缩放外部化的 tikz 图片

Question 1

这个想法cfr 的答案绝对合理：如果/当命令不想被记忆时，它应该发出\mmzAbort。这正是 Memoize 本身处理\refs 的方式：它会中止记忆，直到引用被定义。

我发布新的答案只是为了解决一些细节问题，其中一些与记忆有关，一些则无关。

枚举自动缩放的图片的缺点是，在插入或删除图片时需要重新编译它们。
cfr 检测缩放因子是否稳定的机制对于记忆化来说是绝对必要的——否则，就无法判断图片何时准备好了。然而，她的修改带来了一个问题：当目标宽度/高度发生变化时，图片不会调整大小。
类似地，一旦被记忆，图片就永远不会被重新编译。当\columnwidth发生变化时，问题就会出现。（当图片的代码发生变化时，这不是问题，例如当0.3\columnwidth更改为时0.5\columnwidth。）
自动缩放代码应该在有或没有 Memoize 的情况下都能工作。

下面的代码解决了所有这些问题。此外，我还擅自将其分成一个包（autoscale.sty）和文档，并根据自己的喜好设计 UI ;-)

问题 (1) 也与 TikZexternal库有关，Memoize 通过引用图片源代码的 md5sums 解决了这个问题。这里的问题当然是获取源代码，但 Memoize 使用的机制也可以被其他软件包轻松使用，因为它是作为单独的软件包 Advice 提供的。下面，Advice 的配置是，每当tikzpicture调用环境时，\storemdfivesum都会执行。这个宏将整个环境作为参数，并且可以轻松计算其 md5sum — 然后调用原始的tikzpicture。

我通过将.aux缩放因子存储到控制序列\autoscale@factor@<md5sum> @<目标维度> 中来解决问题 (2)。每当目标宽度或高度发生变化时，中的因子.aux根本不适用，并且调整大小从头开始。

对于 (3)，参数被autoscale width/height附加到 Memoize 的上下文中 — 每当上下文的值（即扩展）发生变化时，extern 都会被重新编译。虽然\mmzset/\mmznext{context={columnwidth=\the\columnwidth}}文档本身中的某些内容可以工作，但下面的自动缩放宏也可以做到这一点，只需将任何参数粘贴到autoscale width/height上下文中（并说明在图片被记忆时可以附加上下文）。

(4) 对于希望支持它的软件包，Memoize 有一个内置解决方案：软件包存根memoizable，它将所有 Memoize 命令定义为虚拟命令。

%%%%%%%%% autoscale.sty %%%%%%%%%

% cwestiwn: https://tex.stackexchange.com/questions/699289/scaling-externalized-tikz-pictures

% When a package uses Memoize commands, one should say
% \RequirePackage{memoizable} to freely use \mmzset etc. even when Memoize is
% not loaded.
% 
% I found two bugs in Memoize v1.0.0, however --- I forgot to load pgfkeys and
% define \mmzAbort in packages memoizable/nomemoize --- thus the workaround
% below (until v1.0.1).

\RequirePackage{pgfkeys}
\ifdefined\mmzAbort\else\let\mmzAbort\relax\fi
\RequirePackage{memoizable}

\RequirePackage{tikz}
\usetikzlibrary{calc}

% Automatically compute the md5sum of every tikzpicture environment; the md5sum
% is available, within and after the picture, in \currentmdfivesum.
\RequirePackage{advice} % actually unnecessary when Memoize is loaded
\pgfqkeys{/md5sum}{
  .install advice,
  advice={tikzpicture}{inner handler=\storemdfivesum},
}
\RequirePackage{pdftexcmds}
\ifdefined\luatexversion
\long\def\pdf@mdfivesum#1{%
  \directlua{%
    oberdiek.pdftexcmds.mdfivesum("\luaescapestring{#1}", "byte")%
  }%
}%
\fi
\def\storemdfivesum#1{%
  \xdef\currentmdfivesum{\pdf@mdfivesum{\unexpanded{#1}}}%
  \AdviceOriginal#1%
}

% The definition of autoscale begins here.

