Re: Can I Map[] this code?
- To: mathgroup at smc.vnet.net
- Subject: [mg95965] Re: Can I Map[] this code?
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Sat, 31 Jan 2009 01:12:15 -0500 (EST)
- References: <glvk8r$e47$1@smc.vnet.net>
Hi, what is with function1[points_, values_] := Function[{v}, Mean[Inner[function2, #, v] & /@ points]] /@ values two Map[] one Inner[], one Mean[] ... ? Regards Jens Andreas wrote: > As I have more experience with procedural programming, I'd like to better understand how to use Mathematica's capabilities to do operations to or mapping functions to lists. > > As an example I have two lists of lists: > > values = {{1, 1, 1, 1}, {1.03, 1.01, .90, .87}, {1.15, .987, 1.1, 1}, {.925, 1.1, 1.03, 1}} > > points = { > {0.0842331, 0.445974, 0.0762394, 0.393553}, > {0.0507857, 0.316297, 0.217557, 0.415361}, > {0.0772796, 0.715707, 0.0966355, 0.110378}, > {0.407287, 0.0992621, 0.294046, 0.199405}, > {0.115973, 0.483231, 0.125979, 0.274817}, > {0.0819106, 0.64151, 0.0656714, 0.210908}, > {0.0240671, 0.164786, 0.230353, 0.580795}, > {0.0402821, 0.582524, 0.131371, 0.245823}, > {0.374207, 0.242838, 0.0277256, 0.355229}, > {0.130812, 0.459584, 0.331101, 0.078503} > } > > I have a named function: > > function2[point_, value_] := If[value == 0, 0, 1 + ((value - 1) * point)] > > That I want to apply across the elements in the list in a function like the following: > > function1[points_, values_] := > Table[ > Sum[ > Sum[ > function2[points[[j, k]], values[[i, k]]], > {k, 1, Length[values[[1]]]} > ], {j, 1, Length[points]} > ]/Length[points], > {i, 1, Length[values]} > ] > > function1 works OK. I just wonder if I can do this kind of calculation more elegantly using something like the Map[] function and how I would do it in a situation like the above. > > I also have a concern about processing speed as the lengths of both lists of lists can get quite large. > > The larger question goes to this. In what kind of situations should one use iterative functions like Table[], Sum[], etc and when does one better use Map[] or other such functions? What advantages and disadvantages does either approach have over the other? > > Any guidance much appreciated. >