Re: Evaluate, Replace, and Hold

*To*: mathgroup at smc.vnet.net*Subject*: [mg77191] Re: Evaluate, Replace, and Hold*From*: Ray Koopman <koopman at sfu.ca>*Date*: Tue, 5 Jun 2007 06:50:54 -0400 (EDT)*References*: <f40gib$65a$1@smc.vnet.net>

On Jun 4, 12:55 am, grenan... 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. In[1]:= model = Function[{a,b,x}, a x + b]; In[2]:= f[points_,params_] := model[a,b,points]/.params In[3]:= p1 = {a->1, b->0}; p2 = {a->1, b->1}; pts = Range[10]; In[6]:= f[pts,p1] Out[6]= {1,2,3,4,5,6,7,8,9,10} In[7]:= f[pts,p2] Out[7]= {2,3,4,5,6,7,8,9,10,11}