## Meeting 2015 09 04 » History » Version 7

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Nicolas Ponieman, 09/02/2015 08:30 PM

# Meeting 2015 09 04¶

## Generic settings¶

/N02/det/trackMaxSteps 1000000000
/N02/det/trackMaxLen 10 km
/gun/energy 10.9181415106 MeV
/N02/prec/setDeltaOne 1.0e-2 mm
/N02/prec/setDeltaInt 1.0e-5 mm
/N02/prec/setEpsilonMin 1.0e-3
/N02/prec/setEpsilonMax 1.0e-3
/N02/prec/setDeltaChord 0.25 mm

MSE is the Mean Squared Error
MSE = 1/N * sum_{i=1}^{n} (G4_i - AN_i)^2
N = Number of output points
r_err

## Experiment 1 - Vary epsilon in G4¶

(see August 21 meeting)

/N02/det/stepMax 20. mm (i.e., stepMax = 20mm)
epsilonMax = epsilonMin = epsilon
The mean square error doesn't seem to vary.
The error, however, keeps growing with distance.

epsilon Simulation Time RHS evaluation steps Mean Square Error [mm^2] sqrt(MSE) [mm] Max(X_Error) [mm]
1.0e-3 0m13.725s 16500010 291.21 17.06 30.54
1.0e-4 0m13.725s 16500010 291.21 17.06 30.54
1.0e-5 0m13.725s 16500010 291.21 17.06 30.54
1.0e-6 0m21.815s 38500010 294.09 17.14 30.68
1.0e-7 0m27.980s 60500010 294.22 17.15 30.69
1.0e-8 0m41.054s 104499999 294.22 17.15 30.69
1.0e-9 0m55.830s 159500010 294.22 17.15 30.69
1.0e-10 1m25.948s 269499999 294.22 17.15 30.69
1.0e-11 2m17.996s 456500010 294.22 17.15 30.69
1.0e-12 3m50.224s 786518324 294.22 17.15 30.69

A few plots for different values of epsilon:

The 3 plots look exactly the same!
The output for those epsilon values is different, though.

## Experiment 2 - Vary stepMax in G4¶

/N02/prec/setEpsilonMin 1.0e-3 (i.e, epsilon = 1.0e-3)
/N02/prec/setEpsilonMax 1.0e-3
Errors were measured for first 2 km (the file size for 10 km in the case of stepMax=0.2mm was too big)

stepMax [mm] Simulation Time RHS evaluation steps Mean Square Error [mm^2] sqrt(MSE)[mm] Max(X_Error) [mm]
0.2 13m34.816s 550000011 12.12 3.48 6.16
1 2m51.026s 110000000 12.11 3.48 6.15
2 1m28.192s 55000000 12.11 3.48 6.15
5 0m33.121s 22000000 12.11 3.48 6.15
10 0m21.907s 22000010 12.08 3.47 6.14
20 0m13.797s 16500010 11.98 3.46 6.12
50 0m8.319s 13200010 11.71 3.42 6.03
100 0m7.179s 13200020 11.25 3.35 5.89
150 0m6.848s 13200020 10.79 3.28 5.76
200 0m6.382s 12650020 10.35 3.21 5.65

Although all the errors look similar, there is a clear and counterintuitive tendency for the error to become smaller as stepMax is increased.
A few plots for different values of stepMax:

## Experiment 3 - Vary DeltaQ in PD¶

Simulated with QSS3 method
DeltaQmin = DeltaQ * 1e-3
Several values of the table were left blank deliberately as they weren't calculated yet

DeltaQ Simulation Time Equivalente in PD to RHS eval steps Mean Square Error [mm^2] sqrt(MSE)[mm] Max(X_Error) [mm]
1.0e-1 0.41s 5.60e5
1.0e-2 0.42s 6.40e5
1.0e-3 1.33s 2.40e6 704.43 26.54 38.08
1.0e-4 8.89s 1.42e7 568.32 23.83 37.89
1.0e-5 16.3s 3.08e7 86.89 9.32 18.41
1.0e-6 35.6s 6.64e7 56.79 7.54 14.80
1.0e-7 77.6s 1.43e8 57.45 7.58 15.03
1.0e-8 165s 3.09e8
1.0e-9 354s 6.64e8
1.0e-10 740s 1.43e9
1.0e-11 1630s 3.09e9
1.0e-12

A few plots for different values of DeltaQ:

The last two plots look exactly the same