From f0c46ce4d21d333772c7a967b3c8965379fd8699 Mon Sep 17 00:00:00 2001 From: Florian Forster Date: Tue, 11 Jan 2011 19:00:36 +0100 Subject: [PATCH] =?utf8?q?F=C3=BCge=20ein=20paar=20Bilder=20hinzu.?= MIME-Version: 1.0 Content-Type: text/plain; charset=utf8 Content-Transfer-Encoding: 8bit Sie lagen schon eine Weile in images/ rum, wurden aber nie eingecheckt. --- images/16-ec-from-bs32-normalized.tex | 290 ++++++++ images/16-ec-from-bs32.tex | 1128 ++++++++++++++++++++++++++++++ images/16-ec-from-ps32.tex | 286 ++++---- images/16-pairwise.tex | 278 ++++++++ images/32-ec-1277190372.tex | 858 ----------------------- images/32-ec-from-bs64.tex | 858 +++++++++++++++++++++++ images/32-pairwise-cut-16-pairwise.tex | 798 +++++++++++++++++++++ images/gamma_dist.gnuplot | 10 + images/markov-comparators-12-pct.data | 41 ++ images/markov-comparators-12-pct.gnuplot | 166 +++++ images/markov-comparators-14-pct.data | 49 ++ images/markov-comparators-14-pct.gnuplot | 162 +++++ images/markov-comparators-16-pct.data | 54 ++ images/markov-comparators-16-pct.gnuplot | 219 ++++++ images/markov-comparators-8-pct.data | 30 + images/oe-merge.tex | 48 ++ images/oe-mergesort-8.tex | 108 +++ images/oe-post-recursive-diff0.tex | 50 ++ images/oe-post-recursive-diff1.tex | 50 ++ 19 files changed, 4482 insertions(+), 1001 deletions(-) create mode 100644 images/16-ec-from-bs32-normalized.tex create mode 100644 images/16-ec-from-bs32.tex create mode 100644 images/16-pairwise.tex delete mode 100644 images/32-ec-1277190372.tex create mode 100644 images/32-ec-from-bs64.tex create mode 100644 images/32-pairwise-cut-16-pairwise.tex create mode 100644 images/gamma_dist.gnuplot create mode 100644 images/markov-comparators-12-pct.data create mode 100644 images/markov-comparators-12-pct.gnuplot create mode 100644 images/markov-comparators-14-pct.data create mode 100644 images/markov-comparators-14-pct.gnuplot create mode 100644 images/markov-comparators-16-pct.data create mode 100644 images/markov-comparators-16-pct.gnuplot create mode 100644 images/markov-comparators-8-pct.data create mode 100644 images/oe-merge.tex create mode 100644 images/oe-mergesort-8.tex create mode 100644 images/oe-post-recursive-diff0.tex create mode 100644 images/oe-post-recursive-diff1.tex diff --git a/images/16-ec-from-bs32-normalized.tex b/images/16-ec-from-bs32-normalized.tex new file mode 100644 index 0000000..9585843 --- /dev/null +++ b/images/16-ec-from-bs32-normalized.tex @@ -0,0 +1,290 @@ +\begin{tikzpicture}[auto] +\node[vertex] (v0) at (0.85,0.00) {}; 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+\path[comp] (v442) -- (v443); + +\node[vertex inactive maximum] (v444) at (13.79,11.75) {}; +\node[vertex inactive maximum] (v445) at (13.79,12.59) {}; +\path[comp inactive maximum] (v444) -- (v445); + +\node[vertex inactive maximum] (v446) at (13.95,12.17) {}; +\node[vertex inactive maximum] (v447) at (13.95,13.01) {}; +\path[comp inactive maximum] (v446) -- (v447); + +\node[vertex inactive minimum] (v448) at (14.48,0.00) {}; +\node[vertex inactive minimum] (v449) at (14.48,0.42) {}; +\path[comp inactive minimum] (v448) -- (v449); + +\node[vertex inactive minimum] (v450) at (14.48,0.84) {}; +\node[vertex inactive