
Example of Convergence Tester 

          Koi, Tatsumi
          SLAC / SCCS
          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.
    What we must remember is
	Large number of history does not valid result of simulation.
	Small Relative Error does not valid result of simulation
To provide statistical information to assist establishing valid confidence intervals for Monte Carlo results for users.

Geometry and Physics are same to exampleN03. Please see README.N03

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Output example

// Part I.A
// Basic statistics values 

EFFICIENCY = 0.99438477
MEAN = 78.477718
VAR = 225.50178
SD = 15.016717
R = 0.0029898448
SHIFT = -13.902917
VOV = 0.0019924127
FOM = 909.19362

// 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 = 117.3797 and it happend at 510th event
Affected Mean = 78.487213 and its ratio to orignal is 1.000121
Affected VAR = 225.81611 and its ratio to orignal is 1.0013939
Affected R = 0.0029912008 and its ratio to orignal is 1.0004535
Affected SHIFT = -13.862598 and its ratio to orignal is 0.99709995
Affected FOM = 908.89814 and its ratio to orignal is 0.99967501

// Part I.C
// Convergence tests results

MEAN distribution is not RANDOM
r follows 1/sqrt(N)
r is monotonically decrease 1
r is less than 0.1. r = 0.0029898448
VOV follows 1/sqrt(N)
VOV is monotonically decrease 1
FOM distribution is RANDOM
SLOPE is large enough
This result passes 7 / 8 Convergence Test.

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

i/16 till_ith  mean  var  sd  r  vov  fom  shift  e  r2eff  r2int
1 255 76.935633 252.45045 15.888689 0.012907453 0.038596366 787.70557 -17.661167 0.984375 6.2003968e-05 0.00010394759
2 511 77.389232 257.4632 16.04566 0.0091630923 0.017298474 773.88648 -16.441348 0.98632812 2.707302e-05 5.6725251e-05
3 767 77.665817 248.62651 15.767895 0.0073259372 0.012144321 826.64625 -16.585523 0.98828125 1.5439723e-05 3.8159751e-05
4 1023 77.969112 245.54395 15.669842 0.0062804686 0.0086792682 841.98653 -16.027547 0.99023438 9.6307939e-06 2.9774973e-05
5 1279 78.061919 228.9236 15.130221 0.0054175269 0.0067481801 897.34046 -14.687306 0.9921875 6.1515748e-06 2.3175093e-05
6 1535 77.870133 231.84589 15.226486 0.004989226 0.0054405699 879.44272 -14.43874 0.99283854 4.6960383e-06 2.0180132e-05
7 1791 78.045703 224.72573 14.990855 0.004537414 0.0046643478 908.22153 -14.045519 0.99386161 3.446599e-06 1.7130038e-05
8 2047 78.107287 226.09338 15.036402 0.0042539011 0.0041397452 902.08658 -14.202387 0.99365234 3.1192414e-06 1.4967598e-05
9 2303 78.129941 222.08125 14.902391 0.0039737195 0.0036662056 916.62223 -13.945849 0.99392361 2.6534449e-06 1.3130148e-05
10 2559 78.225505 223.59764 14.953181 0.0037780287 0.0032772248 910.22344 -13.934949 0.99414062 2.3023084e-06 1.1965617e-05
11 2815 78.250797 222.51845 14.917052 0.003592344 0.0029353727 915.19704 -13.768958 0.99431818 2.0292208e-06 1.0871132e-05
12 3071 78.377339 220.83103 14.860385 0.0034208098 0.002628038 928.36413 -13.3624 0.99479167 1.7042976e-06 9.9938329e-06
13 3327 78.364284 221.49591 14.882739 0.0032921001 0.0024634602 923.51719 -13.660307 0.99489183 1.5427886e-06 9.2918778e-06
14 3583 78.464175 220.63749 14.853871 0.0031621629 0.0022668889 928.57248 -13.539324 0.99497768 1.4083908e-06 8.5880937e-06
15 3839 78.420541 224.71581 14.990524 0.0030847599 0.002080651 911.9934 -13.68267 0.99479167 1.363438e-06 8.1498278e-06
16 4095 78.477718 225.50178 15.016717 0.0029898448 0.0019924127 909.4893 -13.902917 0.99438477 1.3786483e-06 7.5583414e-06


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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

