SN-Markov-Graphen ausgebaut.

diff --git a/diplomarbeit.tex b/diplomarbeit.tex
index a1145c4..2f8aed2 100644 (file)
--- a/diplomarbeit.tex
+++ b/diplomarbeit.tex
@@ -1012,7 +1012,7 @@ sich die Resultate auch in der ersten Schicht nicht unterscheiden.
 
 \begin{figure}
   \begin{center}
 
 \begin{figure}
   \begin{center}

-    \includegraphics[viewport=0 0 360 216,width=15cm]{images/count-cuts-16.pdf}
+    \includegraphics[viewport=0 0 425 262,width=15cm]{images/count-cuts-16.pdf}

   \end{center}
   \caption{Anzahl der \emph{unterschiedlichen} Sortiernetzwerke, die durch
   8-Schnittmuster aus $\operatorname{OES}(16)$, $\operatorname{BS}(16)$ und
   \end{center}
   \caption{Anzahl der \emph{unterschiedlichen} Sortiernetzwerke, die durch
   8-Schnittmuster aus $\operatorname{OES}(16)$, $\operatorname{BS}(16)$ und


@@ -1071,7 +1071,7 @@ unterschiedlichen Schnittmuster abschätzen.
 
 \begin{figure}
   \begin{center}
 
 \begin{figure}
   \begin{center}

-    \includegraphics[viewport=0 0 360 216,width=15cm]{images/collisions-10000-1000000-32.pdf}
+    \includegraphics[viewport=0 0 425 262,width=15cm]{images/collisions-10000-1000000-32.pdf}

   \end{center}
   \caption{Abschnätzung der unterschiedlichen Schnittmuster mit der
   \emph{Monte-Carlo-Methode} für $\operatorname{OES}(32)$ und
   \end{center}
   \caption{Abschnätzung der unterschiedlichen Schnittmuster mit der
   \emph{Monte-Carlo-Methode} für $\operatorname{OES}(32)$ und


@@ -1194,21 +1194,21 @@ Algorithmus vorschnell in Richtung eines lokalen Optimums optimiert.
 Die in \textsc{SN-Evolution} implementierte Selektion lässt sich mithilfe von
 Pseudocode wie folgt beschreiben:
 \begin{verbatim}
 Die in \textsc{SN-Evolution} implementierte Selektion lässt sich mithilfe von
 Pseudocode wie folgt beschreiben:
 \begin{verbatim}

-Guetesumme := 0
+Gütesumme := 0

 Auswahl := (leer)
 
 Auswahl := (leer)
 

-fuer jedes Individuum in Population
+für jedes Individuum in Population

 {
 {

-  reziproke Guete := 1.0 / Guete(Individuum)
-  Wahrscheinlichkeit P := reziproke Guete / (reziproke Guete + Guetesumme)
-  Guetesumme := Guetesumme + reziproke Guete
+  reziproke Güte := 1.0 / Guete(Individuum)
+  Wahrscheinlichkeit P := reziproke Güte / (reziproke Güte + Gütesumme)
+  Gütesumme := Gütesumme + reziproke Güte

 
   mit Wahrscheinlichkeit P
   {
     Auswahl := Individuum
   }
 }
 
   mit Wahrscheinlichkeit P
   {
     Auswahl := Individuum
   }
 }

-gebe Auswahl zurueck
+gib Auswahl zurück

 \end{verbatim}
 
 \subsection{Rekombination}
 \end{verbatim}
 
 \subsection{Rekombination}


@@ -1543,13 +1543,17 @@ gegebenen Sortiernetzwerk. Um von einem Sortiernetzwerk zum Nächsten zu
 gelangen, rekombiniert der Algorithmus das aktuelle Sortiernetzwerk mit sich
 selbst und erhält so einen zufälligen Nachfolger.
 
 gelangen, rekombiniert der Algorithmus das aktuelle Sortiernetzwerk mit sich
 selbst und erhält so einen zufälligen Nachfolger.
 

-\begin{itemize}
-  \item $n \leftarrow \mathrm{Input}$
-  \item \texttt{while} \textit{true}
-  \begin{itemize}
-    \item $n \leftarrow \operatorname{recombine} (n, n)$
-  \end{itemize}
-\end{itemize}
+\begin{verbatim}
+  Netzwerk := Eingabe
+
+  für n Iterationen
+  {
+    Nachfolger := kombiniere (Netzwerk, Netzwerk)
+    Netzwerk   := Nachfolger
+  }
+
+  gib Netzwerk zurück
+\end{verbatim}

 
 \begin{itemize}
   \item Beste erreichte Netzwerke (gleich zu \emph{OE-Mergesort}).
 
 \begin{itemize}
   \item Beste erreichte Netzwerke (gleich zu \emph{OE-Mergesort}).


