calculate de Jong function

Hello,

I don't know how I should implement the first de jong function:

f(x)=Sum((x_i)^2)
where x is a Vector with n dimensions and x_i is the value of the i-th 
Dimension.
i.e. all Values of the Vector are squared and added.

My problem is that I don't know how many Dimensions there are, so I 
can't define the borders of the SUM function.

thanks in advance for help

Stefan

x={x1,x2,x3,x4};

Use Dot

f1[x_?VectorQ] := x.x;

f1[x]

x1^2 + x2^2 + x3^2 + x4^2

or

f2[x_?VectorQ] := Tr[x^2];

f2[x]

x1^2 + x2^2 + x3^2 + x4^2

or

f3[x_?VectorQ] := Plus@@(x^2);

f3[x]

x1^2 + x2^2 + x3^2 + x4^2

or

f4[x_?VectorQ] := Inner[Times,x,x];

f4[x]

x1^2 + x2^2 + x3^2 + x4^2


Bob Hanlon

Hi,

your vector is a list and the dimension of the 
vector is the
length of the list

f[x_]:=x.x

does what you want.

Regards
  Jens


"Stefan Schuster" 
<bi1169*delete_from_star_to_star*@fh-weihenstephan.de> 
schrieb im Newsbeitrag 

Hi Stefan,
there is the Length function that gives you the length of e.g. a vector, 
that is the dimension of your x.
In version 5.1 there is the function Norm that can make your life still 
easier.
Sincerely, Daniel

x=some vector

f[x_]=x.x



On 5/11/05, Stefan Schuster




-- 
Chris Chiasson
 http://www.**--****.com/ 
1 (810) 265-3161

Hi!

f[x_List] := Sum[x[[i]]^2, {i, 1, Length[x]}]

or

f[x_List] := Plus@@x^2

since Powers are Listable

with kind regards


On Wed, 11 May 2005 05:24:54 -0400 (EDT)




-- Christoph Lhotka --
University of Vienna
Institute for Astronomy

Stefen,

Is this what you want?

deJong[vector_] := Plus @@ (vector^2)

Mapping it onto a list of vectors of varying length...

deJong /@ {{1, 1, 1}, {1, 2, 3, 4}, {a, b}}
{3, 30, a^2 + b^2}

The marvels of Mathematica functional programming!

David Park
 XXXX@XXXXX.COM 
 http://www.**--****.com/ ~djmp/ 

From: Stefan Schuster
[mailto:bi1169*delete_from_star_to_star*@fh-weihenstephan.de]
Subject:  calculate de Jong function


Hello,

I don't know how I should implement the first de jong function:

f(x)=Sum((x_i)^2)
where x is a Vector with n dimensions and x_i is the value of the i-th 
Dimension.
i.e. all Values of the Vector are squared and added.

My problem is that I don't know how many Dimensions there are, so I 
can't define the borders of the SUM function.

thanks in advance for help

Stefan