分段定义函数颜色很差

Question

我想绘制这个

\documentclass{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{calc}
\pgfplotsset{compat=newest}% <- set a compat!! (current version is 1.14)
%%%%%%%
\pgfkeys{/pgf/declare function={argsinh(\x) = ln(\x + sqrt(\x^2+1));}}
\pgfkeys{/pgf/declare function={argcosh(\x) = ln(x + sqrt(-1 + x)*sqrt(1 + x));}}
%%%%%%
\begin{document}
\begin{tikzpicture}
\begin{axis}[   
    cycle list name= color list,    
    tick align=center,
    axis lines = left,
    xmin = 0,
    xmax = 2,
    ymin = 0,
    ymax = 1.1,   
    ylabel = {$\mathopen|H(j\Omega)\mathclose|$},    
    xtick = {1,1.2},
    xticklabels = {1, $\Omega_s$},
    ytick = {0,0.1, 0.5, 1},
    yticklabels = {0, $\frac{1}{1+\varepsilon^2/k_1^2}$,$\frac{1}{1+\varepsilon^2}$,1},  
    ]

    \foreach \n in {5,6} {
    \addplot+[domain=0:1,samples=201]{1/(1+1^2*(cos(\n*(acos(\x))))^(2))};

   \addplot+[domain=1:2,samples=201]{1/(1+1^2*(cosh(\n*(argcosh(\x))))^(2))};
    }

    \addplot[black,dotted] coordinates {
        (1.2,1)
        (1.2,.1)
        (2,.1)
    };
    \addplot[black,dotted] coordinates {
        (0,.5)
        (1,.5)
        (1,0)
    };
\end{axis}
\end{tikzpicture}
\end{document}

但我必须避免使用这四种颜色，而只使用两种颜色来表示 \n。然后我意识到，可以通过定义新的单个分段函数来实现

%%%%%%
\begin{tikzpicture}[
\declare function={
chebyshev(\x)= (\x<=1) * (1/(1+1^2*(cos(\n*(acos(\x))))^(2)))+
     and(\x>1) * (1/(1+1^2*(cosh(\n*(argcosh(\x))))^(2)));
     }]
%%%%%% ...

\foreach \n in {5,6} {

    \addplot+[domain=0:2,samples=400]{chebyshev(\x)};

}

但每次都出现错误，我根本不知道问题出在哪里。你能帮助我吗？

Answer 1

问题是acos(x)仅针对 定义x \in [0,1]，而您尝试针对 进行绘制x \in [0,2]。最简单的做法是坚持使用两个函数变体，并在使用 绘制第二个函数之前将颜色索引备份一\pgfplotsset{cycle list shift=-1}。

\documentclass{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{calc}
\pgfplotsset{compat=newest}% <- set a compat!! (current version is 1.14)
%%%%%%% 
\pgfkeys{/pgf/declare function={argsinh(\x) = ln(\x + sqrt(\x^2+1));}}
\pgfkeys{/pgf/declare function={argcosh(\x) = ln(x + sqrt(-1 + x)*sqrt(1 + x));}}
%%%%%% 
\begin{document}
\begin{tikzpicture}
  \begin{axis}[   
    cycle list name= color list,    
    tick align=center,
    axis lines = left,
    xmin = 0,
    xmax = 2,
    ymin = 0,
    ymax = 1.1,   
    ylabel = {$\mathopen|H(j\Omega)\mathclose|$},    
    xtick = {1,1.2},
    xticklabels = {1, $\Omega_s$},
    ytick = {0,0.1, 0.5, 1},
    yticklabels = {0, $\frac{1}{1+\varepsilon^2/k_1^2}$,$\frac{1}{1+\varepsilon^2}$,1},  
    ]

    \foreach \n in {5,6} {
      \addplot+[domain=0:1,samples=201]{1/(1+1^2*(cos(\n*(acos(\x))))^(2))};
      \pgfplotsset{cycle list shift=-1}
      \addplot+[domain=1:2,samples=201]{1/(1+1^2*(cosh(\n*(argcosh(\x))))^(2))};
    }

    \addplot[black,dotted] coordinates {
      (1.2,1)
      (1.2,.1)
      (2,.1)
    };
    \addplot[black,dotted] coordinates {
      (0,.5)
      (1,.5)
      (1,0)
    };
  \end{axis}
\end{tikzpicture}
\end{document}