Ewart's function in tacit version: trian=: 13 :'-:y*>:y' indsy=: 13 :'(>.|:i.y)+/tri i.y' indsy 4 0 1 3 6 1 2 4 7 2 3 5 8 3 4 6 9 trian [: -: ] * >: indsy ([: >. [: |: i.) +/ [: tri i. Linda
-----Original Message----- From: programming-boun...@forums.jsoftware.com [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Henry Rich Sent: Wednesday, August 22, 2012 6:46 PM To: programm...@jsoftware.com Subject: Re: [Jprogramming] Creating random symmetric matrices Why yes, that's much better. Very clever way of filling the triangle. Henry Rich On 8/22/2012 4:28 PM, Ric Sherlock wrote: > Note that Ewart Shaw has responded to this on the Wiki with a solution > that only generates the required number of random numbers: > http://www.jsoftware.com/jwiki/EwartShaw/RandomSymmetricMatrix > > On Wed, Aug 22, 2012 at 5:30 PM, Ric Sherlock <tikk...@gmail.com> wrote: >> The other option is not to add them in the first place? >> >> load 'stats/distribs' >> (|: + ~: zeroTri ) >: zeroTri rnorm 5 5 >> 0.346799 _1.22161 0.57274 0.556122 _0.329658 >> _1.22161 0.149955 _1.77435 _1.76668 0.831557 >> 0.57274 _1.77435 0.77674 _0.0690683 _0.967551 >> 0.556122 _1.76668 _0.0690683 0.720588 _0.195658 >> _0.329658 0.831557 _0.967551 _0.195658 _0.12314 >> >> In other words zero the items above the diagonal then transpose and >> add to the non-diagonal items. >> >> Where zeroTri is an adverb defined as below: >> >> NB.*zeroTri a Zeros triangular items of matrix determined by verb to left >> NB. EG: < zeroTri mat NB. zeros lower-tri items of mat >> NB. EG: <: zeroTri mat NB. zeros lower-tri, off-diag items of mat >> NB. EG: > zeroTri mat NB. zeros upper tri items of mat >> NB. EG: = zeroTri mat NB. zeros all off-diag items of mat >> NB. EG: ~: zeroTri mat NB. zeros diag items of mat >> zeroTri=: 1 :'([: u/~ i.@#) * ]' >> >> This is somewhat wasteful in that you generate a bunch of random >> numbers that you then discard, but if that was an issue you could >> work around it. >> >> >> On Wed, Aug 22, 2012 at 5:07 PM, Owen Marschall >> <omarschal...@amherst.edu> wrote: >>> You read my mind. I was thinking about this same problem tonight while at the opera, and I couldn't think of any way to only divide the diagonals by sqrt(2) a second time--without loops, of course. I don't quite yet understand why your solution works, but I'm sure with enough staring and dictionary help I'll get it. >>> >>> Thanks, >>> Owen >>> >>> On Aug 21, 2012, at 8:25 PM, Henry Rich wrote: >>> >>>> If you have a matrix a of standard normal deviates, you can make it >>>> symmetric with >>>> >>>> asymm =: (+ |:) a >>>> >>>> but what is the variance of the items of a? >>>> >>>> The variance of values off the principal diagonal will be the sum of the variance of two independent standard normal deviates. i.e. 2. >>>> >>>> To return these values to variance 1 you need to divide by sqrt(2). >>>> >>>> But the variance of values ON the principal diagonal will be the sum of two perfectly correlated random variables, i. e. 4. >>>> >>>> So you need to treat the principal diagonal differently. You can reduce its variance by scaling it differently after the conversion to symmetric, dividing the diagonal by sqrt(4) and the rest by sqrt(2): >>>> >>>> asymmgood =: asymm % %: +: >: e. i. # asymm >>>> >>>> (The e. i. bit is a standard idiom for making an identity matrix. Another one you see around is = i. but I avoid that because I think monad = was wrongly defined and should be assigned for other purposes) >>>> >>>> If I've made a statistical blunder I'm sure someone will tell me. >>>> >>>> Henry Rich >>>> >>>> On 8/21/2012 3:10 PM, Owen Marschall wrote: >>>>> Ah, just what I needed. Thanks! >>>>> >>>>> On Aug 21, 2012, at 1:06 PM, Ric Sherlock wrote: >>>>> >>>>>> The primitive ( |: ) is transpose. E.g. : >>>>>> >>>>>> |: i. 3 4 >>>>>> 0 4 8 >>>>>> 1 5 9 >>>>>> 2 6 10 >>>>>> 3 7 11 >>>>>> On Aug 22, 2012 6:55 AM, "Owen Marschall" <omarschal...@amherst.edu> wrote: >>>>>> >>>>>>> Anyone know of an easy way to create a random symmetric matrix >>>>>>> (more specifically, a matrix whose entires are each picked from >>>>>>> a standard Gaussian distribution)? I can start by doing >>>>>>> >>>>>>> load 'stats' >>>>>>> R=:normalrand N N >>>>>>> >>>>>>> but this is not symmetric, and I don't know of any way to >>>>>>> symmetrize it without thinking in loops, which I'm training >>>>>>> myself not to. If I could somehow take a transpose, that would >>>>>>> solve the problem, but I don't know how to do that either. >>>>>>> >>>>>>> Thanks, >>>>>>> Owen >>>>>>> ---------------------------------------------------------------- >>>>>>> ------ 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 > ---------------------------------------------------------------------- > 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
