如何使用“tikz”在路径图中绘制观测值和残差方差？

Question 1

ext.paths.arcto我的图书馆tikz-ext包裹允许指定要绘制的圆弧的起点和终点以及半径。arc to路径操作需要两个附加信息，即方向和大小，以确定您需要两点之间的四个圆弧中的哪一个。在本例中，它们是counter clockwise（因为起点和终点按逆时针顺序排列）和large（因为我们想要绘制圆的较大部分）。

可以与或路径操作circle loop = <direction>一起使用，这样您只需指定一次节点名称，其他所有计算都由样式完成。使用和的值。扩展定义了节点边界上起点和终点之间的角度差。toedgecircle loop radiuscircle loop spread

参数<direction>指定此圆环的中间位置。目前，这需要一个实际数字。再多花点功夫，我们就可以允许circle loop = west或circle loop = east工作。不过，你总是可以定义cloop right/.style={circle loop = 0}等等，类似于TikZ 的循环键。

代码

\documentclass[tikz]{standalone}
\usepackage{tikz}
\usetikzlibrary{
  chains,          % easy placement of nodes in a row
  arrows.meta,     %
  bending,         % for flex option (for arrow tips on tightly curved paths)
  ext.paths.arcto} % for arcto path operation
\tikzset{
  math nodes/.style={execute at begin node=$, execute at end node=$},
  circle loop radius/.initial=.5cm,
  circle loop spread/.initial=60,
  circle loop/.style={
    to path={
      (\tikztostart.{#1-(\pgfkeysvalueof{/tikz/circle loop spread})/2})
      arc to[counter clockwise, large,
             radius=\pgfkeysvalueof{/tikz/circle loop radius}]
      (\tikztostart.{#1+(\pgfkeysvalueof{/tikz/circle loop spread})/2})
      \tikztonodes }}}
\begin{document}
\begin{tikzpicture}[
  rect/.style={shape=rectangle, draw, minimum size=+1cm},
  circ/.style={shape=circle,    draw, minimum size=+.8cm},
%  Tri/.tip={Triangle[length=+.25cm, width=+.2cm]},
  Tri/.tip={Triangle[angle'=45, scale=1.15]}, % scales with line width
  > = Tri,
  arr/.style={very thick, nodes={fill=white}, shape=circle, inner sep=+.15em},
  math nodes,
]
\begin{scope}[start chain=going right, nodes=on chain]
\node[rect] (X) {X};
\node       (b) {\beta};
\node[rect] (Y) {Y};
\node[circ] (e) {\varepsilon};
\end{scope}
\path[arr] (X) edge (b)
           (b) edge[->] (Y)
           (Y) edge[<-] (e)
           (X) edge[<->, circle loop=180] node {\theta} ()
           (e) edge[<->, circle loop=  0] node {\theta} ()
               edge[<->, gray, thick, % changing the spread
                         circle loop=  0, circle loop spread=90] ()
;
\end{tikzpicture}
\end{document}

输出

Answer

ext.paths.arcto我的图书馆tikz-ext包裹允许指定要绘制的圆弧的起点和终点以及半径。arc to路径操作需要两个附加信息，即方向和大小，以确定您需要两点之间的四个圆弧中的哪一个。在本例中，它们是counter clockwise（因为起点和终点按逆时针顺序排列）和large（因为我们想要绘制圆的较大部分）。

可以与或路径操作circle loop = <direction>一起使用，这样您只需指定一次节点名称，其他所有计算都由样式完成。使用和的值。扩展定义了节点边界上起点和终点之间的角度差。toedgecircle loop radiuscircle loop spread

参数<direction>指定此圆环的中间位置。目前，这需要一个实际数字。再多花点功夫，我们就可以允许circle loop = west或circle loop = east工作。不过，你总是可以定义cloop right/.style={circle loop = 0}等等，类似于TikZ 的循环键。

