Multi-dimensional adaptive integration

Roofit and RooStats
1

Hi,

I didn’t find any documentation about the usage of multi-dimensional adaptive integration in ROOT. I looked at the source code and the tutorial mathmoreIntegration.C and came up with the following approach. Is it OK or should I use something else? It calculates the volume of a sphere with radius R=2 in spherical coordinates.

#include "TMath.h"
#include "Math/WrappedFunction.h"
#include "Math/IntegratorMultiDim.h"
#include <iostream>

Double_t func(const Double_t *x){ 
    return x[0]*x[0]*TMath::Sin(x[1]);
}

void multiDimIntegration()
{
    Double_t R = 2.0;  // sphere radius
    // numeric integration
    ROOT::Math::WrappedMultiFunction<> f1(func,3);
    ROOT::Math::IntegratorMultiDim ig(f1);
    Double_t xmin[3] = {0.0, 0.0, 0.0};
    Double_t xmax[3] = {R, TMath::Pi(), 2*TMath::Pi()};
    Double_t volume1 = ig.Integral(xmin, xmax);
    // analytic formula
    Double_t volume2 = 4.0/3*TMath::Pi()*R*R*R;
    
    std::cout << scientific;
    std::cout << "volume1 = " << volume1 << std::endl;
    std::cout << "volume2 = " << volume2 << std::endl;
}

The compiled version works OK, the interpreted version crashes:

root [] .x multiDimIntegration.C++ // works OK
Info in <ACLiC>: unmodified script has already been compiled and loaded
Info in <ACLiC>: it will be regenerated and reloaded!
Info in <TUnixSystem::ACLiC>: creating shared library /home/malusek/work/root/./multiDimIntegration_C.so
volume1 = 3.351032e+01
volume2 = 3.351032e+01

root [] .x multiDimIntegration.C  // crashes
Syntax error /lw/root/5.22.00/include/Math/WrappedFunction.h:159:
Error: Symbol FreeMultiFunctionPtrfFunc is not defined in current scope  /lw/root/5.22.00/include/Math/WrappedFunction.h:183:
Warning: Error occurred during reading source files
Warning: Error occurred during dictionary source generation
!!!Removing /home/malusek/work/root/AutoDict_ROOT__Math__WrappedMultiFunction_FreeMultiFunctionPtr__cxx_ACLiC_dict.cxx /home/malusek/work/root/AutoDict_ROOT__Math__WrappedMultiFunction_FreeMultiFunctionPtr__cxx_ACLiC_dict.h !!!
Error: /lw/root/5.22.00/bin/rootcint: error loading headers...
Error in <ACLiC>: Dictionary generation failed!
Syntax error Math/WrappedFunction.h:159:
Error: abstract class object 'WrappedMultiFunction<FreeMultiFunctionPtr> f1' declared multiDimIntegration.C:14:

 *** Break *** segmentation violation
Using host libthread_db library "/lib/libthread_db.so.1".
Attaching to program: /proc/10171/exe, process 10171
[Thread debugging using libthread_db enabled]
[New Thread 0xb6c156d0 (LWP 10171)]
0xffffe410 in __kernel_vsyscall ()
#1  0xb6cd7123 in waitpid () from /lib/libc.so.6
#2  0xb6c7fb5b in ?? () from /lib/libc.so.6
#3  0xb6d8950d in system () from /lib/libpthread.so.0
#4  0xb79e57bd in TUnixSystem::Exec () from /lw/root/5.22.00/lib/libCore.so
#5  0xb79ec453 in TUnixSystem::StackTrace ()
   from /lw/root/5.22.00/lib/libCore.so
#6  0xb79ea0f6 in TUnixSystem::DispatchSignals ()
   from /lw/root/5.22.00/lib/libCore.so
#7  0xb79ea1dd in SigHandler () from /lw/root/5.22.00/lib/libCore.so
#8  0xb79e2fdd in sighandler () from /lw/root/5.22.00/lib/libCore.so
#9  <signal handler called>
#10 0x083da2d2 in ?? ()
#11 0x083d7fd8 in ?? ()
#12 0x6f722f77 in ?? ()
#13 0x083cf150 in ?? ()
#14 0xb7246eab in G__defined_templateclass ()
   from /lw/root/5.22.00/lib/libCint.so
#15 0xb70f8d95 in Cint::G__ExceptionWrapper ()
   from /lw/root/5.22.00/lib/libCint.so
#16 0xb71b2816 in G__execute_call () from /lw/root/5.22.00/lib/libCint.so
#17 0xb71b3990 in G__call_cppfunc () from /lw/root/5.22.00/lib/libCint.so
#18 0xb7187091 in G__interpret_func () from /lw/root/5.22.00/lib/libCint.so
#19 0xb71757e7 in G__getfunction () from /lw/root/5.22.00/lib/libCint.so
#20 0xb71962f0 in G__basedestructor () from /lw/root/5.22.00/lib/libCint.so
#21 0xb7176f31 in G__getfunction () from /lw/root/5.22.00/lib/libCint.so
#22 0xb7229307 in G__destroy_upto_vararray ()
   from /lw/root/5.22.00/lib/libCint.so
#23 0xb722973d in G__destroy_upto () from /lw/root/5.22.00/lib/libCint.so
#24 0xb718a7df in G__interpret_func () from /lw/root/5.22.00/lib/libCint.so
#25 0xb7175932 in G__getfunction () from /lw/root/5.22.00/lib/libCint.so
#26 0xb7149a0b in G__getitem () from /lw/root/5.22.00/lib/libCint.so
#27 0xb715074d in G__getexpr () from /lw/root/5.22.00/lib/libCint.so
#28 0xb715c402 in G__calc_internal () from /lw/root/5.22.00/lib/libCint.so
#29 0xb71f0bb1 in G__process_cmd () from /lw/root/5.22.00/lib/libCint.so
#30 0xb79d33a0 in TCint::ProcessLine () from /lw/root/5.22.00/lib/libCore.so
#31 0xb79d305f in TCint::ProcessLineSynch ()
   from /lw/root/5.22.00/lib/libCore.so
#32 0xb78fc984 in TApplication::ExecuteFile ()
   from /lw/root/5.22.00/lib/libCore.so
#33 0xb78fcf54 in TApplication::ProcessFile ()
   from /lw/root/5.22.00/lib/libCore.so
#34 0xb78fa164 in TApplication::ProcessLine ()
   from /lw/root/5.22.00/lib/libCore.so
#35 0xb6edeae1 in TRint::HandleTermInput ()
   from /lw/root/5.22.00/lib/libRint.so
#36 0xb6edce75 in TTermInputHandler::Notify ()
   from /lw/root/5.22.00/lib/libRint.so
#37 0xb6edf594 in TTermInputHandler::ReadNotify ()
   from /lw/root/5.22.00/lib/libRint.so
#38 0xb79e9dd5 in TUnixSystem::CheckDescriptors ()
   from /lw/root/5.22.00/lib/libCore.so
#39 0xb79ea8af in TUnixSystem::DispatchOneEvent ()
   from /lw/root/5.22.00/lib/libCore.so
#40 0xb7959771 in TSystem::InnerLoop () from /lw/root/5.22.00/lib/libCore.so
#41 0xb795cef1 in TSystem::Run () from /lw/root/5.22.00/lib/libCore.so
#42 0xb78f8a07 in TApplication::Run () from /lw/root/5.22.00/lib/libCore.so
#43 0xb6edf090 in TRint::Run () from /lw/root/5.22.00/lib/libRint.so
#44 0x08048ef5 in main ()
The program is running.  Quit anyway (and detach it)? (y or n) [answered Y; input not from terminal]
Detaching from program: /proc/10171/exe, process 10171
Root > Function multiDimIntegration() busy flag cleared

