One problem w/adding the random discrepancy back into a set is that you
will go out of the 1-72 band - then you have to handle that piddling
difference. At some point, it's faster to grab the low-hanging fruit and
be on your way. Whether or not any of this matters depends mainly on the
exact problem domain.
On Wed, Jun 27, 2018 at 8:50 PM, Skip Cave <s...@caveconsulting.com> wrote:
> All,
>
> Wow! Chris Burke's suggestion about rounddist works better than what I
> expected.
>
> g=.1 rounddist "1 (* 172 % +/"1)"1 ] f01
> +/172=+/"1 g
>
> 100000 NB. Now ALL the 6-digit vectors generated sum to 172!!
>
>
> NB. To check:
>
> >./,g
>
> 145
>
> <./,g
>
> 0
>
>
> NB. However, some of the vectors contain integers > 70, and/or some include
> a zero, which is out-of-spec:
>
> NB. Find & count 6 integer vectors in g that have integers > 70 in them
>
>
> #g#~+./"1]100000 6 $70<,g
>
> 5006
>
> NB. So there are still about 5% of the 6 integer vectors that miss the
> original spec of integers 1-70
>
> #g#~+./"1]100000 6 $0=,g
>
> 4250
>
> And another 4.2% that contain zeros
>
>
> Skip
>
>
> Skip Cave
>
> Cave Consulting LLC
>
>
> On Wed, Jun 27, 2018 at 6:09 PM chris burke <cbu...@jsoftware.com> wrote:
>
> > Perhaps use the distributed rounding function from the numeric script?
> For
> > example:
> >
> > load 'numeric'
> >
> > (+/,]) 1 rounddist a * 172 % +/a=. 42 23 5 20 41 40
> > 172 42 23 5 21 41 40
> >
> > (+/,]) 1 rounddist a * 172 % +/a=. 50 35 50 8 19 11
> > 172 50 35 49 8 19 11
> >
> >
> > On Wed, Jun 27, 2018 at 3:47 PM, Skip Cave <s...@caveconsulting.com>
> > wrote:
> >
> > > Devon,
> > >
> > > That 0-1 fraction method is a really nice way to generate lots of sets
> > of 6
> > > random integers 1-70 that sum to 172.
> > > That got me to thinking -- shouldn't we be able to make all the
> generated
> > > 6-integer sets sum to 172?
> > >
> > > f01=. 1e5 6?@$0 NB. Generating the fractions
> > >
> > > NB. Now if we instument your verb a bit more:
> > >
> > > itt1=. f01#~c=.172=+/"1 b=.([: <. 0.5 + ] * 172 % +/"1)"1 ] f01
> > >
> > > $itt1
> > >
> > > 55085 6
> > >
> > > NB. Not bad. Over half of the strings sum to 172.
> > >
> > >
> > > NB. What about the other half (invert the c selection vector)?
> > >
> > > 5{.b#~-.c
> > >
> > > 42 23 5 20 41 40
> > >
> > > 50 35 50 8 19 11
> > >
> > > 37 34 34 17 22 27
> > >
> > > 49 10 25 2 34 53
> > >
> > > 30 14 44 15 32 38
> > >
> > >
> > > How far off are the rest of these strings ?
> > >
> > > d=.172-+/"1 b#~-.-.c
> > >
> > > 20{.d
> > >
> > > 1 _1 1 _1 _1 _1 1 1 _1 1 1 _1 1 1 1 1 1 1 _1 1
> > >
> > > _20{.d
> > >
> > > 1 1 _1 _1 1 1 _1 _1 _1 _1 _1 1 _1 2 _2 1 1 _1 _1 1
> > >
> > >
> > > >./d
> > >
> > > 2
> > >
> > > <./d
> > >
> > > _2
> > >
> > > NB. Looks like the rest of the strings are off by as much as +/- 2
> > >
> > >
> > > So we should be able find the discrepancy in the remaining strings, and
> > > randomly pick one or more of the integers in each of the strings to add
> > or
> > > subtract 1 or 2 to. Then all the strings will sum to 172.
> > >
> > >
> > > I'll leave that exercise to the reader...
> > >
> > >
> > > Skip
> > >
> > ----------------------------------------------------------------------
> > 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
Quantitative Consultant
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
