Re: composing functions
- To: mathgroup at smc.vnet.net
- Subject: [mg45544] Re: [mg45527] composing functions
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Tue, 13 Jan 2004 04:03:58 -0500 (EST)
- References: <200401120715.CAA29367@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
On 12 Jan 2004, at 07:15, Pedro L wrote:
> Hi!
>
> I would like to find a way for composing a list of functions over a
> list of numbers.
>
> I have the list {{f, g, h}, {a, b, c, d}}
> (f, g, h are functions and a, b, c, d are numbers)
> I would like to obtain h[g[f[a, b], c], d]
>
> Since it's for a real program, I had to do it in "any" way. So I did
> it as I show below:
>
>
> In[1]:= kk = {{f, g, h}, {a, b, c, d}}
>
> Out[1]= {{f, g, h}, {a, b, c, d}}
>
> In[2]:= result1 = {kk[[2,1]]}; For[i = 1, i < Length[kk[[2]]], i++,
> AppendTo[result1, kk[[1,i]]];
> AppendTo[result1, kk[[2,i + 1]]]]; result1
>
> Out[2]= {a, f, b, g, c, h, d}
>
> In[3]:= result2 = StringJoin @@ ToString /@ result1
>
> Out[3]= afbgchd
>
> In[4]:= result3 = StringInsert[result2, "~", Range[2,
> StringLength[result2]]]
>
> Out[4]= a~f~b~g~c~h~d
>
> In[5]:= result4 = ToExpression[result3]
>
> Out[5]= h[g[f[a, b], c], d]
>
>
>
>
> But I'm really sure that it can be done much better.
>
> Could you help me?
>
>
>
>
>
One possible way:
ListCompose[l_List, k_List] := Module[{F = l},
Fold[First[F = RotateRight[F]][#1, #2] & , First[k],
Rest[k]]]
Now:
ListCompose[{h, g, f}, {a, b, c, d}]
Out[2]=
h[g[f[a, b], c], d]
ListCompose[{h, g, f, k}, {a, b, c, d, e}]
h[g[f[k[a, b], c], d], e]
etc.
Andrzej Kozlowski
Chiba, Japan
http://www.mimuw.edu.pl/~akoz/
- References:
- composing functions
- From: Pedro L <pedrito6@softhome.net>
- composing functions