\tikzset{
  % #1 = target width/height
  autoscale width/.code={\autoscale{#1}{width}{\x1}},
  autoscale height/.code={\autoscale{#1}{height}{\y1}},
}

% #1 = target width/height, #2 = "width"/"height", #3 = "\x1"/"\y1"
\def\autoscale#1#2#3{%
  \ifcsdef{autoscale@factor@\currentmdfivesum @\the\dimexpr#1\relax}{%
    \letcs\autoscale@factor{autoscale@factor@\currentmdfivesum @\the\dimexpr#1\relax}%
  }{%
    \def\autoscale@factor{1}%
  }%
  \pgfkeysalso{%
    execute at end picture=\autoscale@size@to@aux{#1}{#2}{#3},
    scale=\autoscale@factor,
  }%
}

% #1 = target width/height, #2 = "width"/"height", #3 = "\x1"/"\y1"
\def\autoscale@size@to@aux#1#2#3{%
  \path let
  \p1=($(current bounding box.north east)-(current bounding box.south west)$),
  \n1={\autoscale@factor*\x1},
  \n2={#1/#3}
  in \pgfextra{%
    \autoscale@if@roughly@equal{0.1pt}{#1}{\n1}{%
      \immediate\write\@mainaux{%
        \csgdef{autoscale@factor@\currentmdfivesum @\the\dimexpr#1\relax}{\autoscale@factor}%
      }%
      \mmzset{context={target #2=\the\dimexpr#1\relax}}%
    }{%
      \immediate\write\@mainaux{%
        \csgdef{autoscale@factor@\currentmdfivesum @\the\dimexpr#1\relax}{\n2}%
        }%
      \mmzAbort
    }%
  };
}

% Such a macro is actually already defined by Memoize, but as we want autoscale
% to work without Memoize as well, I copied the definition here.  This macro
% checks whether the given dimensions (|#2| and |#3|) are equal within the
% tolerance given by |#1|. (We don't use |\ifpdfabsdim|, because it is
%   unavailable in \hologo{XeTeX}.)
\def\autoscale@if@roughly@equal#1#2#3{%
  \dimen0=\dimexpr#2-#3\relax
  \ifdim\dimen0<0pt
    \dimen0=-\dimen0\relax
  \fi
  \ifdim\dimen0>#1\relax
    \expandafter\@secondoftwo
  \else
    \expandafter\@firstoftwo
  \fi
}%

以及文件：

\documentclass[twocolumn,landscape]{article}

% Memoize must be loaded before autoscale, because autoscale supports
% Memoize. And it must be loaded before tkz-fct, because the latter loads TikZ
% library "fadings".
\usepackage{memoize}
\usepackage{autoscale} % loads TikZ as well
\usepackage{tkz-fct}

\usepackage{lipsum}
\begin{document}

\lipsum[1]

\noindent
\begin{tikzpicture}[autoscale width=\columnwidth]
  \tkzInit[xmin=-1,xmax=3,ymin=-1,ymax=1.2]
  \tkzDrawX
  \tkzDrawY
  % Fonction 
  \tkzClip
  \tkzFct[thick,domain=0.55:5]{(\x*\x+\x-1)/(\x**3)}
  \tkzDefPointByFct(1.39)\tkzGetPoint{A}\tkzDrawPoint[size=3](A)
  \draw[dotted,thick] (1.39,0) -- (1.39, 0.86) -- (0,0.86) node[left] {\( f(x) \)};
  \draw[thick] (1.39,-0.1) node[below] {\( x \)} -- (1.39,0.1);
  % Annotations
  \draw[<->,ultra thick] (1,-0.35) -- (2,-0.35);
  \node at (1.5,-0.45){\(A\)};
  \draw[dashed] (1, 0) -- (1, 1) -- (0, 1);
  \draw[dashed] (2, 0) -- (2, 0.625) -- (0, 0.625);
  \draw[<->,ultra thick] (-0.6,0.625) -- (-0.6,1);
\end{tikzpicture}%

\lipsum[2]

\end{document}

Answer

这个想法cfr 的答案绝对合理：如果/当命令不想被记忆时，它应该发出\mmzAbort。这正是 Memoize 本身处理\refs 的方式：它会中止记忆，直到引用被定义。

