From 03513af39ecf9914870e33eae56f5357a93016ab Mon Sep 17 00:00:00 2001 From: treecity Date: Tue, 13 Mar 2012 12:43:00 +0000 Subject: [PATCH] [doc] Beispiele Eingebunden git-svn-id: https://drops.fb12.tu-berlin.de/svn/bacc/trunk@102 26120e32-c555-405d-b3e1-1f783fb42516 --- doc/doc1.pdf | Bin 165331 -> 165325 bytes doc/doc1.tex | 2 +- doc/doc2.tex | 167 ++++++++++++++++ doc/fig/Net_Neigh.eps | 272 ++++++++++++++++++++++++++ doc/fig/Net_Neigh.pdf | Bin 0 -> 6651 bytes doc/fig/Net_Neigh.svg | 378 ++++++++++++++++++++++++++++++++++++ doc/fig/exmpl1_coo.tex | 13 ++ doc/fig/exmpl1_ele.tex | 9 + doc/fig/exmpl1_f2s.tex | 16 ++ doc/fig/exmpl1_nei.tex | 9 + doc/fig/exmpl1_ref.eps | 302 ++++++++++++++++++++++++++++ doc/fig/exmpl1_ref.pdf | Bin 0 -> 5485 bytes doc/fig/exmpl2_coo.tex | 23 +++ doc/fig/exmpl2_ele.tex | 16 ++ doc/fig/exmpl2_f2s.tex | 9 + doc/fig/exmpl2_nei.tex | 16 ++ doc/fig/exmpl2_ref.eps | 323 ++++++++++++++++++++++++++++++ doc/fig/exmpl2_ref.pdf | Bin 0 -> 5649 bytes 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q&pf=c-{d9k*PPtHuk_VMj}os^l(LQt$*0{0mX1stGpc1Z&F8O^6Cnnc+1`p-yAz;PsN zzmVflAmk9hMlbx{O(=pQ*yDOis74@=?ViY;2!(1mO0i*j4#Nd%7=f{S^&Eu?I25JX z4~d){C7>XIv&tmyGg>HzUlEw+vYY`Vp2trAUE3I13 zA%a_z6hzoYJ%rNdiNf4=Q60EGjR$RYT<;S18|z=or~ZEi3n|Xo}?36(BUb zBSB=vkR&b)#~{xx00D*br69ogqrt@i{@UO$oL_MSCn2tPhWR=l2!s|w&O(7OgoxmR z5DM&v5b}iqgw)r4uh$0vqTk5`0~EiXAV&SC8UJyH%Y(nV03-l^WpNme^E(2P4B+p3 z4nR>}n{XI`@iCm648C>TR1y4!CoocA34wzz8eIPWeS`o>5&!P7uPq_DmB1I_9tf0= zabf(`1h_|r|L0Y8w#aDK)JBxr;uj6f2>_!x>q{tO@}jtfQ{!y!ZR zJV7v=fV}BLa7YlmOgN091@AEqfdC^>;o{_~@I~Y6rAA|XpSa%z-1hx;6>u0Se6?ws zKZ*#!{jA_$h5#t}&3RI;`~<-GYlOpanm2YFMxeq2NdjfvR*58jhy=k=9KnH94rMq( lLpd#xky1)Z$RvoIAbcFW{$B`NxJqPWOq)78%f`q}{|3ib&HexY diff --git a/doc/doc1.tex b/doc/doc1.tex index 7b9937b..b8eb387 100644 --- a/doc/doc1.tex +++ b/doc/doc1.tex @@ -70,7 +70,7 @@ Berechnet werden soll: \section{Gitter} Alle Gitter bestehen nur aus achsenorientierten Rechtecken. -Entscheidend für die Tests sind Gitter in einer Ebene und Ganze Körper... +Entscheidend für die Tests sind Gitter in einer Ebene und Körper... \chapter{Analytische Berechnung der Integrale} diff --git a/doc/doc2.tex b/doc/doc2.tex new file mode 100644 index 0000000..0545be6 --- /dev/null +++ b/doc/doc2.tex @@ -0,0 +1,167 @@ +\documentclass[a4paper,10pt,fleqn]{report} +\usepackage{fullpage} %Seiten etwas Größer +\usepackage{amsmath,amssymb} %Mathematische Symbole +%\usepackage{moreverb} +\usepackage{graphicx,psfrag,subfig} %Grafiken einbinden/Texte ersetzen/Bilder nebeneinander +%\usepackage{ifthen} +%\usepackage{showkeys} +%\usepackage[final,numbered]{mcode} +\usepackage{colortbl} %Einfache Färbungen in Tabellen +\usepackage{color} %Farben benutzen und Definieren +\usepackage{subfig} %mehrere Figuren in einer +\usepackage{hyperref} %Links im Inhaltsverzeichnis +\hypersetup{linkbordercolor={1 1 1},citebordercolor={1 1 1},urlbordercolor={1 1 1}} + + +\usepackage[ngerman]{babel} %Sprachpacket für Überschriften +\usepackage[utf8]{inputenc} %Eingabekodierung +\usepackage{fixltx2e} %Deutschsprach Bugs + +\definecolor{gray}{gray}{.95} + +\def\todo#1{\textcolor{red}{#1}} +\def\why#1{\textcolor{blue}{#1}} +\def\Matlab{{\sc Matlab}} +\def\q{\Q} + +\def\Ea{$E$} +\def\Eb{$\tilde E$} +\def\v{\boldsymbol{v}} +\def\D{\mathcal{D}} +\def\Q{\mathcal{Q}} +\def\G{\mathcal{G}} +\def\L{\mathcal{L}} +\def\T{\mathcal{T}} +\def\oder{\vee} +\def\und{\wedge} + +\newcommand{\dif}[2]{\frac{\partial#1}{\partial#2}} +\newcommand{\enorm}[1]{\left| \! \left| \! \left|#1\right| \! \right| \! \right|} +\newcommand{\norm}[1]{\lVert#1\rVert} +\newcommand{\abs}[1]{\lvert#1\rvert} +\newcommand{\showMesh}[2][]{\begin{figure}[ht] +\caption{#1} +\label{#2} +\centering +\subfloat[Lage]{\includegraphics[width=0.5\textwidth]{fig/#2_ref}} +\subfloat[Koordinaten]{\input{fig/#2_coo}}\\ +\subfloat[Elemente]{\input{fig/#2_ele}} +\subfloat[Nachbarn]{\input{fig/#2_nei}} +\end{figure}} + +\def\N{\mathbb{N}} +\def\R{\mathbb{R}} + +\author{P. Schaefer} + +\begin{document} +\tableofcontents +\clearpage +\chapter{Implementierung} + + +\section{Datenstruktur} +Alle Koordinaten werden in einer $ N \times 3,N \in \N$ Matrix abgespeichert. +\begin{displaymath} + COO[i,1:3] = C_i := (x_1,x_2,x_3)^{-1} \text{ wobei } x_1,x_2,x_3 \in \R \und i \in \{1,2 \dots N\} +\end{displaymath} +Jedes Element wird dann durch jeweils vier Koordinatenindizes als $M \times 4, M\in\N$ Matrix gespeichert. Wobei die Koordinaten links herum durchgegangen werden. +\begin{displaymath} + ELE[i,1:4] = E_i := (v_1,v_2,v_3,v_4) \text{ wobei } v_1,v_2,v_3,v_4 \in C \und i \in \{1,2 \dots M\} +\end{displaymath} +Aufgrund der Netzstabilität wollen wir maximal zwei Nachbarn an einer Kante zulassen, weshalb wir nur $2*4$ Einträge für die Nachbarschaftsrelationen pro Element benötigen. In der $M \times 8$ Matrix sind die Indizes der Nachbarn $n_1,n_2 \in E$ der Kante $(v_k, v_{k^{+1}}) | k\in \{1,2,3,4\}$ des Elements $E_i$ an den Stellen $NEI[i,[k,k+4]]$ gespeichert. Sollte eine Seite keinen Nachbarn haben markieren wir diese mit einer $0$. Außerdem wird an Kanten mit nur einem Nachbarn der erste Index auf den Nachbarn gesetzt und der zweite auf $0$.