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.
>

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