我发布新的答案只是为了解决一些细节问题，其中一些与记忆有关，一些则无关。

枚举自动缩放的图片的缺点是，在插入或删除图片时需要重新编译它们。
cfr 检测缩放因子是否稳定的机制对于记忆化来说是绝对必要的——否则，就无法判断图片何时准备好了。然而，她的修改带来了一个问题：当目标宽度/高度发生变化时，图片不会调整大小。
类似地，一旦被记忆，图片就永远不会被重新编译。当\columnwidth发生变化时，问题就会出现。（当图片的代码发生变化时，这不是问题，例如当0.3\columnwidth更改为时0.5\columnwidth。）
自动缩放代码应该在有或没有 Memoize 的情况下都能工作。

下面的代码解决了所有这些问题。此外，我还擅自将其分成一个包（autoscale.sty）和文档，并根据自己的喜好设计 UI ;-)

问题 (1) 也与 TikZexternal库有关，Memoize 通过引用图片源代码的 md5sums 解决了这个问题。这里的问题当然是获取源代码，但 Memoize 使用的机制也可以被其他软件包轻松使用，因为它是作为单独的软件包 Advice 提供的。下面，Advice 的配置是，每当tikzpicture调用环境时，\storemdfivesum都会执行。这个宏将整个环境作为参数，并且可以轻松计算其 md5sum — 然后调用原始的tikzpicture。

我通过将.aux缩放因子存储到控制序列\autoscale@factor@<md5sum> @<目标维度> 中来解决问题 (2)。每当目标宽度或高度发生变化时，中的因子.aux根本不适用，并且调整大小从头开始。

对于 (3)，参数被autoscale width/height附加到 Memoize 的上下文中 — 每当上下文的值（即扩展）发生变化时，extern 都会被重新编译。虽然\mmzset/\mmznext{context={columnwidth=\the\columnwidth}}文档本身中的某些内容可以工作，但下面的自动缩放宏也可以做到这一点，只需将任何参数粘贴到autoscale width/height上下文中（并说明在图片被记忆时可以附加上下文）。

(4) 对于希望支持它的软件包，Memoize 有一个内置解决方案：软件包存根memoizable，它将所有 Memoize 命令定义为虚拟命令。

%%%%%%%%% autoscale.sty %%%%%%%%%

% cwestiwn: https://tex.stackexchange.com/questions/699289/scaling-externalized-tikz-pictures

% When a package uses Memoize commands, one should say
% \RequirePackage{memoizable} to freely use \mmzset etc. even when Memoize is
% not loaded.
% 
% I found two bugs in Memoize v1.0.0, however --- I forgot to load pgfkeys and
% define \mmzAbort in packages memoizable/nomemoize --- thus the workaround
% below (until v1.0.1).

\RequirePackage{pgfkeys}
\ifdefined\mmzAbort\else\let\mmzAbort\relax\fi
\RequirePackage{memoizable}

\RequirePackage{tikz}
\usetikzlibrary{calc}

% Automatically compute the md5sum of every tikzpicture environment; the md5sum
% is available, within and after the picture, in \currentmdfivesum.
\RequirePackage{advice} % actually unnecessary when Memoize is loaded
\pgfqkeys{/md5sum}{
  .install advice,
  advice={tikzpicture}{inner handler=\storemdfivesum},
}
\RequirePackage{pdftexcmds}
\ifdefined\luatexversion
\long\def\pdf@mdfivesum#1{%
  \directlua{%
    oberdiek.pdftexcmds.mdfivesum("\luaescapestring{#1}", "byte")%
  }%
}%
\fi
\def\storemdfivesum#1{%
  \xdef\currentmdfivesum{\pdf@mdfivesum{\unexpanded{#1}}}%
  \AdviceOriginal#1%
}

% The definition of autoscale begins here.

