IntegratorMultiDim accuracy

ROOT
1

Hello,

I was trying to learn how to use IntegratorMultiDim by calculating a volume of ball with a following macro:
testIntegral.C (727 Bytes)

On ROOT v6-12-04 it gives the following result:
exact : 4.18879
kDEFAULT : 4.17793 , error: 0
kADAPTIVE : 4.17793 , error: 0
kVEGAS : 4.18659 , error: 0
kMISER : 4.20576 , error: 0
kPLAIN : 4.20984 , error: 0

Why with tolerance settings at 1e-9 I have accuracy worse than 1e-3?

Best regards,
Antoni

2

What concerns “intergration”, see for example:

3

OK, so I guess kADAPTIVE fails on a discontinuity at r = 1, while accuracy of MC integrators is defined by ncall parameter, not by tolerances.

@moneta Maybe it would be better to put some more info in documentation of IntegratorMultiDim or IntegrationMultiDim::Type ? Currently information

  • about tolerance vs ncall for MC integration is given in the description of GSLMCIntegrator ctor (with which we don’t interact normally)
  • regarding discontinuity is given in AdaptiveIntegratorMultiDim description “usually works best for smooth functions”, but again we don’t really interact with it directly and the statement seems to weak as here we get a bias not e.g. long convergence time
4

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