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Re: Replace Table[Sum...]...] with Functional code

  • To: mathgroup at smc.vnet.net
  • Subject: [mg98550] Re: Replace Table[Sum...]...] with Functional code
  • From: Ray Koopman <koopman at sfu.ca>
  • Date: Sun, 12 Apr 2009 03:48:42 -0400 (EDT)
  • References: <grn1l3$n0t$1@smc.vnet.net>

On Apr 10, 1:57 am, Andreas <aa... at ix.netcom.com> wrote:
> I use the following two functions to analyze time series:
>
> mm[data_,period_] := Table[Sum[(Log[data[[t]]] - Log[data[[t-i]]])/
>    Sqrt[i], {i,1,period}] / period, {t, period+1, Length[data]}]
>
> mr[data_,period_] := Table[Sum[Log[data[[t-i]]/data[[-i + t-1]]] *
>   (Sqrt[i] - Sqrt[i-1]), {i,1,period}],{t, period+2, Length[data]}]
>
> They have a similar structure, Table[Sum[...]...], which sums a
> bunch of stuff from the time series at each point in the series.
>
> I'd like to convert them into functional programing constructs, but
> as the increments in the Table function come into play in the Sum,
> I haven't been able to figure out a way to do it.
>
> I've tried Map with Partition and a bunch of other things,
> but I could use some pointers.
>
> Any help much appreciated.

Here is a third pair of suggestions. This mm is about as fast
as the second version but is perhaps a little more elegant.

mm[data_, period_] :=
   (Append[-#,Tr@#]&[1/(Sqrt@Range[period,1,-1]*period)]).
    Transpose@Partition[Log@data,period+1,1]

This mr is faster than the second version.

mr[data_, period_] :=
    Partition[Rest@#-Most@#&@Log@data,period,1].
   (Reverse[Rest@#-Most@#]&@Sqrt@Range[0,period])


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