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

*To*: mathgroup at smc.vnet.net*Subject*: [mg89503] Re: Transform list of numbers into pure functions using replace rule*From*: "David Park" <djmpark at comcast.net>*Date*: Wed, 11 Jun 2008 03:17:54 -0400 (EDT)*References*: <g2lb8t$964$1@smc.vnet.net>

Mac, It is often easier to use actual Function expressions than to use slot notation. So you could try something like this: {1, 2, f[x]} /. x_?NumberQ -> Function[x] {1 &, 2 &, f[x]} But there is some danger in that because I don't know what f[x] is. It looks like it is not a function but an expression. Is 'f' a function you have already predefined? If it is an expression then it may contain numbers that would also be replaced by the rule. The following might be safer: {1, 2, f[x]} /. data : List[args__] :> (If[NumberQ[#], Function[x, #], #] & /@ data) Function[x, 1], Function[x, 2], f[x]} If f[x] is actually an expression in x then why not use the following, which does give everything as a Function? {1, 2, 2 x + x^2} /. data : List[args__] :> (Function[x, #] & /@ data) {Function[x, 1], Function[x, 2], Function[x, 2 x + x^2]} And why use a replacement rule at all, rather than just mapping directly onto the data list? -- David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ "Mac" <mwjdavidson at googlemail.com> wrote in message news:g2lb8t$964$1 at smc.vnet.net... > 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 > >