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Adapting function to input type

  • To: mathgroup at smc.vnet.net
  • Subject: [mg86480] Adapting function to input type
  • From: Mac <mwjdavidson at googlemail.com>
  • Date: Wed, 12 Mar 2008 00:13:24 -0500 (EST)

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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