(Siehe Figur:\ref{exmpl3:nei:part}) +\\\noindent +Ein ausführliches Beispiel ist in Figure \ref{exmpl3} dargestellt. +\showMesh[Beispiel 3]{exmpl3} +\begin{figure}[ht] +\caption{Nachbarschaftsrelationen Element 4 aus \ref{exmpl3}} +\label{exmpl3:nei:part} +\centering + \subfloat[Lage]{\includegraphics{fig/Net_Neigh}} + \subfloat[Nachbarn]{\input{fig/exmpl3_nei_part}} +\end{figure} + + + + + +\section{Verfeinern} +Da wir im weiteren Verlauf sowohl adaptive also auch anisotrope Netzverfeinerung zulassen wollen, ist es sinnvoll eine Verfeinerungsfunktion zu implementieren, die alle Möglichen Teilungsprozesse auf einem Element unterstützt. Dabei sind vier nur wirklich relevant: +\begin{enumerate} + \item keine Teilung + \item volle Teilung in vier gleich große Elemente + \item halbe Teilung in zwei gleichgroße horizontal liegende Elemente + \item halbe Teilung in zwei gleichgroße vertikal liegende Elemente +\end{enumerate} +Zusätzlich wurde auch Typ 5. belegt, welcher als Ergebnis eine volle Teilung 2. ausführt, diese aber schrittweise durch eine 3. Teilung und zwei 4. Teilungen. + +Damit jedem Element $E_i$ eine Teilungsart zugeordnet werden kann, haben wir einen Markierungsvektor $marked \in {1,2,3,4,5}^M$ eingeführt. Dabei entspricht $marked_i$ der Art der Teilung für das Element $E_i$. Um isotrope und auch uniforme Teilungen zu erleichtern kann statt dem Vektor $marked$ auch nur ein Skalar übergeben werden $marked \in {1,2\dots5}$, wodurch jedes Element mit der gewählten Art verfeinert wird. + +Relevant zum Verfeinern eines Netzes sind also die Koordinaten $COO$, Elemente $ELE$ sowie die Nachbarschaftsrelationen $NEI$ und der Markierungsvektor $marked$. + +Da wir später einen Fehlerschätzer berechnen wollen, ist es wichtig sich zu jedem Element seine Teilelemente zu merken. Dazu legen wir während der Teilung eine $M \times 4$ Matrix an, in der die maximal vier Elementindizes gespeichert sind. Wenn wir also ein Element in vier gleich große Teile verfeinern, so wird das neue Element links unten das erste sein und alle weiteren folgen im Kreis links herum. Teilen wir ein Element in zwei gleich große Elemente, so werden die doppelt belegten Quadranten auch doppelt eingetragen. Ein gar nicht geteiltes Element wird also vier mal den alten Indizes speichern. Dadurch wird sicher gestellt, dass das arithmetische Mittel über die Elemente immer gültig auszuführen ist. +(Siehe Figur:\ref{exmpl3:f2s}) + +$[COO_{fine}, ELE_{fine}, NEI_{fine}, F2S ] = refineQuad(COO, ELE, NEI, marked);$ + +\begin{figure}[ht] +\caption{VaterSohn} +\centering +\subfloat[VaterSohn