minimum] (v451) at (14.48,1.26) {}; +\path[comp inactive minimum] (v450) -- (v451); + +\node[vertex inactive minimum] (v452) at (14.48,1.68) {}; +\node[vertex inactive minimum] (v453) at (14.48,2.10) {}; +\path[comp inactive minimum] (v452) -- (v453); + +\node[vertex inactive minimum] (v454) at (14.48,2.52) {}; +\node[vertex inactive minimum] (v455) at (14.48,2.94) {}; +\path[comp inactive minimum] (v454) -- (v455); + +\node[vertex inactive minimum] (v456) at (14.48,3.36) {}; +\node[vertex inactive minimum] (v457) at (14.48,3.78) {}; +\path[comp inactive minimum] (v456) -- (v457); + +\node[vertex inactive minimum] (v458) at (14.48,4.20) {}; +\node[vertex inactive minimum] (v459) at (14.48,4.62) {}; +\path[comp inactive minimum] (v458) -- (v459); + +\node[vertex] (v460) at (14.48,5.03) {}; +\node[vertex] (v461) at (14.48,5.45) {}; +\path[comp] (v460) -- (v461); + +\node[vertex] (v462) at (14.48,5.87) {}; +\node[vertex] (v463) at (14.48,6.29) {}; +\path[comp] (v462) -- (v463); + +\node[vertex] (v464) at (14.48,6.71) {}; +\node[vertex] (v465) at (14.48,7.13) {}; +\path[comp] (v464) -- (v465); + +\node[vertex] (v466) at (14.48,7.55) {}; +\node[vertex] (v467) at (14.48,7.97) {}; +\path[comp] (v466) -- (v467); + +\node[vertex] (v468) at (14.48,8.39) {}; +\node[vertex] (v469) at (14.48,8.81) {}; +\path[comp] (v468) -- (v469); + +\node[vertex] (v470) at (14.48,9.23) {}; +\node[vertex] (v471) at (14.48,9.65) {}; +\path[comp] (v470) -- (v471); + +\node[vertex] (v472) at (14.48,10.07) {}; +\node[vertex] (v473) at (14.48,10.49) {}; +\path[comp] (v472) -- (v473); + +\node[vertex active maximum] (v474) at (14.48,10.91) {}; +\node[vertex active maximum] (v475) at (14.48,11.33) {}; +\path[comp active maximum] (v474) -- (v475); + +\node[vertex inactive maximum] (v476) at (14.48,11.75) {}; +\node[vertex inactive maximum] (v477) at (14.48,12.17) {}; +\path[comp inactive maximum] (v476) -- (v477); + +\node[vertex inactive maximum] (v478) at (14.48,12.59) {}; +\node[vertex inactive maximum] (v479) at (14.48,13.01) {}; +\path[comp inactive maximum] (v478) -- (v479); + +\end{tikzpicture} diff --git a/images/16-ec-from-ps32.tex b/images/16-ec-from-ps32.tex index 9e94974..3d94d3a 100644 --- a/images/16-ec-from-ps32.tex +++ b/images/16-ec-from-ps32.tex @@ -1,270 +1,270 @@ -\begin{tikzpicture}[scale=0.60,auto] -\node[vertex] (v0) at (1.50,0) {}; -\node[vertex] (v1) at (1.50,2) {}; +\begin{tikzpicture}[auto] +\node[vertex] (v0) at (0.93,0.00) {}; 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-\node[vertex] (v113) at (20.95,2) {}; +\node[vertex] (v112) at (14.07,0.75) {}; +\node[vertex] (v113) at (14.07,1.49) {}; \path[comp] (v112) -- (v113); -\node[vertex] (v114) at (20.95,3) {}; -\node[vertex] (v115) at (20.95,4) {}; +\node[vertex] (v114) at (14.07,2.24) {}; +\node[vertex] (v115) at (14.07,2.98) {}; \path[comp] (v114) -- (v115); -\node[vertex] (v116) at (20.95,5) {}; -\node[vertex] (v117) at (20.95,6) {}; +\node[vertex] (v116) at (14.07,3.73) {}; +\node[vertex] (v117) at (14.07,4.47) {}; \path[comp] (v116) -- (v117); -\node[vertex] (v118) at (20.95,7) {}; -\node[vertex] (v119) at (20.95,8) {}; +\node[vertex] (v118) at (14.07,5.22) {}; +\node[vertex] (v119) at (14.07,5.96) {}; \path[comp] (v118) -- (v119); -\node[vertex] (v120) at (20.95,9) {}; -\node[vertex] (v121) at (20.95,10) {}; +\node[vertex] (v120) at (14.07,6.71) {}; +\node[vertex] (v121) at (14.07,7.45) {}; \path[comp] (v120) -- (v121); -\node[vertex] (v122) at (20.95,11) {}; -\node[vertex] (v123) at (20.95,12) {}; 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+\path[comp inactive minimum] (v112) -- (v113); + +\node[vertex inactive minimum] (v114) at (14.15,2.05) {}; +\node[vertex inactive minimum] (v115) at (14.15,2.73) {}; +\path[comp inactive minimum] (v114) -- (v115); + +\node[vertex] (v116) at (14.15,3.41) {}; +\node[vertex] (v117) at (14.15,4.09) {}; +\path[comp] (v116) -- (v117); + +\node[vertex] (v118) at (14.15,4.77) {}; +\node[vertex] (v119) at (14.15,5.45) {}; +\path[comp] (v118) -- (v119); + +\node[vertex] (v120) at (14.15,6.14) {}; +\node[vertex] (v121) at (14.15,6.82) {}; +\path[comp] (v120) -- (v121); + +\node[vertex inactive maximum] (v122) at (14.15,7.50) {}; +\node[vertex inactive maximum] (v123) at (14.15,8.18) {}; +\path[comp inactive maximum] (v122) -- (v123); + +\node[vertex inactive maximum] (v124) at (14.15,8.86) {}; +\node[vertex inactive maximum] (v125) at (14.15,9.55) {}; +\path[comp inactive maximum] (v124) -- (v125); + +\end{tikzpicture} diff --git a/images/32-ec-1277190372.tex b/images/32-ec-1277190372.tex deleted file mode 100644 index 485d6ed..0000000 --- a/images/32-ec-1277190372.tex +++ /dev/null @@ -1,858 +0,0 @@ -\begin{tikzpicture}[scale=0.35,auto] -\node[vertex] (v0) at (1.50,0) {}; 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- -\node[vertex] (v78) at (10.45,16) {}; -\node[vertex] (v79) at (10.45,30) {}; -\path[comp] (v78) -- (v79); - -\node[vertex] (v80) at (9.05,24) {}; -\node[vertex] (v81) at (9.05,25) {}; -\path[comp] (v80) -- (v81); - -\node[vertex] (v82) at (9.05,28) {}; -\node[vertex] (v83) at (9.05,29) {}; -\path[comp] (v82) -- (v83); - -\node[vertex] (v84) at (11.95,0) {}; -\node[vertex] (v85) at (11.95,4) {}; -\path[comp] (v84) -- (v85); - -\node[vertex] (v86) at (12.30,1) {}; -\node[vertex] (v87) at (12.30,21) {}; -\path[comp] (v86) -- (v87); - -\node[vertex] (v88) at (12.65,2) {}; -\node[vertex] (v89) at (12.65,20) {}; -\path[comp] (v88) -- (v89); - -\node[vertex] (v90) at (13.00,3) {}; -\node[vertex] (v91) at (13.00,5) {}; -\path[comp] (v90) -- (v91); - -\node[vertex] (v92) at (11.95,6) {}; -\node[vertex] (v93) at (11.95,10) {}; -\path[comp] (v92) -- (v93); - -\node[vertex] (v94) at (13.00,7) {}; -\node[vertex] (v95) at (13.00,9) {}; -\path[comp] (v94) -- (v95); - -\node[vertex] (v96) at (13.35,8) {}; 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+\node[vertex inactive minimum] (v359) at (14.58,2.70) {}; +\path[comp inactive minimum] (v358) -- (v359); + +\node[vertex] (v360) at (14.58,3.04) {}; +\node[vertex] (v361) at (14.58,3.38) {}; +\path[comp] (v360) -- (v361); + +\node[vertex] (v362) at (14.58,3.72) {}; +\node[vertex] (v363) at (14.58,4.06) {}; +\path[comp] (v362) -- (v363); + +\node[vertex] (v364) at (14.58,4.39) {}; +\node[vertex] (v365) at (14.58,4.73) {}; +\path[comp] (v364) -- (v365); + +\node[vertex] (v366) at (14.58,5.07) {}; +\node[vertex] (v367) at (14.58,5.41) {}; +\path[comp] (v366) -- (v367); + +\node[vertex] (v368) at (14.58,5.75) {}; +\node[vertex] (v369) at (14.58,6.08) {}; +\path[comp] (v368) -- (v369); + +\node[vertex] (v370) at (14.58,6.42) {}; +\node[vertex] (v371) at (14.58,6.76) {}; +\path[comp] (v370) -- (v371); + +\node[vertex] (v372) at (14.58,7.10) {}; +\node[vertex] (v373) at (14.58,7.44) {}; +\path[comp] (v372) -- (v373); + +\node[vertex inactive maximum] (v374) at (14.58,7.77) {}; +\node[vertex inactive maximum] (v375) at (14.58,8.11) {}; +\path[comp inactive maximum] (v374) -- (v375); + +\node[vertex inactive maximum] (v376) at (14.58,8.45) {}; +\node[vertex inactive maximum] (v377) at (14.58,8.79) {}; +\path[comp inactive maximum] (v376) -- (v377); + +\node[vertex inactive maximum] (v378) at (14.58,9.13) {}; +\node[vertex inactive maximum] (v379) at (14.58,9.46) {}; +\path[comp inactive maximum] (v378) -- (v379); + +\node[vertex inactive maximum] (v380) at (14.58,9.80) {}; +\node[vertex inactive maximum] (v381) at (14.58,10.14) {}; +\path[comp inactive maximum] (v380) -- (v381); + +\end{tikzpicture} diff --git a/images/gamma_dist.gnuplot b/images/gamma_dist.gnuplot new file mode 100644 index 0000000..d62cace --- /dev/null +++ b/images/gamma_dist.gnuplot @@ -0,0 +1,10 @@ +_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)) +gamma_offset = 0.0 +gamma_k = 15.7880378786862 +gamma_theta = 0.980078674752871 +gamma_fit(x) = 100.0 * dgamma(x - gamma_offset, gamma_k, gamma_theta) +#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 * gamma_dist(x - gamma_offset) + diff --git a/images/markov-comparators-12-pct.data b/images/markov-comparators-12-pct.data new file mode 100644 index 0000000..87d460b --- /dev/null +++ b/images/markov-comparators-12-pct.data @@ -0,0 +1,41 @@ +41 0.091900 +42 0.347600 +43 1.120700 +44 3.481000 +45 7.939400 +46 12.061400 +47 14.087900 +48 13.914800 +49 11.997600 +50 9.773000 +51 7.513400 +52 5.488200 +53 3.909200 +54 2.752300 +55 1.899600 +56 1.255700 +57 0.835600 +58 0.531400 +59 0.357700 +60 0.242700 +61 0.143700 +62 0.090700 +63 0.063200 +64 0.039200 +65 0.023500 +66 0.013800 +67 0.009200 +68 0.005600 +69 0.003900 +70 0.003000 +71 0.001200 +72 0.000800 +73 0.000400 +74 0.000200 +75 0.000100 +76 0.000200 +77 0.000000 +78 0.000100 +79 0.000000 +80 0.000000 +81 0.000100 diff --git a/images/markov-comparators-12-pct.gnuplot b/images/markov-comparators-12-pct.gnuplot new file mode 100644 index 0000000..718b7a0 --- /dev/null +++ b/images/markov-comparators-12-pct.gnuplot @@ -0,0 +1,166 @@ +#!/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 wxt 0 +# set output +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 inside right top vertical Right noreverse enhanced autotitles nobox +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 [41.0000:81.0000] ) +set x2range [ * : * ] noreverse nowriteback # (currently [41.0000:81.0000] ) +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 [0.00000:16.0000] ) +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 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 +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) +_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 +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)" +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 +# EOF diff --git a/images/markov-comparators-14-pct.data b/images/markov-comparators-14-pct.data new file mode 100644 index 0000000..dff3e84 --- /dev/null +++ b/images/markov-comparators-14-pct.data @@ -0,0 +1,49 @@ +53 0.023000 +54 0.076800 +55 0.346200 +56 0.985900 +57 2.245000 +58 4.447600 +59 7.318500 +60 9.956200 +61 11.628000 +62 11.749200 +63 11.005500 +64 9.528900 +65 7.816700 +66 6.207400 +67 4.703300 +68 3.507500 +69 2.525400 +70 1.839200 +71 1.300700 +72 0.882900 +73 0.621900 +74 0.421000 +75 0.288000 +76 0.193000 +77 0.132600 +78 0.082900 +79 0.055200 +80 0.038000 +81 0.025900 +82 0.016600 +83 0.012000 +84 0.006800 +85 0.004000 +86 0.002800 +87 0.001700 +88 0.001300 +89 0.000800 +90 0.000500 +91 0.000100 +92 0.000200 +93 0.000200 +94 0.000200 +95 0.000000 +96 0.000100 +97 0.000000 +98 0.000100 +99 0.000100 +100 0.000000 +101 0.000100 diff --git a/images/markov-comparators-14-pct.gnuplot b/images/markov-comparators-14-pct.gnuplot new file mode 100644 index 0000000..d8a3937 --- /dev/null +++ b/images/markov-comparators-14-pct.gnuplot @@ -0,0 +1,162 @@ +#!/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 wxt 0 +# set output +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 inside right top vertical Right noreverse enhanced autotitles nobox +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 [53.0000:101.000] ) +set x2range [ * : * ] noreverse nowriteback # (currently [53.0000:101.000] ) +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 [0.00000:12.0000] ) +set y2range [ * : * ] noreverse nowriteback # (currently [0.00000:11.7492] ) +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 +_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)) +gamma_fit(x) = 100.0 * dgamma(x - gamma_offset, gamma_k, gamma_theta) +GNUTERM = "wxt" +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))" +gamma_offset = 52 +gamma_k = 9.52243956215441 +gamma_theta = 0.866869465480136 +GPFUN_gamma_fit = "gamma_fit(x) = 100.0 * dgamma(x - gamma_offset, gamma_k, gamma_theta)" +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 +# EOF diff --git a/images/markov-comparators-16-pct.data b/images/markov-comparators-16-pct.data new file mode 100644 index 0000000..515fc83 --- /dev/null +++ b/images/markov-comparators-16-pct.data @@ -0,0 +1,54 @@ +63 0.00036 +64 0.00148 +65 0.00420 +66 0.01019 +67 0.03000 +68 0.06674 +69 0.18834 +70 0.45496 +71 1.01551 +72 2.08409 +73 3.92942 +74 6.10824 +75 8.35161 +76 9.88771 +77 10.63978 +78 10.38984 +79 9.52167 +80 8.31205 +81 6.89893 +82 5.57473 +83 4.35112 +84 3.31039 +85 2.47437 +86 1.82548 +87 1.33113 +88 0.95592 +89 0.68841 +90 0.48849 +91 0.33511 +92 0.23689 +93 0.16438 +94 0.11395 +95 0.08025 +96 0.05561 +97 0.03840 +98 0.02602 +99 0.01815 +100 0.01064 +101 0.00747 +102 0.00510 +103 0.00362 +104 0.00300 +105 0.00161 +106 0.00143 +107 0.00125 +108 0.00067 +109 0.00031 +110 0.00027 +111 0.00031 +112 0.00004 +113 0.00013 +114 0.00000 +115 0.00013 +116 0.00009 diff --git a/images/markov-comparators-16-pct.gnuplot b/images/markov-comparators-16-pct.gnuplot new file mode 100644 index 0000000..0751469 --- /dev/null +++ b/images/markov-comparators-16-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 wxt 0 +# set