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

*To*: mathgroup at smc.vnet.net*Subject*: [mg98588] Re: [mg98556] Re: Replace Table[Sum...]...] with Functional code*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Mon, 13 Apr 2009 03:36:06 -0400 (EDT)*References*: <grpilf$ltq$1@smc.vnet.net> <200904120749.DAA27315@smc.vnet.net>*Reply-to*: drmajorbob at bigfoot.com

Here's a simpler version (I think): functionalMR2[data_, period_] := ListConvolve[Rest@# - Most@# &@Sqrt@Range[0, period], Log[Rest@data/Most@data]] Comparing it with yours: functionalMR[data_, period_] := Module[{kernel, ls}, kernel = Table[(Sqrt[i] - Sqrt[i - 1]), {i, period}]; ls = ListCorrelate[{1, 1}, data, {1, -1}, 1, Times, Log[#2/#1] &]; ListConvolve[kernel, ls, {-1, 1}, 0]] data = Array[a, 10]; Table[functionalMR[data, p] == functionalMR2[data, p], {p, 0, 10}] {True, True, True, True, True, True, True, True, True, True, True} I haven't looked at Ray Koopman's code; it may be the same as mine, for all I know. Bobby On Sun, 12 Apr 2009 02:49:46 -0500, <mike.honeychurch at gmail.com> wrote: > On Apr 11, 2:59 am, Bob Hanlon <hanl... at cox.net> wrote: >> mm[data_, period_] := >> Table[ >> Sum[(Log[data[[t]]] - Log[data[[t - i]]])/Sqrt[i], >> {i, 1, period}]/period, >> {t, period + 1, Length[data]}] >> >> mm2[data_, period_] := Module[ >> {logData = Log[data], d = Sqrt[Range[period, 1, -1]]}, >> Mean[#/d] & /@ >> (Drop[logData, period] - >> Most[Partition[logData, period, 1]])] >> >> data = Array[x, {500}]; >> >> period = Random[Integer, {20, 100}] >> >> 41 >> >> Timing[r1 = mm[data, period];] >> >> {0.459393,Null} >> >> Timing[r2 = mm2[data, period];] >> >> {0.228474,Null} >> >> %/%% >> >> {0.497339,1} >> >> r1 == r2 >> >> True >> >> Bob Hanlon >> >> ---- 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 >> th= > e increments in the Table function come into play in the Sum, I haven't > bee= > n able to figure out a way to do it. >> >> I've tried Map with Partition and a bunch of other things, but I could >> us= > e some pointers. >> >> Any help much appreciated. > > By using Table and Sum you are repeating a lot of calculations. Once > "period" has been set all the possible values of (Sqrt[i] - Sqrt[i - > 1]) and Log[data[[t - i]] / data[[-i + t - 1]]] are set. Therefore: > > kernel=Table[(Sqrt[i]-Sqrt[i-1]),{i,period}]; > > ls=ListCorrelate[{1,1},data,{1,-1},1,Times,Log[#2/#1]&]; > > so now combine them: > > ListConvolve[kernel,ls,{-1,1},0] > > functionalMR[data_,period_]:=Module[{kernel,ls}, > kernel=Table[(Sqrt[i]-Sqrt[i-1]),{i,period}]; > ls=ListCorrelate[{1,1},data,{1,-1},1,Times,Log[#2/#1]&]; > ListConvolve[kernel,ls,{-1,1},0] > ] > > This is a little bit slower than Ray Koopman's code but I just like > using ListCorrelate and ListConvolve as replacements for Table[Sum > [ ...]...] > > :) > > Mike > -- DrMajorBob at bigfoot.com

**References**:**Re: Replace Table[Sum...]...] with Functional code***From:*mike.honeychurch@gmail.com