# Meeting 2015 09 11¶

## 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

• All measured times correspond to executions (both of G4 or PD) which don't produce output at all (or produce a minimum logging).
• MSE is the Mean Squared Error of the position
• MSE = 1/N * sum_{i=1}^{N} (G4x_i - ANx_i)^2 + (G4y_i - ANy_i)^2
• N = Number of output points
• r_Error = sqrt(MSE)
• max(X_Error) is the maximum of all the absolute errors in x, i.e. max(abs(G4x_i - ANx_i))

## 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 X_Error, however, keeps growing with distance.

epsilon Simulation Time RHS evaluation steps r_Error [mm] Max(X_Error) [mm] r_Error [mm] Max(X_Error) [mm] r_Error [mm] Max(X_Error) [mm] r_Error [mm] Max(X_Error) [mm] 10 km 1 km 100 m 10 m 1.0e-3 13.72s 1.65e7 1.71E+01 3.05E+01 1.73E+00 3.11E+00 1.73E-01 3.07E-01 1.73E-02 2.96E-02 1.0e-4 13.72s 1.65e7 1.71E+01 3.05E+01 1.73E+00 3.11E+00 1.73E-01 3.07E-01 1.73E-02 2.96E-02 1.0e-5 13.72s 1.65e7 1.71E+01 3.05E+01 1.73E+00 3.11E+00 1.73E-01 3.07E-01 1.73E-02 2.96E-02 1.0e-6 21.81s 3.85e7 1.72E+01 3.07E+01 1.74E+00 3.12E+00 1.74E-01 3.09E-01 1.74E-02 2.98E-02 1.0e-7 27.98s 6.05e7 1.72E+01 3.07E+01 1.74E+00 3.12E+00 1.74E-01 3.09E-01 1.74E-02 2.98E-02 1.0e-8 41.05s 1.04e8 1.72E+01 3.07E+01 1.74E+00 3.12E+00 1.74E-01 3.09E-01 1.74E-02 2.98E-02 1.0e-9 55.83s 1.59e8 1.72E+01 3.07E+01 1.74E+00 3.12E+00 1.74E-01 3.09E-01 1.74E-02 2.98E-02 1.0e-10 85.94s 2.69e8 1.72E+01 3.07E+01 1.74E+00 3.12E+00 1.74E-01 3.09E-01 1.74E-02 2.98E-02 1.0e-11 137.99s 4.56e8 1.72E+01 3.07E+01 1.74E+00 3.12E+00 1.74E-01 3.09E-01 1.74E-02 2.98E-02 1.0e-12 230.22s 7.86e8 1.72E+01 3.07E+01 1.74E+00 3.12E+00 1.74E-01 3.09E-01 1.74E-02 2.98E-02
epsilon Simulation Time RHS evaluation steps r_Error [mm] Max(X_Error) [mm] r_Error [mm] Max(X_Error) [mm] r_Error [mm] Max(X_Error) [mm] r_Error [mm] Max(X_Error) [mm] 1 m 100 mm 10 mm 1 mm 1.0e-3 13.72s 1.65e7 1.72E-03 2.78E-03 1.26E-04 2.30E-04 500001 3.03e-2 1.0e-4 13.72s 1.65e7 1.72E-03 2.78E-03 1.26E-04 2.30E-04 500001 3.03e-2 1.0e-5 13.72s 1.65e7 1.72E-03 2.78E-03 1.26E-04 2.30E-04 500001 3.03e-2 1.0e-6 21.81s 3.85e7 1.73E-03 2.79E-03 1.30E-04 2.40E-04 500001 1.30e-2 1.0e-7 27.98s 6.05e7 1.74E-03 2.80E-03 1.30E-04 2.40E-04 500001 8.26e-3 1.0e-8 41.05s 1.04e8 1.74E-03 2.80E-03 1.30E-04 2.40E-04 500001 4.81e-3 1.0e-9 55.83s 1.59e8 1.74E-03 2.80E-03 1.30E-04 2.40E-04 500001 3.14e-3 1.0e-10 85.94s 2.69e8 1.74E-03 2.80E-03 1.30E-04 2.40E-04 500001 1.86e-3 1.0e-11 137.99s 4.56e8 1.74E-03 2.80E-03 1.30E-04 2.40E-04 500001 1.09e-3 1.0e-12 230.22s 7.86e8 1.74E-03 2.80E-03 1.30E-04 2.40E-04 500001 6.36e-4

