花式箭头表示 pmatrix 的延续

Question

我觉得我的要求有点难，但我还是在努力。我有这个align环境

\begin{align} \nonumber
    \f = \begin{pmatrix}
    f(x_1, y_1) \\ f(x_2, y_1) \\ \vdots \\ f(x_{N - 1}, y_1) \\ f(x_N, y_1)
    \end{pmatrix}
    &&
    \begin{pmatrix}
    f(x_1, y_2) \\ f(x_2, y_2) \\ \vdots \\ f(x_{N - 1}, y_2) \\ f(x_N, y_2)
    \end{pmatrix}
    &&
    \begin{pmatrix}
    f(x_1, y_N) \\ f(x_2, y_N) \\ \vdots \\ f(x_{N - 1}, y_N) \\ f(x_N, y_N)
    \end{pmatrix}
\end{align}

我想以pmatrix这种方式在 '之间制作箭头

有什么方法吗？

先感谢您。

Answer 1

您可以将它们放入tikzpicture并绘制箭头。

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{arrows.meta,bending,matrix}
\begin{document}
\begin{align*} 
    f = \begin{tikzpicture}[baseline=(P.base),>={Latex[bend]}]
    \node[inner sep=0pt,outer sep=0pt](P){\vphantom{1}};
    \path (P) node[inner sep=0pt,outer sep=0pt,matrix of math nodes,
        ampersand replacement=\&,column sep=1ex
        ] (M){
    {\begin{pmatrix}
    f(x_1, y_1) \\ f(x_2, y_1) \\ \vdots \\ f(x_{N - 1}, y_1) \\ f(x_N, y_1)
    \end{pmatrix}}
    \& \phantom{\vdots}\&
    {\begin{pmatrix}
    f(x_1, y_2) \\ f(x_2, y_2) \\ \vdots \\ f(x_{N - 1}, y_2) \\ f(x_N, y_2)
    \end{pmatrix}}
    \& \textcolor{blue}{\boldsymbol{\vdots}}\&
    {\begin{pmatrix}
    f(x_1, y_N) \\ f(x_2, y_N) \\ \vdots \\ f(x_{N - 1}, y_N) \\ f(x_N, y_N)
    \end{pmatrix}}
    \\
    };
    \draw[blue,thick,->] (M-1-1.south) to[out=-90,in=-90] (M-1-1.south-|M-1-2)
    -- (M-1-3.north-|M-1-2) to[out=90,in=90] (M-1-3.north);
    \draw[blue,thick,->] (M-1-3.south) to[out=-90,in=-90] (M-1-3.south-|M-1-4)
    -- ([yshift=-1ex]M-1-4.south) (M-1-4.north) -- (M-1-5.north-|M-1-4) to[out=90,in=90] (M-1-5.north);
\end{tikzpicture}   
\end{align*}
\end{document}

Answer 2

一个解决方案是pstricks：每个矩阵定义为一个 BoxNodes，它们通过中间节点与\ncangles命令链接。

\documentclass[svgnames]{article}
\usepackage{amsmath, bm}
\usepackage{pst-node}

\begin{document}

\[ \bm{f} =
    \psDefBoxNodes{M1}{\begin{pmatrix}
    f(x_1, y_1) \\ f(x_2, y_1) \\ \vdots \\ f(x_{N - 1}, y_1) \\ f(x_N, y_1)
    \end{pmatrix}}
   \enspace \pnode{I}\enspace
    \psDefBoxNodes{M2}{\begin{pmatrix}
    f(x_1, y_2) \\ f(x_2, y_2) \\ \vdots \\ f(x_{N - 1}, y_2) \\ f(x_N, y_2)
    \end{pmatrix}}
     \enspace \Rnode{D}{\textcolor{blue}{\boldsymbol{\vdots}}}\enspace
    \psDefBoxNodes{M3}{\begin{pmatrix}
    f(x_1, y_N) \\ f(x_2, y_N) \\ \vdots \\ f(x_{N - 1}, y_N) \\ f(x_N, y_N)
    \end{pmatrix}}
%%arrows
\psset{linewidth=1pt, linecolor=RoyalBlue, arrowinset=0.12, linearc=0.3}
\ncangles[angleA=-90, armA=0.5cm, angleB=-90]{M1:bC}{I}\ncangles[angleA=90, armA=0.5cm, angleB=90, arrows=<-]{M2:tC}{I}
\ncangles[angleA=-90, armA=0.5cm, angleB=-90, nodesepB=3pt]{M2:bC}{D}\ncangles[angleA=90, armA=0.5cm, angleB=90, arrows=<-, nodesepB=-2pt]{M3:tC}{D}
\]

\end{document}