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experimentes nearly done

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toni
2017-05-06 01:04:48 +02:00
parent b4720ae288
commit 5b2e1b0c65
26 changed files with 45206 additions and 23 deletions
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4
code/filter/KLB.h
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@@ -211,8 +211,8 @@ struct ModeProbabilityTransitionNormal : public K::MarkovTransitionProbability<M
//create the matrix
Eigen::MatrixXd m(2,2);
m << expKld, 1.0 - expKld, 1 - qualityWifi, qualityWifi;
//m << expKld, 1.0 - expKld, 0.00000000000000000001, 0.99999999999999999999;
//m << expKld, 1.0 - expKld, 1 - qualityWifi, qualityWifi;
m << 1, 0, 0, 1.0;
return m;

10
code/main.cpp
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@@ -305,8 +305,8 @@ K::Statistics<float> run(DataSetup setup, int numFile, std::string folder, std::
//plot.setEst(estPos);
//plot.setGT(gtPos);
//plot.addParticles1(IMMAPF.getModes()[0].getParticles());
//plot.addParticles2(IMMAPF.getModes()[1].getParticles());
plot.addParticles1(IMMAPF.getModes()[0].getParticles());
plot.addParticles2(IMMAPF.getModes()[1].getParticles());
plot.addEstimationNode(estPos);
//plot.addEstimationNodeSmoothed(IMMAPF.getModes()[1].getEstimation().position.inMeter());
@@ -354,8 +354,8 @@ K::Statistics<float> run(DataSetup setup, int numFile, std::string folder, std::
wifiFile << __QUALITY << "\n";
//plot.show();
//usleep(10*10);
plot.show();
usleep(10*10);
lastTimestamp = ts;
@@ -456,7 +456,7 @@ int main(int argc, char** argv) {
K::Statistics<float> statsQuantil;
K::Statistics<float> tmp;
for(int i = 0; i < 25; ++i){
for(int i = 0; i < 1; ++i){
// Settings::useKLB = false;
// errorPair = run(data.IPIN2017, 1, "ipin2017", Settings::Paths_IPIN2017::path1);
// run(data.IPIN2017, 0, "ipin2017", Settings::Paths_IPIN2017::path1);

2
tex/bare_conf.tex
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@@ -118,7 +118,7 @@
% gfx include folder
\graphicspath{ {gfx/} }
\graphicspath{ {gfx/} {gfx/eval}}
% correct bad hyphenation here

20
tex/chapters/conclusion.tex
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@@ -1,2 +1,20 @@
\section{Conclusion}
Kommt schon noch.
In this work we presented .. which is easy to adapt to many existing localisation systems.
combining different filter shemes using an IMMPF
enables us to combine beliebie transition models.
Looking at the results / experiments
we were able to satisfy the need of diversity and focues to reduce the recover from sample impoverishment in context of indoor localization.
The benefits of our approach demonstrated
This further
future work completely different localisation approaches, not only transitions.
more then 2 filters
a more advanced wi-fi quality factor
incorporating a smoothing filter as mode, so we are able to draw new particles from a smoothed particle set. ..

124
tex/chapters/experiments.tex
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@@ -2,26 +2,36 @@
% allgemeine infos über pfade und gebäude. wo
% bild: mit pfaden drauf und eventl. wifi qualität in jeweiligen bereichen? (kann frank das)
All upcoming experiments were carried out on four floors of a \SI{77}{m} x \SI{55}{m} sized faculty building.
\begin{figure}
\centering
\input{gfx/eval/paths.tex}
\caption{Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy }
\label{fig:paths}
\end{figure}
%
All upcoming experiments were carried out on four floors (0 to 3) of a \SI{77}{m} x \SI{55}{m} sized faculty building.
It includes several staircases and elevators and has a ceiling height of about \SI{3}{m}.
Nevertheless, the grid was generated for the complete campus and thus outdoor areas like the courtyard are also walkable.
As Wi-Fi is attenuated by obstacles and walls, it does not provide a consistent quality over the complete building.
In fig. \ref{} we illustrate the quality obtained by the wall attenuation factor model presented earlier.
Here, green indicates a high coverage and thus a good quality for localisation, while red does the opposite.
