From 32219a1257de0ea2fb64ac4e6146a60d23840929 Mon Sep 17 00:00:00 2001 From: Florian Forster Date: Sat, 29 Jan 2011 13:32:05 +0100 Subject: [PATCH] SN-Markov-Graphen ausgebaut. --- diplomarbeit.tex | 50 ++++--- images/markov-comparators-12-pct.gnuplot | 23 ++-- images/markov-comparators-14-pct.gnuplot | 10 +- images/markov-comparators-16-pct.gnuplot | 10 +- images/markov-comparators-18-pct.data | 60 +++++++++ images/markov-comparators-18-pct.gnuplot | 219 +++++++++++++++++++++++++++++++ 6 files changed, 332 insertions(+), 40 deletions(-) create mode 100644 images/markov-comparators-18-pct.data create mode 100644 images/markov-comparators-18-pct.gnuplot diff --git a/diplomarbeit.tex b/diplomarbeit.tex index a1145c4..2f8aed2 100644 --- a/diplomarbeit.tex +++ b/diplomarbeit.tex @@ -1012,7 +1012,7 @@ sich die Resultate auch in der ersten Schicht nicht unterscheiden. \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 @@ -1071,7 +1071,7 @@ unterschiedlichen Schnittmuster abschätzen. \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 @@ -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} -Guetesumme := 0 +Gütesumme := 0 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 } } -gebe Auswahl zurueck +gib Auswahl zurück \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. -\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}). @@ -1560,7 +1564,7 @@ selbst und erhält so einen zufälligen Nachfolger. \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 @@ -1570,7 +1574,7 @@ selbst und erhält so einen zufälligen Nachfolger. \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 @@ -1580,7 +1584,7 @@ selbst und erhält so einen zufälligen Nachfolger. \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 @@ -1588,6 +1592,16 @@ selbst und erhält so einen zufälligen Nachfolger. \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} diff --git a/images/markov-comparators-12-pct.gnuplot b/images/markov-comparators-12-pct.gnuplot index 718b7a0..bde07ad 100644 --- 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' -# 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 @@ -44,7 +44,7 @@ set format cb "% g" 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 @@ -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 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 "" @@ -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 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] ) @@ -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) +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) -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 @@ -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__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 -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 diff --git a/images/markov-comparators-14-pct.gnuplot b/images/markov-comparators-14-pct.gnuplot index d8a3937..21e29ae 100644 --- 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' -# 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 @@ -44,7 +44,7 @@ set format cb "% g" 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 @@ -157,6 +157,6 @@ FIT_CONVERGED = 1 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 diff --git a/images/markov-comparators-16-pct.gnuplot b/images/markov-comparators-16-pct.gnuplot index 0751469..4e93bc4 100644 --- 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' -# 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 @@ -44,7 +44,7 @@ set format cb "% g" 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 @@ -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))" -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 diff --git a/images/markov-comparators-18-pct.data b/images/markov-comparators-18-pct.data new file mode 100644 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 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 -- 2.11.0