Re: problem with integrating an interpolated list
- To: mathgroup at smc.vnet.net
- Subject: [mg103024] Re: problem with integrating an interpolated list
- From: antononcube <antononcube at gmail.com>
- Date: Fri, 4 Sep 2009 03:15:54 -0400 (EDT)
- References: <h7b04r$d8$1@smc.vnet.net> <h7o85i$nht$1@smc.vnet.net>
On Sep 3, 7:57 pm, Harutyun Amirjanyan <amirjan... at gmail.com> wrote:
[...]
> WithNIntegrate, the nonsmooth behavior of InterpolatingFunction near
> the boundaries of pieces produces an error message and requires many
> recursive steps to evaluate accurately.
This is true and it is relevant given the definition of NewFunction.
Your statement also hints the solution of the problem Tobias has. We
need to define NewFunction as a piecewise function. Then NIntegrate
can use its piecewise pre-processing and gives quickly a result.
NNewFunction[x_, y_] :=
Piecewise[{{0, x < 2}, {0, y < 0}, {0, x > MaxResolution - 2}, {0, y
> MaxResolution - 2}, {MyFunction[x, y], True}}]
In[74]:= NIntegrate[NNewFunction[x + 2, y + 2], {x, -10, 10}, {y, -10,
10}] // Timing
Out[74]= {0.142061, 11.0756}
These plots can be used for further validation and clarification:
Needs["Integration`NIntegrateUtilities`"]
Plot3D[NNewFunction[x + 2, y + 2], {x, -10, 10}, {y, -10, 10},
PlotPoints -> 50]
Plot3D[NewFunction[{x + 2, y + 2}], {x, -10, 10}, {y, -10, 10},
PlotPoints -> 50]
NIntegrateSamplingPoints@NIntegrate[NNewFunction[x + 2, y + 2], {x,
-10, 10}, {y, -10, 10}]
Anton Antonov