To obtain this information we measured Wi-Fi at $666$ different points and interpolated the results as described in \cite{}.
In fig. \ref{fig:paths} we illustrate the quality obtained by the wall attenuation factor model presented earlier.
Here, the intensity of red indicates a low coverage and thus a bad quality for localisation.
To obtain this information we interpolated the Wi-Fi quality factor given by all test walks using $l_{\text{max}} = \SI{-75}{\dBm}$ and $l_{\text{min}} = \SI{-90}{\dBm}$.
As mentioned before, we omit any time-consuming calibration processes and use the same values for all access-points. That would be $P_{0_{\text{wifi}}} = \SI{-46}{\dBm}, \mPLE_{\text{wifi}} = \SI{2.7}{}, \mWAF_{\text{wifi}} = \SI{8}{\dB}$.
The position of the access-points (about five per floor) is known beforehand.
Due to legal terms, we are not allowed to depict their positions and therefore omit this information within the figures.
% gewählte parameter (auch mal die optimieren wifi parameter testen)
We arranged three distinct walks (see also fig. \ref{}).
We arranged three distinct walks (see also fig. \ref{fig:paths}).
The measurements for the walks were recorded using a Motorola Nexus 6 at 2.4 GHz band only.
The computation was done offline as described in algorithm \ref{}.
For each walk we deployed $xx$ MC runs using 5000 Particles for each mode.
The computation was done offline as described in algorithm \ref{fig:paths}.
For each walk we deployed $50$ MC runs using 5000 Particles for each mode.
Instead of an initial position and heading, all walks start with a uniform distribution (random position and heading) as prior.
For the filtering we used $\sigma_\text{wifi} = 8.0$ as uncertainties, both growing with each measurement's age.
While the pressure change was assumed to be \SI{0.105}{$\frac{\text{\hpa}}{\text{\meter}}$}, all other barometer-parameters are determined automatically.
The step size $\mStepSize$ for the transition was configured to be \SI{70}{\centimeter} with an allowed derivation of \SI{10}{\percent}. The heading deviation was set to \SI{25}{\degree}.
The step size $\mStepSize$ for the transition was configured to be \SI{70}{\centimeter} with an allowed derivation of \SI{10}{\percent}.
The heading deviation was set to \SI{25}{\degree}.
The pedestrian's position (state) was estimated using the weighted arithmetic mean of
the particle set.
% wie für die kld gezogen? begründen warum wir nun keine parzenschätzung machen (weil ähnliche ergebnisse)
To calculate \eqref{equ:KLD} and thus the Kullback-Leibler divergence, we need to sample densities from both modes likewise.
@@ -39,6 +49,7 @@ The density of a specific point $\hat\mStateVec_{t} = \fPos{\mVertexA}$ is then
while $d^i_{\text{KL}}$ is the euclidean distance between the considered point's $\hat\mStateVec_{t}$ and all particles $\fPos{\vec{X}_t^{i,m_t}}$ of the mode. The variance $\sigma_{\text{KL}}$ is set to \SI{1}{m}.
It is well known, that the computation of the kernel density estimation is rather slow, thus we also used a much simpler estimation by assuming a multivariate Gaussian distribution for both modes.
Here, the mean is given by weighted arithmetic mean of the particles and the variance is defined by the sample covariance matrix.
Calculating a meaningful $D_{\text{KL}}$, both estimation methods performed almost identical and therefore we used the multivariate Gaussian distribution for both modes with $\lambda = 0.03$ for the upcoming experimental discussion.
% ground truth
The ground truth is measured by recording a timestamp at marked spots on the walking route. When passing a marker, the pedestrian clicked a button on the smartphone application.
@@ -46,21 +57,106 @@ Between two consecutive points, a constant movement speed is assumed.
Thus, the ground truth might not be \SI{100}{\percent} accurate, but fair enough for error measurements.
The approximation error is then calculated by comparing the interpolated ground truth position with the current estimation \cite{Fetzer2016OMC}.
% maß für die streuung der verteilung (diversity von partikeln)
error at the beginning always very high. about 44 meters. therefore the median is better value oder 75 quantil.
%error at the beginning always very high. about 44 meters. therefore the median is better value oder 75 quantil.
