbers such as (2p1) or >> >transcendental functions such as monadic (^). If (y) is rational then (PoU >> >y) is algebraic, so transcendence is not needed. The precision seems OK, >> >even without the use of ((**|)&.+.) >> > >> > n,.PoU(n=.i.8)%8 >> >0 1 >> >1 0.707107j0.707107 >> >2 0j1 >> >3 _0.707107j0.707107 >> >4 _1 >> >5 _0.707107j_0.707107 >> >6 0j_1 >> >7 0.707107j_0.707107 >> >---------------------------------------------------------------------- >> >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
