Re: Help on compiling a function

• To: mathgroup at smc.vnet.net
• Subject: [mg115657] Re: Help on compiling a function
• From: Peter Pein <petsie at dordos.net>
• Date: Mon, 17 Jan 2011 05:41:48 -0500 (EST)
• References: <iguiqe\$8sv\$1@smc.vnet.net>

```On 16.01.2011 11:55, Ramiro wrote:
> Hi everyone,
>
> I had written about this but wanted to revisit the problem in light of
> 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
>
> Thanks in advance,
> 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?
>

Hi Ramiro,

make use of LogGamma and logarithmic laws:

In[1]:= example2 =
Compile[{{n, _Real, 1}, {a, _Real}, {b, _Real}, {t, _Real, 1}},
Block[{tn = Total[n]},
Exp[LogGamma[a + tn] - Total[LogGamma[1 + n]] - LogGamma[a] +
a Log[b] + n.Log[t] - (tn + a) Log[Total[t] + b]]]];

In[2]:= example2[{97.6203, 8.4788, 21.4204, 46.1755}, 1, 1, {39.9342,
7.5820, 5.8656, 10.0553}]

Out[2]= 1.06265*10^-11

Cheers,
Peter

```

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