% zeigen das es stucken verhindert (eventl. hier eine andere aufnahme die mitten drinnen stecken bleibt)
% bild: stucken im raum + nicht mehr stucken im raum + kld mit anzeigen
\begin{figure}
\centering
\input{gfx/eval/path3.tex}
\input{gfx/eval/path3-kld.tex}
\caption{Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy }
\label{fig:path3}
\end{figure}
%
At first, we discuss the results of path 3, starting at the left-hand side of the building.
Exemplary estimation results, using the modes standalone and combined within the IMMPF, can be seen in fig. \ref{fig:path3}.
As mentioned above, every run of a walk starts with a uniform distribution as prior.
Due to a low Wi-Fi coverage at the starting point, the pedestrian's position is falsely estimated into a room instead of the corridor.
All three filters are able to overcome this false detection.
However, the common particle filter (red) gets then indissoluble captured within a room, because of its restrictive behaviour and the aftereffects of the initial Wi-Fi readings.
It provides an \SI{75}{\percent}-quantil of $\tilde{x}_{0.75} = \SI{3884}{\centimeter}$ and got captured in \SI{100}{\percent} of all runs.
As expected and discussed earlier, the simple transition (blue) is less prone to bad observations and provides not so accurate, but very robust results of $\tilde{x}_{0.75}= \SI{809}{\centimeter}$ and a standard deviation over all results of $\bar{\sigma} = \SI{529}{\centimeter}$.
Looking at $D_{\text{KL}}$ over time confirms our assumption made in section \ref{sec:immpf}.
It is clearly visible, that the Kullback-Leibler divergence between both modes (purple) is a very good indicator to observe, if the dominant filter gets stuck or loses track.
Following, the IMMPF (green) results in a very natural and straight path estimation and a low $D_{\text{KL}}$ between modes and no sticking.
The benefits of mixing both filtering schemes within the scenario of path 3 are thus obvious.
The IMMPF filters with an error of $\tilde{x}_{0.75} = \SI{667}{\centimeter}$ and $\bar{\sigma} = \SI{558}{\centimeter}$.
% zeigen das schlechtes wi-fi (zu hohe diversity) behoben wird.
% bild: lauf auf der rechten seite des gebäudes zeige mit und ohne wifi faktor (schlechtes wifi einzeichnen)
\begin{figure}[b]
\centering
\input{gfx/eval/path2.tex}
\input{gfx/eval/path2-wifi-quality.tex}
\caption{Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy }
\label{fig:path2}
\end{figure}
%
Next, we investigate the performance of our approach by considering the scenario in path 2.
Here, the overall Wi-Fi quality is rather low, especially in the zig-zag stairwell on the buildings back and the small entrance area at floor 1 (cf. fig. \ref{fig:paths}).
Path 2 starts in the second floor, walking town the centred stairs into the first floor, then making a right turn and walking the stairs down to zero floor, from there we walk back to second floor using the zig-zag stairwell and after finally crossing a room we are back at the start.
This is a very challenging scenario, at first the estimation got stuck on the first floor in a room's corner and after that the Wi-Fi is highly attenuated.
Looking at fig. \ref{fig:path2}, one can observe the impact of the Wi-Fi quality factor within the Markov transition matrix.
Without it, the position estimation (red) is drifting in the courtyard, missing the stairwell and producing high errors between \SI{80}{th} and \SI{130}{th} second.
As described before, the bad Wi-Fi readings are causing $D_{\text{KL}}$ to grow.
It follows that the accurate dominant filter draws new particles from the uncertain support and therefore worsen the position estimation.
In this scenario it is cold comfort that the system is able to recover thanks to its high diversity during situations with uncertain measurements.
Only by adding the Wi-Fi quality factor the system is able to improve the approximated path (green) and the overall estimation results from $\tilde{x}_{0.75} = \SI{1278}{\centimeter}$ with $\bar{\sigma} = \SI{948}{\centimeter}$ to $\tilde{x}_{0.75} = \SI{811}{\centimeter}$ with $\bar{\sigma} = \SI{340}{\centimeter}$.
However, this is far from perfect and in some cases ($\sim \SI{9}{\percent}$) the quality factor was not able to prevent the estimation to drift in the courtyard.
