Re: ? ? ? ! ?
- To: mathgroup at smc.vnet.net
- Subject: [mg8270] Re: ? ? ? ! ?
- From: "P.J. Hinton" <paulh>
- Date: Sat, 23 Aug 1997 01:59:10 -0400
- Organization: Wolfram Research, Inc.
- Sender: owner-wri-mathgroup at wolfram.com
Lou Talman wrote:
>
> Can anyone explain what v3.0 of Mathematica thinks it's doing when it
> executes
>
> Plot[Abs'[x], {x, -3/10, 3/10}]
>
> ???
>
> Note the prime: The first argument of Plot was Abs'[x], not Abs[x].
The strange plot you are observing is being caused by artifcats
introduced by the numerical approximation of D[Abs[x],x].
The kernel does not evaluate D[Abs[x],x] /. x -> x0 with the
analytical formula (which I think you're expecting)
Which[x < 0, -1, x > 0, 1, x == 0, Indeterminate]
Rather it's taking finite difference approximations as one would do
with the ND function in NumericalMath`NLimit`. The discontinuity
in the derivative of Abs[x] at x == 0 throws a wrench into the
machinery.
A way to compensate for your problem is to do the following.
In[1]:= <<NumericalMath`NLimit`
In[2]:= Plot[ND[Abs[x],x,x0,Scale -> 0.001],{x0,-3/10,3/10}]
The Scale option in ND forces the kernel to approximate the derivative
with a smaller stepsize, which reduces the prominence of the artifact
at x==0.
--
P.J. Hinton
Mathematica Programming Group paulh at wolfram.com
Wolfram Research, Inc. http://www.wolfram.com/~paulh/