• To: mathgroup at smc.vnet.net
• Subject: [mg112465] Re: Advice on Compile
• From: "Carl K. Woll" <carlw at wolfram.com>
• Date: Thu, 16 Sep 2010 06:00:59 -0400 (EDT)

```On 9/15/2010 7:02 PM, Niels R. Walet wrote:
> I am trying to write the following code (simplified, Mathematica 7.0.2)
> setZu[subs_] :=
>   Block[{Zmint}, Zmint = Evaluate[EFRp[q] /. subs]; Clear[Zmn];
>    Zmn = Compile[{{k, _Real}},
>      NIntegrate[Evaluate[Zmint], {q, 0, k}]];]
> I call
> setZu[EFRp ->  Function[{q}, q^2/(1 + q^2)^2]]
> and than
> Zmn[1.]
> gives an error (because Zmint has not been expanded).
> Of course I can move the assigment on Zmint within the compile, but it
> leads to ugly code, and I am not sure how efficient the compile is (does
> it do the substitution every time, or is it "compiled out"?). In real
> life the integrals I calculate are extremely expensive, and give me the
> coefficients for an ODE I try to solve, so extreme efficiency would be
> appreciated: I want to compile the expression with the substitution
> done, not the substitution process itself.
> Any light on this issue would be appreciated.
> Niels
>
>

You need to use something like With to get Zmint evaluated:

setZu[subs_] := With[{Zmint = EFRp[q] /. subs},
Zmn = Compile[{{k, _Real}},
NIntegrate[Evaluate[Zmint], {q, 0, k}]];]

However, for this particular integral, it would be worth considering
doing something like:

nint = f /.
First@NDSolve[{f'[q] == q^2/(1 + q^2)^2, f[0] == 0}, f, {q, 0, 10}]

nint[2.3]//Timing
Zmn[2.3]//Timing

Also, care to share what the real integrals you are trying to do
numerically?

Carl Woll
Wolfram Research

```

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