This solely happened when particles were sampled directly onto the courtyard while changing from first to zero floor.
Those particles then received a high weight due to the attenuated measurements, causing a weight degeneracy.
Adapting the bounds $l_{\text{max}}$ and $l_{\text{min}}$ of the quality factor or optimizing the access-points parameters can resolve this problem \cite{}.
% zeigen das immpf nicht viel schlechter als normaler pf (ohne stucken) ist.
% bild: er schafft es nicht die treppe rauf + er schafft es immpf + er schafft es normal filter
\begin{figure}[t]
\centering
\input{gfx/eval/path1.tex}
\input{gfx/eval/path1-time.tex}
\caption{Lorem Ipsum is simply dummy text of the printing and typesetting industry. Lorem Ipsum has been the industry's standard dummy }
\label{fig:path1}
\end{figure}
%
An exemplary result for path 1 is illustrated in fig. \ref{fig:path1}.
The path starts on the first floor and finishes on the third after walking two straight stairs.
Using the grid-based particle filter for localisation, we were able to provide an very accurate path (blue) in \SI{80}{\percent} of the MC runs providing $\tilde{x}_{0.75} = \SI{526}{\centimeter}$ with $\bar{\sigma} = \SI{316}{\centimeter}$.
Due to a lack of particles near the stairs, the other \SI{20}{\percent} failed to detect the first floor change (red).
Using our approach (green), we were able detect all floor changes and thus never lost track.
It performs with $\tilde{x}_{0.75} = \SI{544}{\centimeter}$ and $\bar{\sigma} = \SI{281}{\centimeter}$.
Those very similar estimation results confirm the efficiency of the mixing and how it is able to keep the accuracy while providing a higher robustness against failures.
% gegenüberstellung aller pfade und werte in tabelle
\definecolor{header}{rgb}{.8, .8, .8}
\begin{table}
\caption{Median error for all conducted walks.}
\label{tbl:err}
\centering
\begin{tabular}{|l|c|c|c|c|c|c|c|c|c|}
\hline
& \multicolumn{3}{c}{Path 1} & \multicolumn{3}{|c|}{Path 2} & \multicolumn{3}{|c|}{Path 3}\\
\hline
& $\bar{x}$ & $\bar{\sigma}$ & $\tilde{x}_{0.75}$ & $\bar{x}$ & $\bar{\sigma}$ & $\tilde{x}_{0.75}$ & $\bar{x}$ & $\bar{\sigma}$ & $\tilde{x}_{0.75}$ \\
\hline
PF_{\text{grid}}& $x$ & $x$ & $x$ & $x$ & $x$ & $x$ & $x$ & $x$ & $x$ \\
\hline
PF_{\text{simple}}& $x$ & $x$ & $x$ & $x$ & $x$ & $x$ & $x$ & $x$ & $x$ \\
\hline
IMMPF & $x$ & $x$ & $x$ & $x$ & $x$ & $x$ & $x$ & $x$ & $x$ \\
\hline
\end{tabular}
\end{table}
An overview of all localisation results can be seen in table \ref{tbl:err}.
Again, it should be noted that the localisation system used for the experiments is very basic and can be seen as a slimmed version of our previous works \cite{}.
Optimizing the Wi-Fi parameters and adding additional methods will improve the localisation results significantly.
More importantly, the here presented approach was able to recover in all situations and thus never got completely stuck within a demarcated area.
All results were similar or more accurate then the ones provided by the standalone filters, even when the localisation did not suffer from any problems.
%how the Markov transition matrix regulates the impact of the supporting filter in the right amount.