\tikzset{
  % #1 = target width/height
  autoscale width/.code={\autoscale{#1}{width}{\x1}},
  autoscale height/.code={\autoscale{#1}{height}{\y1}},
}

% #1 = target width/height, #2 = "width"/"height", #3 = "\x1"/"\y1"
\def\autoscale#1#2#3{%
  \ifcsdef{autoscale@factor@\currentmdfivesum @\the\dimexpr#1\relax}{%
    \letcs\autoscale@factor{autoscale@factor@\currentmdfivesum @\the\dimexpr#1\relax}%
  }{%
    \def\autoscale@factor{1}%
  }%
  \pgfkeysalso{%
    execute at end picture=\autoscale@size@to@aux{#1}{#2}{#3},
    scale=\autoscale@factor,
  }%
}

% #1 = target width/height, #2 = "width"/"height", #3 = "\x1"/"\y1"
\def\autoscale@size@to@aux#1#2#3{%
  \path let
  \p1=($(current bounding box.north east)-(current bounding box.south west)$),
  \n1={\autoscale@factor*\x1},
  \n2={#1/#3}
  in \pgfextra{%
    \autoscale@if@roughly@equal{0.1pt}{#1}{\n1}{%
      \immediate\write\@mainaux{%
        \csgdef{autoscale@factor@\currentmdfivesum @\the\dimexpr#1\relax}{\autoscale@factor}%
      }%
      \mmzset{context={target #2=\the\dimexpr#1\relax}}%
    }{%
      \immediate\write\@mainaux{%
        \csgdef{autoscale@factor@\currentmdfivesum @\the\dimexpr#1\relax}{\n2}%
        }%
      \mmzAbort
    }%
  };
}

% Such a macro is actually already defined by Memoize, but as we want autoscale
% to work without Memoize as well, I copied the definition here.  This macro
% checks whether the given dimensions (|#2| and |#3|) are equal within the
% tolerance given by |#1|. (We don't use |\ifpdfabsdim|, because it is
%   unavailable in \hologo{XeTeX}.)
\def\autoscale@if@roughly@equal#1#2#3{%
  \dimen0=\dimexpr#2-#3\relax
  \ifdim\dimen0<0pt
    \dimen0=-\dimen0\relax
  \fi
  \ifdim\dimen0>#1\relax
    \expandafter\@secondoftwo
  \else
    \expandafter\@firstoftwo
  \fi
}%

以及文件：

\documentclass[twocolumn,landscape]{article}

% Memoize must be loaded before autoscale, because autoscale supports
% Memoize. And it must be loaded before tkz-fct, because the latter loads TikZ
% library "fadings".
\usepackage{memoize}
\usepackage{autoscale} % loads TikZ as well
\usepackage{tkz-fct}

\usepackage{lipsum}
\begin{document}

\lipsum[1]

\noindent
\begin{tikzpicture}[autoscale width=\columnwidth]
  \tkzInit[xmin=-1,xmax=3,ymin=-1,ymax=1.2]
  \tkzDrawX
  \tkzDrawY
  % Fonction 
  \tkzClip
  \tkzFct[thick,domain=0.55:5]{(\x*\x+\x-1)/(\x**3)}
  \tkzDefPointByFct(1.39)\tkzGetPoint{A}\tkzDrawPoint[size=3](A)
  \draw[dotted,thick] (1.39,0) -- (1.39, 0.86) -- (0,0.86) node[left] {\( f(x) \)};
  \draw[thick] (1.39,-0.1) node[below] {\( x \)} -- (1.39,0.1);
  % Annotations
  \draw[<->,ultra thick] (1,-0.35) -- (2,-0.35);
  \node at (1.5,-0.45){\(A\)};
  \draw[dashed] (1, 0) -- (1, 1) -- (0, 1);
  \draw[dashed] (2, 0) -- (2, 0.625) -- (0, 0.625);
  \draw[<->,ultra thick] (-0.6,0.625) -- (-0.6,1);
\end{tikzpicture}%

\lipsum[2]

\end{document}

Question 2

我思考此版本有效。需要 3 次编译才能使输出稳定。并且（最终！）输出（希望）保持稳定。

这使用memoize而不是external库。如果您使用默认perl提取方法或python版本，则不需要完整的 shell-escape。

基本思想是，autoscale除非新计算的比例因子相差不大，否则不要使用新计算的比例因子，以防止原始代码所需的连续重新编译，否则该因子在每次编译时都会发生变化。（这与外部化无关。它只是原始代码的一个功能。）

