Re: Transform list of numbers into pure functions using replace rule

• To: mathgroup at smc.vnet.net
• Subject: [mg89486] Re: Transform list of numbers into pure functions using replace rule
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Tue, 10 Jun 2008 07:14:36 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <g2lb8t\$964\$1@smc.vnet.net>

```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]}
>
> Any help would be appreciated.
>
> Mac
>
>

Either one of the following expressions returns the desired result {1 &,
2 &, f[x]}.

{1, 2, f[x]} /. x_ /; NumberQ[x] -> (x &)

{1, 2, f[x]} /. x_ /; NumberQ[x] -> Function[x]

Regards,
-- Jean-Marc

```

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