1454
tex/gfx/eval/path1-time.eps Executable file
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File diff suppressed because it is too large Load Diff

617
tex/gfx/eval/path1-time.gp Executable file
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@@ -0,0 +1,617 @@
set terminal epslatex color dashed size 3.38583,1.29921
set output "/mnt/vm/paper/OTHER2017/for_toni/out//path1-time.tex"
set xtics autofreq
set format x '\footnotesize{%h}'
set xlabel '\footnotesize{time (seconds)}' offset 0,0.3
unset x2tics
unset x2label
set yrange [0.000000:15.000000]
set ytics 3.000000
set format y '\footnotesize{%h}'
set ylabel '\footnotesize{error (meter)}' offset 2.5,0
unset y2tics
unset y2label
set grid
set key opaque samplen 1 right top width -4
set lmargin 4.3
set rmargin 0.2
set tmargin 0.1
set bmargin 2
plot '-' with lines linecolor rgb '#0000ff' linewidth 1.500000 dashtype 1 title '\footnotesize{PF (good)}' axes x1y1 , '-' with lines linecolor rgb '#00ff00' linewidth 1.500000 dashtype 1 title '\footnotesize{IMMPF}' axes x1y1 , '-' with lines linecolor rgb '#ff0000' linewidth 1.500000 dashtype 1 title '\footnotesize{PF (bad)}' axes x1y1 ,
0 29.1668
0.5 11.6316
1 10.2128
1.5 9.74814
2 9.34261
2.5 9.39509
3 9.05017
3.5 8.84955
4 8.55709
4.5 8.31611
5 8.08367
5.5 8.00224
6 8.0398
6.5 7.87502
7 7.86332
7.5 7.6833
8 7.42124
8.5 6.48534
9 6.09727
9.5 5.70414
10 5.42138
10.5 5.11964
11 4.99812
11.5 4.70494
12 4.33738
12.5 4.16511
13 3.93357
13.5 3.74014
14 3.4985
14.5 3.14284
15 3.38153
15.5 4.53088
16 4.81591
16.5 5.02615
17 4.96308
17.5 4.59334
18 4.34389
18.5 4.18784
19 3.90874
19.5 3.63752
20 3.39695
20.5 3.01859
21 2.7376
21.5 2.45909
22 2.1811
22.5 1.79169
23 1.4758
23.5 1.20587
24 0.917463
24.5 0.764496
25 0.605617
25.5 0.601277
26 0.716062
26.5 0.949812
27 1.07112
27.5 1.44326
28 1.49711
28.5 1.48652
29 1.02773
29.5 1.03352
30 1.0778
30.5 1.15188
31 1.37333
31.5 1.51402
32 1.75634
32.5 2.14538
33 2.47978
33.5 2.75338
34 3.042
34.5 3.31619
35 3.48865
35.5 3.05748
36 0.786165
36.5 2.03559
37 2.36072
37.5 2.31036
38 2.22851
38.5 2.09333
39 1.84259
39.5 1.61101
40 1.34202
40.5 1.0714
41 0.853001
41.5 0.725106
42 0.696079
42.5 0.793333
43 1.01948
43.5 1.23781
44 1.42128
44.5 1.61879
45 1.77851
45.5 1.98664
46 2.05386
46.5 1.9643
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47.5 2.03714
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48.5 2.67713
49 3.17032
49.5 3.80009
50 4.26093
50.5 4.81178
51 5.38053
51.5 5.94291
52 6.58634
52.5 7.1211
53 7.72214
53.5 8.22617
54 8.75811
54.5 8.87446
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55.5 8.99755
56 8.91654
56.5 8.70647
57 8.42571
57.5 7.9835
58 8.14601
58.5 7.95408
59 7.57623
59.5 7.04313
60 6.65536
60.5 6.24699
61 6.5037
61.5 6.22684
62 5.93405
62.5 5.59862
63 5.3826
63.5 5.84229
64 5.54944
64.5 5.30337
65 5.01541
65.5 4.63842
66 4.19257
66.5 4.16871
67 3.67205
67.5 3.2661
68 2.87546
