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
