Example of Convergence Tester
Koi, Tatsumi
SLAC National Accelerator Laboratory / PPA
tkoi@slac.stanford.eedu
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 README.B1
Note that in this example, the classes with the code added for
the purpose of demonstration of the Convergence Tester start with a prefix
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
Gabriele Cosmo