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Re: procedures
*To*: mathgroup at smc.vnet.net
*Subject*: [mg96950] Re: [mg96937] procedures
*From*: Sseziwa Mukasa <mukasa at jeol.com>
*Date*: Sat, 28 Feb 2009 06:40:15 -0500 (EST)
*References*: <200902271116.GAA21679@smc.vnet.net> <7F1970D7-0EE8-42D6-BC3E-6095D648BBA6@jeol.com> <1235749530.4275.7.camel@linux-sslk.site>
On Feb 27, 2009, at 10:45 AM, Davide Venturelli wrote:
> Thank you for the answer!
>
>> What is the purpose of assigning its value to
>> itself?
>
> I am evaluating a recursive function.
> I want to store every computed value in such a way that next time the
> code calls it, it remembers if it has already evaluated it.
> So while I need := for definition of the recursive functions, I use
> the
> Do loop to assign actual values to the array.
>
> Do you have a better idea?
You can implement functions with memory as
F[x_]:=f[x]=(*body goes here*)
This would obviate the need for Do loop, just evaluating D[x,n] would
be sufficient.
Search for FunctionsThatRememberValuesTheyHaveFound in the
Mathematica help documentation (for v7).
> I now have another problem, anyway!
>
> When I do FindRoot[f[x],{x,0}] it looks for all instances of x in the
> definition of the function, and THEN evaluate the function for the
> symbol X.
I think this occurs because FindRoot defaults to Newton's method and
it needs to take the derivative of the expression.
> What I want is to override this symbolic method and call f[x] with the
> numerical value of x, since in the definition of f[x] I have recursive
> functions that would imply to evaluate a huge polynomial of x, and
> keeping track of all the terms is really lengthy.
> While if I substitute x=x0 at each recursive step, the computation is
> less costy.
>
> So is there a way to tell mathematica in FindRoot to call the function
> with numerical values, like it was a black box?
This comes up from time to time on this mailing list. The usual
suggestion is to make the function definition valid only for numeric
arguments see
http://groups.google.com/group/comp.soft-sys.math.mathematica/
browse_thread/thread/a076ff6d9b72b462
for example.
Hope that helped,
Sseziwa Mukasa
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