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 r_Error [mm] Max(X_Error) [mm] r_Error [mm] Max(X_Error) [mm] r_Error [mm] Max(X_Error) [mm] r_Error [mm] Max(X_Error) [mm] 10 km 1 km 100 m 10 m 0.2 814.81s 5.50e8 1.07E+01 1.99E+01 1.74E+00 3.15E+00 1.74E-01 3.15E-01 1.74E-02 3.14E-02 1 171.02s 1.10e8 1.72E+01 3.07E+01 1.74E+00 3.15E+00 1.74E-01 3.13E-01 1.74E-02 3.11E-02 2 88.19s 5.50e7 1.72E+01 3.07E+01 1.74E+00 3.15E+00 1.74E-01 3.13E-01 1.74E-02 3.09E-02 5 33.12s 2.20e7 1.72E+01 3.07E+01 1.74E+00 3.15E+00 1.74E-01 3.13E-01 1.74E-02 3.06E-02 10 21.90s 2.20e7 1.71E+01 3.07E+01 1.74E+00 3.13E+00 1.74E-01 3.12E-01 1.74E-02 3.06E-02 20 13.79s 1.65e7 1.71E+01 3.05E+01 1.73E+00 3.11E+00 1.73E-01 3.07E-01 1.73E-02 2.96E-02 50 8.31s 1.32e7 1.69E+01 3.02E+01 1.71E+00 3.08E+00 1.71E-01 2.99E-01 1.71E-02 2.89E-02 100 7.17s 1.32e7 1.65E+01 2.97E+01 1.68E+00 3.01E+00 1.68E-01 2.93E-01 1.67E-02 2.83E-02 150 6.84s 1.32e7 1.62E+01 2.91E+01 1.64E+00 2.96E+00 1.64E-01 2.80E-01 1.64E-02 2.69E-02 200 6.38s 1.26e7 1.59E+01 2.85E+01 1.61E+00 2.90E+00 1.61E-01 2.82E-01 1.59E-02 2.72E-02
stepMax [mm] Simulation Time RHS evaluation steps r_Error [mm] Max(X_Error) [mm] r_Error [mm] Max(X_Error) [mm] r_Error [mm] Max(X_Error) [mm] r_Error [mm] Max(X_Error) [mm] Output Steps Output steps / RHS steps ratio 1 m 100 mm 10 mm 1 mm 0.2 814.81s 5.50e8 1.76E-03 3.02E-03 1.67E-04 3.36E-04 4.09E-06 7.20E-06 3.44E-07 5.98E-07 1 171.02s 1.10e8 1.76E-03 2.83E-03 1.66E-04 3.35E-04 3.86E-06 6.36E-06 10000001 9.10e-2 2 88.19s 5.50e7 1.76E-03 2.83E-03 1.64E-04 3.35E-04 3.63E-06 6.36E-06 5000001 9.10e-2 5 33.12s 2.20e7 1.75E-03 2.83E-03 1.58E-04 3.09E-04 2.61E-06 3.62E-06 2000001 9.10e-2 10 21.90s 2.20e7 1.74E-03 2.81E-03 1.45E-04 2.78E-04 1000001 4.55e-2 20 13.79s 1.65e7 1.72E-03 2.78E-03 1.26E-04 2.30E-04 500001 3.03e-2 50 8.31s 1.32e7 1.66E-03 2.76E-03 6.91E-05 9.14E-05 200001 1.52e-2 100 7.17s 1.32e7 1.56E-03 1.98E-03 100001 7.58e-3 150 6.84s 1.32e7 1.58E-03 1.77E-03 66668 5.05e-3 200 6.38s 1.26e7 1.36E-03 1.76E-03 50001 3.97e-3

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 Equivalent in PD to RHS eval steps r_Error [mm] Max(X_Error) [mm] r_Error [mm] Max(X_Error) [mm] r_Error [mm] Max(X_Error) [mm] r_Error [mm] Max(X_Error) [mm] 10 km 1 km 100 m 10 m 1.0e-1 0.41s 5.60e5 1.0e-2 0.42s 6.40e5 1.0e-3 1.33s 2.40e6 2.65E+01 3.81E+01 2.17E+01 3.75E+01 6.11E+00 1.25E+01 7.48E-01 1.43E+00 1.0e-4 8.89s 1.42e7 2.38E+01 3.79E+01 6.44E+00 1.32E+01 7.89E-01 1.57E+00 8.28E-02 1.57E-01 1.0e-5 16.3s 3.08e7 9.32E+00 1.84E+01 1.09E+00 2.20E+00 1.13E-01 2.24E-01 1.14E-02 2.19E-02 1.0e-6 35.6s 6.64e7 7.53E+00 1.48E+01 7.68E-01 1.51E+00 7.69E-02 1.51E-01 7.71E-03 1.51E-02 1.0e-7 77.6s 1.43e8 7.58E+00 1.50E+01 7.64E-01 1.52E+00 7.65E-02 1.52E-01 7.62E-03 1.51E-02 1.0e-8 165s 3.09e8 1.0e-9 354s 6.64e8 1.0e-10 740s 1.43e9 1.0e-11 1630s 3.09e9
DeltaQ Simulation Time Equivalente in PD to RHS eval steps r_Error [mm] Max(X_Error) [mm] r_Error [mm] Max(X_Error) [mm] r_Error [mm] Max(X_Error) [mm] r_Error [mm] Max(X_Error) [mm] 1 m 100 mm 10 mm 1 mm 1.0e-1 0.41s 5.60e5 1.0e-2 0.42s 6.40e5 1.0e-3 1.33s 2.40e6 8.17E-02 1.35E-01 7.27E-03 9.15E-03 4.84E-04 5.73E-04 2.52E-12 0.00E+00 1.0e-4 8.89s 1.42e7 8.65E-03 1.44E-02 8.32E-04 9.69E-04 5.13E-05 1.35E-04 1.21E-05 1.71E-05 1.0e-5 16.3s 3.08e7 1.18E-03 2.17E-03 1.09E-04 1.74E-04 8.47E-06 2.08E-05 7.82E-07 1.49E-06 1.0e-6 35.6s 6.64e7 7.64E-04 1.50E-03 8.00E-05 1.67E-04 7.36E-06 1.72E-05 5.95E-07 1.29E-06 1.0e-7 77.6s 1.43e8 7.67E-04 1.50E-03 7.64E-05 1.56E-04 7.48E-06 1.87E-05 7.49E-07 1.59E-06 1.0e-8 165s 3.09e8 1.0e-9 354s 6.64e8 1.0e-10 740s 1.43e9 1.0e-11 1630s 3.09e9

A few plots for different values of DeltaQ: