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can Mathematica generate itself a function?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg31769] can Mathematica generate itself a function?
*From*: "Romoscanu, Alexandre" <alexandre.romoscanu at imes.mavt.ethz.ch>
*Date*: Sat, 1 Dec 2001 02:45:34 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
Hello
I am trying to set Mathematica to create itself a function, and then
consider it as a function definition.
Suppose I want to create a function of the form
function[w,a1,...aN]
where w is a variable and a1...aN, a total of N parameters (such a
function can for example be used as a fitting model with N parameters in
NonlinearRegress, etc...)
In some cases, 2 parameters will be requested, i.e. N=2.
In some, one would like the function to have 5 parameters(N=5) to
define, say a 1-variable, 5-parameter fitting model.
I would like to program Mathematica to create the function itself on a
given pattern, my only input being the number of parameters (here, N). I
just do not want to retype a new function each time for the cases I want
2 paramaters, or 10...or N.
Keeping in mind that a function is defined as f[x_,y_]=Sin[x+y] (for
instance), if the total number of parameter pairs is defined by the
positive integer
NumberOfModules (=5 for example)
then the following expressions obviously create the left part of a
potential definition statement (like "f[x_,y_]=Sin[x+y]"):
In[1]:= AddUnderscore2[varname_String] := varname <> "_";
In[2]:= function[w_,
Sequence @@ (ToExpression[
AddUnderscore2 /@ (ToString /@ Array[a, NumberOfModules])])
give
Out[2]:= function[w_, a[1] _, a[2] _, a[3] _, a[4] _, a[5] _]
because NumberOfModules was chosen to be 5.(+notice the problematic
blank in front of the _.)
The right part could look as
Sum[(a[i]*w^2)/(1 + a[i]^2*w^2), {i, 1, NumberOfModules}]
Hence,
function[x_, y_,
Sequence @@ (AddUnderscore2 /@ (ToString /@ Array[a,
NumberOfModules]))] =
Sum[(a[i]*w^2)/(1 + a[i]^2*w^2), {i, 1, NumberOfModules}]
Looks like the definition of a formula.
My problem is the last step...Mathematica does not (without surprize)
look at the expression right above as it looks to "f[x_,y_]=Sin[x+y]".
There must be a trick with ToExpression, ToString, or some other
low-level Mathematica command.
Thank you for any hint-
Alexandre Romoscanu
Grad Student, ETH Zurich
PS Please, mail me a copy of a potential reply, my newsgroup access is
quite unreliable.
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