Re: Problem with nested NIntegrate[]
- To: mathgroup at smc.vnet.net
- Subject: [mg70235] Re: Problem with nested NIntegrate[]
- From: dimmechan at yahoo.com
- Date: Sun, 8 Oct 2006 02:05:00 -0400 (EDT)
- References: <eg83ok$nc3$1@smc.vnet.net>
First the behavior is not paradoxical; you could say it is feature (at
least to me).
Second here is the the analytic result
Integrate[Integrate[y, {x, -1, 1}], {y, -1, 1}]
0
Third see that despite of the presence of these NIntegrate::inum :
messages
you got the right answer
NIntegrate[NIntegrate[y, {x, -1, 1}], {y, -1, 1}]
NIntegrate::inum (...)
General::stop: (...)
NIntegrate::ploss : (...)
0.
I believe when integrating numerically y over {x,-1,1} NIntegrate
samples some
points where the integrand is not numerically.
I can think right now many alternatives in order to avoid the messages.
The first is the most desired.
NIntegrate[y, {x, -1, 1}, {y, -1, 1}]
0.
NIntegrate[NIntegrate[y, {y, -1, 1}], {x, -1, 1}, AccuracyGoal -> 20]
0.
Off[NIntegrate::inum]
NIntegrate[NIntegrate[y, {x, -1, 1}], {y, -1, 1}, AccuracyGoal -> 20]
0.
(*AccuracyGoal ->20 is necessay to supress NIntegrate::ploss :
message.*)
On[NIntegrate::inum]
Block[{Message}, NIntegrate[NIntegrate[y, {x, -1, 1}], {y, -1, 1}]]
0.
Block[{$Messages = {}}, NIntegrate[NIntegrate[y, {x, -1, 1}], {y, -1,
1}]]
0.
Regards
Î?/Î? Eckhard ÎγÏ?αÏ?ε:
> Hello,
>
> I encountered some strange behaviour of NIntegrate when I use a
> somewhat neseted structure of several - in my example of two -
> NIntegrate[] functions
>
> NIntegrate[NIntegrate[y,{x,-1,1}],{y,-1,1}]
>
> This gives me the error
>
> NIntegrate::"num Integrand y is not numerical at {x) = 0
>
> Why does the inner NIntegrate function not know, what value is
> currently assigned to y...
>
> I hope someone can shed a little light on that seemingly paradoxical
> behaviour.
>
> thanks in advance
>
> Eckhard