Re: Re: Riddle with Ordering
- To: mathgroup at smc.vnet.net
- Subject: [mg78020] Re: [mg77934] Re: Riddle with Ordering
- From: DrMajorBob <drmajorbob at bigfoot.com>
- Date: Thu, 21 Jun 2007 05:51:15 -0400 (EDT)
- References: <f58dbg$8gi$1@smc.vnet.net> <16868914.1182336134968.JavaMail.root@m35>
- Reply-to: drmajorbob at bigfoot.com
Allowing ties, you get something like this, then:
Clear[rawRanking, ranks]
rawRanking[x_List] := Ordering@Ordering@x
ranks[int_List] := Module[{raw = rawRanking@int},
Mean[Pick[raw, int, #]] & /@ int
]
{integers = RandomInteger[{0, 10}, 14], Sort@integers,
rawRanking@integers, ranks@integers} // TableForm
2 1 5 10 3 6 4 1 6 7 2 2 9 9
1 1 2 2 2 3 4 5 6 6 7 9 9 10
3 1 8 14 6 9 7 2 10 11 4 5 12 13
4 3/2 8 14 6 19/2 7 3/2 19/2 11 4 4 25/2 25/2
Bobby
On Wed, 20 Jun 2007 04:28:07 -0500, <nazdrovje at gmail.com> wrote:
> I got this reply by Andrzej Kozlowski, which was very close but not
> what I intended.
>
> ****Begin quote
>
> Iit's not much of a riddle for anyone who has been reading carefully
> this forum for a while as it has turned up more than once. It gives
> you the permutation which will turn Sort[AnyList] into AnyList. In
> other words:
>
> Sort[AnyList][[Ordering[Ordering[AnyList]]]] == Anylist
>
>
> This means, in particular, that if AnyPermuation is any permutation:
>
> Ordering[Ordering[AnyPermuation]]==AnyPermutation
>
> Moreover, AnyList does not have to be a list of reals, or even a list
> of numbers, and its elements need not be distinct.
> *****End quote
>
>
> The intended answer is that the above construct replaces each number
> with its rank in the list. This is useful for all kinds of statistics
> involving ranks, such as Spearman rank correlation (although
> Mathematica has this already built-in). The reason I required the
> numbers to be unique is that otherwise equal numbers would get unequal=
> (successive) ranks. Usually, a set of equal numbers is mapped to a set=
> of equal ranks (the average of the ranks that would be obtained for
> the set by the above method).
>
> Naz
>
>
>
> On Jun 19, 1:06 pm, nazdro... at gmail.com wrote:
>> Just a gem I discovered with Ordering[ ].
>>
>> Anyone have an idea what
>>
>> SomeArrayWithUniqueReals // Ordering // Ordering
>>
>> does?
>>
>> I like this, especially the double use of Ordering. Answer tomorrow.
>
>
>
-- =
DrMajorBob at bigfoot.com