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Re: compile a numerical integral

• To: mathgroup at smc.vnet.net
• Subject: [mg124596] Re: compile a numerical integral
• From: Gabriel Landi <gtlandi at gmail.com>
• Date: Thu, 26 Jan 2012 03:25:04 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <jflvvs$jr4$1@smc.vnet.net> <201201251205.HAA06021@smc.vnet.net>

You may profit considerably from "SymbolicProcessing"->0. For instance

In[106]:= tab1 = Table[
    NIntegrate[x^n Exp[x], {x, -1, 1}], {n, 2, 40, 2}]; // AbsoluteTiming

Out[106]= {0.282903, Null}

In[116]:= tab2 = Table[NIntegrate[x^n Exp[x], {x, -1, 1}, Method -> {"GlobalAdaptive"}     ], {n, 2, 40, 2}]; // AbsoluteTiming

Out[116]= {0.273898, Null}

In[117]:= tab3 = Table[
    NIntegrate[x^n Exp[x], {x, -1, 1},
     Method -> {"GlobalAdaptive", "SymbolicProcessing" -> 0}
     ], {n, 2, 40, 2}]; // AbsoluteTiming

Out[117]= {0.069791, Null}

And

In[114]:= tab1 - tab2
Out[114]= {0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.}

In[115]:= tab1 - tab3
Out[115]= {0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.}

Best regards,

Gabriel

On Jan 25, 2012, at 10:05 AM, Oleksandr Rasputinov wrote:

> On Tue, 24 Jan 2012 10:09:00 -0000, Ruth Lazkoz S=E1ez <ruth.lazkoz at ehu.es> 
> wrote:
>
>> Hi wise people,
>>
>> I am working to make a code faster using compile and failed at the very
>> beginning.
>> Is there a way to make a version that works?
>>
>> f=Compile[{u},NIntegrate[x*u,{x,0.,#}]&/@{1,2,3}]
>>
>> Best,
>>
>> Ruth Lazkoz
>>
>
> Sorry to disappoint, but no. NIntegrate cannot be compiled and, even if it 
> could, it wouldn't provide any meaningful performance improvement 
> (although sometimes the integrand can be compiled; if this is likely to be 
> beneficial it will be done automatically, but you can try it manually 
> using the option Compiled->True). However, one can often benefit by 
> changing the Method option appropriately (see 
> tutorial/NIntegrateIntegrationRules), although this can be quite involved 
> and is obviously not a panacea. It is worth persisting, however: in an 
> example from my own work, optimizing the Method yielded a fourfold 
> reduction in calculation time versus the default setting when evaluating
> some complicated projection integrals, and I was only able to improve on
> this slightly (by another 40% or so) by pre-calculating the integration
> bounds analytically for special cases of the integrand instead of letting 
> NIntegrate find the bounds itself.
>

• References:
  • Re: compile a numerical integral
    • From: "Oleksandr Rasputinov" <oleksandr_rasputinov@hmamail.com>