aus \ref{exmpl2}]{\input{fig/exmpl2_f2s}} +\subfloat[VaterSohn aus \ref{exmpl3}]{\input{fig/exmpl3_f2s}} +\end{figure} + +\section{Fehlerschätzer} +\begin{eqnarray*} +\mu_h^2 & = & \norm{\varrho_h^{1/2}(\phi_{\frac h 2}-\Pi_h\phi_{\frac h 2})}_{\L^2(\T)}^2 \\ +& = &\sum_{T\in \T_h}\mu_h(T)^2\\ +\mu_h(T)^2 & = & \norm{\varrho_h^{1/2}(\phi_{\frac h 2}-\Pi_h\phi_{\frac h 2})}_{\L^2(\T)}^2 \\ +& = & h_{min}(T)\norm{\phi_{\frac h 2}-\Pi_h\phi_{\frac h 2}}_{\L^2(\T)}^2 \\ +&& T_j \in \tau_h, t_j^{(1)},\dots,t_j^{(4)} \in \tau_{\frac h 2} \\ +\phi_{\frac h 2}|_{T_j} & = &x_j^{(1)}\chi_{t_j^{(1)}}+\dots+x_j^{(4)}\chi_{t_j^{(4)}}\\ +\Pi_h\phi_{\frac h 2}|_{T_j}&=&\frac 1 {\abs{T_j}}\int_{T_j}\phi_{\frac h 2}d\Gamma\\ +& =&\frac 1 {\abs{T_j}}\sum_{k=1}^4x_j^{(k)}\int_{t^{(k)}}1d\Gamma\\ +& =&\frac 1 {\abs{T_j}}\sum_{k=1}^4x_j^{(k)}\abs{t_j^{(k)}}\\ +& =&\frac 1 {\abs{T_j}}\sum_{k=1}^4x_j^{(k)}\frac {\abs{T_j}} 4 \\ +& =&\frac 1 4 (x_j^{(1)} +\dots+x_j^{(4)} )=: m_j\\ +\norm{\phi_{\frac h 2} - \Pi_h\phi_{\frac h 2}}_{\L^2(T_j)}^2 +&=&\sum_{k=1}^4\norm{\phi_{\frac h 2} - \Pi_h\phi_{\frac h 2}}_{\L^2\left(t_j^{(k)}\right)}^2\\ +&=&\sum_{k=1}^4 \int_{t_j^{(k)}}(\phi_{\frac h 2} - \Pi_h\phi_{\frac h 2})^2d\Gamma\\ +&=&\sum_{k=1}^4 \int_{t_j^{(k)}}(x_j^{(k)}-m_j)^2d\Gamma\\ +&=&\sum_{k=1}^4 \abs{t_j^{(k)}}(x_j^{(k)}-m_j)^2\\ +&=&\frac {\abs{T_j}} 4\sum_{k=1}^4 (x_j^{(k)}-m_j)^2\\ +\mu_e(T_j)^2 & = & \frac{\why{ h_{min}(T_j)} \abs{T_j}}{4} \sum_{k=1}^4{(x_j^{(k)}-m_j)^2} +\end{eqnarray*} + +$mu = computeEstSlpMuTilde(x_{fine}, COO, ELE, F2S);$ + +\section{Markieren} +Bestimme $M_e \subseteq T_e$ mit minimaler Kardinalität +\begin{eqnarray*} +\theta \sum_{T\in T_e} \mu_e(T)^2 & \leq & \sum_{T\in M_e} \mu_e(T)^2 +\end{eqnarray*} +Zur anisotropen Verfeinerung wird weiterhin berechnet: +\begin{eqnarray*} +\begin{pmatrix} + C_j^{(1)}\\ C_j^{(2)}\\C_j^{(3)}\\ C_j^{(4)} +\end{pmatrix} +& = & \frac 1 4 +\begin{pmatrix} +1 & 1 & 1 & 1\\ +1 & -1 & 1 & -1\\ +1 & 1 & -1 & -1\\ +1 & -1 & -1 & 1\\ +\end{pmatrix} +\begin{pmatrix} + x_j^{(1)}\\ x_j^{(2)}\\x_j^{(3)}\\ x_j^{(4)} +\end{pmatrix} +\end{eqnarray*} + +\begin{eqnarray*} +\eta \abs{ C_j^{(3)}} & \geq & \sqrt{\abs{ C_j^{(2)}}^2 + \abs{ C_j^{(4)}}^2}\\ +\eta \abs{ C_j^{(4)}} & \geq & \sqrt{\abs{ C_j^{(2)}}^2 + \abs{ C_j^{(3)}}^2} +\end{eqnarray*} + +$xF2S := x_{fine}[F2S]$\\ +$marked = computeEstSlpMuTilde(xF2S, mu, theta, eta);$ +\end{document} diff --git a/doc/fig/Net_Neigh.eps b/doc/fig/Net_Neigh.eps new file mode 100644 index 0000000..0c21686 --- /dev/null +++ b/doc/fig/Net_Neigh.eps @@ -0,0 +1,272 