@@ -1560,7 +1564,7 @@ selbst und erhält so einen zufälligen Nachfolger.
 
 \begin{figure}
   \begin{center}
 
 \begin{figure}
   \begin{center}

-  \includegraphics[viewport=0 0 360 216,width=15cm]{images/markov-comparators-12-pct.pdf}
+  \includegraphics[viewport=0 0 425 262,width=15cm]{images/markov-comparators-12-pct.pdf}

   \end{center}
   \caption{Anzahl der Komparatoren von Sortiernetzwerken (mit 12~Leitungen),
   die von {\sc SN-Markov} durchlaufen wurden. Grün eingezeichnet ist die
   \end{center}
   \caption{Anzahl der Komparatoren von Sortiernetzwerken (mit 12~Leitungen),
   die von {\sc SN-Markov} durchlaufen wurden. Grün eingezeichnet ist die


@@ -1570,7 +1574,7 @@ selbst und erhält so einen zufälligen Nachfolger.
 
 \begin{figure}
   \begin{center}
 
 \begin{figure}
   \begin{center}

-  \includegraphics[viewport=0 0 360 216,width=15cm]{images/markov-comparators-14-pct.pdf}
+  \includegraphics[viewport=0 0 425 262,width=15cm]{images/markov-comparators-14-pct.pdf}

   \end{center}
   \caption{Anzahl der Komparatoren von Sortiernetzwerken (mit 14~Leitungen),
   die von {\sc SN-Markov} durchlaufen wurden. Grün eingezeichnet ist die
   \end{center}
   \caption{Anzahl der Komparatoren von Sortiernetzwerken (mit 14~Leitungen),
   die von {\sc SN-Markov} durchlaufen wurden. Grün eingezeichnet ist die


@@ -1580,7 +1584,7 @@ selbst und erhält so einen zufälligen Nachfolger.
 
 \begin{figure}
   \begin{center}
 
 \begin{figure}
   \begin{center}

-  \includegraphics[viewport=0 0 360 216,width=15cm]{images/markov-comparators-16-pct.pdf}
+  \includegraphics[viewport=0 0 425 262,width=15cm]{images/markov-comparators-16-pct.pdf}

   \end{center}
   \caption{Anzahl der Komparatoren von Sortiernetzwerken (mit 16~Leitungen),
   die von {\sc SN-Markov} durchlaufen wurden. Grün eingezeichnet ist die
   \end{center}
   \caption{Anzahl der Komparatoren von Sortiernetzwerken (mit 16~Leitungen),
   die von {\sc SN-Markov} durchlaufen wurden. Grün eingezeichnet ist die


@@ -1588,6 +1592,16 @@ selbst und erhält so einen zufälligen Nachfolger.
   \label{fig:markov-comparators-16}
 \end{figure}
 
   \label{fig:markov-comparators-16}
 \end{figure}
 

+\begin{figure}
+  \begin{center}
+  \includegraphics[viewport=0 0 425 262,width=15cm]{images/markov-comparators-18-pct.pdf}
+  \end{center}
+  \caption{Anzahl der Komparatoren von Sortiernetzwerken (mit 18~Leitungen),
+  die von {\sc SN-Markov} durchlaufen wurden. Grün eingezeichnet ist die
+  \emph{Gamma-Verteilung} $f(x - 81)$ mit $k = 10,724$ und $\theta = 0,766$.}
+  \label{fig:markov-comparators-18}
+\end{figure}
+

 \newpage
 \section{Empirische Beobachtungen}
 
 \newpage
 \section{Empirische Beobachtungen}
 

diff --git a/images/markov-comparators-12-pct.gnuplot b/images/markov-comparators-12-pct.gnuplot
index 718b7a0..bde07ad 100644 (file)
--- a/images/markov-comparators-12-pct.gnuplot
+++ b/images/markov-comparators-12-pct.gnuplot
@@ -13,8 +13,8 @@
 #      faq, bugs, etc:   type "help seeking-assistance"
 #      immediate help:   type "help"
 #      plot window:      hit 'h'
 #      faq, bugs, etc:   type "help seeking-assistance"
 #      immediate help:   type "help"
 #      plot window:      hit 'h'

-# set terminal wxt 0
-# set output
+set terminal pdfcairo  size 15.00cm, 9.27cm 
+set output 'markov-comparators-12-pct.pdf'

 unset clip points
 set clip one
 unset clip two
 unset clip points
 set clip one
 unset clip two


