Re: Re: how to be as efficient as Mean[list] - efficient summing of function applied to list

*To*: mathgroup at smc.vnet.net*Subject*: [mg28580] Re: [mg28539] Re: how to be as efficient as Mean[list] - efficient summing of function applied to list*From*: BobHanlon at aol.com*Date*: Sat, 28 Apr 2001 21:36:05 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

You can get a slight improvement by noting that Log is Listable (which also makes f Listable). Using 300,000 data points: data= Table[Random[Real,{.1,10}],{300000}]; Tr[Map[-Log[#]&,data]]//Timing {0.9833333333335759*Second, -404534.38111083925} Tr[-Log[data]]//Timing {0.8499999999985448*Second, -404534.38111083925} Bob Hanlon In a message dated 2001/4/25 7:40:50 PM, hay at haystack.demon.co.uk writes: >First: be as direct as possible with the function: > >data= Table[Random[Real,{.1,10}],{30000}]; >f[x_] := -Log[x]; > >Apply[Plus,Map[f[#1]&,data]]//Timing > > {6.15 Second,-40363.9} > >Apply[Plus,Map[f,data]]//Timing > > {5.11 Second,-40363.9} > >Apply[Plus,Map[-Log[#]&,data]]//Timing > > {0.55 Second,-40363.9} > >Second, use the same method as the package Statistics`DescriptiveStatistics` >for summing (use Tr} > >Tr[Map[-Log[#]&,data]]//Timing > > {0.22 Second,-40363.9} >-- >Allan >--------------------- >Allan Hayes >Mathematica Training and Consulting >Leicester UK >www.haystack.demon.co.uk >hay at haystack.demon.co.uk >Voice: +44 (0)116 271 4198 >Fax: +44 (0)870 164 0565 > >"Matthew D. Langston" <langston at SLAC.Stanford.EDU> wrote in message >news:9c5o3v$iv1 at smc.vnet.net... >> I have a one dimensional list of 28,900 data points. I want to apply >a >> function, called f[x_], to each element of this list and sum the resulting >> list to obtain one number. For the following example, f[x_] := -Log[x]. >My >> naive idea was to do something like this: >> >> Length[data] >> 28900 >> >> Apply[Plus,Map[f[#1]&,data]]//Timing >> {32.136 Second,-69627.8} >> >> However, this seemed to take to long when compared to other built-in >> Mathematic functions that iterate over a list and perform a sum. For >> example, the Mean function on the same data takes two orders of magnitude >> less time than my function: >> >> Mean[data]//Timing >> {0.13 Second,-0.0296526} >> >> Is the "Apply[Plus[...]]" method the right method to use for what I want >to >> do? Or, is it just that the time it takes my function f[x_] to perform >one >> calculation, when amortized over the whole 28,900 data points, just adds >up >> to a lot of time (32 seconds in my example). >> >> Regards, Matt >> >> -- >> Matthew D. Langston >> SLD, Stanford Linear Accelerator Center >> langston at SLAC.Stanford.EDU >