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: cairo 1.10.2 (http://cairographics.org) +%%CreationDate: 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+\begin{tabular}{>{\columncolor{gray}}rcccc} +\rowcolor{gray} + Index & c1 & c2 & c3 & c4\\ + 1 & 2 & 5 & 6 & 3\\ + 2 & 5 & 8 & 9 & 6\\ + 3 & 4 & 7 & 8 & 5\\ + 4 & 1 & 4 & 5 & 2 +\end{tabular} +\label{exmpl1:ele} \ No newline at end of file diff --git a/doc/fig/exmpl1_f2s.tex b/doc/fig/exmpl1_f2s.tex new file mode 100644 index 0000000..5037733 --- /dev/null +++ b/doc/fig/exmpl1_f2s.tex @@ -0,0 +1,16 @@ +\begin{tabular}{>{\columncolor{gray}}rcccc} +\rowcolor{gray} + Index & e1 & e2 & e3 & e4\\ + 1 & 1 & 1 & 1 & 1\\ + 2 & 2 & 2 & 2 & 2\\ + 3 & 3 & 3 & 3 & 3\\ + 4 & 4 & 4 & 4 & 4\\ + 5 & 12 & 14 & 13 & 5\\ + 6 & 6 & 6 & 6 & 6\\ + 7 & 7 & 7 & 7 & 7\\ + 8 & 8 & 8 & 8 & 8\\ + 9 & 9 & 9 & 9 & 9\\ + 10 & 10 & 10 & 10 & 10\\ + 11 & 11 & 11 & 11 & 11 +\end{tabular} +\label{exmpl1:f2s} \ No newline at end of file diff --git a/doc/fig/exmpl1_nei.tex b/doc/fig/exmpl1_nei.tex new file mode 100644 index 0000000..8d7f3c9 --- /dev/null +++ b/doc/fig/exmpl1_nei.tex @@ -0,0 +1,9 @@ +\begin{tabular}{>{\columncolor{gray}}rcccccccc} +\rowcolor{gray} + Index & n1 & n2 & n3 & n4 & n5 & n6 & n7 & n8\\ + 1 & 4 & 2 & 0 & 0 & 0 & 0 & 0 & 0\\ + 2 & 3 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\ + 3 & 0 & 0 & 2 & 4 & 0 & 0 & 0 & 0\\ + 4 & 0 & 3 & 1 & 0 & 0 & 0 & 0 & 0 +\end{tabular} +\label{exmpl1:nei} \ No newline at end of file diff --git a/doc/fig/exmpl1_ref.eps b/doc/fig/exmpl1_ref.eps new file mode 100644 index 0000000..f5c1c4a --- /dev/null +++ b/doc/fig/exmpl1_ref.eps @@ -0,0 +1,302 @@ +%!PS-Adobe-2.0 EPSF-1.2 +%%Creator: MATLAB, The MathWorks, Inc. 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a/doc/fig/exmpl2_coo.tex b/doc/fig/exmpl2_coo.tex new file mode 100644 index 0000000..4597de8 --- /dev/null +++ b/doc/fig/exmpl2_coo.tex @@ -0,0 +1,23 @@ +\begin{tabular}{>{\columncolor{gray}}rccc} +\rowcolor{gray} + Index & x1 & x2 & x3\\ + 1 & 0.0000 & 0.0000 & 0.0000\\ + 2 & 0.0000 & 0.2500 & 0.0000\\ + 3 & 0.0000 & 0.5000 & 0.0000\\ + 4 & 0.0000 & 0.7500 & 0.0000\\ + 5 & 0.0000 & 1.0000 & 0.0000\\ + 6 & 0.2500 & 0.0000 & 0.0000\\ + 7 & 0.2500 & 0.2500 & 0.0000\\ + 8 & 0.2500 & 0.5000 & 0.0000\\ + 9 & 0.2500 & 0.7500 & 0.0000\\ + 10 & 0.2500 & 1.0000 & 0.0000\\ + 11 & 0.5000 & 0.0000 & 0.0000\\ + 12 & 0.5000 & 0.2500 & 0.0000\\ + 13 & 0.5000 & 0.5000 & 0.0000\\ + 14 & 0.5000 & 0.7500 & 0.0000\\ + 15 & 0.5000 & 1.0000 & 0.0000\\ + 16 & 1.0000 & 0.0000 & 0.0000\\ + 17 & 1.0000 & 0.5000 & 0.0000\\ + 