output +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 inside right top vertical Right noreverse enhanced autotitles nobox +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 [63.0000:116.000] ) +set x2range [ * : * ] noreverse nowriteback # (currently [63.0000:116.000] ) +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 [0.00000:12.0000] ) +set y2range [ * : * ] noreverse nowriteback # (currently [0.00000:10.6398] ) +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) +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) +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_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 = 17.9390580825481 +gamma_theta = 1.09113152299828 +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 = 62 +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))" +y = 0 +FIT_CONVERGED = 1 +a = 240000 +a0 = 2.0 +FIT_NDF = 52 +FIT_STDFIT = 0.15913245106829 +FIT_WSSR = 1.31680312311609 +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))" +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 +# EOF diff --git a/images/markov-comparators-8-pct.data b/images/markov-comparators-8-pct.data new file mode 100644 index 0000000..4b8d983 --- /dev/null +++ b/images/markov-comparators-8-pct.data @@ -0,0 +1,30 @@ +19 0.534628 +20 1.38496 +21 2.96327 +22 13.6184 +23 22.6531 +24 18.8797 +25 14.8193 +26 9.94546 +27 6.1938 +28 3.8068 +29 2.30663 +30 1.29686 +31 0.702513 +32 0.398067 +33 0.226193 +34 0.122834 +35 0.0688669 +36 0.0349614 +37 0.0206483 +38 0.01138 +39 0.00363692 +40 0.00305032 +41 0.00199444 +42 0.00152516 +43 0.00035196 +44 0.0005866 +45 0.00035196 +46 0 +47 0 +48 0.00011732 diff --git a/images/oe-merge.tex b/images/oe-merge.tex new file mode 100644 index 0000000..3cb4146 --- /dev/null +++ b/images/oe-merge.tex @@ -0,0 +1,48 @@ +\begin{tikzpicture}[scale=0.80,auto] + +% Draw the odd lines +\foreach \line in {0, 1, 2, 3} + \path[edge,rounded corners,color=red] + (1+2*\line, 9.0) -- (1+2*\line, 5.5) + -- (1+ \line, 4.5) -- (1+ \line, 1.5) + -- (1+2*\line, 0.5) -- (1+2*\line,-1.0); + +% Draw the even lines +\foreach \line in {0, 1, 2, 3} + \path[edge,rounded corners,color=blue] + (2+2*\line, 9.0) -- (2+2*\line, 5.5) + -- (5+ \line, 4.5) -- (5+ \line, 1.5) + -- (2+2*\line, 0.5) -- (2+2*\line,-1.0); + +% Line labels +\foreach \line in {0, 1, 2, 3} + \node at (1+\line,9.3) {$u_\line$}; +\foreach \line in {0, 1, 2, 3} + \node at (5+\line,9.3) {$v_\line$}; +\foreach \line in {0, ..., 7} + \node at (1+\line,-1.3) {$w_\line$}; + +% Left sorted list box +\draw[fill=white] (0.75,6) rectangle (4.25,8); +\path[gray box] (1,6.25) -- (4,7.75) -- (4,6.25) -- cycle; + +% Right sorted list box +\draw[fill=white] (4.75,6) rectangle (8.25,8); +\path[gray box] (8,6.25) -- (8,7.75) -- (5,6.25) -- cycle; + +% Left OEM block +\draw[fill=white] (0.75,2) rectangle (4.25,4); +\node at (2.5,3) {\small $\textrm{OEM}\left(\left\lceil\frac{n}{2}\right\rceil, \left\lceil\frac{m}{2}\right\rceil\right)$}; + +% Right OEM block +\draw[fill=white] (4.75,2) rectangle (8.25,4); +\node at (6.5,3) {\small $\textrm{OEM}\left(\left\lfloor\frac{n}{2}\right\rfloor, \left\lfloor\frac{m}{2}\right\rfloor\right)$}; + +\foreach \line in {0, 1, 2} +{ + \path[comp,very