@@ -44,7 +44,7 @@ set format cb "% g"
 set angles radians
 unset grid
 set key title ""
 set angles radians
 unset grid
 set key title ""

-set key inside right top vertical Right noreverse enhanced autotitles nobox
+set key outside center bottom horizontal Right noreverse enhanced autotitles box linetype -1 linewidth 1.000

 set key noinvert samplen 4 spacing 1 width 0 height 0 
 unset label
 unset arrow
 set key noinvert samplen 4 spacing 1 width 0 height 0 
 unset label
 unset arrow


@@ -105,8 +105,8 @@ set timestamp ""
 set timestamp  offset character 0, 0, 0 font "" norotate
 set rrange [ * : * ] noreverse nowriteback  # (currently [8.98847e+307:-8.98847e+307] )
 set trange [ * : * ] noreverse nowriteback  # (currently [-5.00000:5.00000] )
 set timestamp  offset character 0, 0, 0 font "" norotate
 set rrange [ * : * ] noreverse nowriteback  # (currently [8.98847e+307:-8.98847e+307] )
 set trange [ * : * ] noreverse nowriteback  # (currently [-5.00000:5.00000] )

-set urange [ * : * ] noreverse nowriteback  # (currently [-5.00000:5.00000] )
-set vrange [ * : * ] noreverse nowriteback  # (currently [-5.00000:5.00000] )
+set urange [ * : * ] noreverse nowriteback  # (currently [-10.0000:10.0000] )
+set vrange [ * : * ] noreverse nowriteback  # (currently [-10.0000:10.0000] )

 set xlabel "Komparatoren" 
 set xlabel  offset character 0, 0, 0 font "" textcolor lt -1 norotate
 set x2label "" 
 set xlabel "Komparatoren" 
 set xlabel  offset character 0, 0, 0 font "" textcolor lt -1 norotate
 set x2label "" 


@@ -121,7 +121,7 @@ set yrange [ * : * ] noreverse nowriteback  # (currently [0.00000:16.0000] )
 set y2range [ * : * ] noreverse nowriteback  # (currently [0.00000:14.0879] )
 set zlabel "" 
 set zlabel  offset character 0, 0, 0 font "" textcolor lt -1 norotate
 set y2range [ * : * ] noreverse nowriteback  # (currently [0.00000:14.0879] )
 set zlabel "" 
 set zlabel  offset character 0, 0, 0 font "" textcolor lt -1 norotate

-set zrange [ * : * ] noreverse nowriteback  # (currently [8.98847e+307:-8.98847e+307] )
+set zrange [ * : * ] noreverse nowriteback  # (currently [-10.0000:10.0000] )

 set cblabel "" 
 set cblabel  offset character 0, 0, 0 font "" textcolor lt -1 rotate by -270
 set cbrange [ * : * ] noreverse nowriteback  # (currently [8.98847e+307:-8.98847e+307] )
 set cblabel "" 
 set cblabel  offset character 0, 0, 0 font "" textcolor lt -1 rotate by -270
 set cbrange [ * : * ] noreverse nowriteback  # (currently [8.98847e+307:-8.98847e+307] )


@@ -144,9 +144,9 @@ set fit noerrorvariables
 gamma_gamma(x) = (floor(x - 0.5))!
 gamma_dist(x) = x**(gamma_k - 1) * exp((-1.0) * x / gamma_theta) / (gamma_theta**gamma_k * gamma(gamma_k))
 gamma_fit(x) = 100.0 * dgamma(x - gamma_offset, gamma_k, gamma_theta)
 gamma_gamma(x) = (floor(x - 0.5))!
 gamma_dist(x) = x**(gamma_k - 1) * exp((-1.0) * x / gamma_theta) / (gamma_theta**gamma_k * gamma(gamma_k))
 gamma_fit(x) = 100.0 * dgamma(x - gamma_offset, gamma_k, gamma_theta)

+dgamma(x, shape, rate) = (x<0)? 0 : (x==0)? ((shape<1)? 1/0 : (shape==1)? rate : 0) : (rate==0)? 0 : exp(_ln_dgamma(x, shape, rate))

 _ln_dgamma(x, a, b) = a*log(b) - lgamma(a) + (a-1)*log(x) - b*x
 pgamma(x, shape, rate) = (x<0)? 0 : igamma(shape, x*rate)
 _ln_dgamma(x, a, b) = a*log(b) - lgamma(a) + (a-1)*log(x) - b*x
 pgamma(x, shape, rate) = (x<0)? 0 : igamma(shape, x*rate)

-dgamma(x, shape, rate) = (x<0)? 0 : (x==0)? ((shape<1)? 1/0 : (shape==1)? rate : 0) : (rate==0)? 0 : exp(_ln_dgamma(x, shape, rate))