代码

\documentclass[tikz]{standalone}
\usepackage{tikz}
\usetikzlibrary{
  chains,          % easy placement of nodes in a row
  arrows.meta,     %
  bending,         % for flex option (for arrow tips on tightly curved paths)
  ext.paths.arcto} % for arcto path operation
\tikzset{
  math nodes/.style={execute at begin node=$, execute at end node=$},
  circle loop radius/.initial=.5cm,
  circle loop spread/.initial=60,
  circle loop/.style={
    to path={
      (\tikztostart.{#1-(\pgfkeysvalueof{/tikz/circle loop spread})/2})
      arc to[counter clockwise, large,
             radius=\pgfkeysvalueof{/tikz/circle loop radius}]
      (\tikztostart.{#1+(\pgfkeysvalueof{/tikz/circle loop spread})/2})
      \tikztonodes }}}
\begin{document}
\begin{tikzpicture}[
  rect/.style={shape=rectangle, draw, minimum size=+1cm},
  circ/.style={shape=circle,    draw, minimum size=+.8cm},
%  Tri/.tip={Triangle[length=+.25cm, width=+.2cm]},
  Tri/.tip={Triangle[angle'=45, scale=1.15]}, % scales with line width
  > = Tri,
  arr/.style={very thick, nodes={fill=white}, shape=circle, inner sep=+.15em},
  math nodes,
]
\begin{scope}[start chain=going right, nodes=on chain]
\node[rect] (X) {X};
\node       (b) {\beta};
\node[rect] (Y) {Y};
\node[circ] (e) {\varepsilon};
\end{scope}
\path[arr] (X) edge (b)
           (b) edge[->] (Y)
           (Y) edge[<-] (e)
           (X) edge[<->, circle loop=180] node {\theta} ()
           (e) edge[<->, circle loop=  0] node {\theta} ()
               edge[<->, gray, thick, % changing the spread
                         circle loop=  0, circle loop spread=90] ()
;
\end{tikzpicture}
\end{document}

输出

Question 2

还没有解决方案，只是进行一些清理，以便更好地看到树林中的森林，即相关结构：

%\documentclass{article}
\documentclass[10pt,border=3mm,tikz]{standalone}
\usepackage{amsmath}
%\usepackage{tikz}% already included, see above

% Page style.
%\pagestyle{empty}

% `tikz` options.
\usetikzlibrary{positioning}
\usetikzlibrary{arrows.meta}

\begin{document}

% Picture.
\begin{tikzpicture}[% some clean-up via self defined styles
        nda/.style={draw, rectangle, minimum width=1cm, minimum height=1cm,fill=white},
        ndb/.style={draw, circle, minimum width=0.8cm, minimum height=0.8cm,},
        dra/.style={very thick, arrows={-Triangle[length=0.25cm, width=0.2cm]}},
        drb/.style={very thick, arrows={[length=0.25cm, width=0.2cm]Triangle-Triangle[length=0.25cm, width=0.2cm]}, looseness=4,},
    ]
    % Define the nodes.
    \node[nda]                      (X) {$X$};
    \node[nda, right=2.5cm of X]    (Y) {$Y$};
    \node[ndb, right=1cm of Y]      (E) {$\varepsilon$};

    % Draw the arrows.
    \draw[dra] (X) -- (Y) node[midway, fill=white] {$\beta$};
    \draw[dra] (E) -- (Y);

    % Draw variances.
    \draw [drb, bend right=105] (X.145) to 
            node [midway, fill=white] {$\sigma^{2}$} (X.215);

    \draw [drb, bend left=105]  (E.45 ) to 
            node [midway, fill=white] {$\theta$} (E.315);
\end{tikzpicture}

\end{document}

Answer

还没有解决方案，只是进行一些清理，以便更好地看到树林中的森林，即相关结构：

%\documentclass{article}
\documentclass[10pt,border=3mm,tikz]{standalone}
\usepackage{amsmath}
%\usepackage{tikz}% already included, see above