18 & 1.0000 & 0.7500 & 0.0000\\ + 19 & 1.0000 & 1.0000 & 0.0000 +\end{tabular} diff --git a/doc/fig/exmpl2_ele.tex b/doc/fig/exmpl2_ele.tex new file mode 100644 index 0000000..8d7c7da --- /dev/null +++ b/doc/fig/exmpl2_ele.tex @@ -0,0 +1,16 @@ +\begin{tabular}{>{\columncolor{gray}}rcccc} +\rowcolor{gray} + Index & c1 & c2 & c3 & c4\\ + 1 & 4 & 9 & 10 & 5\\ + 2 & 14 & 18 & 19 & 15\\ + 3 & 11 & 16 & 17 & 13\\ + 4 & 2 & 7 & 8 & 3\\ + 5 & 3 & 8 & 9 & 4\\ + 6 & 13 & 17 & 18 & 14\\ + 7 & 7 & 12 & 13 & 8\\ + 8 & 6 & 11 & 12 & 7\\ + 9 & 1 & 6 & 7 & 2\\ + 10 & 9 & 14 & 15 & 10\\ + 11 & 8 & 13 & 14 & 9 +\end{tabular} +\label{exmpl2:ele} \ No newline at end of file diff --git a/doc/fig/exmpl2_f2s.tex b/doc/fig/exmpl2_f2s.tex new file mode 100644 index 0000000..c7d66b4 --- /dev/null +++ b/doc/fig/exmpl2_f2s.tex @@ -0,0 +1,9 @@ +\begin{tabular}{>{\columncolor{gray}}rcccc} +\rowcolor{gray} + Index & e1 & e2 & e3 & e4\\ + 1 & 5 & 11 & 10 & 1\\ + 2 & 6 & 6 & 2 & 2\\ + 3 & 3 & 3 & 3 & 3\\ + 4 & 9 & 8 & 7 & 4 +\end{tabular} +\label{exmpl2:f2s} \ No newline at end of file diff --git a/doc/fig/exmpl2_nei.tex b/doc/fig/exmpl2_nei.tex new file mode 100644 index 0000000..9da83b6 --- /dev/null +++ b/doc/fig/exmpl2_nei.tex @@ -0,0 +1,16 @@ +\begin{tabular}{>{\columncolor{gray}}rcccccccc} +\rowcolor{gray} + Index & n1 & n2 & n3 & n4 & n5 & n6 & n7 & n8\\ + 1 & 5 & 10 & 0 & 0 & 0 & 0 & 0 & 0\\ + 2 & 6 & 0 & 0 & 10 & 0 & 0 & 0 & 0\\ + 3 & 0 & 0 & 6 & 8 & 0 & 0 & 0 & 7\\ + 4 & 9 & 7 & 5 & 0 & 0 & 0 & 0 & 0\\ + 5 & 4 & 11 & 1 & 0 & 0 & 0 & 0 & 0\\ + 6 & 3 & 0 & 2 & 11 & 0 & 0 & 0 & 0\\ + 7 & 8 & 3 & 11 & 4 & 0 & 0 & 0 & 0\\ + 8 & 0 & 3 & 7 & 9 & 0 & 0 & 0 & 0\\ + 9 & 0 & 8 & 4 & 0 & 0 & 0 & 0 & 0\\ + 10 & 11 & 2 & 0 & 1 & 0 & 0 & 0 & 0\\ + 11 & 7 & 6 & 10 & 5 & 0 & 0 & 0 & 0 +\end{tabular} +\label{exmpl2:nei} \ No newline at end of file diff --git a/doc/fig/exmpl2_ref.eps b/doc/fig/exmpl2_ref.eps new file mode 100644 index 0000000..fe1ab01 --- /dev/null +++ b/doc/fig/exmpl2_ref.eps @@ -0,0 +1,323 @@ +%!PS-Adobe-2.0 EPSF-1.2 +%%Creator: MATLAB, The MathWorks, Inc. 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0.0000\\ + 4 & 0.0000 & 0.6250 & 0.0000\\ + 5 & 0.0000 & 0.7500 & 0.0000\\ + 6 & 0.0000 & 1.0000 & 0.0000\\ + 7 & 0.1250 & 0.5000 & 0.0000\\ + 8 & 0.1250 & 0.6250 & 0.0000\\ + 9 & 0.1250 & 0.7500 & 0.0000\\ + 10 & 0.2500 & 0.0000 & 0.0000\\ + 11 & 0.2500 & 0.2500 & 0.0000\\ + 12 & 0.2500 & 0.5000 & 0.0000\\ + 13 & 0.2500 & 0.6250 & 0.0000\\ + 14 & 0.2500 & 0.7500 & 0.0000\\ + 15 & 0.2500 & 1.0000 & 0.0000\\ + 16 & 0.5000 & 0.0000 & 0.0000\\ + 17 & 0.5000 & 0.2500 & 0.0000\\ + 18 & 0.5000 & 0.5000 & 0.0000\\ + 19 & 0.5000 & 0.7500 & 0.0000\\ + 20 & 0.5000 & 1.0000 & 0.0000\\ + 21 & 1.0000 & 0.0000 & 0.0000\\ + 22 & 1.0000 & 0.5000 & 0.0000\\ + 23 & 1.0000 & 0.7500 & 0.0000\\ + 24 & 1.0000 & 1.0000 & 0.0000 +\end{tabular} diff --git a/doc/fig/exmpl3_ele.tex b/doc/fig/exmpl3_ele.tex new file mode 100644 index 0000000..e1f4e9d --- /dev/null +++ b/doc/fig/exmpl3_ele.tex @@ -0,0 +1,19 @@ +\begin{tabular}{>{\columncolor{gray}}rcccc} +\rowcolor{gray} + Index & c1 & c2 & c3 & c4\\ + 1 & 5 & 14 & 15 & 6\\ + 2 & 19 & 23 & 24 & 20\\ + 3 & 16 & 21 & 22 & 18\\ + 4 & 2 & 11 & 12 & 3\\ + 5 & 4 & 8 & 9 & 5\\ + 6 & 18 & 22 & 23 & 19\\ + 7 & 11 & 17 & 18 & 12\\ + 8 & 10 & 16 & 17 & 11\\ + 9 & 1 & 10 & 11 & 2\\ + 10 & 14 & 19 & 20 & 15\\ + 11 & 12 & 18 & 19 & 14\\ + 12 & 3 & 7 & 8 & 4\\ + 13 & 8 & 13 & 14 & 9\\ + 14 & 7 & 12 & 13 & 8 +\end{tabular} +\label{exmpl3:ele} \ No newline at end of file diff --git a/doc/fig/exmpl3_f2s.tex b/doc/fig/exmpl3_f2s.tex new file mode 100644 index 0000000..3a0d666 --- /dev/null +++ b/doc/fig/exmpl3_f2s.tex @@ -0,0 +1,16 @@ +\begin{tabular}{>{\columncolor{gray}}rcccc} +\rowcolor{gray} + Index & e1 & e2 & e3 & e4\\ + 1 & 1 & 1 & 1 & 1\\ + 2 & 2 & 2 & 2 & 2\\ + 3 & 3 & 3 & 3 & 3\\ + 4 & 4 & 4 & 4 & 4\\ + 5 & 12 & 14 & 13 & 5\\ + 6 & 6 & 6 & 6 & 6\\ + 7 & 7 & 7 & 7 & 7\\ + 8 & 8 & 8 & 8 & 8\\ + 9 & 9 & 9 & 9 & 9\\ + 10 & 10 & 10 & 10 & 10\\ + 11 & 11 & 11 & 11 & 11 +\end{tabular} +\label{exmpl3:f2s} \ No newline at end of file diff --git a/doc/fig/exmpl3_nei.tex b/doc/fig/exmpl3_nei.tex new file mode 100644 index 0000000..483a265 --- /dev/null +++ b/doc/fig/exmpl3_nei.tex @@ -0,0 +1,19 @@ +\begin{tabular}{>{\columncolor{gray}}rcccccccc} +\rowcolor{gray} + Index & n1 & n2 & n3 & n4 & n5 & n6 & n7 & n8\\ + 1 & 13 & 10 & 0 & 0 & 5 & 0 & 0 & 0\\ + 2 & 6 & 0 & 0 & 10 & 0 & 0 & 0 & 0\\ + 3 & 0 & 0 & 6 & 8 & 0 & 0 & 0 & 7\\ + 4 & 9 & 7 & 12 & 0 & 0 & 0 & 14 & 0\\ + 5 & 12 & 13 & 1 & 0 & 0 & 0 & 0 & 0\\ + 6 & 3 & 0 & 2 & 11 & 0 & 0 & 0 & 0\\ + 7 & 8 & 3 & 11 & 4 & 0 & 0 & 0 & 0\\ + 8 & 0 & 3 & 7 & 9 & 0 & 0 & 0 & 0\\ + 9 & 0 & 8 & 4 & 0 & 0 & 0 & 0 & 0\\ + 10 & 11 & 2 & 0 & 1 & 0 & 0 & 0 & 0\\ + 11 & 7 & 6 & 10 & 14 & 0 & 0 & 0 & 13\\ + 12 & 4 & 14 & 5 & 0 & 0 & 0 & 0 & 0\\ + 13 & 14 & 11 & 1 & 5 & 0 & 0 & 0 & 0\\ + 14 & 4 & 11 & 13 & 12 & 0 & 0 & 0 & 0 +\end{tabular} +\label{exmpl3:nei} \ No newline at end of file diff --git a/doc/fig/exmpl3_nei_part.tex b/doc/fig/exmpl3_nei_part.tex new file mode 100644 index 0000000..a1cc1a3 --- /dev/null +++ b/doc/fig/exmpl3_nei_part.tex @@ -0,0 +1,6 @@ +\begin{tabular}{>{\columncolor{gray}}rcccccccc} +\rowcolor{gray} + Index & n1 & n2 & n3 & n4 & n5 & n6 & n7 & n8\\ + 4 & 9 & 7 & 12 & 0 & 0 & 0 & 14 & 0 +\end{tabular} +\label{exmpl3:nei} diff --git a/doc/fig/exmpl3_ref.eps b/doc/fig/exmpl3_ref.eps new file mode 100644 index 0000000..fc682fd --- /dev/null +++ b/doc/fig/exmpl3_ref.eps @@ -0,0 +1,332 @@ +%!PS-Adobe-2.0 EPSF-1.2 +%%Creator: MATLAB, The MathWorks, Inc. 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+/bpage {/pgsv save def} bdef +/epage {pgsv restore} bdef +/bplot /gsave ldef +/eplot {stroke grestore} bdef +% orientation switch +/portraitMode 0 def /landscapeMode 1 def /rotateMode 2 def +% coordinate system mappings +/dpi2point 0 def +% font control +/FontSize 0 def +/FMS {/FontSize xstore findfont [FontSize 0 0 FontSize neg 0 0] + makefont setfont} bdef +/reencode {exch dup where {pop load} {pop StandardEncoding} ifelse + exch dup 3 1 roll findfont dup length dict begin + { 1 index /FID ne {def}{pop pop} ifelse } forall + /Encoding exch def currentdict end definefont pop} bdef +/isroman {findfont /CharStrings get /Agrave known} bdef +/FMSR {3 1 roll 1 index dup isroman {reencode} {pop pop} ifelse + exch FMS} bdef +/csm {1 dpi2point div -1 dpi2point div scale neg translate + dup landscapeMode eq {pop -90 rotate} + {rotateMode eq {90 rotate} if} ifelse} bdef +% line types: solid, dotted, dashed, dotdash +/SO { [] 0 setdash } bdef +/DO { [.5 dpi2point mul 4 dpi2point mul] 0 setdash 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1 asub + dup 0 get exch 1 get 7 -1 roll astore } bdef +/compute_transform { + dmat dtri tri_to_matrix tmat1 invertmatrix + smat stri tri_to_matrix tmat2 concatmatrix } bdef +/ds {stri astore pop} bdef +/dt {dtri astore pop} bdef +/db {2 copy /cols xdef /rows xdef mul dup 3 mul string + currentfile exch readhexstring pop + dup 0 3 index getinterval /rbmap xdef + dup 2 index dup getinterval /gbmap xdef + 1 index dup 2 mul exch getinterval /bbmap xdef pop pop}bdef +/it {gs np dtri aload pop moveto lineto lineto cp c + cols rows 8 compute_transform + rbmap gbmap bbmap true 3 colorimage gr}bdef +/il {newpath moveto lineto stroke}bdef +currentdict end def +%%EndProlog + +%%BeginSetup +MathWorks begin + +0 cap + +end +%%EndSetup + +%%Page: 1 1 +%%BeginPageSetup +%%PageBoundingBox: 58 199 546 589 +MathWorks begin +bpage +%%EndPageSetup + +%%BeginObject: obj1 +bplot + +/dpi2point 8.33333 def +portraitMode 0150 5100 csm + + 334 190 4067 3251 MR c np +85 dict begin %Colortable dictionary +/c0 { 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