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
