Integration over irregular region

ROOT
1

Hi there,

I am trying to do the following integral (over some irregular region):

|+1      |+sqrt(1-x^2)
|        |
|   dx   |     dy  f(x,y)
|        |
|-1      |-sqrt(1-x^2)

Obviously, there are a couple of numerical C-recipes to get the job done.
However, I was wondering if there is ROOT way to do it. More specifically,
using GLSIntegrator. I am going through the documentation (including the
mathmore/test folder) but it seems to me that GSL integrands requires a
regular region for the integration limit e.g.,

|+1      |+c
|        |
|   dx   |     dy  f(x,y)
|        |
|-1      |-d

Am I totally misunderstanding the documentation? Otherwise, could you please point me to the right direction!

Thank you as always

erdos

Root 5.18
osx 10.4.9

2

Hi,

you would need to build two integrand functions one in x and one in y and then do the two integrations.

The attached example shows how to do using a simple case for f(x,y).

Best Regards

Lorenzo
exampleDoubleIntegral.C (1.85 KB)

3

Hi Lorenzo,

Thank you very much for the example. It worked beautifully! However, just to check my understanding, I made an attempt (albeit childish!) to generalize your example to a TripleIntegral. It quits with some bus errors.

I attach my attempt! I would greatly appreciate if you would take a look at it (time permitting of course!).

Thanks in advance
erdos
exampleTripleIntegral.C (2.68 KB)

4

Hi,

just replace line 92 of your macro:

  WrappedFunction<IntegrandFunctionX> wf(fx);

with

  WrappedFunction<const IntegrandFunctionX &> wf(fx);

This avoids the copying of the IntegrandFunctionX object, which has as data member a pointer to a GSLIntegrator and therefore it is not handled correctly.
It is strange that using ACLIC you did not get a compiler error, due to the private copy constructor of IntegrandFunctionX . Compiling directly the macro you will have this error.

Best Regards

Lorenzo