然后，我们将得到的缩放因子与上一次编译时得到的缩放因子进行比较（如果有的话）。如果因子不同，我们将中止记忆化。如果因子相同，我们将继续。记忆化是否真正完成取决于进一步观察的情况memoize。我们只是不会强行停止它。

无论如何，这不是一个理想的解决方案，因为我们没有使用适当的记忆机制来确定何时编译外部映像。但我思考它确实有效。但我仍然不知道它失败的所有情况。

\documentclass[twocolumn,landscape]{article}
% cwestiwn: https://tex.stackexchange.com/questions/699289/scaling-externalized-tikz-pictures
\usepackage[extract=perl]{memoize}
\usepackage{tikz,tkz-fct}
\usetikzlibrary{calc}

\makeatletter
\ExplSyntaxOn
\msg_new:nnn { nilcouv } { duplicate-figure-id }
{ duplicate~figure~identifier:~'#1'. }

% Sequence recording all figure identifiers (for the 'scale to max size' TikZ
% style) found so far
\seq_new:N \g__nilcouv_scale_to_max_style_figure_ids_seq
% Counter used when generating automatic figure identifiers for 'autoscale'
\int_new:N \g_nilcouv_last_autogenerated_figure_nb_int

\cs_new_protected:Npn \__nilcouv_check_unique_id:n #1
{
  \seq_if_in:NnTF \g__nilcouv_scale_to_max_style_figure_ids_seq {#1}
  { \msg_error:nnn { nilcouv } { duplicate-figure-id } {#1} }
  { \seq_gput_right:Nn \g__nilcouv_scale_to_max_style_figure_ids_seq {#1} }
}

% Automatic generation of figure ids (the pattern is defined here)
\cs_new:Npn \__nilcouv_autogenerated_id:n #1 { nilcouv~autogenerated~id~#1 }

\cs_generate_variant:Nn \__nilcouv_autogenerated_id:n { V }

\cs_new_protected:Npn \__nilcouv_autoscale:nnn #1#2#3
{ 
  \tikzset { scale~to~max~size={#1}{#2}{#3} } 
}

\cs_generate_variant:Nn \__nilcouv_autoscale:nnn { x }

\cs_new_protected:Npn \__nilcouv_autoscale_autoid:nn #1#2
{
  % Increment the counter
  \int_gincr:N \g_nilcouv_last_autogenerated_figure_nb_int
  % Call the 'autoscale' style with the new id
  \__nilcouv_autoscale:xnn
  { \__nilcouv_autogenerated_id:V
    \g_nilcouv_last_autogenerated_figure_nb_int
  }
  {#1}
  {#2}
}


% Set up aliases using LaTeX2e naming style
\cs_new_eq:NN \nilcouv@check@unique@id \__nilcouv_check_unique_id:n
\cs_new_eq:NN \nilcouv@autoscale@autoid \__nilcouv_autoscale_autoid:nn
\ExplSyntaxOff

% Autoscaling technique that doesn't affect font sizes in TikZ pictures.
% (based on code from marmot: <https://tex.stackexchange.com/a/497749/73317>)
%
% #1: unique per-picture id allowing several pictures to use this mechanism
%     in a given document (it should contain no control sequence token nor
%     active character)
% #2: target width
% #3: target height
\newcommand*{\nilcouv@ExportBB}[3]{%
  \path let
  \p1=($(current bounding box.north east)-(current bounding box.south west)$),
  \n1={#2/\x1},\n2={#3/\y1}
  in \pgfextra{\pgfmathsetmacro{\nilcouv@figscale}{min(\n1,\n2)}%
    \ifcsname nilcouv@auto@figscale@#1\endcsname
      \edef\nilcouv@tmpb{\csname nilcouv@auto@figscale@#1\endcsname}%
      \pgfmathsetmacro \nilcouv@tmpc{\nilcouv@tmpb - \nilcouv@figscale}%
      \ifdim \nilcouv@tmpc pt<0.1pt
        \relax
      \else
        \expandafter\xdef\csname nilcouv@auto@figscale@#1\endcsname{%
          \nilcouv@figscale}%
      \fi
      \else
        \expandafter\xdef\csname nilcouv@auto@figscale@#1\endcsname{%
          \nilcouv@figscale}%
      \fi
      \edef\nilcouv@tmpe{\csname nilcouv@auto@figscale@old@#1\endcsname}%
      \ifx\nilcouv@tmpe\nilcouv@tmpb
        \relax
      \else
        \mmzAbort
      \fi
    };
  \immediate\write\@mainaux{%
    \string\expandafter
    \gdef\string\csname\space nilcouv@auto@figscale@old@#1\string\endcsname{%
      \csname nilcouv@auto@figscale@#1\endcsname}%
    \string\expandafter
    \gdef\string\csname\space nilcouv@auto@figscale@#1\string\endcsname{%
      \csname nilcouv@auto@figscale@#1\endcsname}}%
}