68.5 2.60504
69 2.93793
69.5 2.85513
70 2.79062
70.5 2.56077
71 2.46195
71.5 2.35365
72 2.5718
72.5 2.2802
73 2.10541
73.5 2.06427
74 2.04606
74.5 2.108
75 2.17339
75.5 1.97367
76 1.72986
76.5 1.65501
77 1.38293
77.5 1.34031
78 1.13435
78.5 1.22212
79 1.12113
79.5 1.00369
80 0.705503
80.5 1.04979
81 0.855131
81.5 0.808121
82 0.81775
82.5 0.866265
83 0.871328
83.5 1.36589
84 1.13568
84.5 1.1479
85 1.08519
85.5 1.18977
86 1.1685
86.5 1.63406
87 1.69501
87.5 1.55964
88 1.35852
88.5 1.12659
89 1.27025
89.5 1.06438
90 1.03155
90.5 0.9086
91 0.754012
91.5 0.902826
92 0.780396
92.5 0.760737
93 0.696015
93.5 0.773882
94 1.12057
94.5 1.12057
e
0 26.2437
0.5 12.8498
1 11.024
1.5 10.6972
2 10.5548
2.5 10.4043
3 10.1949
3.5 10.2909
4 10.3893
4.5 10.4647
5 10.0473
5.5 9.65996
6 9.34478
6.5 9.18746
7 8.69
7.5 8.20884
8 7.86488
8.5 7.42611
9 6.96206
9.5 6.39218
10 5.95967
10.5 5.49403
11 5.25366
11.5 4.84596
12 4.4542
12.5 4.10828
13 3.81587
13.5 3.76986
14 3.50454
14.5 3.31728
15 3.27288
15.5 3.67125
16 4.38447
16.5 4.99138
17 5.24937
17.5 5.33139
18 5.02794
18.5 4.9746
19 4.90096
19.5 5.11832
20 5.12293
20.5 5.22722
21 5.38345
21.5 5.33466
22 5.31933
22.5 5.10233
23 5.21385
23.5 5.14401
24 5.35493
24.5 5.27135
25 5.49211
25.5 5.6808
26 5.9894
26.5 5.96252
27 6.19049
27.5 5.9796
28 5.88978
28.5 5.44923
29 5.01207
29.5 4.94766
30 4.56213
30.5 4.17241
31 4.2799
31.5 4.36084
32 4.65659
32.5 5.34477
33 5.82144
33.5 5.81139
34 5.82742
34.5 5.61091
35 5.33078
35.5 5.07171
36 4.81134
36.5 4.48861
37 4.30611
37.5 4.07908
38 3.87895
38.5 3.56325
39 3.31669
39.5 3.04869
40 2.75216
40.5 2.5083
41 2.24089
41.5 1.96629
42 1.72239
42.5 1.49381
43 1.20818
43.5 0.985968
44 0.849934
44.5 0.771279
45 0.814509
45.5 0.967511
46 0.966517
46.5 0.904176
47 1.34459
47.5 1.80965
48 1.74528
48.5 1.92738
49 2.17443
49.5 2.32521
50 2.09174
50.5 2.38807
51 2.70073
51.5 2.34883
52 2.33251
52.5 2.31544
53 2.39796
53.5 2.4732
54 2.16275
54.5 1.91952
55 2.06186
55.5 2.2352
56 2.45439
56.5 2.39521
57 2.39349
57.5 2.39714
58 2.45876
58.5 2.48195
59 2.57504
59.5 2.65016
60 2.77777
60.5 2.9007
61 3.17483
61.5 3.16315
62 3.42473
62.5 3.68636
63 3.91929
63.5 4.16612
64 4.29741
64.5 4.11238
65 4.24851
65.5 4.36475
66 4.60441
66.5 4.78642
67 4.49453
67.5 4.66655
68 4.62524
68.5 4.65164
69 4.21202
69.5 4.35684
70 4.36084
70.5 4.46367
71 4.5158
71.5 4.04398
72 4.20174
72.5 4.2305
73 4.29608
73.5 4.35748
74 4.20325
74.5 4.13695
75 3.98376
75.5 3.89505
76 3.92486
76.5 4.04962
77 3.99406
77.5 4.19799
78 4.47754
78.5 4.81633
79 4.73471
79.5 3.93321
80 3.54553
80.5 2.6374
81 2.24239
81.5 2.18865
82 2.01895
82.5 1.93168
83 1.69827
83.5 1.21597
84 1.11463
84.5 0.986728
85 0.854302
85.5 0.865358
86 1.13848
86.5 1.44028
87 1.64155
87.5 1.86381
88 2.31665
88.5 2.66694
89 2.62039
89.5 2.98849
90 2.71409
90.5 2.53784
91 2.8018
91.5 2.82705
92 2.46118
92.5 2.04663
93 2.11185
93.5 1.61724
94 1.38254
94.5 1.25669
95 1.55395