 GNUTERM = "wxt"
 GPFUN_gamma_gamma = "gamma_gamma(x) = (floor(x - 0.5))!"
 gamma_k = 8.26729758801638
 GNUTERM = "wxt"
 GPFUN_gamma_gamma = "gamma_gamma(x) = (floor(x - 0.5))!"
 gamma_k = 8.26729758801638


@@ -154,13 +154,12 @@ gamma_theta = 0.961930249498844
 GPFUN_gamma_dist = "gamma_dist(x) = x**(gamma_k - 1) * exp((-1.0) * x / gamma_theta) / (gamma_theta**gamma_k * gamma(gamma_k))"
 gamma_offset = 40
 GPFUN_gamma_fit = "gamma_fit(x) = 100.0 * dgamma(x - gamma_offset, gamma_k, gamma_theta)"
 GPFUN_gamma_dist = "gamma_dist(x) = x**(gamma_k - 1) * exp((-1.0) * x / gamma_theta) / (gamma_theta**gamma_k * gamma(gamma_k))"
 gamma_offset = 40
 GPFUN_gamma_fit = "gamma_fit(x) = 100.0 * dgamma(x - gamma_offset, gamma_k, gamma_theta)"

+GPFUN__ln_dgamma = "_ln_dgamma(x, a, b) = a*log(b) - lgamma(a) + (a-1)*log(x) - b*x"
+GPFUN_pgamma = "pgamma(x, shape, rate) = (x<0)? 0 : igamma(shape, x*rate)"
+GPFUN_dgamma = "dgamma(x, shape, rate) = (x<0)? 0 : (x==0)? ((shape<1)? 1/0 : (shape==1)? rate : 0) : (rate==0)? 0 : exp(_ln_dgamma(x, shape, rate))"

 FIT_CONVERGED = 1
 FIT_NDF = 39
 FIT_STDFIT = 0.222936770551606
 FIT_WSSR = 1.9383313428952
 FIT_CONVERGED = 1
 FIT_NDF = 39
 FIT_STDFIT = 0.222936770551606
 FIT_WSSR = 1.9383313428952

-GPFUN__ln_dgamma = "_ln_dgamma(x, a, b) = a*log(b) - lgamma(a) + (a-1)*log(x) - b*x"
-GPFUN_pgamma = "pgamma(x, shape, rate) = (x<0)? 0 : igamma(shape, x*rate)"
-GPFUN_dgamma = "dgamma(x, shape, rate) = (x<0)? 0 : (x==0)? ((shape<1)? 1/0 : (shape==1)? rate : 0) : (rate==0)? 0 : exp(_ln_dgamma(x, shape, rate))"
-plot [x=41:81] './images/markov-comparators-12-pct.data' title 'Gemessene Daten', gamma_fit(x) title 'Gamma-Verteilung'
-## fit gamma_fit(x) 'images/markov-comparators-12-pct.data' via gamma_k, gamma_theta
+plot [x=41:81] 'markov-comparators-12-pct.data' title 'Gemessene Daten', gamma_fit(x) title 'Gamma-Verteilung'

 #    EOF
 #    EOF

diff --git a/images/markov-comparators-14-pct.gnuplot b/images/markov-comparators-14-pct.gnuplot
index d8a3937..21e29ae 100644 (file)
--- a/images/markov-comparators-14-pct.gnuplot
+++ b/images/markov-comparators-14-pct.gnuplot
@@ -13,8 +13,8 @@
 #      faq, bugs, etc:   type "help seeking-assistance"
 #      immediate help:   type "help"
 #      plot window:      hit 'h'
 #      faq, bugs, etc:   type "help seeking-assistance"
 #      immediate help:   type "help"
 #      plot window:      hit 'h'

-# set terminal wxt 0
-# set output
+set terminal pdfcairo  size 15.00cm, 9.27cm 
+set output 'markov-comparators-14-pct.pdf'

 unset clip points
 set clip one
 unset clip two
 unset clip points
 set clip one
 unset clip two


@@ -44,7 +44,7 @@ set format cb "% g"
 set angles radians
 unset grid
 set key title ""
 set angles radians
 unset grid
 set key title ""

-set key inside right top vertical Right noreverse enhanced autotitles nobox
+set key outside center bottom horizontal Right noreverse enhanced autotitles box linetype -1 linewidth 1.000

 set key noinvert samplen 4 spacing 1 width 0 height 0 
 unset label
 unset arrow
 set key noinvert samplen 4 spacing 1 width 0 height 0 
 unset label
 unset arrow


