Re: Problem with NIntegrate -- Monte Carlo

• To: mathgroup at smc.vnet.net
• Subject: [mg39225] Re: Problem with NIntegrate -- Monte Carlo
• From: "Carl K. Woll" <carlw at u.washington.edu>
• Date: Tue, 4 Feb 2003 02:23:10 -0500 (EST)
• Organization: University of Washington
• References: <b1idic\$bjv\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Alan,

The error message occurs because the NIntegrate within ComplicatedF is
complaining about its input. For some reason, the MonteCarlo NIntegrate is
examining the quantity ComplicatedF[x] where x is not numerical. Try
inputting simply ComplicatedF[x] and you will see the same error message.

The way to avoid this situation is to change the function by restricting its
input to only numeric quantities:

Clear[ComplicatedF]
ComplicatedF[x_?NumericQ] := Re [NIntegrate [E^(- (I x+y+I)^2), {y,0,1}] ]

Now try your Monte Carlo integration and you will see no errors.

Carl Woll
Physics Dept
U of Washington

"Alan Lewis" <alanlewis at optioncity.net> wrote in message
news:b1idic\$bjv\$1 at smc.vnet.net...
> I have a rather complicated function that Mathematica can't seem to handle
> with
> NIntegrate, Method->MonteCarlo.
>
> This is not my function, but it shows the essence of the problem.
> Suppose we have
>
>    ComplicatedF[x_] :=  Re [NIntegrate [E^(- (I x+y+I)^2), {y,0,1}] ]
>
> Then, if you try:
>
> NIntegrate[ComplicatedF[x], {x,0,2}, Method->MonteCarlo]
>
> Mathematica will complain that the integrand is not numerical.
> But of course it is numerical and removing the Method->MonteCarlo option
>
> Now my actual function is quite complicated which is why
> I want to try the MonteCarlo method. Any suggestions?
>
>

```

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