Your results agree with mine - of the three versions of "hft" only Raul's appears to turn an arbitrary random, complex, square matrix into one that passes "ishermitian".
On Tue, Jan 15, 2013 at 11:05 PM, Linda Alvord <lindaalv...@verizon.net>wrote: > Have I gotten all the definitions correct? The only one that consistently > works on a random matrix provided by Kip was provided by Raul > > ishermitian =: -: +@|: > ]K=:hermy=. (([: <: [: +: 0 ?@$~ ,~) j. [: <: [: +: 0 ?@$~ ,~) 3 > 0.681691j_0.530679 0.105724j0.221189 0.140368j_0.982508 > _0.469356j_0.623093 0.71661j0.893344 _0.125895j0.532656 > _0.882974j_0.727597 0.0632899j_0.0448332 _0.975941j_0.730788 > hft =: + +@|:@(- ] * =@i.@#) NB. Kip > ishermitian hft K > 0 > hft=: (+ +@|: * >/~@i.@#) NB. Ai > ishermitian hft K > 0 > hft=: (% 1 + =@i.@#)@:+ +@|: NB. Raul > ishermitian hft K > 1 > hft=:((23 b.&.(a.&i.)&.(2&(3!:5))&.+. +@|:)) NB. Henry > ishermitian hft K > 0 > hft=: 0&=`(,: +@|:)} > ishermitian hft K > 0 > > Linda > > > -----Original Message----- > From: programming-boun...@forums.jsoftware.com > [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Henry Rich > Sent: Tuesday, January 15, 2013 6:21 PM > To: programm...@jsoftware.com > Subject: Re: [Jprogramming] Hermitian from triangular > > Nah, that's not beyond impish. The devilish solution is to take the > bitwise > OR of the matrix with its conjugate transpose (but that's easier in > assembler language than in J: > (23 b.&.(a.&i.)&.(2&(3!:5))&.+. +@|:)) > ). And you need to be sure that the zeros on the lower diagonal and below > are true zeros! > > Henry Rich > > On 1/15/2013 6:03 PM, km wrote: > > Oh, boy! (v1`v2) } y <--> (v1 y) } (v2 y) > > > > Brief and devilish, take care for your soul, Henry! > > > > --Kip > > > > Sent from my iPad > > > > > > On Jan 15, 2013, at 3:39 PM, Henry Rich <henryhr...@nc.rr.com> wrote: > > > >> hft =: 0&=`(,: +@|:)} > >> > >> Henry Rich > >> > >> On 1/15/2013 5:25 AM, km wrote: > >>> This is an easy one. A Hermitian matrix matches its conjugate > transpose. Write a verb hft that creates a Hermitian matrix from a > triangular one that has a real diagonal. > >>> > >>> ishermitian =: -: +@|: > >>> ]A =: 2 2 $ 1 2j3 0 4 > >>> 1 2j3 > >>> 0 4 > >>> ]B =: hft A > >>> 1 2j3 > >>> 2j_3 4 > >>> ishermitian A > >>> 0 > >>> ishermitian B > >>> 1 > >>> > >>> Kip Murray > >>> > >>> Sent from my iPad > >>> -------------------------------------------------------------------- > >>> -- 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 > -- Devon McCormick, CFA ^me^ at acm. org is my preferred e-mail ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
