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创建吸收马尔可夫链的图表

tag-icon • tag-icon tikz-pgf graphs
创建吸收马尔可夫链的图表

我在创建以下图表时遇到了问题 在此处输入图片描述

它应该具有以下样式 在此处输入图片描述

代码如下

\documentclass{article}
\usepackage[margin=1in]{geometry}
\usepackage{amsmath,amssymb}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric,automata,positioning} 
\newcommand{\N}{\mathbb{N}} % natuerliche Zahlen
    \newcommand{\Z}{\mathbb{Z}} % ganze Zahlen
    \newcommand{\Q}{\mathbb{Q}} % rationale Zahlen
    \newcommand{\R}{\mathbb{R}} % reelle Zahlen
    \newcommand{\Prob}{\mathbb{P}} % Symbol fuer Wahrscheinlichkeitsmaß
    \newcommand{\E}{\mathbb{E}} % Symbol fuer Erwartungswert
    \newcommand{\QAt}{\mathbf{Q}_{A_{2}A_{2}}}
    \newcommand{\QAo}{\mathbf{Q}_{A_{1}A_{1}}}
    \newcommand{\QAot}{\mathbf{Q}_{A_{1}A_{2}}}
    \newcommand{\QAto}{\mathbf{Q}_{A_{2}A_{1}}}
    \newcommand{\QAtC}{\mathbf{Q}_{A_{2}C}}
    \newcommand{\QAtw}{\mathbf{Q}_{A_{2}\{\omega\}}}
    \newcommand{\QAow}{\mathbf{Q}_{A_{1}\{\omega\}}}
    \newcommand{\I}{\mathbf{I}}
    \newcommand{\vf}{\mathbf{v}}
    \newcommand{\Df}{\mathbf{D}}
    \newcommand{\af}{\pmb{\alpha}}
    \newcommand{\eef}{\mathbf{e}}
    \newcommand{\Psf}{\pmb{\Psi}}
    \newcommand{\Phf}{\pmb{\Phi}}
    \newcommand{\bef}{\pmb{\beta}}
    \newcommand{\Pf}{\mathbf{P}}
    \newcommand{\Qf}{\mathbf{Q}}
    \newcommand{\mf}{\mathbf{m}}
    \newcommand{\ef}{\pmb{\varepsilon}}
    \newcommand{\Hf}{\mathbf{H}}
    \newcommand{\Ef}{\mathbf{E}}
    \newcommand{\Mf}{\mathbf{M}}
    \newcommand{\Vf}{\mathbf{V}}
    \newcommand{\gf}{\mathbf{g}}
    \newcommand{\QSo}{\mathbf{Q}_{S' S'}}
    \newcommand{\QSot}{\mathbf{Q}_{S' S''}}
    \newcommand{\QSt}{\mathbf{Q}_{S'' S''}}
    \newcommand{\UP}[2]{\makebox[0pt]{\smash{\raisebox{1.5em}{$\phantom{#2}#1$}}}#2}
    \newcommand{\LF}[1]{\makebox[0pt]{$#1$\hspace{4.5em}}}
    \newcommand{\zfo}{\mathbf{z}_{1}}
    \newcommand{\zft}{\mathbf{z}_{2}}
    \newcommand{\zf}{\mathbf{z}}
\begin{document}}


    \begin{tikzpicture}[->,>=stealth,shorten >=1pt,auto,node distance=2.5cm,
                        semithick]
      \tikzset{every state/.append style={fill=red,draw=none,text=white}}

      \node[state]         (A)                    {$\{\omega\}$};
      \node[state]         (B) [below=of A] {$A_{2}(1)$};
      \node[state]         (C) [below=of B] {$A_{1}(1)$};
      \node[state]         (D) [below=of C] {$\{\omega\}$};
      \node[state]         (F) [right=of B] {$A_{2}(2)$};
      \node[state]         (E) [above=of F] {$\{\omega\}$};
      \node[state]         (G) [below=of F] {$A_{1}(2)$};
      \node[state]         (H) [below=of G] {$\{\omega\}$};
      \node[state]         (J) [right=of F] {$A_{2}(m)$};
      \node[state]         (I) [above=of J] {$\{\omega\}$};
      \node[state]         (K) [below=of J] {$A_{1}(m)$};
      \node[state]         (L) [below=of K] {$\{\omega\}$};
      \node[state]         (M) [right=of J] {$A_{2}$\scriptsize(m+1)};


      \path (B) edge              node {$\mathbf{Q}_{A_{2}\{\omega\}}$} (A)
                edge [loop left]  node {$\QAt$}                         (B)
                edge              node {$\QAto$}                        (C)
            (C) edge [loop left]  node {$\QAo$}                         (C)
                edge              node {$\mathbf{Q}_{A_{1}\{\omega\}}$} (D)
                edge [right]      node {$\QAot$}                        (F)
            (F) edge              node {$\mathbf{Q}_{A_{2}\{\omega\}}$} (E)
                edge [loop left]  node {$\QAt$}                         (F)
                edge              node(aux) {$\QAto$}                        (G)
            (G) edge [loop left]  node {$\QAo$}                         (G)
                edge              node {$\mathbf{Q}_{A_{1}\{\omega\}}$} (H)
            (J) edge              node {$\mathbf{Q}_{A_{2}\{\omega\}}$} (I)
                edge [loop left]  node {$\QAt$}                         (J)
                edge              node {$\QAto$}                        (K)
            (K) edge [loop left]  node {$\QAo$}                         (K)
                edge              node {$\mathbf{Q}_{A_{1}\{\omega\}}$} (L)
                edge [right]      node {$\QAot$}                        (M)
            (M) edge [loop left]  node {$\I$}                           (M);
     \node[right=2mm of aux,font=\bfseries\Huge]{\dots};
    \end{tikzpicture}
\end{document}

