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>