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Re: SetDelayed and Evaluate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104497] Re: SetDelayed and Evaluate
  • From: Szabolcs Horvát <szhorvat at gmail.com>
  • Date: Sun, 1 Nov 2009 17:57:00 -0500 (EST)
  • References: <hcjiul$jmr$1@smc.vnet.net>

On 2009.11.01. 10:04, Peter wrote:
> Hi group,
>
> after years of experience with Mathematica I've got a simple (?)
> problem:
>
> When answering to a question on the student support forum (http://
> forums.wolfram.com/student-support/topics/21448/) I tried fo myself
> the folowing variants:
> f[z_?NumericQ]:=Compile[{{x,_Real}},x-x^2][z];
> g[z_?NumericQ]:=Evaluate[Compile[{{x,_Real}},x-x^2]][z];
> and got the following results:
> In[6]:= Timing[Do[NMaximize[f[x],x],{1000}]]
> Out[6]= {35.871,Null}
> In[7]:= Timing[Do[NMaximize[g[x],x],{1000}]]
> Out[7]= {35.962,Null}
>
> ~1 ms per NMaximize is OK, because there are background-processes
> running.
>
> But I expect f to compile x-x^2 at every call to f and g to compile
> once on time of definition. Therefore I expected g to be significantly
> faster than f.
>
> Where am I wrong?
>

Dear Peter,

If you look under 'More Information' in the documentation, you'll see

"Evaluate only overrides HoldFirst, etc. attributes when it appears 
directly as the head of the function argument that would otherwise be held."

This is not true for SetDelayed in your example because of the presence 
of [z] after Evaluate[...].  You can check that the Compile[...] part is 
not evaluated before the definition is created using Information[g].

I would like to note though that (unless I'm mistaken), NMaximize should 
automatically compile the function it's given.  So the simplest 
solution, NMaximize[x - x^2, x], is likely also the fastest.


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