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Re: Adapting function to input type

  • To: mathgroup at smc.vnet.net
  • Subject: [mg86500] Re: Adapting function to input type
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Wed, 12 Mar 2008 05:27:59 -0500 (EST)
  • Organization: Uni Leipzig
  • References: <fr7op0$38l$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de

Hi,

and adding the rule

pbiomass[obs_, err_?NumericQ, forwardmodel_]:=
   pbiomass[obs, err &, forwardmodel]

before your definition will not help ?

Regards
   Jens

Mac wrote:
> I'm convinced from what I know of Mathematica that a function can be
> programmed to adapt the calculation according to function input
> parameter types (scalar or function), but I'm still not sure exactly
> how to do it.
> 
> As an example of a current calculation I calculate the probability
> curve for an observation "obs", with error "err" and forward model
> "forwardmodel" as a function of forest biomass. Here the error
> parameter is assumed to be a function (i.e. err[#] in the expression
> for pbiomass)
> 
> pbiomass[obs_, err_, forwardmodel_] := Module[{biomass},
>    biomass = Range[1, 1000, 1];
>    Exp[-1*(forwardmodel[#] - obs)^2/(2 err[#]^2)] & /@ biomass
>    ];
> 
> I have several possibilities for error models including
> 
> (* a constant error of 4m in height*)
> errmod3[b_] := 4;
> 
> (* a relative error expressed as a percentage of the forward model -
> here 10% of forward model *)
> errmod2[b_] := forwardmodel[b] 0.1;
> 
> Using errmod2 or errmod3 I can call the pbiomass function without
> problem using the syntax
> 
> pbiomass[somenumber,errmod2,forwardmodel]
> 
> or
> 
> pbiomass[somenumber,errmod3,forwardmodel]
> 
> Ideally however I would like to have the option of calling pbiomass[]
> using a scalar value for err[] as well as a function, for instance in
> the case of a 4m height error
> 
> pbiomass[somenumber,4,forwardmodel]
> 
> instead of having to define a separate err function for a constant
> value and use this in the call. I'm stumped as to how to implement
> this in Mathematica but I'm pretty sure it is possible so I thought I
> would pose the question and hopefully learn from the answers.
> 
> Many thanks
> 
> Mac
> 


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