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Re: N-dimensional NIntegrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg79100] Re: [mg79066] N-dimensional NIntegrate
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Wed, 18 Jul 2007 03:04:08 -0400 (EDT)
  • Reply-to: hanlonr at cox.net

x = ToExpression[Table["x" <> ToString[n], {n, 3}]];

Fold[Integrate[#1, #2] &, f @@ x, x]

Integrate[Integrate[Integrate[
       f[x1, x2, x3], x1], x2], x3]

Fold[Integrate[#1, {#2, -Infinity, Infinity}] &, f @@ x, x]

Integrate[Integrate[Integrate[
       f[x1, x2, x3], {x1, -Infinity, 
         Infinity}], {x2, -Infinity, 
       Infinity}], {x3, -Infinity, 
     Infinity}]


Bob Hanlon

---- mfedert at gmail.com wrote: 
> Hi everyone,
> 
> I want to define an N-dimensional definite integral---numerical
> integration rather than symbolic.
> 
> Eg,
> 
> compute integral of f(x) dx
> 
> where x can be an N-vector.  I want to define the integral for general
> N.  (Obviously before evaluating the integral, I'll specify N.)  I
> can't think how to define the range of integration in a neat way in
> the general case.  Eg if the variables are x_{1}, x_{2}, ... x_{N},
> how can I specify that the integration range is
> (say) R^{N}?
> 
> Something like
> 
> NIntegrate[ f(x), {x_{1}, -inf, inf}, {x_{2}, -inf, inf}, ..., {x_{N},
> -inf, inf} ]
> 
> is what I want... would be neat to have x defined as a list or
> something.
> 
> There must be a neat way to do this.   Sorry for being such an
> amateur.
> 
> Cheers,
> MF
> 
> 



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