Re: ? ? ? ! ?
- To: mathgroup at smc.vnet.net
- Subject: [mg8298] Re: [mg8223] ? ? ? ! ?
- From: David Withoff <withoff>
- Date: Sun, 24 Aug 1997 04:46:42 -0400
- Sender: owner-wri-mathgroup at wolfram.com
> 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 behavior I see appears both on a PowerMac 7200/120 running
> Mac OS 7.5.3 and on a Wintel box running Windoze 95, so I presume that
> it isn't platform dependent--or at least, not fully so.
>
> --Lou Talman
Mathematica here computes numerical derivatives of the (non-differentiable)
Abs function. The result looks surprisingly good to me, given that the
task that the computer is asked to do here is basically impossible. That
is, it is impossible by purely numerical means to get reliable results
for numerical derivatives without any information about the scale of
variation of the function. The built-in automatic differentiation that
is used here works fine for reasonably smooth functions.
For numerical differentiation of non-smooth functions, or anything where
it is necessary to specify the scale, you might want to use the ND function
(from the NumericalMath`NLimit` package) instead.
In[1]:= Needs["NumericalMath`NLimit`"]
In[2]:= Plot[ND[Abs[t], t, x, Scale -> Sign[x]], {x, -3/10, 3/10}]
Out[2]= -Graphics-
Dave Withoff
Wolfram Research