Example of Convergence Tester

      Koi, Tatsumi \n
      SLAC National Accelerator Laboratory / PPA  \n
      tkoi@slac.stanford.eedu \n

This example shows how to use convergece tester in Geant4. The aim of Convergence Tester

After a Monte Carlo simulation, we get an answer. However how to estimate quality of the answer. The answer is usually given in a form of average value. But sometimes the value is strongly affected by single or a few events in the full calculation. In such case, we must concern about quality of the value.

What we must remember is

Large number of history does not valid result of simulation.
Small Relative Error does not valid result of simulation Convergence tester provides statistical information to assist establishing valid confidence intervals for Monte Carlo results for users.

Geometry and Physics are same to exampleB1. Please see Example B1. Also run1.mac and run2.mac are like in exampleB1, with the only diffrence slightly increased number of events in run1.mac. Note that in this example, the classes with the code added for the purpose of demonstration of the Convergence Tester are defined in the namespace B1Con instead of B1 and also the executable and the test macro names are changed in exampleB1Con and exampleB1Con.in.

Known problem: Computing time of T cannot be gotten properly in current MT migration of example of B1Con. Therefore FOM (=1/(R^2T) where R is relative error and T is computing time) relates numbers are unusable.

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Output example

// Part I.A
// Basic statistics values

G4ConvergenceTester Output Result of DOSE_TALLY
       EFFICIENCY =         0.601
             MEAN =   4.81721e-12
              VAR =   2.15334e-23
               SD =   4.64041e-12
                R =     0.0304622
            SHIFT =   2.22459e-13
              VOV =   0.000166754
              FOM =       1238.68

// Part I.B
// If the largeset scored events happen at next to the last event,
// then how much the event effects the statistics values of the calculation

THE LARGEST SCORE =   1.07301e-11 and it happend at 487th event
    Affected Mean =   4.82311e-12 and its ratio to orignal is 1.00123
     Affected VAR =   2.15468e-23 and its ratio to orignal is 1.00062
       Affected R =     0.0304192 and its ratio to orignal is 0.998587
   Affected SHIFT =    2.1804e-13 and its ratio to orignal is 0.980133
     Affected FOM =       1238.68 and its ratio to orignal is 1

// Part I.C
// Convergence tests results

MEAN distribution is  RANDOM
r follows 1/std::sqrt(N)
r is monotonically decrease
r is less than 0.1. r = 0.0304622
VOV follows 1/std::sqrt(N)
VOV is monotonically decrease
FOM distribution is not RANDOM
SLOPE is not large enough
This result passes 6 / 8 Convergence Test.

// Part II
// Profile of statistics values in the history

G4ConvergenceTester Output History of DOSE_TALLY
i/16 till_ith      mean          var           sd            r          vov          fom        shift            e        r2eff        r2int
   1    62  4.94618e-12  2.04631e-23  4.52362e-12     0.115225   0.00313634      86.5745 -1.73435e-14     0.619048   0.00976801   0.00329797
   2   124  4.69364e-12  2.10698e-23  4.59018e-12    0.0874712     0.001597      150.228  3.11143e-13          0.6   0.00533333   0.00225666
   3   187  4.72161e-12  2.14009e-23  4.62612e-12    0.0714575   0.00101852      225.105   3.1009e-13     0.590426   0.00368986   0.00138916
   4   249  4.95617e-12  2.13982e-23  4.62582e-12    0.0590299  0.000690138      329.865  9.71971e-14         0.62   0.00245161   0.00101898
   5   312   4.8529e-12  2.13482e-23  4.62041e-12    0.0538155  0.000573301      396.887  1.95662e-13     0.607029   0.00206827  0.000818582
   6   374  5.14255e-12  2.15736e-23  4.64474e-12     0.046641  0.000432121      528.379 -6.42963e-14     0.637333   0.00151743  0.000652145
   7   437  5.03849e-12  2.13484e-23  4.62043e-12    0.0438173  0.000379317      598.673  2.54207e-14     0.636986   0.00130112  0.000614447
   8   499  4.96962e-12   2.1429e-23  4.62914e-12    0.0416574  0.000329007      662.364  9.27708e-14         0.63    0.0011746  0.000557264
   9   562  4.91513e-12  2.14709e-23  4.63367e-12    0.0397316  0.000285324       728.13  1.33544e-13     0.623446    0.0010728  0.000502991
  10   624  4.82995e-12  2.13825e-23  4.62412e-12    0.0382954  0.000272664      783.766  2.19101e-13        0.616  0.000997403  0.000466792
  11   687  4.79197e-12  2.13975e-23  4.62574e-12    0.0368022  0.000251788      848.661  2.48547e-13     0.606105  0.000944593  0.000407838
  12   749  4.77183e-12  2.15116e-23  4.63807e-12    0.0354912  0.000227501      912.513   2.6728e-13     0.601333  0.000883962  0.000373986
  13   812  4.76087e-12  2.14479e-23  4.63119e-12    0.0341162  0.000212259      987.548  2.70437e-13     0.597786  0.000827601  0.000334885
  14   874  4.81359e-12  2.13296e-23   4.6184e-12    0.0324353    0.0001976      1092.56  2.14521e-13     0.603429  0.000751082  0.000299767
  15   937  4.82018e-12  2.14558e-23  4.63204e-12    0.0313767  0.000181379      1167.52  2.18545e-13     0.601279  0.000706952  0.000276498
  16   999  4.81721e-12  2.15334e-23  4.64041e-12    0.0304622  0.000166754      1238.68  2.22459e-13        0.601  0.000663894  0.000263125


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Reference of this Convergence tests:
MCNP(TM) -A General Monte Carlo N-Particle Transport Code
Version 4B
Judith F. Briesmeister, Editor
LA-12625-M, Issued: March 1997, UC 705 and UC 700
CHAPTER 2. GEOMETRY, DATA, PHYSICS, AND MATHEMATICS
VI. ESTIMATION OF THE MONTE CARLO PRECISION