Multiple Integration methods in CERN ROOT library

Question

I've been converting some old Fortran code to C++ and I've run into a bit of a bind. There's a section that involves the cernlib function DGMLT, Gaussian Quadrature for Multiple Integration, which is defined at http://hep.fi.infn.it/cernlib.pdf

I've been scouring online and I can't find a suitable method in ROOT to replicate this process. The few examples of multiple integration functions I've found (ROOT::Math::AdaptiveIntegratorMultiDim() and the like) don't have any code examples.

Basically, I need some sample code for multiple integration, possibly using ROOT.

Answer 1

Below is a snippet using AdaptiveIntegratorMultiDim::Integral to compute multidimensional gaussian integrals with dimension 2--15:

for(unsigned int dim=2; dim<kMaxSyst; ++dim){
    NdimNormal nDimNormal(dim);
    ROOT::Math::Functor func(nDimNormal,dim);
    ROOT::Math::IntegratorMultiDim im(func);
    volNom = im.Integral(xminNom, xmaxNom);
    volSys = im.Integral(xminSys, xmaxSys);
    cout<<"dim = "<<dim
        <<" : volNom = "<<volNom
        <<" , volSys = "<<volSys
        <<endl;
}

The class NdimNormal is an N-dimensional function object, see its definition in the full code here: gist link. Note that AdaptiveIntegratorMultiDim::Integral can only handle integrals with dimension between 1 and 16. For higher dimensions you might want to consider gsl.