Re: couple of small problems
- To: mathgroup at smc.vnet.net
- Subject: [mg40880] Re: couple of small problems
- From: Oliver Ruebenkoenig <ruebenko at imtek.uni-freiburg.de>
- Date: Wed, 23 Apr 2003 01:15:47 -0400 (EDT)
- Organization: Rechenzentrum der Universitaet Freiburg, Germany
- References: <b80k2i$m3n$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi Jake,
On Mon, 21 Apr 2003, Jake Rodriguez Rosales wrote:
> First, suppose I have a function which behaves one way in a certain
> interval and behaves another way in a different interval. Suppose:
>
> f1[x_] := Cos[x] 0 < Cos[x] < 0.6
> and
> f2[x_] := (1 + Sin[x]/3)*Cos[x] -1 < Cos[x] < 0
>
> How do I combine these two functions into one main function, FMain[x],
> which incorporates the behaviour in both intervals (i.e. which gives
> me f1[x] if 0 < Cos[x] < 0.6 and gives me f2[x] for the other interval)?
> Is there a specific command in Mathematica to deal with this?
f[ x_ ] /; 0 < Cos [ x ] < 0.6 := Cos[ x ] ;
f[ x_ ] /; -1 < Cos[ x ] < 0 := ( 1 + Sin[ x ] / 3 ) * Cos[ x ];
f[ x_ ] := 0; (* else *)
Plot[ f[x], {x, -5, 5} ]
See the Help Browser for Condition
>
> The next problem mainly concerns with looping structures. I initially have
> an empty list, say Blist, which I want to continually fill up until
> I have say, 100 elements in the list. I do this by appending an
> element x, to the list, if the element satisfies some particular
> condition. So, for example, say I have two functions, h[x] and
> g[x]. I generate x (how I generate x is not important), and check if
> h[x] < g[x]. If it is, I decide to keep x and append it to the
> list Blist. I want to do this until the Length[Blist] = 100.
> I tried this code:
>
> Blist = {}
>
> While[Length[Blist] < 100, x = Random[];
> If[h[x] < g[x], Blist = AppendTo[Blist, x]]]
Blist = {};
h[ x_ ] := Cos[ x ];
g[ x_ ] := Sin[ x ];
While[
Length[ Blist ] < 100, x = Random[];
If[ h[ x ] < g[ x ], AppendTo[ Blist, x ] ]
]
hope that helps,
oliver
Oliver Ruebenkoenig, <ruebenko at imtek.de>
Phone: ++49 +761 203 7293