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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg89487] Re: Transform list of numbers into pure functions using replace rule
  • From: Mac <mwjdavidson at googlemail.com>
  • Date: Tue, 10 Jun 2008 07:14:47 -0400 (EDT)
  • References: <g2lb8t$964$1@smc.vnet.net>

On Jun 10, 9:42 am, Mac <mwjdavid... at googlemail.com> 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

Hello,

Many thanks for your very quick reply. Your solution doesn't quite
work because I would also like to transform lists of this type (it was
in the first example I gave):

In[3]:= {1, 2, f[x], 3 &} /. x_ /; NumberQ[x] -> (x &)

Out[3]= {1 &, 2 &, f[x], 3 & &}

The problem is the "3&&" which I would like to be "3&".

Any magic that you can propose ?

many thanks in any case

Mac


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