Re: Help on compiling a function

• To: mathgroup at smc.vnet.net
• Subject: [mg115648] Re: Help on compiling a function
• From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
• Date: Mon, 17 Jan 2011 05:40:02 -0500 (EST)
• References: <iguiqe\$8sv\$1@smc.vnet.net>

```Small error correction in the timing calculations & added
parallelization (example4):

In[134]:=
x0 = Table[
example0[{97.6203, 8.4788, 21.4204, 46.1755 + i}, 1,
1, {39.9342, 7.5820, 5.8656, 10.0553}], {i, 0, 1, 0.00001}] //
Timing;
x1 = Table[
example1[{97.6203, 8.4788, 21.4204, 46.1755 + i}, 1,
1, {39.9342, 7.5820, 5.8656, 10.0553}], {i, 0, 1, 0.00001}] //
Timing;
x2 = Table[
example2[{97.6203, 8.4788, 21.4204, 46.1755 + i}, 1,
1, {39.9342, 7.5820, 5.8656, 10.0553}], {i, 0, 1, 0.00001}] //
Timing;
x3 = Table[
example3[{97.6203, 8.4788, 21.4204, 46.1755 + i}, 1,
1, {39.9342, 7.5820, 5.8656, 10.0553}], {i, 0, 1, 0.00001}] //
Timing;
x4 = Table[
example4[{97.6203, 8.4788, 21.4204, 46.1755 + i}, 1,
1, {39.9342, 7.5820, 5.8656, 10.0553}], {i, 0, 1, 0.00001}] //
Timing;

In[146]:=
{First[x0]/First[x1], First[x0]/First[x2], First[x0]/First[x3],
First[x0]/First[x4]}

Out[146]= {0.956921, 7.11966, 7.97129, 8.08738}

Cheers -- Sjoerd

On Jan 16, 11:55 am, Ramiro <ramiro.barran... at gmail.com> wrote:
> Hi everyone,
>
> the latest Mathematica options for compiling (C and parallelization),
> which I was hoping to try to use on this function, which is the main
> arithmetic and time-consuming part of my simulation.
>
> I have the following code:
>
> example1 =
>   Compile[{{n, _Real, 1}, {a, _Real}, {b, _Real}, {t, _Real, 1}},
>    Gamma[Total[n] + a]/(Times @@ (Gamma[n + 1])*Gamma[a])*b^a*
>     Times @@ (t^n)/(Total[t] + b)^(Total[n] + a)];
>
> but under input such as the following it breaks:
>
> example1[{97.6203, 8.4788, 21.4204, 46.1755}, 1, 1, {39.9342, 7.5820,
> 5.8656, 10.0553}]
> CompiledFunction::cfse: Compiled expression
> 1.33128164105722332870399207`12.920368310128136*^315 should be a
> machine-size real number. >>
> CompiledFunction::cfex: Could not complete external evaluation at
> instruction 4; proceeding with uncompiled evaluation. >>
>
> the problem is just that in the calculation Gamma ends up being really
> big, larger than \$MaxMachineNumber so it complains.
>
> Anybody see a way around this?  This is the workhorse function of my
> simulation, so any gain in speed helps a lot
>
> Ramiro
>
> Longer explanation (if interested):
>
> example =
>  Compile[{{n, _Real, 1}, {a, _Real}, {b, _Real}, {t, _Real, 1}},
>   Module[{totaln, totalt, gammanp1times, tpowntimes, times1, div1,
>     times2, times3, pow1, gammatotnpa}, totaln = Total[n];
>    totalt = Total[t];
>    gammanp1times = Apply[Times, Gamma[n + 1]];
>    tpowntimes = Apply[Times, t^n];
>    times1 = Times[gammanp1times, Gamma[a]];
>    gammatotnpa = Gamma[totaln + a];
>    div1 = Divide[gammatotnpa, times1];
>    times2 = Times[div1, b^a];
>    times3 = Times[times2, tpowntimes];
>    pow1 = Power[totalt + b, totaln + a];
>    Divide[times3, pow1]]
>   ]
> example[{97.6203, 8.4788, 21.4204, 46.1755}, 1, 1, {39.9342, 7.5820,
>   5.8656, 10.0553}]
>
> the result of gammatotnpa is greater than 10^315 which is greater than
> \$MaxMachineNumber on my machine.  Any suggestions?

```

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