@@ -157,6 +157,6 @@ FIT_CONVERGED = 1
 FIT_NDF = 47
 FIT_STDFIT = 0.125963571262577
 FIT_WSSR = 0.745740600405454
 FIT_NDF = 47
 FIT_STDFIT = 0.125963571262577
 FIT_WSSR = 0.745740600405454

-plot [x=53:101] 'images/markov-comparators-14-pct.data' title 'Gemessene Daten', gamma_fit(x) title 'Gamma-Verteilung'
-## fit gamma_fit(x) 'images/markov-comparators-14-pct.data' via gamma_k, gamma_theta
+plot [x=53:101] 'markov-comparators-14-pct.data' title 'Gemessene Daten', gamma_fit(x) title 'Gamma-Verteilung'
+## fit gamma_fit(x) 'markov-comparators-14-pct.data' via gamma_k, gamma_theta

 #    EOF
 #    EOF

diff --git a/images/markov-comparators-16-pct.gnuplot b/images/markov-comparators-16-pct.gnuplot
index 0751469..4e93bc4 100644 (file)
--- a/images/markov-comparators-16-pct.gnuplot
+++ b/images/markov-comparators-16-pct.gnuplot
@@ -13,8 +13,8 @@
 #      faq, bugs, etc:   type "help seeking-assistance"
 #      immediate help:   type "help"
 #      plot window:      hit 'h'
 #      faq, bugs, etc:   type "help seeking-assistance"
 #      immediate help:   type "help"
 #      plot window:      hit 'h'

-# set terminal wxt 0
-# set output
+set terminal pdfcairo  size 15.00cm, 9.27cm 
+set output 'markov-comparators-16-pct.pdf'

 unset clip points
 set clip one
 unset clip two
 unset clip points
 set clip one
 unset clip two


@@ -44,7 +44,7 @@ set format cb "% g"
 set angles radians
 unset grid
 set key title ""
 set angles radians
 unset grid
 set key title ""

-set key inside right top vertical Right noreverse enhanced autotitles nobox
+set key outside center bottom horizontal Right noreverse enhanced autotitles box linetype -1 linewidth 1.000

 set key noinvert samplen 4 spacing 1 width 0 height 0 
 unset label
 unset arrow
 set key noinvert samplen 4 spacing 1 width 0 height 0 
 unset label
 unset arrow


@@ -214,6 +214,6 @@ GPFUN_gamma = "gamma(x) = x**(gamma_k - 1) * exp((-1.0) * x / gamma_theta) / (ga
 GPFUN__ln_dgamma = "_ln_dgamma(x, a, b) = a*log(b) - lgamma(a) + (a-1)*log(x) - b*x"
 GPFUN_pgamma = "pgamma(x, shape, rate) = (x<0)? 0 : igamma(shape, x*rate)"
 GPFUN_dgamma = "dgamma(x, shape, rate) = (x<0)? 0 : (x==0)? ((shape<1)? 1/0 : (shape==1)? rate : 0) : (rate==0)? 0 : exp(_ln_dgamma(x, shape, rate))"
 GPFUN__ln_dgamma = "_ln_dgamma(x, a, b) = a*log(b) - lgamma(a) + (a-1)*log(x) - b*x"
 GPFUN_pgamma = "pgamma(x, shape, rate) = (x<0)? 0 : igamma(shape, x*rate)"
 GPFUN_dgamma = "dgamma(x, shape, rate) = (x<0)? 0 : (x==0)? ((shape<1)? 1/0 : (shape==1)? rate : 0) : (rate==0)? 0 : exp(_ln_dgamma(x, shape, rate))"

-plot [x=63:116] 'images/markov-comparators-16-pct.data' title 'Gemessene Daten', gamma_fit(x) title "Gamma-Verteilung"
-## fit gamma_fit(x) 'images/markov-comparators-16-pct.data' via gamma_k, gamma_theta
+plot [x=63:116] 'markov-comparators-16-pct.data' title 'Gemessene Daten', gamma_fit(x) title "Gamma-Verteilung"
+## fit gamma_fit(x) 'markov-comparators-16-pct.data' via gamma_k, gamma_theta