\tikzset{
  % Arguments: figure identifier, target width, target height
  scale to max size/.style n args={3}{%
    execute at end picture={\nilcouv@ExportBB{#1}{#2}{#3}},
    /utils/exec={\nilcouv@check@unique@id{#1}%
      \ifcsname nilcouv@auto@figscale@#1\endcsname
        \wlog{Found autoscale value for picture '#1'}%
      \else
        \typeout{Automatically-scaled pictures: please recompile
          for picture '#1'.}%
        \expandafter\gdef
        \csname nilcouv@auto@figscale@#1\endcsname{1}%
      \fi
    },
    scale=\csname nilcouv@auto@figscale@#1\endcsname,
  },
  % Same style except the id is automatically generated using a counter
  autoscale autoid/.style 2 args={%
    /utils/exec={%
      \nilcouv@autoscale@autoid{#1}{#2}%
    },
  },
}
% End of the code based on <https://tex.stackexchange.com/a/497749/73317>
\makeatother

\begin{document}
\begin{tikzpicture}[autoscale autoid={0.3\columnwidth}{\maxdimen}]
  \tkzInit[xmin=-1,xmax=3,ymin=-1,ymax=1.2]
  \tkzDrawX
  \tkzDrawY
  % Fonction 
  \tkzClip
  \tkzFct[thick,domain=0.55:5]{(\x*\x+\x-1)/(\x**3)}
  \tkzDefPointByFct(1.39)\tkzGetPoint{A}\tkzDrawPoint[size=3](A)
  \draw[dotted,thick] (1.39,0) -- (1.39, 0.86) -- (0,0.86) node[left] {\( f(x) \)};
  \draw[thick] (1.39,-0.1) node[below] {\( x \)} -- (1.39,0.1);
  %Annotations
  \draw[<->,ultra thick] (1,-0.35) -- (2,-0.35);
  \node at (1.5,-0.45){\(A\)};
  \draw[dashed] (1, 0) -- (1, 1) -- (0, 1);
  \draw[dashed] (2, 0) -- (2, 0.625) -- (0, 0.625);
  \draw[<->,ultra thick] (-0.6,0.625) -- (-0.6,1);
\end{tikzpicture}%

width is 96.05pt and height is 6.83331pt

width is 97.16948pt and height is 6.83331pt

width is 132.29497pt and height is 6.83331pt



abcdefghijklmnopqrstuvwxyz

\end{document}

編輯記錄：

\mmzPrefix {.//prawf.}
\mmzUsedCMemo {.//prawf.AB565A279548684A84116CD5604FF9BE.memo}
\mmzUsedExtern {.//prawf.AB565A279548684A84116CD5604FF9BE-E778DCCCB8AAB0BBD3F6CFEEFD2421F8.pdf}
\mmzUsedCCMemo {.//prawf.AB565A279548684A84116CD5604FF9BE-E778DCCCB8AAB0BBD3F6CFEEFD2421F8.memo}
\endinput

文件：

prawf.AB565A279548684A84116CD5604FF9BE-E778DCCCB8AAB0BBD3F6CFEEFD2421F8.memo  
prawf.AB565A279548684A84116CD5604FF9BE.memo  
prawf.mmz.log
prawf.AB565A279548684A84116CD5604FF9BE-E778DCCCB8AAB0BBD3F6CFEEFD2421F8.pdf   
prawf.mmz

Answer