Re: Evaluate, Replace, and Hold

*To*: mathgroup at smc.vnet.net*Subject*: [mg77165] Re: [mg77118] Evaluate, Replace, and Hold*From*: DrMajorBob <drmajorbob at bigfoot.com>*Date*: Tue, 5 Jun 2007 06:37:23 -0400 (EDT)*References*: <8194080.1180946234421.JavaMail.root@m35>*Reply-to*: drmajorbob at bigfoot.com

Here's a function that allows several different interfaces: Clear[f] f[a_, b_][x_] := a x + b; f[{a_, b_}][x_] := f[a, b][x]; f[r : {_ -> a_, _ -> b_}][x_] := f[a, b][x] p1 = {a -> 1, b -> 0}; p2 = {1, 1}; p3 = Sequence[1, 2]; pts = Range[10]; f[p1] /@ pts f[p2] /@ pts f[p3] /@ pts {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} {2, 3, 4, 5, 6, 7, 8, 9, 10, 11} {3, 4, 5, 6, 7, 8, 9, 10, 11, 12} f /@ {p1, p2} {f[{a -> 1, b -> 0}], f[{1, 1}]} # /@ pts & /@ (f /@ {p1, p2}) {{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, {2, 3, 4, 5, 6, 7, 8, 9, 10, 11}} (The Sequence interface doesn't work in the last two examples.) Set also works (rather than SetDelayed): Clear[f, a, b, x] f[a_, b_][x_] = a x + b; f[{a_, b_}][x_] = f[a, b][x]; f[r : {_ -> a_, _ -> b_}][x_] = f[a, b][x]; Set is faster, when it works at all for the application. Bobby On Mon, 04 Jun 2007 02:49:10 -0500, <grenander at gmail.com> wrote: > > This is a newbie question. I have a parametric form of a model and I > would like to evaluate it with different parameters on a list of > values. > > model = a x + b; > > Different sets of parameters: > > p1 = {a->1, b->0}; > p2 = {a->1, b->1}; > > x for which I'd like to evaluate the model: > > pts = Range[10]; > > I would like to define a function to evaluate the model at pts using > any of the sets of paramters: > > f[pts, p1] > f[pts, p2] > > I would also like it to work for single points: > > f[1, p1] > f[2, p1] > > I've tried various forms for a function definition that dont work. I > can do the following for a particular set of parameters: > > Function[{x}, Evaluate[model /. p1]] /@ pts > > but how can I turn it into a function of also the parameters. The > below doesn't work, for example: > > f[pts_, p_]:=Function[{x}, Evaluate[model /. p] ] /@ pts > > What I know is from descending the documentation tree (v6.0) starting > from the examples in FindFit. I have a fundamental misunderstanding of= > replacement rules and delayed evaluation. > > Thanks. > > > -- = DrMajorBob at bigfoot.com