 #    EOF
 #    EOF

diff --git a/images/markov-comparators-18-pct.data b/images/markov-comparators-18-pct.data
new file mode 100644 (file)
index 0000000..657e905
--- /dev/null
+++ b/images/markov-comparators-18-pct.data
@@ -0,0 +1,60 @@
+# Iterations: 2000000
+# Average: 95.121195
+82   0.002700
+83   0.017850
+84   0.083150
+85   0.234150
+86   0.525100
+87   1.081900
+88   2.119950
+89   3.715400
+90   5.601700
+91   7.519850
+92   8.935550
+93   9.665700
+94   9.740400
+95   9.213650
+96   8.254850
+97   7.111550
+98   5.918750
+99   4.800000
+100  3.808500
+101  2.986000
+102  2.264700
+103  1.717150
+104  1.275150
+105  0.948300
+106  0.685250
+107  0.507100
+108  0.359150
+109  0.261650
+110  0.186650
+111  0.139800
+112  0.095150
+113  0.068650
+114  0.043950
+115  0.032450
+116  0.022750
+117  0.014950
+118  0.011150
+119  0.009450
+120  0.006450
+121  0.004150
+122  0.002950
+123  0.001700
+124  0.001550
+125  0.000800
+126  0.000600
+127  0.000350
+128  0.000400
+129  0.000250
+130  0.000150
+131  0.000100
+132  0.000050
+133  0.000100
+134  0.000150
+135  0.000050
+136  0.000000
+137  0.000050
+138  0.000000
+139  0.000050