Platform: ROOT 5.22/00 on openSUSE 10.3 (x86).

2

Hi,

just replace the line

ROOT::Math::WrappedMultiFunction<> f1(func,3);

with

ROOT::Math::Functor f1(func,3);

and your macro will work in interpreted mode. In the previous case CINT had some problem understanding the template class.

Regards

Lorenzo

3

Hi,

Thanks for your reply. It works with CINT but it doesn’t work with ACLiC now. How can I fix it so that it works with both?

#ifndef __CINT__
#include "TMath.h"
#include "Math/Functor.h"
#include "Math/IntegratorMultiDim.h"
#include <iostream>
#endif

Double_t func(const Double_t *x){ 
    return x[0]*x[0]*TMath::Sin(x[1]);
}

void multiDimIntegration()
{
    Double_t R = 2.0;  // sphere radius
    // numeric integration
    ROOT::Math::Functor f1(func,3); 
    ROOT::Math::IntegratorMultiDim ig(f1);
    Double_t xmin[3] = {0.0, 0.0, 0.0};
    Double_t xmax[3] = {R, TMath::Pi(), 2*TMath::Pi()};
    Double_t volume1 = ig.Integral(xmin, xmax);
    // analytic formula
    Double_t volume2 = 4.0/3*TMath::Pi()*R*R*R;
    
    std::cout << scientific;
    std::cout << "volume1 = " << volume1 << std::endl;
    std::cout << "volume2 = " << volume2 << std::endl;
}
root [] .x multiDimIntegration.C++
Info in <TUnixSystem::ACLiC>: creating shared library /home/malusek/work/root/./multiDimIntegration_C.so
/lw/root/5.22.00/include/Math/Functor.h: In instantiation of ‘ROOT::Math::FunctorHandler<ROOT::Math::Functor, Double_t ()(const Double_t*)>’:
/lw/root/5.22.00/include/Math/Functor.h:370:   instantiated from ‘ROOT::Math::Functor::Functor(const Func&, unsigned int) [with Func = Double_t ()(const Double_t*)]’
/home/malusek/work/root/./multiDimIntegration.C:16:   instantiated from here
/lw/root/5.22.00/include/Math/Functor.h:99: error: field ‘ROOT::Math::FunctorHandler<ROOT::Math::Functor, Double_t ()(const Double_t*)>::fFunc’ invalidly declared function type
g++: /home/malusek/work/root/./multiDimIntegration_C_ACLiC_dict.o: není souborem ani adresářem
Error in <ACLiC>: Compilation failed!
Error: Function multiDimIntegration() is not defined in current scope  :0:
*** Interpreter error recovered ***
1 Like
4

Sorry for the previous post, the correct syntax working in C++ and CINT is:

 ROOT::Math::Functor f1(&func,3);

Lorenzo

5

It works now. Thank you for your help.

It would be nice to have simple examples available in the reference documentation, e.g. in http://root.cern.ch/root/html522/ROOT__Math__IntegratorMultiDim.html. Has anybody thought about it? It takes much less time to adapt a simple example than to start from scratch by studying the source code.

1 Like
6

I agree with your point. We are in did working now on improving the documentation and examples.
Thank you for your feedback

Best Regards
Lorenzo

1 Like