Re: Re:Mapping down two lists

*To*: mathgroup at smc.vnet.net*Subject*: [mg25534] Re: [mg25515] Re:Mapping down two lists*From*: "Carl K. Woll" <carlw at u.washington.edu>*Date*: Sat, 7 Oct 2000 03:35:39 -0400 (EDT)*References*: <200010060350.XAA24897@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

John, A faster approach then the ones you have listed is to use Dot, as in #.#&@(lst1[[All,1]]-lst2) At least, in my tests this was almost 5 times faster than your In[5] version. Carl ----- Original Message ----- From: "John Satherley" <js1 at liverpool.ac.uk> To: mathgroup at smc.vnet.net Subject: [mg25534] [mg25515] Re:Mapping down two lists > Many thanks to all those who sent in suggestions as to how to speed up > calculations involving lists as per my original request below. > > I've collected together the suggestions, added some of my own and done some > timing tests: > > In[1]=lst1 = Table[{Random[], Random[]}, {1000000}]; > In[2]=lst2 = Table[Random[], {1000000}]; > > In[3]=compiledfunction = Compile[{{x, _Real, 2}, {y, _Real, 1}}, Plus @@ > (First[Transpose[x]] - y)^2]; > > In[4]= Plus @@ ((#[[1]] - #[[3]])^2 & /@ Transpose[Join[Transpose[lst1], > {lst2}]]) // Timing > In[5]= Plus @@ (First[Transpose[lst1]] - lst2)^2 // Timing > In[6]= Plus @@ (Transpose[lst1][[1]] - lst2)^2 // Timing > In[7]= Plus @@ (Take[Transpose[lst1], 1][[1]] - lst2)^2 //Timing > In[8]= Plus @@ (#^2 & /@ (Transpose[lst1][[1])] - lst2) // Timing > In[9]= Plus @@ (#^2 & /@ (#[[1]] & /@ lst1 - lst2)) // Timing > In[10]= compiledfunction[lst1, lst2] // Timing > > Out[4]= {10.71 Second, 166795.} > Out[5]= {4.4 Second, 166795.} > Out[6]= {4.34 Second, 166795.} > Out[7]= {4.39 Second, 166795.} > Out[8]= {4.89 Second, 166795.} > Out[9]= {7.74 Second, 166795.} > Out[10]= {2.37 Second, 166795.} > > As you can see there is quite a range in the calculation speed. Compiling > the functions gives a speed enhancement by almost a factor of 2 compared to > the other fastest time. I noted that, if compiled then, all the functions > take about the same time to complete hence I only show one of them here. In > the noncompiled versions its likely that the speed increase arises from > carrying out a minimum number of calculations. The first in the list clearly > does the most and takes the longest to complete. > > John Satherley > > > > > > Hi MathGroup > I'm trying to sharpen up my functional programming skills and have come > across a problem which is probably very trivial but I can't find a > satisfactory solution. > > I have two lists of equal length, one 2 dimensional and the other 1 > dimensional: > lst1={{1,2},{2,3},{1,3},......} > lst2={1,2,2,3,4,5.....} > > What I want to do is find the difference between lst1[[i,1]] and lst2[[i]] > square it and then sum up all the terms over the length of the list. > > It is easy to do this in terms of Tables but I'm trying to find a fast > solution for long lists that uses map and other functional programming > tools. > > The best I have come up with is: > Apply[Plus,([#[[1]]&/@lst1-lst2)^2] > but I'm wondering if it is possible to map directly onto the two lists > without first having to extract the elements of the first list? Map seems to > only work down a single list. > > I would be most grateful of any hints as to how this might be performed in > an efficient manner. > > Thanks for help > Dr. John Satherley > Dept of Chem > University of Liverpool > Liverpool L69 7ZD > UK > js1 at liv.ac.uk > > > > >

**References**:**Re:Mapping down two lists***From:*"John Satherley" <js1@liverpool.ac.uk>