diff --git a/images/markov-comparators-18-pct.gnuplot b/images/markov-comparators-18-pct.gnuplot
new file mode 100644 (file)
index 0000000..3ebe8bf
--- /dev/null
+++ b/images/markov-comparators-18-pct.gnuplot
@@ -0,0 +1,219 @@
+#!/usr/bin/gnuplot -persist
+#
+#    
+#      G N U P L O T
+#      Version 4.4 patchlevel 0
+#      last modified March 2010
+#      System: Linux 2.6.32-5-amd64
+#    
+#      Copyright (C) 1986-1993, 1998, 2004, 2007-2010
+#      Thomas Williams, Colin Kelley and many others
+#    
+#      gnuplot home:     http://www.gnuplot.info
+#      faq, bugs, etc:   type "help seeking-assistance"
+#      immediate help:   type "help"
+#      plot window:      hit 'h'
+set terminal pdfcairo  size 15.00cm, 9.27cm 
+set output 'markov-comparators-18-pct.pdf'
+unset clip points
+set clip one
+unset clip two
+set bar 1.000000 front
+set border 31 front linetype -1 linewidth 1.000
+set xdata
+set ydata
+set zdata
+set x2data
+set y2data
+set timefmt x "%d/%m/%y,%H:%M"
+set timefmt y "%d/%m/%y,%H:%M"
+set timefmt z "%d/%m/%y,%H:%M"
+set timefmt x2 "%d/%m/%y,%H:%M"
+set timefmt y2 "%d/%m/%y,%H:%M"
+set timefmt cb "%d/%m/%y,%H:%M"
+set boxwidth
+set style fill  empty border
+set style rectangle back fc  lt -3 fillstyle   solid 1.00 border lt -1
+set dummy x,y
+set format x "% g"
+set format y "% g"
+set format x2 "% g"
+set format y2 "% g"
+set format z "% g"
+set format cb "% g"
+set angles radians
+unset grid
+set key title ""
+set key outside center bottom horizontal Right noreverse enhanced autotitles box linetype -1 linewidth 1.000
+set key noinvert samplen 4 spacing 1 width 0 height 0 
+unset label
+unset arrow
+set style increment default
+unset style line
+unset style arrow
+set style histogram clustered gap 2 title  offset character 0, 0, 0
+unset logscale
+set offsets 0, 0, 0, 0
+set pointsize 1
+set encoding default
+unset polar
+unset parametric
+unset decimalsign
+set view 60, 30, 1, 1  
+set samples 100, 100
+set isosamples 10, 10
+set surface
+unset contour
+set clabel '%8.3g'
+set mapping cartesian
+set datafile separator whitespace
+unset hidden3d
+set cntrparam order 4
+set cntrparam linear
+set cntrparam levels auto 5
+set cntrparam points 5
+set size ratio 0 1,1
+set origin 0,0
+set style data points
+set style function lines
+set xzeroaxis linetype -2 linewidth 1.000
+set yzeroaxis linetype -2 linewidth 1.000
+set zzeroaxis linetype -2 linewidth 1.000
+set x2zeroaxis linetype -2 linewidth 1.000
+set y2zeroaxis linetype -2 linewidth 1.000
+set ticslevel 0.5
+set mxtics default
+set mytics default
+set mztics default
+set mx2tics default
+set my2tics default
+set mcbtics default
+set xtics border in scale 1,0.5 mirror norotate  offset character 0, 0, 0
+set xtics autofreq  norangelimit
+set ytics border in scale 1,0.5 mirror norotate  offset character 0, 0, 0
+set ytics autofreq  norangelimit
+set ztics border in scale 1,0.5 nomirror norotate  offset character 0, 0, 0
+set ztics autofreq  norangelimit
+set nox2tics
+set noy2tics
+set cbtics border in scale 1,0.5 mirror norotate  offset character 0, 0, 0
+set cbtics autofreq  norangelimit
+set title "" 
+set title  offset character 0, 0, 0 font "" norotate
+set timestamp bottom 
+set timestamp "" 
+set timestamp  offset character 0, 0, 0 font "" norotate
+set rrange [ * : * ] noreverse nowriteback  # (currently [8.98847e+307:-8.98847e+307] )
+set trange [ * : * ] noreverse nowriteback  # (currently [-5.00000:5.00000] )
+set urange [ * : * ] noreverse nowriteback  # (currently [-5.00000:5.00000] )
+set vrange [ * : * ] noreverse nowriteback  # (currently [-5.00000:5.00000] )
+set xlabel "Komparatoren" 
+set xlabel  offset character 0, 0, 0 font "" textcolor lt -1 norotate
+set x2label "" 
+set x2label  offset character 0, 0, 0 font "" textcolor lt -1 norotate
+set xrange [ * : * ] noreverse nowriteback  # (currently [82.0000:139.000] )
+set x2range [ * : * ] noreverse nowriteback  # (currently [82.0000:139.000] )
+set ylabel "Prozent" 
+set ylabel  offset character 0, 0, 0 font "" textcolor lt -1 rotate by -270
+set y2label "" 
+set y2label  offset character 0, 0, 0 font "" textcolor lt -1 rotate by -270
+set yrange [ * : * ] noreverse nowriteback  # (currently [0.00000:10.0000] )
+set y2range [ * : * ] noreverse nowriteback  # (currently [0.00000:9.74040] )
+set zlabel "" 
+set zlabel  offset character 0, 0, 0 font "" textcolor lt -1 norotate
+set zrange [ * : * ] noreverse nowriteback  # (currently [8.98847e+307:-8.98847e+307] )
+set cblabel "" 
