You should look at f K and g K, see how they are related to K. Pay attention to the diagonals. Kip
Sent from my iPad On Jan 16, 2013, at 2:45 AM, "Linda Alvord" <lindaalv...@verizon.net> wrote: > Here's another slant on Raul's solution: > > > > ishermitian=: -:[:+|: > > J=:hermy=. (([: <: [: +: 0 ?@$~ ,~) j. [: <: [: +: 0 ?@$~ ,~) 3 > > UT=:(i.3)<:/i.3 > > ]K=:UT*J > > _0.763071j_0.749387 0.904219j0.649481 _0.284142j_0.657158 > 0 _0.500527j0.695882 _0.927555j_0.590524 > 0 0 _0.0310291j0.525098 > > f=: (% 1 + =@i.@#)@:+ +@|: NB. Raul > > g=:[:(% (1 + [: = [: i. #)) (+ [:+ |:) NB. Linda > > (f K)-:g K > > 1 > > 5!:4 <'f' > > -- % > │ -- 1 > -----+ +- + > │ L---+ -- = > -- @: -+ │ -- @ -+- i. > │ │ L- @ -+- # > │ L- + > --+ > │ -- + > L- @ --+- |: > > 5!:4 <'g' > > -- [: > │ -- % > │ │ -- 1 > +----+ +- + > │ L---+ -- [: > --+ │ +- = > │ L----+ -- [: > │ L----+- i. > │ L- # > │ -- + > L----+ -- [: > L---+- + > L- |: > > > > Linda > > > > -----Original Message----- > From: programming-boun...@forums.jsoftware.com > [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Linda Alvord > Sent: Wednesday, January 16, 2013 1:56 AM > To: programm...@jsoftware.com > Subject: Re: [Jprogramming] Hermitian from triangular > > > > I sort of wondered about that word "triangular" but no one else seemed to > worry about it. I should have noticed that A was a triangular matrix when K > showed up > > > > ishermitian=: -:[:+|: > > ]J=:hermy=. (([: <: [: +: 0 ?@$~ ,~) j. [: <: [: +: 0 ?@$~ ,~) 3 > > 0.82045j_0.713947 _0.216061j_0.616151 _0.560927j_0.861101 > > 0.101964j_0.151381 0.350483j_0.440496 0.58375j0.501941 > > 0.00170859j0.457596 0.637767j0.161541 0.333754j_0.975332 > > ]UT=:(i.3)<:/i.3 > > 1 1 1 > > 0 1 1 > > 0 0 1 > > ]K=:UT*J > > 0.82045j_0.713947 _0.216061j_0.616151 _0.560927j_0.861101 > > 0 0.350483j_0.440496 0.58375j0.501941 > > 0 0 0.333754j_0.975332 > > hft =: + +@|:@(- ] * <mailto:=@i.@#> =@i.@#) NB. Kip > > ishermitian hft K > > 0 > > hft=: (+ +@|: * > <mailto:/~@i.@#> /~@i.@#) NB. Ai > > ishermitian hft K > > 0 > > hft=: (% 1 + <mailto:=@i.@#)@> =@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 > > Does K sufficient to test these programs, Kip? > > > > Linda > > > > > > -----Original Message----- > > From: <mailto:programming-boun...@forums.jsoftware.com> > programming-boun...@forums.jsoftware.com > > [ <mailto:programming-boun...@forums.jsoftware.com> > mailto:programming-boun...@forums.jsoftware.com] On Behalf Of km > > Sent: Wednesday, January 16, 2013 1:31 AM > > To: <mailto:programm...@jsoftware.com> programm...@jsoftware.com > > Subject: Re: [Jprogramming] Hermitian from triangular > > > > Linda and Devon, the assignment was to turn a triangular matrix that has a > real diagonal into a Hermitian matrix. A triangular matrix can be "upper > triangular" like > > > > 1 2 3 > > 0 4 5 > > 0 0 6 > > > > or "lower triangular" like > > > > 1 0 0 > > 2 3 0 > > 4 5 6 > > > > The "diagonal" is always the one running from the upper left corner to the > lower right corner, containing 1 4 6 in the first example and 1 3 6 in the > second example. The following upper triangular matrix has a real diagonal > but some numbers off the diagonal are not real. > > > > 1 _2j3 0 > > 0 _4 5j_6 > > 0 0 7 > > > > Although the numbers in my examples have patterns, in general the numbers in > a triangular matrix need have no pattern except that either numbers below > the diagonal are all 0's or numbers above the diagonal are all 0's. > > > > Kip Murray > > > > Sent from my iPad > > > > > > On Jan 15, 2013, at 11:19 PM, Devon McCormick < <mailto:devon...@gmail.com> > devon...@gmail.com> wrote: > > > >> 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 > > < <mailto:lindaalv...@verizon.net> 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 =: + +@|:@(- ] * <mailto:=@i.@#> =@i.@#) NB. Kip > >>> ishermitian hft K > >>> 0 > >>> hft=: (+ +@|: * > <mailto:/~@i.@#> /~@i.@#) NB. Ai > >>> ishermitian hft K > >>> 0 > >>> hft=: (% 1 + <mailto:=@i.@#)@> =@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: <mailto:programming-boun...@forums.jsoftware.com> > programming-boun...@forums.jsoftware.com > >>> [ <mailto: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: <mailto:programm...@jsoftware.com> 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 < <mailto:henryhr...@nc.rr.com> > 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> > http://www.jsoftware.com/forums.htm > >>>>> ------------------------------------------------------------------- > >>>>> -- > >>>>> - For information about J forums see > >>>>> <http://www.jsoftware.com/forums.htm> > http://www.jsoftware.com/forums.htm > >>>> -------------------------------------------------------------------- > >>>> -- For information about J forums see > >>>> <http://www.jsoftware.com/forums.htm> > http://www.jsoftware.com/forums.htm > >>> --------------------------------------------------------------------- > >>> - For information about J forums see > >>> <http://www.jsoftware.com/forums.htm> > http://www.jsoftware.com/forums.htm > > >>> --------------------------------------------------------------------- > >>> - For information about J forums see > >>> <http://www.jsoftware.com/forums.htm> > 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> > http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- > > For information about J forums see <http://www.jsoftware.com/forums.htm> > http://www.jsoftware.com/forums.htm > > > > ---------------------------------------------------------------------- > > For information about J forums see <http://www.jsoftware.com/forums.htm> > 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
