Re: Speed challenge: Improve on integer frequencies from Count?
- To: mathgroup at smc.vnet.net
- Subject: [mg67777] Re: [mg67739] Speed challenge: Improve on integer frequencies from Count?
- From: Sseziwa Mukasa <mukasa at jeol.com>
- Date: Fri, 7 Jul 2006 07:12:55 -0400 (EDT)
- References: <200607061052.GAA28442@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
On Jul 6, 2006, at 6:52 AM, Gareth Russell wrote:
> Hi,
>
> A challenge for the efficiency gurus:
>
> Given a list of integers whose possible values lie in the range 0 to
> maxInt, with any given integer represented 0, 1 or multiple times,
> e.g., what you would get from
>
> Table[Random[Integer, {0, maxInt}], {1000}]
>
> create a list of frequencies of values including ALL possible values
> (i.e., not the basic output of Frequencies[], because that only
> includes values present in the list.
>
> The fastest I have been able to come up with is the obvious use of
> Count[]...
>
> In[256]:=
> myFrequencies=Compile[{{myList,_Integer,1},{
> maxInt,_Integer}},Table[Count[myList,i],{i,0,maxInt}]]
>
> Out[256]=
> CompiledFunction[{myList,maxInt},Table[Count[myList,i],{i,
> 0,maxInt}],-\
> CompiledCode-]
>
> In[278]:=
> testList=Table[Random[Integer,{0,500}],{1000}];
>
> In[281]:=
> Timing[Do[myFrequencies[testList,500];,{1000}]]
>
> Out[281]=
> {2.3103 Second,Null}
>
> However, it seems to me that this should be able to be improved upon,
> because it scans the whole list maxInt times. One should be able to
> scan the list once, and increment a frequency list in the right
> places,
> perhaps with a For[] loop. But try as I might, I can't come up with a
> version that is faster than the compiled Count[] version above.
>
> Can anyone do it?
On my machine Frequencies is faster than myFrequencies. The missing
values can be filled in with:
{0,#}&/@Complement[Range[0,maxInt],Flatten[Last/@result]]]
where result is the result of calling Frequencies. Combining the two
I get:
myFrequencies2[lst_,maxInt_]:=Block[{freqs=Frequencies[lst]},Join
[freqs,{0,#}&/@Complement[Range[0,maxInt],Flatten[Last/@freqs]]]]
which is faster than myFrequencies on my machine. Of course in this
case the list is not sorted, adding a sort makes it much slower than
myFrequencies. Alternatively, you could just keep the list of zero
frequency items separate.
Regards,
Ssezi
- References:
- Speed challenge: Improve on integer frequencies from Count?
- From: Gareth Russell <russell@njit.edu>
- Speed challenge: Improve on integer frequencies from Count?