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

*To*: mathgroup at smc.vnet.net*Subject*: [mg89484] Re: Transform list of numbers into pure functions using replace rule*From*: Albert Retey <awnl at arcor.net>*Date*: Tue, 10 Jun 2008 07:14:13 -0400 (EDT)*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 &] This is the correct syntax for Condition: {1, 2, f[x]} /. x_ /; NumberQ[x] -> Function[x] This is what I would probably do: {1, 2, f[x]} /. x_?NumericQ -> Function[x] I would also strongly suggest to not use arguments in your function descriptions, then you can treat everything the same: f[x_]:=x^3 parameters = { 1, 2,f, Sin, Abs, Interpolation[Table[{x, Sin[x^2]}, {x, 0, 1, 0.1}]], Compile[{x},Exp[1/x]], Function[{y}, Piecewise[{{Abs[y], y > -10}}]] } functions = Replace[parameters, {x_?NumericQ -> Function[x]}, {1}] Map[#[0.5] &, functions] note that you need to be careful to make this work with interpolating and compiled functions, too... hth, albert