+set cblabel  offset character 0, 0, 0 font "" textcolor lt -1 rotate by -270
+set cbrange [ * : * ] noreverse nowriteback  # (currently [8.98847e+307:-8.98847e+307] )
+set zero 1e-08
+set lmargin  -1
+set bmargin  -1
+set rmargin  -1
+set tmargin  -1
+set locale "en_US.UTF-8"
+set pm3d explicit at s
+set pm3d scansautomatic
+set pm3d interpolate 1,1 flush begin noftriangles nohidden3d corners2color mean
+set palette positive nops_allcF maxcolors 0 gamma 1.5 color model RGB 
+set palette rgbformulae 7, 5, 15
+set colorbox default
+set colorbox vertical origin screen 0.9, 0.2, 0 size screen 0.05, 0.6, 0 front bdefault
+set loadpath 
+set fontpath 
+set fit noerrorvariables
+binom(n,k) = (n!) / ((k!) * ((n-k)!))
+binv(n,k,p) = binom(n,k) * (p**k) * ((1-p)**(n-k))
+bin(x) = binv(n,floor(x),p)
+gauss(x) = (a1 / sigma) * exp((-0.5) * ((x - mu) / sigma)**2.0)
+poisson_int(x) = exp((-1.0) * lambda) * (lambda**x) / (x!)
+poisson(x) = poisson_int(floor(x + 0.5))
+erl(x) = gamma * exp(-1.0 * gamma * x) * (gamma * x)**(n_erl - 1) / ((n_erl - 1)!)
+binomial_int(x) = binomial_coeff(n, x) * p**x * (1-p)**(n-x)
+binomial_coeff(n,k) = (n!) / ((k!) * ((n-k)!))
+binomial(x) = binomial_int(floor(x + 0.5))
+binomial_fit(x) = 100.0 * binomial(x-19.0)
+poisson_fit(x) = 100.0 * poisson(x - offset)
+gauss_fit(x) = 100.0 * gauss(x)
+cauchy(x) = (1.0 / pi) * s / (s**2.0 + (x - t)**2)
+cauchy_fit(x) = 100.0 * cauchy(x)
+erlang_fit(x) = 100.0 * erl(x - erl_offset)
+gamma_dist(x) = x**(gamma_k - 1) * exp((-1.0) * x / gamma_theta) / (gamma_theta**gamma_k * gamma(gamma_k))
+gamma_fit(x) = 100.0 * dgamma(x - gamma_offset, gamma_k, gamma_theta)
+dgamma(x, shape, rate) = (x<0)? 0 : (x==0)? ((shape<1)? 1/0 : (shape==1)? rate : 0) : (rate==0)? 0 : exp(_ln_dgamma(x, shape, rate))
+foo_fit(x) = foo_a0 * exp(foo_a1 * (x - 62))
+_ln_dgamma(x, a, b) = a*log(b) - lgamma(a) + (a-1)*log(x) - b*x
+pgamma(x, shape, rate) = (x<0)? 0 : igamma(shape, x*rate)
+GNUTERM = "wxt"
+GPFUN_binom = "binom(n,k) = (n!) / ((k!) * ((n-k)!))"
+GPFUN_binv = "binv(n,k,p) = binom(n,k) * (p**k) * ((1-p)**(n-k))"
+n = 29
+p = 0.172562132555044
+GPFUN_bin = "bin(x) = binv(n,floor(x),p)"
+a1 = 0.398942280401433
+sigma = 1.88445909011715
+mu = 23.800757470569
+GPFUN_gauss = "gauss(x) = (a1 / sigma) * exp((-0.5) * ((x - mu) / sigma)**2.0)"
+lambda = 5.10554056666183
+GPFUN_poisson_int = "poisson_int(x) = exp((-1.0) * lambda) * (lambda**x) / (x!)"
+GPFUN_poisson = "poisson(x) = poisson_int(floor(x + 0.5))"
+gamma = 1.90073273091251
+n_erl = 54
+GPFUN_erl = "erl(x) = gamma * exp(-1.0 * gamma * x) * (gamma * x)**(n_erl - 1) / ((n_erl - 1)!)"
+GPFUN_binomial_int = "binomial_int(x) = binomial_coeff(n, x) * p**x * (1-p)**(n-x)"
+GPFUN_binomial_coeff = "binomial_coeff(n,k) = (n!) / ((k!) * ((n-k)!))"
+GPFUN_binomial = "binomial(x) = binomial_int(floor(x + 0.5))"
+GPFUN_binomial_fit = "binomial_fit(x) = 100.0 * binomial(x-19.0)"
+offset = 19
+GPFUN_poisson_fit = "poisson_fit(x) = 100.0 * poisson(x - offset)"
+GPFUN_gauss_fit = "gauss_fit(x) = 100.0 * gauss(x)"
+s = 1.39871428165847
+t = 23.5320369849105
+GPFUN_cauchy = "cauchy(x) = (1.0 / pi) * s / (s**2.0 + (x - t)**2)"
+GPFUN_cauchy_fit = "cauchy_fit(x) = 100.0 * cauchy(x)"
+erl_offset = 49.8425987940659
+GPFUN_erlang_fit = "erlang_fit(x) = 100.0 * erl(x - erl_offset)"
+gamma_k = 10.7234521744736
+gamma_theta = 0.76572583751246
+GPFUN_gamma_dist = "gamma_dist(x) = x**(gamma_k - 1) * exp((-1.0) * x / gamma_theta) / (gamma_theta**gamma_k * gamma_gamma(gamma_k))"
+gamma_offset = 81
+GPFUN_gamma_fit = "gamma_fit(x) = 100.0 * dgamma(x - gamma_offset, gamma_k, gamma_theta)"
+foo_a0 = 0.000540217815483465
+foo_a1 = 0.838098058527587
+GPFUN_foo_fit = "foo_fit(x) = foo_a0 * exp(foo_a1 * (x - 62))"
+GPFUN__ln_dgamma = "_ln_dgamma(x, a, b) = a*log(b) - lgamma(a) + (a-1)*log(x) - b*x"
+GPFUN_pgamma = "pgamma(x, shape, rate) = (x<0)? 0 : igamma(shape, x*rate)"
+GPFUN_dgamma = "dgamma(x, shape, rate) = (x<0)? 0 : (x==0)? ((shape<1)? 1/0 : (shape==1)? rate : 0) : (rate==0)? 0 : exp(_ln_dgamma(x, shape, rate))"
+y = 0
+FIT_CONVERGED = 1
+a = 240000
+a0 = 2.0
+FIT_NDF = 56
+FIT_STDFIT = 0.0927264844441511
+FIT_WSSR = 0.481499251372798
+lamdba = 14.0
+scale = 5000000
+GPFUN_gamma_gamma = "gamma_gamma(x) = (floor(x - 0.5))!"
+GPFUN_gamma = "gamma(x) = x**(gamma_k - 1) * exp((-1.0) * x / gamma_theta) / (gamma_theta**gamma_k * gamma_gamma(k))"
+plot [x=82:139] 'markov-comparators-18-pct.data' title 'Gemessene Daten', gamma_fit(x) title "Gamma-Verteilung"
+## fit gamma_fit(x) 'markov-comparators-18-pct.data' via gamma_k, gamma_theta
+#    EOF