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Re: Making a function dynamically define another conditional function...
*To*: mathgroup at smc.vnet.net
*Subject*: [mg21761] Re: [mg21733] Making a function dynamically define another conditional function...
*From*: Hartmut Wolf <hwolf at debis.com>
*Date*: Thu, 27 Jan 2000 22:56:42 -0500 (EST)
*Organization*: debis Systemhaus
*References*: <200001260845.DAA02315@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Paul Howland schrieb:
>
> How can I make a function dynamically define a conditional function?
>
> Given a list of arguments {{a,A}, {b,B}, ...} I want to write a function
> that will take these arguments, and generate a new function, f say,
> which is defined as (for example):
> f[x_] := x+a /; x==A
> f[x_] := x+b /; x==B
> etc.
>
> So, the obvious solution is to define a function as follows:
>
> In[1] := TestFn[data_List] := Module[{args},
> ClearAll[f];
> Do[
> args = data[[i]];
> f[x_] = x + args[[1]] /; x==args[[2]],
> {i, Length[data]}
> ]]
>
> and call it using something like TestFn[{{1,2},{3,4},{5,6}}].
>
> But this doesn't work (see attached notebook) as it appears that
> Mathematica does not evaluate any part of the condition at the time of
> definition, so args[[2]] remains unevaluated. As a consequence, the
> resulting function definition is not properly defined.
>
> So, the obvious solution to this is to wrap Evaluate[] around the
> condition (i.e. define the function as f[x_] = x + args[[1]] /;
> Evaluate[x == args[[2]]]. And this appears to work. If you do ?f, then
> you see a function comprising a number of conditional definitions.
> However, if you come to use the function, then it appears that
> Mathematica does not perform the condition test that appears in the
> definition! It simply uses the first definition it finds.
>
> What is going on?! How can I make this work?
>
Hello Paul,
in your definitions above you seem to define function values only for
certain discrete arguments, so I understand your function to be
equivalent with
f[A] = A+a
f[B] = B+b
etc.
For that just do
In[25]:= Apply[(f[#2] = #1 + #2) &, {{1, 2}, {3, 4}, {5, 6}}, {1}];
In[26]:= Information["f", LongForm -> False]
"Global`f"
f[2] = 3
f[4] = 7
f[6] = 11
To make up another example, and to fully show the metaprogramming
method, e.g. if you want to have
ff[x_] := a /; x <= A
ff[x_] := b /; x <= B
etc.
In[35]:= makeFun[f_Symbol, data_] :=
(Apply[(f[x_] := #1 /; x <= #2) &, data, {1}])
In(36]:= makeFun[ff, {{1, 2}, {3, 4}, {5, 6}}];
In[37]:= Information["ff", LongForm -> False]
"Global`ff"
ff[x_] := 1 /; x <= 2
ff[x_] := 3 /; x <= 4
ff[x_] := 5 /; x <= 6
Regard that parentheses enclosing Set or SetDelayed in the defining
functions are neccessary.
Kind Regards, Hartmut
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