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Re: Functions of Arrays

  • To: mathgroup at smc.vnet.net
  • Subject: [mg102650] Re: [mg102590] Functions of Arrays
  • From: Leonid Shifrin <lshifr at gmail.com>
  • Date: Mon, 17 Aug 2009 04:32:19 -0400 (EDT)
  • References: <200908161039.GAA01145@smc.vnet.net>

Hi,

you should really define your function on lists, of which arrays are a
special case. Lists are the  data structure most used in Mathematica, and it
has many functions to conveniently work with lists - using them, you can
make your programs brief and efficient.

If you simply want your function to take a list (array) and return a sum of
squares,
here are some ways:

sumsq1[x_List] := Total[x^2];

sumsq2[x_List] := x.x;

With the following test array (list):

In[1] = test = Range[10]

Out[1] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

You get:

In[2] = sumsq1[test]

Out[2] = 385

In[3] = sumsq2[test]

Out[3] = 385

If you plan to use Mathematica often, it is a good idea to read some simple
account on
basic Mathematica programming with lists. Mathematica book and online
documentation are both
pretty good. A very good book is by Paul Wellin et al.   Also, I have
devoted a chapter to this
topic in my book:

http://www.mathprogramming-intro.org/

It is free, you may want to check it out.


Regards,
Leonid


On Sun, Aug 16, 2009 at 2:39 PM, zak <u.gotzes at googlemail.com> wrote:

> Functions can be defined via
>
> f[x1_, x2_] := x1^2 + x2^2
>
> in Mathematica.
>
>
> But how can I manage it to define a function depending on an array?
> I would like to do something like
>
> Array[x,2]
> f[x[1]_,x[2]_]:=x[1]^2+x[2]^2
>
> because the length of the array varies in my application.
>
>



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