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Re: Transform list of numbers into pure functions using replace rule
*To*: mathgroup at smc.vnet.net
*Subject*: [mg89480] Re: Transform list of numbers into pure functions using replace rule
*From*: Oliver Ruebenkoenig <ruebenko at uni-freiburg.de>
*Date*: Tue, 10 Jun 2008 07:13:28 -0400 (EDT)
*References*: <g2lb8t$964$1@smc.vnet.net>
Malcolm,
here is a better one:
On Tue, 10 Jun 2008, Mac wrote:
> Hello,
>
> I'm developed a program to invert satellite observations into
> geophysical variables such as forest biomass. One of the input
> parameters are the errors in the observation channels which can be
> either constant or a function. To be consistent the program expects
> all errors to be functions but they can also be constant functions
> e.g. if the error is 4 then the input parameter is "4&".
>
> I've however hit a problem with the replacement rule that allows me to
> transform all input errors into a function. The following works as
> expected in that constants in the list are transformed into virtual
> functions and functions in the list are left alone.
>
> In[40]:= If[NumberQ[#], ToExpression[ToString[#] <> "&"], #] & /@ {1,
> 2, 3 &, f[x]}
>
> Out[40]= {1 &, 2 &, 3 &, f[x]}
>
> However, I cannot find a replacement rule to do the same job. Here is
> one try:
>
> In[39]:= {1, 2, f[x]} /. x_ /; NumberQ -> Hold[x &]
>
> Out[39]= {1, 2, f[x]}
{1, 2, f[x], 3 &} /. x_Function :> x[[1]] /. x_Integer :> (x &)
{1 &, 2 &, f[x], 3 &}
this one treats the function separately and it only works for expressions
like Function[3] but not for Function[x,y].
I was not able to find a pattern that does the transformation in one
step.
Since
{1, 2, f[x], 3 & } /. x_?NumberQ :> (x &)
matches the function but
NumberQ /@ {1, 2, f[x], 3 & }
{True, True, False, False}
indicates otherwise.
This behavior makes sense in the following scenario:
{2.3, 4, 7/8, a, b, 3 &} /. (x_ /; NumberQ[x]) -> x^2
but is unwanted in your case.
hth,
oliver
>
> Any help would be appreciated.
>
> Mac
>
>
>
Oliver Ruebenkoenig, <ruebenko AT uni-freiburg.de>
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