% Page style.
%\pagestyle{empty}

% `tikz` options.
\usetikzlibrary{positioning}
\usetikzlibrary{arrows.meta}

\begin{document}

% Picture.
\begin{tikzpicture}[% some clean-up via self defined styles
        nda/.style={draw, rectangle, minimum width=1cm, minimum height=1cm,fill=white},
        ndb/.style={draw, circle, minimum width=0.8cm, minimum height=0.8cm,},
        dra/.style={very thick, arrows={-Triangle[length=0.25cm, width=0.2cm]}},
        drb/.style={very thick, arrows={[length=0.25cm, width=0.2cm]Triangle-Triangle[length=0.25cm, width=0.2cm]}, looseness=4,},
    ]
    % Define the nodes.
    \node[nda]                      (X) {$X$};
    \node[nda, right=2.5cm of X]    (Y) {$Y$};
    \node[ndb, right=1cm of Y]      (E) {$\varepsilon$};

    % Draw the arrows.
    \draw[dra] (X) -- (Y) node[midway, fill=white] {$\beta$};
    \draw[dra] (E) -- (Y);

    % Draw variances.
    \draw [drb, bend right=105] (X.145) to 
            node [midway, fill=white] {$\sigma^{2}$} (X.215);

    \draw [drb, bend left=105]  (E.45 ) to 
            node [midway, fill=white] {$\theta$} (E.315);
\end{tikzpicture}

\end{document}

Question 3

纯粹为了比较，下面是使用lualatex内置元帖子语言。我尝试遵循一种清晰的方法：定义路径，绘制所有路径，然后添加标签。我使用了方便的cutbefore和cutafter运算符，从圆圈制作出环路。请点击上面的链接获取教程和参考资料。

您需要用来编译它lualatex。

\documentclass[border=5mm]{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
beginfig(1);
  path x_box, y_box, e_circle, sigma_loop, theta_loop, xy_arrow, ey_arrow;

  y_box = unitsquare shifted -(1/2,1/2) scaled 32;
  x_box = y_box shifted 100 left;
  e_circle = fullcircle scaled 24 shifted 42 right;

  xy_arrow = point 3/2 of x_box -- point 7/2 of y_box;
  ey_arrow = point 4 of e_circle -- point 3/2 of y_box;

  sigma_loop = fullcircle scaled 32
               shifted point 7/2 of x_box 
               shifted 12 left
               cutbefore x_box
               cutafter x_box;

  theta_loop = fullcircle scaled 24 rotated 180
               shifted point 0 of e_circle
               shifted 8 right
               cutbefore e_circle
               cutafter e_circle;

  ahangle := 30;
  drawoptions(withpen pencircle scaled 3/4);
  drawarrow xy_arrow;
  drawarrow ey_arrow;
  drawdblarrow sigma_loop;
  drawdblarrow theta_loop;
  drawoptions();

  draw x_box; label("$X$", center x_box);
  draw y_box; label("$Y$", center y_box);
  draw e_circle; label("$\epsilon$", center e_circle);

  vardef do_filled_label(expr t, z) = 
    save p; picture p; p = thelabel(t, z);  unfill bbox p; draw p;
  enddef;

  do_filled_label("$\sigma^2$", point 4 of sigma_loop shifted 2 right);
  do_filled_label("$\theta$", point 4 of theta_loop);
  do_filled_label("$\beta$", point 1/2 of xy_arrow);

endfig;
\end{mplibcode}
\end{document}

Answer

纯粹为了比较，下面是使用lualatex内置元帖子语言。我尝试遵循一种清晰的方法：定义路径，绘制所有路径，然后添加标签。我使用了方便的cutbefore和cutafter运算符，从圆圈制作出环路。请点击上面的链接获取教程和参考资料。

您需要用来编译它lualatex。

\documentclass[border=5mm]{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
beginfig(1);
  path x_box, y_box, e_circle, sigma_loop, theta_loop, xy_arrow, ey_arrow;

  y_box = unitsquare shifted -(1/2,1/2) scaled 32;
  x_box = y_box shifted 100 left;
  e_circle = fullcircle scaled 24 shifted 42 right;

  xy_arrow = point 3/2 of x_box -- point 7/2 of y_box;
  ey_arrow = point 4 of e_circle -- point 3/2 of y_box;

  sigma_loop = fullcircle scaled 32
               shifted point 7/2 of x_box 
               shifted 12 left
               cutbefore x_box
               cutafter x_box;