95.5 1.24532
96 1.11499
96.5 1.05108
97 1.12895
97.5 1.86952
98 2.73255
98.5 3.24558
99 4.15926
99.5 4.15926
e
0 29.5556
0.5 13.3102
1 10.1264
1.5 9.07331
2 8.49031
2.5 8.11966
3 7.85434
3.5 7.62143
4 7.67484
4.5 8.01264
5 8.24019
5.5 8.30282
6 8.28996
6.5 8.56366
7 8.6518
7.5 8.61524
8 8.48531
8.5 8.16305
9 8.42124
9.5 8.237
10 8.17581
10.5 8.02198
11 7.35719
11.5 6.6522
12 6.20554
12.5 5.71834
13 5.2016
13.5 5.77752
14 4.48564
14.5 3.65346
15 2.98181
15.5 2.562
16 3.17028
16.5 2.76856
17 4.83808
17.5 8.59553
18 9.60292
18.5 10.0396
19 10.1362
19.5 10.5114
20 10.5223
20.5 10.645
21 10.6585
21.5 10.8138
22 10.6796
22.5 10.6699
23 10.7855
23.5 10.6712
24 10.3308
24.5 9.71392
25 9.36427
25.5 9.01536
26 8.5206
26.5 8.07526
27 7.73007
27.5 7.41328
28 7.12922
28.5 6.73203
29 6.37419
29.5 6.22036
30 6.09736
30.5 6.00089
31 5.80289
31.5 5.50559
32 5.41869
32.5 5.37924
33 5.2886
33.5 5.25041
34 5.19367
34.5 5.09686
35 5.02554
35.5 5.03853
36 4.99254
36.5 5.04511
37 4.94632
37.5 4.87316
38 4.73606
38.5 4.68232
39 4.66752
39.5 4.6091
40 4.43919
40.5 4.58321
41 5.72669
41.5 7.33098
42 8.06384
42.5 8.07509
43 8.24887
43.5 8.48035
44 8.19151
44.5 8.29384
45 8.06327
45.5 7.90187
46 7.52695
46.5 7.55486
47 7.68559
47.5 7.74938
48 7.58331
48.5 7.6776
49 7.75357
49.5 7.88098
50 7.85943
50.5 8.15009
51 8.41695
51.5 8.37477
52 8.47293
52.5 8.58861
53 8.72836
53.5 8.92246
54 8.94162
54.5 9.07386
55 9.27395
55.5 9.44222
56 9.63087
56.5 9.69
57 9.96572
57.5 10.1888
58 10.5297
58.5 10.7611
59 11.2903
59.5 11.4246
60 11.7431
60.5 11.5697
61 10.2123
61.5 8.46815
62 7.55504
62.5 7.50106
63 7.6269
63.5 7.78617
64 7.79366
64.5 7.59865
65 7.58353
65.5 7.50437
66 7.48414
66.5 7.28797
67 7.12839
67.5 7.05964
68 6.93637
68.5 6.86925
69 6.84725
69.5 6.84186
70 6.82544
70.5 6.80564
71 6.80053
71.5 6.81689
72 6.80295
72.5 6.80444
73 6.80685
73.5 6.8133
74 6.86771
74.5 6.87548
75 6.88196
75.5 6.91905
76 6.90703
76.5 6.95847
77 7.05938
77.5 7.0889
78 7.14634
78.5 7.21662
79 7.28326
79.5 7.21443
80 7.134
80.5 7.01858
81 6.87917
81.5 6.79338
82 6.45476
82.5 5.13587
83 4.97396
83.5 4.76141
84 4.58683
84.5 4.4757
85 4.50247
85.5 4.54596
86 4.29589
86.5 4.3642
87 4.45278
87.5 4.53018
88 4.57392
88.5 4.30883
89 4.28239
89.5 4.12876
90 3.93727
90.5 3.80566
91 3.60028
91.5 3.51017
92 3.45539
92.5 3.41999
93 3.46701
93.5 3.64712
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97.5 5.5051
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99 6.21296
99.5 6.21296
e

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set terminal epslatex color dashed size 3.38583,0.984252
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}{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}%
\renewcommand\includegraphics[2][]{}%
}%
\providecommand\rotatebox[2]{#2}%
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% no textcolor at all
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% gray or color?
