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Re: Adapting function to input type

  • To: mathgroup at smc.vnet.net
  • Subject: [mg86493] Re: Adapting function to input type
  • From: Szabolcs <szhorvat at gmail.com>
  • Date: Wed, 12 Mar 2008 05:26:41 -0500 (EST)
  • References: <fr7op0$38l$1@smc.vnet.net>

On Mar 12, 6:13=A0am, Mac <mwjdavid... at googlemail.com> 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},
> =A0 =A0biomass = Range[1, 1000, 1];
> =A0 =A0Exp[-1*(forwardmodel[#] - obs)^2/(2 err[#]^2)] & /@ biomass
> =A0 =A0];
>
> 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.

You could use an anonymous function:

pbiomass[somenumber, 4&, forwardmodel]

Or you can extend pbiomass to recognize numbers and construct the
anonymous function automatically:

pbiomass[a_, num_?NumericQ, b_] := pbiomass[a, num &, b]

> 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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