  theta_loop = fullcircle scaled 24 rotated 180
               shifted point 0 of e_circle
               shifted 8 right
               cutbefore e_circle
               cutafter e_circle;

  ahangle := 30;
  drawoptions(withpen pencircle scaled 3/4);
  drawarrow xy_arrow;
  drawarrow ey_arrow;
  drawdblarrow sigma_loop;
  drawdblarrow theta_loop;
  drawoptions();

  draw x_box; label("$X$", center x_box);
  draw y_box; label("$Y$", center y_box);
  draw e_circle; label("$\epsilon$", center e_circle);

  vardef do_filled_label(expr t, z) = 
    save p; picture p; p = thelabel(t, z);  unfill bbox p; draw p;
  enddef;

  do_filled_label("$\sigma^2$", point 4 of sigma_loop shifted 2 right);
  do_filled_label("$\theta$", point 4 of theta_loop);
  do_filled_label("$\beta$", point 1/2 of xy_arrow);

endfig;
\end{mplibcode}
\end{document}

Question 4

您的解决方案还不错，但并不完全清楚您想要什么。弯曲的行具有圆形形状吗？

在我看来，圆形箭头看起来不太好看……

\documentclass[margin=3mm]{standalone}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{arrows.meta, 
                bending,
                positioning}

\begin{document}
    \begin{tikzpicture}[
alr/.style = {thick, {Triangle[flex']}-{Triangle[flex]}},
arr/.style = {thick, -Triangle},
lbl/.style = {fill=white, inner sep=2pt, midway},
  C/.style = {circle, draw,  minimum width=1cm, inner sep=2pt},
  N/.style = {draw, minimum size =1cm, outer sep=0pt},
                        ]
\node[N] (X) {$X$};
\node[N, right=2.5cm of X] (Y) {$Y$};
\node[C, right=1cm of Y] (E) {$\varepsilon$};
% Draw arrows
\draw[arr] (X) -- node[lbl] {$\beta$} (Y) ;
\draw[arr] (E) -- (Y);
% Draw variances
\draw [alr] (X.west) ++ (0,0.866025/2) arc (60:300:0.5) node [lbl] {$\sigma^2$};% 0.886025=sin(60)
\draw [alr] (E.center) ++ (-60:0.5) arc (-120:120:0.5) node [lbl] {$\theta$};
% test circle, remove in real document
\draw [red, densely dashed, very thin] (X.west) ++ (-0.25,0) circle[radius=0.5];
    \end{tikzpicture}
\end{document}

Answer

您的解决方案还不错，但并不完全清楚您想要什么。弯曲的行具有圆形形状吗？

在我看来，圆形箭头看起来不太好看……

\documentclass[margin=3mm]{standalone}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{arrows.meta, 
                bending,
                positioning}

\begin{document}
    \begin{tikzpicture}[
alr/.style = {thick, {Triangle[flex']}-{Triangle[flex]}},
arr/.style = {thick, -Triangle},
lbl/.style = {fill=white, inner sep=2pt, midway},
  C/.style = {circle, draw,  minimum width=1cm, inner sep=2pt},
  N/.style = {draw, minimum size =1cm, outer sep=0pt},
                        ]
\node[N] (X) {$X$};
\node[N, right=2.5cm of X] (Y) {$Y$};
\node[C, right=1cm of Y] (E) {$\varepsilon$};
% Draw arrows
\draw[arr] (X) -- node[lbl] {$\beta$} (Y) ;
\draw[arr] (E) -- (Y);
% Draw variances
\draw [alr] (X.west) ++ (0,0.866025/2) arc (60:300:0.5) node [lbl] {$\sigma^2$};% 0.886025=sin(60)
\draw [alr] (E.center) ++ (-60:0.5) arc (-120:120:0.5) node [lbl] {$\theta$};
% test circle, remove in real document
\draw [red, densely dashed, very thin] (X.west) ++ (-0.25,0) circle[radius=0.5];
    \end{tikzpicture}
\end{document}

如何使用“tikz”在路径图中绘制观测值和残差方差？

编辑

答案1

代码

输出

答案2

答案3

答案4

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