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Re: Function of several variables
*To*: mathgroup at smc.vnet.net
*Subject*: [mg72203] Re: Function of several variables
*From*: "Ray Koopman" <koopman at sfu.ca>
*Date*: Thu, 14 Dec 2006 05:49:28 -0500 (EST)
*References*: <eljaik$7dv$1@smc.vnet.net>
tlhiv wrote:
> I have created a list of variables that I would like to make a function
> in terms of by
>
> M = 4;
> X = Table[Subscript[x, i], {i, 1, M}]
>
> Now I would like to make a function f that is a function of each of
> these M variables. If I were manually create this function without
> taking advantage of iterators, I would do something like
>
> f[Subscript[x,1]_,Subscript[x,2]_,Subscript[x,3]_,Subscript[x,4]_] =
> 1/(Subscript[x,1]+Subscript[x,2]+Subscript[x,3]+Subscript[x,4])
>
> However, my plan is to significantly increase M, and therefore I don't
> want to have to manually define f in this way. I would like to define
> it in terms of the elements of X and use the Sum in the function
> definition. In the end I'm going to be solving an optimization problem
> where I try to find the "optimal" choice for these elements of X. Can
> someone offer a method for accomplishing this function definition?
>
> Thanks,
>
> --
> Troy Henderson
> Assistant Professor
> Department of Mathematical Sciences
> United States Military Academy
> http://www.tlhiv.org
Here's a toy example, that minimizes Sum[(x[i]-i)^2,{i,n}]
from a (poor) random start:
In[1]:= ranger[n_] := Block[{v, x}, v = Array[x,n];
FindMinimum[#.#&[v - Range@n],
{#,Random[]}&/@v]]
In[2]:= ranger[4]
Out[2]= {0., {x[1] -> 1., x[2] -> 2., x[3] -> 3., x[4] -> 4.}}
This gives a list of the minimizing values:
In[3]:= %[[2,All,2]]
Out[3]= {1.,2.,3.,4.}
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