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% GNUPLOT: LaTeX picture with Postscript
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Package color not loaded in conjunction with
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}{Either use 'blacktext' in gnuplot or load the package
color.sty in LaTeX.}%
\renewcommand\color[2][]{}%
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\providecommand\includegraphics[2][]{%
\GenericError{(gnuplot) \space\space\space\@spaces}{%
Package graphicx or graphics not loaded%
}{See the gnuplot documentation for explanation.%
}{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}%
\renewcommand\includegraphics[2][]{}%
}%
\providecommand\rotatebox[2]{#2}%
\@ifundefined{ifGPcolor}{%
\newif\ifGPcolor
\GPcolortrue
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\@ifundefined{ifGPblacktext}{%
\newif\ifGPblacktext
\GPblacktexttrue
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% define a \g@addto@macro without @ in the name:
\let\gplgaddtomacro\g@addto@macro
% define empty templates for all commands taking text:
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\gdef\gplfronttext{}%
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\ifGPblacktext
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\expandafter\def\csname LTw\endcsname{\color{white}}%
\expandafter\def\csname LTb\endcsname{\color{black}}%
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\expandafter\def\csname LT0\endcsname{\color[rgb]{1,0,0}}%
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% gray
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\def\colorgray#1{\color[gray]{#1}}%
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\put(4431,572){\makebox(0,0)[r]{\strut{}\footnotesize{PF simple}}}%
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\put(4431,352){\makebox(0,0)[r]{\strut{}\footnotesize{IMMPF}}}%
\csname LTb\endcsname%
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}%
\gplbacktext
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\gplfronttext
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% GNUPLOT: LaTeX picture with Postscript
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Package color not loaded in conjunction with
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}{See the gnuplot documentation for explanation.%
}{Either use 'blacktext' in gnuplot or load the package
color.sty in LaTeX.}%
\renewcommand\color[2][]{}%
}%
\providecommand\includegraphics[2][]{%
\GenericError{(gnuplot) \space\space\space\@spaces}{%
Package graphicx or graphics not loaded%
}{See the gnuplot documentation for explanation.%
}{The gnuplot epslatex terminal needs graphicx.sty or graphics.sty.}%
\renewcommand\includegraphics[2][]{}%
}%
\providecommand\rotatebox[2]{#2}%
\@ifundefined{ifGPcolor}{%
\newif\ifGPcolor
\GPcolortrue
}{}%
\@ifundefined{ifGPblacktext}{%
\newif\ifGPblacktext
\GPblacktexttrue
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% define a \g@addto@macro without @ in the name:
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% define empty templates for all commands taking text:
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\gdef\gplfronttext{}%
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\ifGPblacktext
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% gray or color?
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\expandafter\def\csname LTw\endcsname{\color{white}}%
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\expandafter\def\csname LTa\endcsname{\color{black}}%
\expandafter\def\csname LT0\endcsname{\color[rgb]{1,0,0}}%
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\expandafter\def\csname LT5\endcsname{\color[rgb]{1,1,0}}%
\expandafter\def\csname LT6\endcsname{\color[rgb]{0,0,0}}%
\expandafter\def\csname LT7\endcsname{\color[rgb]{1,0.3,0}}%
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% gray
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\def\colorgray#1{\color[gray]{#1}}%
\expandafter\def\csname LTw\endcsname{\color{white}}%
\expandafter\def\csname LTb\endcsname{\color{black}}%
\expandafter\def\csname LTa\endcsname{\color{black}}%
\expandafter\def\csname LT0\endcsname{\color{black}}%
\expandafter\def\csname LT1\endcsname{\color{black}}%
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\expandafter\def\csname LT3\endcsname{\color{black}}%
\expandafter\def\csname LT4\endcsname{\color{black}}%
\expandafter\def\csname LT5\endcsname{\color{black}}%
\expandafter\def\csname LT6\endcsname{\color{black}}%
\expandafter\def\csname LT7\endcsname{\color{black}}%
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\csname LTb\endcsname%
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\csname LTb\endcsname%
\put(4431,1948){\makebox(0,0)[r]{\strut{}path 3}}%
}%
\gplbacktext
\put(0,0){\includegraphics{gfx/eval/paths}}%
\gplfronttext
\end{picture}%
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