thick] (2+2*\line,0) -- (3+2*\line,0); + \draw (2+2*\line,0) circle(5pt)[color=black,fill=black] {}; + \draw (3+2*\line,0) circle(5pt)[color=black,fill=black] {}; +} + +\end{tikzpicture} diff --git a/images/oe-mergesort-8.tex b/images/oe-mergesort-8.tex new file mode 100644 index 0000000..6a8b32b --- /dev/null +++ b/images/oe-mergesort-8.tex @@ -0,0 +1,108 @@ +\begin{tikzpicture}[scale=0.70,auto] + +% Box for lower OEM(4) +\draw[red box] (1,-.333) rectangle (5.35,3.333); + +% Box for upper OEM(4) +\draw[red box] (1,3.667) rectangle (5.35,7.333); + +% Box for even merge block +\draw[blue box] (5.85,-.333) rectangle (7.60,7.333); + +% Box for odd merge block +\draw[blue box] (8.10,-.333) rectangle (9.85,7.333); + +% Box for trailing recursive comparators +\draw[green box] (10.35,-.333) rectangle (11.35,7.333); + +\path[edge] (0,0) -- (12.35,0); +\path[edge] (0,1) -- (12.35,1); +\path[edge] (0,2) -- (12.35,2); +\path[edge] (0,3) -- (12.35,3); +\path[edge] (0,4) -- (12.35,4); +\path[edge] (0,5) -- (12.35,5); +\path[edge] (0,6) -- (12.35,6); +\path[edge] (0,7) -- (12.35,7); + +% lower OEM(4) +\node[vertex] (v0) at (1.50,0) {}; +\node[vertex] (v1) at (1.50,1) {}; +\path[comp] (v0) -- (v1); + +\node[vertex] (v2) at (1.50,2) {}; +\node[vertex] (v3) at (1.50,3) {}; +\path[comp] (v2) -- (v3); + +\node[vertex] (v8) at (3.00,0) {}; +\node[vertex] (v9) at (3.00,2) {}; +\path[comp] (v8) -- (v9); + +\node[vertex] (v10) at (3.35,1) {}; +\node[vertex] (v11) at (3.35,3) {}; +\path[comp] (v10) -- (v11); + +\node[vertex] (v16) at (4.85,1) {}; +\node[vertex] (v17) at (4.85,2) {}; +\path[comp] (v16) -- (v17); + +% upper OEM(4) +\node[vertex] (v4) at (1.50,4) {}; +\node[vertex] (v5) at (1.50,5) {}; +\path[comp] (v4) -- (v5); + +\node[vertex] (v6) at (1.50,6) {}; +\node[vertex] (v7) at (1.50,7) {}; +\path[comp] (v6) -- (v7); + +\node[vertex] (v12) at (3.00,4) {}; +\node[vertex] (v13) at (3.00,6) {}; +\path[comp] (v12) -- (v13); + +\node[vertex] (v14) at (3.35,5) {}; +\node[vertex] (v15) at (3.35,7) {}; +\path[comp] (v14) -- (v15); + +\node[vertex] (v18) at (4.85,5) {}; +\node[vertex] (v19) at (4.85,6) {}; +\path[comp] (v18) -- (v19); + +% Begin of even OE merge (8) +\node[vertex] (v20) at (6.35,0) {}; +\node[vertex] (v21) at (6.35,4) {}; +\path[comp] (v20) -- (v21); + +\node[vertex] (v24) at (6.70,2) {}; +\node[vertex] (v25) at (6.70,6) {}; +\path[comp] (v24) -- (v25); + +\node[vertex] (v28) at (7.10,2) {}; +\node[vertex] (v29) at (7.10,4) {}; +\path[comp] (v28) -- (v29); + +% Begin of odd OE merge (8) +\node[vertex] (v22) at (8.60,1) {}; +\node[vertex] (v23) at (8.60,5) {}; +\path[comp] (v22) -- (v23); + +\node[vertex] (v26) at (8.95,3) {}; +\node[vertex] (v27) at (8.95,7) {}; +\path[comp] (v26) -- (v27); + +\node[vertex] (v30) at (9.35,3) {}; +\node[vertex] (v31) at (9.35,5) {}; +\path[comp] (v30) -- (v31); + +% Trailing recursive comparators +\node[vertex] (v32) at (10.85,1) {}; +\node[vertex] (v33) at (10.85,2) {}; +\path[comp] (v32) -- (v33); + +\node[vertex] (v34) at (10.85,3) {}; +\node[vertex] (v35) at (10.85,4) {}; +\path[comp] (v34) -- (v35); + +\node[vertex] (v36) at (10.85,5) {}; +\node[vertex] (v37) at (10.85,6) {}; +\path[comp] (v36) -- (v37); + +\end{tikzpicture} diff --git a/images/oe-post-recursive-diff0.tex b/images/oe-post-recursive-diff0.tex new file mode 100644 index 0000000..9481f04 --- /dev/null +++ b/images/oe-post-recursive-diff0.tex @@ -0,0 +1,50 @@ +\begin{tikzpicture}[scale=0.66,auto] + +\pgfmathsetmacro{\lastzeroindex}{0} + +% Space between nodes +\pgfmathsetmacro{\spacingx}{1.3} +% Amount even boxes are raised +\pgfmathsetmacro{\offsety}{0.8} + +\pgfmathsetmacro{\totalheight}{4 + \offsety} % Height of one sub-picture. + +% Lines +\foreach \x in {0, ..., 7} + \draw[edge] (\spacingx * \x, 0) -- (\spacingx * \x, \totalheight); + +% Even zero nodes +\foreach \x in {0, ..., \lastzeroindex} +{ + \draw[red box] (2 * \spacingx * \x - .5, 2 + \offsety) rectangle +(1,1); + \draw (2 * \spacingx * \x, 2.5 + \offsety) node {$0$}; +} + +% Even one nodes +\pgfmathsetmacro{\firstoneindex}{\lastzeroindex+1} +\foreach \x in {\firstoneindex, ..., 3} +{ + \draw[blue box] (2 * \spacingx * \x - .5, 2 + \offsety) rectangle +(1,1); + \draw (2 * \spacingx * \x, 2.5 + \offsety) node {$1$}; +} + +% Odd zero nodes +\foreach \x in {0, ..., 0} +{ + \draw[red box] (\spacingx + 2 * \spacingx * \x - .5, 2) rectangle +(1,1); + \draw (\spacingx + 2 * \spacingx * \x, 2.5) node {$0$}; +} + +% Odd one nodes +\foreach \x in {1, ..., 3} +{ + \draw[blue box] (\spacingx + 2 * \spacingx * \x - .5, 2) rectangle +(1,1); + \draw (\spacingx + 2 * \spacingx * \x, 2.5) node {$1$}; +} + +% Comparators +\foreach \x in {0, ..., 2} + \draw[comp] ( \spacingx + 2 * \spacingx * \x, 1) node[vertex] {} + -- (2 * \spacingx + 2 * \spacingx * \x, 1) node[vertex] {}; + +\end{tikzpicture} diff --git a/images/oe-post-recursive-diff1.tex b/images/oe-post-recursive-diff1.tex new file mode 100644 index 0000000..c2d8e60 --- /dev/null +++ b/images/oe-post-recursive-diff1.tex @@ -0,0 +1,50 @@ +\begin{tikzpicture}[scale=0.66,auto] + +\pgfmathsetmacro{\lastzeroindex}{1} + +% Space between nodes +\pgfmathsetmacro{\spacingx}{1.3} +% Amount even boxes are raised +\pgfmathsetmacro{\offsety}{0.8} + +\pgfmathsetmacro{\totalheight}{4 + \offsety} % Height of one sub-picture. + +% Lines +\foreach \x in {0, ..., 7} + \draw[edge] (\spacingx * \x, 0) -- (\spacingx * \x, \totalheight); + +% Even zero nodes +\foreach \x in {0, ..., \lastzeroindex} +{ + \draw[red box] (2 * \spacingx * \x - .5, 2 + \offsety) rectangle +(1,1); + \draw (2 * \spacingx * \x, 2.5 + \offsety) node {$0$}; +} + +% Even one nodes +\pgfmathsetmacro{\firstoneindex}{\lastzeroindex+1} +\foreach \x in {\firstoneindex, ..., 3} +{ + \draw[blue box] (2 * \spacingx * \x - .5, 2 + \offsety) rectangle +(1,1); + \draw (2 * \spacingx * \x, 2.5 + \offsety) node {$1$}; +} + +% Odd zero nodes +\foreach \x in {0, ..., 0} +{ + \draw[red box] (\spacingx + 2 * \spacingx * \x - .5, 2) rectangle +(1,1); + \draw (\spacingx + 2 * \spacingx * \x, 2.5) node {$0$}; +} + +% Odd one nodes +\foreach \x in {1, ..., 3} +{ + \draw[blue box] (\spacingx + 2 * \spacingx * \x - .5, 2) rectangle +(1,1); + \draw (\spacingx + 2 * \spacingx * \x, 2.5) node {$1$}; +} + +% Comparators +\foreach \x in {0, ..., 2} + \draw[comp] ( \spacingx + 2 * \spacingx * \x, 1) node[vertex] {} + -- (2 * \spacingx + 2 * \spacingx * \x, 1) node[vertex] {}; + +\end{tikzpicture} -- 2.11.0