谢谢你的帮助

答案1

以下是一些起点：

\documentclass[tikz, border=3mm]{standalone}
\usetikzlibrary{automata,chains,positioning}

\begin{document}

\begin{tikzpicture}[
  auto,
  node distance = 14mm,
  start chain = going right,
  state/.append style = {
      thick, 
      minimum width=3em,
      on chain,
  fill=red,
  draw=none,
  text=white
 },
]

\node (s0)[state]    {$1$};   
\node (s1)[state]    {$2$};  
\node (s2)[state]    {$3$};  
\node (s3)[state]    {$r-2$};  
\node (s4)[state]    {$r-1$};     

\draw[->] (s0) edge[bend left] node (a1) {p} (s1)
          (s1) edge[bend left] node (b1) {q} (s0)
          (s1) edge[bend left] node (a2) {p} (s2)
          (s2) edge[bend left] node (b2) {q} (s1)
          (s3) edge[bend left] node (a4) {p} (s4)
          (s4) edge[bend left] node (b4) {q} (s3)
          ;

\node[state,node distance=3cm] (a) [below=of s2] {$\alpha$};      
\draw[->] (s4.south west) edge node {p} (a); 
\draw[<-] (a) edge node {q} (s0.south east); 
\node[node distance=0.3cm,right=of s2] {$\ldots$};  
\path (a) edge [loop below] node {Q} (a);    

\end{tikzpicture}

\end{document}

在此处输入图片描述

答案2

编辑：一个新版本。我做了一些改变。你可以改变字符的大小，类似地，有一个大的页和和大1。

在此处输入图片描述

\documentclass[a4paper,12pt]{article}
\usepackage{tikz, tikz-cd,amsmath}
\usepackage{graphicx}
\newcommand*\nci[1]{\tikz[baseline=(char.base)]{
            \node[shape=circle, draw=red, fill=red, draw,inner sep=7pt] (char) {#1};}}
\usepackage{adjustbox}
\begin{document}
\adjustbox{scale=.5,center}{%
\begin{tikzcd}[column sep=1.6in,row sep=1.1in]
\nci{\textcolor{white}{\resizebox{.5cm}{!}{1}}}\arrow[r, "\resizebox{.5cm}{!}{$p$}", bend left=15] \arrow[rrd, "q"'] & \nci{\textcolor{white}{2}} \arrow[l, "q", bend left=15] \arrow[r, "p", bend left=15] & \nci{\textcolor{white}{3}}\cdots  \arrow[l, "q", bend left=15] & \qquad \cdots \nci{\textcolor{white}{$r-2$}} \arrow[r, "p", bend left=10] & \nci{\textcolor{white}{$r-1$}} \arrow[lld, "p"'] \arrow[l, "q", bend left=10] \\
  &  & \alpha &  & 
\end{tikzcd}
}
\end{document}

这里有一个版本tikz-cd只需与您想要的进行比较即可。当然，您可以增加字符的大小等。

在此处输入图片描述

\documentclass[a4paper,12pt]{standalone}
\usepackage{tikz-cd,amsmath}


\begin{document}
\begin{tikzcd}[column sep=1.6in,row sep=1.1in]
1 \arrow[r, "p", bend left=15] \arrow[rrd, "q"'] & 2 \arrow[l, "q", bend left=15] \arrow[r, "p", bend left=15] & 3\cdots  \arrow[l, "q", bend left=15] & \qquad \cdots r-2 \arrow[r, "p", bend left=10] & r-1 \arrow[lld, "p"'] \arrow[l, "q", bend left=10] \\
  &  & \alpha &  & 
\end{tikzcd}
\end{document}

答案3

这是一个使用chainTikZ 概念的解决方案（参见 3.0.1a 手册第 257 页第 19 节）。第一个字符串定义节点1; 2; 3; ...;n-1和n-2。第二个链重用这些节点并将箭头放在相反的方向。

查恩

\documentclass[a4paper,12pt]{article}
\usepackage{tikz}
\usetikzlibrary{graphs,quotes}
\begin{document}

\begin{tikzpicture}
\graph[grow right=20mm,edges=bend left,edge node={node [yshift=3pt, midway]{p}}] {
1 -> 2   -> 3-!-4/$\cdots$   -!- 5/{$n-2$}->6/{$n-1$}  ;
};
\graph[use existing nodes,edges=bend right,grow right=20mm,edge node={node [yshift=3pt, midway]{q}}]  {
1 <- 2   <- 3-!-4/$\cdots$   -!- 5/{$n-2$}<-6/{$n-1$}  ;
};
\node at (5,-2)(a){a}edge [loop below] node {s} ();;
\graph[use existing nodes,edges={bend right=10}]{ 1.south->[edge label'=q](a)<-[edge label=p]6.south;};
\end{tikzpicture}
\end{document}

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