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Re: Defining derivatives

  • To: mathgroup at smc.vnet.net
  • Subject: [mg84499] Re: Defining derivatives
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Sat, 29 Dec 2007 20:02:23 -0500 (EST)
  • References: <fl4uhv$9jb$1@smc.vnet.net>

Hi,

if x is symbolic, Abs[x]>1.0 can't not evaluated and
you should define:

QuarticSpline[x_?NumericQ] := Module[{r}, r = Abs[x];
   If[r > 1.0,
    0.0,
    1 + r^2 (-6 + r (8 - 3 r))
    ]
   ]

QuarticSplineD1[x_?NumericQ] := Module[{r}, r = Abs[x];
   If[r > 1.0,
    0.0,
    Sign[x]*r (-12 + (24 r - 12))
    ]
   ]

  Derivative[1][QuarticSpline][x_] := QuarticSplineD1[x]

Regards
   Jens

KF wrote:
> (I am sorry if this or similar question was already answered. I did 
> archive search, but didn't find anything.)
> 
> I have a function:
> 
>    QuarticSpline[x_] :=
>      Module[
>        { r },
>        r = Abs[x];
>        If [r > 1.0,
>            0.0,
>            1 + r r (-6 + r (8 - 3 r))
>        ]
>      ]
> 
> It's first derivative should be (at least for my purposes :o) :
> 
>    QuarticSplineD1 [x_] :=
>      Module[
>        { r },
>        r = Abs [x];
>        If [r > 1.0,
>            0.0,
>            Sign[x] * r (-12 + (24 r - 12))
>        ]
>      ]
> 
> but D[QuarticSpline[x], x] returns
> 
>    If[Abs[x] > 1., 0, 0]
> 
> Now, Mathematica Tutorial, in chapter Defining Derivatives, says
> 
> "You can define the derivative in Mathematica of a function f of one 
> argument simply by an assignment like f'[x_]=fp[x]."
> 
> But if I try to write
> 
>     QuarticSpline'[x_] = QuarticSplineD1[x]
> 
> I got
> 
>     Set::write: "Tag Function in (If[Abs[#1]>1.,0,0]&)[x_] is Protected."
> 
> Is it possible to define QuarticSpline' to "return" QuarticSplineD1 ?
> 
> Regards,
> 
> K. Fresl
> 
> 
> 


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