So, assuming you're really looking for the possible grade vector
<:6 1 5 2 3 4
5 0 4 1 2 3
You could choose F like this for "W =. 3 9 [L =. 20 16 12"
F=: 4 : 0"0
select. x*y
case. 60 do. 4
case. 180 do. 2
case. 48 do. 1
case. 144 do. 0
case. 36 do. 3
case. 108 do. 5
end.
)
and you ravel the table produced by "L F/ W",
\:,L F/ W
5 0 4 1 2 3
But this hardly seems like a satisfactorily general "F".
A brute force approach also seems fruitless:
F=: 4 : 'x^2 - y^2'
]targ=. <:6 1 5 2 3 4 NB. Targeting a possible grade vector
5 0 4 1 2 3
$W=. {2$<_2 _1 0 1 2 NB. All pairs of these five items
5 5
$L=. {3$<_3 _2 _1 0 1 2 3 NB. All triplets of these five items
7 7 7
$\:"1 ,&>L(F/&.>)/W
7 7 7 5 5 6
$(,/)^:4]\:"1 ,&>L(F/&.>)/W
8575 6
(<targ) e. <"1 (,/)^:4]\:"1 ,&>L(F/&.>)/W
0
NB. Not here...
$targ *./ . =~ (,/)^:4]\:"1 ,&>L(F/&.>)/W
8575
1 e. targ *./ . =~ (,/)^:4]\:"1 ,&>L(F/&.>)/W
0
NB. Try a wider range...
$W=. {2$<_20 _10 2 1 0 1 2 10 20
9 9
3 3{.W
+-------+-------+-----+
|_20 _20|_20 _10|_20 2|
+-------+-------+-----+
|_10 _20|_10 _10|_10 2|
+-------+-------+-----+
|2 _20 |2 _10 |2 2 |
+-------+-------+-----+
$L=. {3$<_30 _20 _10 _3 _2 _1 0 1 2 3 10 20 30
13 13 13
]targ=. <:6 1 5 2 3 4
5 0 4 1 2 3
1 e. targ *./ . =~ (,/)^:4]\:"1 ,&>L(F/&.>)/W
0
NB. Not here either...
This problem seems woefully under-specified.
Regards,
Devon
On Thu, Feb 25, 2010 at 7:48 PM, Yuvaraj Athur Raghuvir <
[email protected]> wrote:
> I have to determine such an F. F is not given. The only known information
> is
> how the values are ordered.
>
> On Thu, Feb 25, 2010 at 4:44 PM, Henry Rich <[email protected]> wrote:
>
> > You are looking for a solution given any F?
> >
> > If F is [, no solution is possible.
> >
> > Henry Rich
> >
> > Yuvaraj Athur Raghuvir wrote:
> > > Dear J Forum,
> > >
> > > I have an interesting problem for which I need more insights to
> proceed.
> > >
> > > I have to determine three unknowns:
> > > (a) W where 2 = $W = w1, w2
> > > (b) L where 3 = $ L = l1 , l2 , l3
> > > (c) F a dyad that takes scalar inputs
> > >
> > > Such that
> > > (6 1 5 2 3 4) -: \:; L F"0 0/ W NB. the order of values is known.
> > >
> > > For example,
> > > F =: *
> > > (6 1 5 2 3 4) -: \:; L F"0 0/ W [W =. 3 9 [L =. 20 16 12
> > > 0
> > >
> > > I designed a test that is essentially a blind brute force on the inputs
> > > assuming F is given:
> > > F =: 4 : 'x^2 - y^2' NB. for example
> > > odometer =: #: i.@(*/)
> > > test =: 3 : 0
> > > n =. y
> > > w =. odometer n,n
> > > l =. odometer n,n,n
> > > NB. I get a length error if I use bigger inputs. So chunking into
> 100's
> > > for_i. i. 100 %~ {. $l do.
> > > for_j. i. 100 %~ {. $w do.
> > > b =. ('' -: I. (6 1 5 2 3 4) -:"1 1 (>@[ \:@,"_1@:(F"0 0/"1 1)
> >@])/
> > > (_100{.(100*>:i){. l);(_100{.(100*>:j){. w))
> > > smoutput i,j
> > > if. b<1 do. break. [smoutput 'found it';i;j end.
> > > end.
> > > end.
> > > ''
> > > )
> > >
> > > I am not convinced that I can find a solution this way since the
> > functional
> > > forms are far too many to be tried out notwithstanding my other
> > assumptions.
> > >
> > >
> > > Any suggestions?
> > >
> > > Regards,
> > > Yuva
> > > ----------------------------------------------------------------------
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> > >
> > ----------------------------------------------------------------------
> > 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
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