我构建了一个宏，通过 中的三角形注释图形的斜率loglogaxis。对于小斜率，它工作正常，但对于大斜率，我得到一个Dimension too large错误。
最小工作示例：
\documentclass[margin=1cm]{standalone}
\usepackage{amsmath}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usetikzlibrary{calc}
%%% START MACRO FOR ANNOTATION OF TRIANGLE WITH SLOPE %%%.
\newcommand{\logLogSlopeTriangle}[5]
{
% #1. Relative offset in x direction.
% #2. Width in x direction, so xA-xB.
% #3. Relative offset in y direction.
% #4. Slope d(y)/d(log10(x)).
% #5. Plot options.
\pgfplotsextra
{
\pgfkeysgetvalue{/pgfplots/xmin}{\xmin}
\pgfkeysgetvalue{/pgfplots/xmax}{\xmax}
\pgfkeysgetvalue{/pgfplots/ymin}{\ymin}
\pgfkeysgetvalue{/pgfplots/ymax}{\ymax}
% Calculate auxilliary quantities.
\pgfmathsetmacro{\xA}{(exp(\xmin))^(1-#1)*(exp(\xmax))^#1}
\pgfmathsetmacro{\yA}{(exp(\ymin))^(1-#3)*(exp(\ymax))^#3}
\pgfmathsetmacro{\xB}{(exp(\xmin))^(1-(#1-#2))*(exp(\xmax))^(#1-#2)}
\pgfmathsetmacro{\yB}{\yA}
\pgfmathsetmacro{\xC}{\xA}
\pgfmathsetmacro{\yC}{\yA/(\xB^#4)*\xA^#4}
% Define coordinates for \draw.
\coordinate (A) at (axis cs:\xA,\yA);
\coordinate (B) at (axis cs:\xB,\yB);
\coordinate (C) at (axis cs:\xC,\yC);
% Draw slope triangle.
\draw[#5] (A)-- node[pos=0.5,anchor=north] {1}
(B)--
(C)-- node[pos=0.5,anchor=west] {#4}
cycle;
}
}
%%% END MACRO FOR ANNOTATION OF TRIANGLE WITH SLOPE %%%.
\begin{document}
\begin{tikzpicture}
\begin{loglogaxis}
[
xlabel=$x$,
ylabel style={rotate=-90},
ylabel=$y$,
grid=major,
clip=false
]
\addplot[blue,line width=1pt,domain=10^1:10^2] {sqrt(x)};
\addplot[red,line width=1pt,domain=10^1:10^2] {x};
%\addplot[green!75!black,line width=1pt,domain=10^1:10^2] {x^3}; % RESULTS IN A 'DIMENSION TOO LARGE ERROR. HOW DO I FIX THIS?'
\logLogSlopeTriangle{0.9}{0.1}{0.1}{0.5}{blue};
\logLogSlopeTriangle{0.75}{0.1}{0.1}{1}{red};
%\logLogSlopeTriangle{0.6}{0.1}{0.1}{3}{green!75!black}; % RESULTS IN A 'DIMENSION TOO LARGE ERROR. HOW DO I FIX THIS?'
\end{loglogaxis}
\end{tikzpicture}
\end{document}
结果：
取消注释\addplot ... {x^3}及其对应的注释\logLogSlopeTriangle{...}，我收到Dimension too large错误。
我该如何解决？
答案1
解决方案是使用相对坐标代替绝对坐标。因此，rel axis cs使用 代替axis cs。
\yCrel如果不使用的话，要推导出表达式需要相当多的数学知识\yC，但这是结果（参见代码），并且它可以正常工作而没有出现错误Dimension too large。
\documentclass[margin=1cm]{standalone}
\usepackage{amsmath}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usetikzlibrary{calc}
%%% START MACRO FOR ANNOTATION OF TRIANGLE WITH SLOPE %%%.
\newcommand{\logLogSlopeTriangle}[5]
{
% #1. Relative offset in x direction.
% #2. Width in x direction, so xA-xB.
% #3. Relative offset in y direction.
% #4. Slope d(y)/d(log10(x)).
% #5. Plot options.
\pgfplotsextra
{
\pgfkeysgetvalue{/pgfplots/xmin}{\xmin}
\pgfkeysgetvalue{/pgfplots/xmax}{\xmax}
\pgfkeysgetvalue{/pgfplots/ymin}{\ymin}
\pgfkeysgetvalue{/pgfplots/ymax}{\ymax}
% Calculate auxilliary quantities, in relative sense.
\pgfmathsetmacro{\xArel}{#1}
\pgfmathsetmacro{\yArel}{#3}
\pgfmathsetmacro{\xBrel}{#1-#2}
\pgfmathsetmacro{\yBrel}{\yArel}
\pgfmathsetmacro{\xCrel}{\xArel}
%\pgfmathsetmacro{\yCrel}{ln(\yC/exp(\ymin))/ln(exp(\ymax)/exp(\ymin))} % REPLACE THIS EXPRESSION WITH AN EXPRESSION INDEPENDENT OF \yC TO PREVENT THE 'DIMENSION TOO LARGE' ERROR.
\pgfmathsetmacro{\lnxB}{\xmin*(1-(#1-#2))+\xmax*(#1-#2)} % in [xmin,xmax].
\pgfmathsetmacro{\lnxA}{\xmin*(1-#1)+\xmax*#1} % in [xmin,xmax].
\pgfmathsetmacro{\lnyA}{\ymin*(1-#3)+\ymax*#3} % in [ymin,ymax].
\pgfmathsetmacro{\lnyC}{\lnyA+#4*(\lnxA-\lnxB)}
\pgfmathsetmacro{\yCrel}{\lnyC-\ymin)/(\ymax-\ymin)} % THE IMPROVED EXPRESSION WITHOUT 'DIMENSION TOO LARGE' ERROR.
% Define coordinates for \draw. MIND THE 'rel axis cs' as opposed to the 'axis cs'.
\coordinate (A) at (rel axis cs:\xArel,\yArel);
\coordinate (B) at (rel axis cs:\xBrel,\yBrel);
\coordinate (C) at (rel axis cs:\xCrel,\yCrel);
% Draw slope triangle.
\draw[#5] (A)-- node[pos=0.5,anchor=north] {1}
(B)--
(C)-- node[pos=0.5,anchor=west] {#4}
cycle;
}
}
%%% END MACRO FOR ANNOTATION OF TRIANGLE WITH SLOPE %%%.
\begin{document}
\begin{tikzpicture}
\begin{loglogaxis}
[
xlabel=$x$,
ylabel style={rotate=-90},
ylabel=$y$,
legend style=
{
at={(1,1)},
anchor=north west,
draw=none,
fill=none
},
legend cell align=left,
grid=major,
clip=false
]
\addplot[blue,line width=1pt,domain=10^1:10^4] {sqrt(x)};
\addplot[red,line width=1pt,domain=10^1:10^4] {x};
\addplot[green!75!black,line width=1pt,domain=10^1:10^4] {x^2};
\addplot[brown,line width=1pt,domain=10^1:10^4] {x^3};
\logLogSlopeTriangle{0.9}{0.1}{0.16}{0.5}{blue};
\logLogSlopeTriangle{0.9}{0.1}{0.29}{1}{red};
\logLogSlopeTriangle{0.9}{0.1}{0.53}{2}{green!75!black};
\logLogSlopeTriangle{0.9}{0.1}{0.79}{3}{brown};
\legend
{
$\sqrt{x}$,
$x$,
$x^2$,
$x^3$
}
\end{loglogaxis}
\end{tikzpicture}
\end{document}
结果：
