## calculate de Jong function

Mathematica

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• 1. Wolfram free input shortcut is "cntrl =" What do we use for underscript now?
Hello group. Is there anyway to turn off the free input in version 8? I just noticed that the shortcut for entering free input query is not only "=" but also "cntrl =" I found out because I was trying to input a limit with underscript in text cell. Instead of putting blanks for underscript, mathematica put the wolfram query thing. The same thing happens in an input cell as well. It seems the only way to put underscript is the use the mouse and click on the underscript button in the palette. It will be nice to have keyboard shortcut back. i wonder which other keyboard shortcuts are gone in version 8? Thanks for any insight in advance. Sean

### 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

```

### Re: calculate de Jong function

```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

```

### Re: calculate de Jong function

```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

```

### Re: calculate de Jong function

```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

```

### Re: calculate de Jong function

```x=some vector

f[x_]=x.x

On 5/11/05, Stefan Schuster

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

```

### Re: calculate de Jong function

```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

```

### Re: calculate de Jong function

```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

```