Can't use K because its diagonal is not real (is not made up of real numbers). Kip
Sent from my iPad On Jan 16, 2013, at 12:55 AM, "Linda Alvord" <lindaalv...@verizon.net> wrote: > 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 =: + +@|:@(- ] * =@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 > > Does K sufficient to test these programs, Kip? > > Linda > > > -----Original Message----- > From: programming-boun...@forums.jsoftware.com > [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of km > Sent: Wednesday, January 16, 2013 1:31 AM > To: 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 <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 > <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 > ---------------------------------------------------------------------- > 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
