% Copyright 2008-2020 by Christian Feuersaenger
%
% This file may be distributed and/or modified
%
% 1. under the LaTeX Project Public License and/or
% 2. under the GNU Public License.
%
% See the file doc/generic/pgf/licenses/LICENSE for more details.
%
% ******************************
% This here is the shared implementation of TeX-dialect specific files
%   tikzlibraryexternal.code.tex
% ******************************
%
%
% This file provides a high-level automatic export feature for tikz pictures.
% It allows to export EACH SINGLE FIGURE into a separate PDF.
%
% The simplest way is to use the 'convert with system call' option; it simply converts every figure using the write18 method. If that is not possible, a list of figure file names is generated and you need to generate these figures manually (or with a script).
%
%
% It replaces \tikzpicture/ \endtikzpicture and \tikz and invokes \beginpgfgraphicnamed ... \endpgfgraphicnamed
% commands if necessary.

% handle with extreme care and only in small, local groups:
\toksdef\t@tikzexternal@tmpa=0
\toksdef\t@tikzexternal@tmpb=1

\newif\iftikzexternal@nestedflag
\newif\iftikzexternal@verboseuptodate
\newif\iftikzexternal@verboseio
\newif\iftikzexternal@genfigurelist
\newif\iftikzexternal@onlynamed
\newif\iftikzexternal@file@isuptodate
\newif\iftikzexternal@force@remake
\newif\iftikzexternal@optimize
\newif\iftikzexternal@export@enabled
\tikzexternal@export@enabledtrue

% must be numeric!
\gdef\c@tikzexternal@version{2}

% This 'if' can be used as part of the public user interface.
%
% It is set by the 'remake next' key.
%
% It disables any up-to-date checks for the *next* picture, forcing a
% remake of it.
%
% It applies only to *one* picture.
\newif\iftikzexternalremakenext
\newif\iftikzexternal@verbose@optimize
\tikzexternal@verbose@optimizetrue

% A global boolean which can be used to skip single figures.
\newif\iftikzexternalexportnext
\tikzexternalexportnexttrue

% Invokes '#1' if the external lib is currently externalizing
% something and '#2' if not.
%
% This command must be called *after* \tikzexternalize.
\def\tikzifexternalizing#1#2{%
    \ifpgf@external@grabshipout #1\else #2\fi
}%
% Invokes '#1' if the external lib is currently externalizing the NEXT FOLLOWING
% tikzpicture. It invokes '#2' if that is not the case.
\def\tikzifexternalizingnext#1#2{%
    \ifpgf@external@grabshipout
        \tikzexternalgetnextfilename\tikzexternal@temp
        \tikzifexternaljobnamematches\tikzexternal@temp{#1}{#2}%
    \else
        #2%
    \fi
}%
% Invokes '#1' if the external lib is currently externalizing the
% current picture. It invokes '#2' if that is not the case.
%
% If the command is invoked outside of a picture, '#2' will be
% invoked.
\def\tikzifexternalizingcurrent#1#2{%
    \ifpgf@external@grabshipout
        \tikzexternalgetcurrentfilename\tikzexternal@temp
        \ifx\tikzexternal@temp\pgfutil@empty
            #2%
        \else
            \tikzifexternaljobnamematches\tikzexternal@temp{#1}{#2}%
        \fi
    \else
        #2%
    \fi
}%

% Invokes '#2' if \jobname equals '#1' and '#3' if not.
% I suppose that '#1' is a macro containing the file name.
%
\def\tikzifexternaljobnamematches#1#2#3{%
    \edef\pgf@tempa{\expandafter\string\csname#1\endcsname}%
    \edef\pgf@tempb{\expandafter\string\csname\pgfactualjobname\endcsname}%
    \ifx\pgf@tempa\pgf@tempb #2\else#3 \fi%
}%


\pgfutil@IfUndefined{pdfshellescape}{%
    % let's hope that \usepackage{pdftexcmds} has been used...
    \pgfutil@IfUndefined{pdf@shellescape}{%
        \def\tikzexternalcheckshellescape{0}%
    }{%
        \let\tikzexternalcheckshellescape=\pdf@shellescape
    }%
}{%
    \let\tikzexternalcheckshellescape=\pdfshellescape
}%
\ifnum\tikzexternalcheckshellescape=1
    \def\tikzexternalcheckshellescape{\pgfkeysvalueof{/tikz/external/shell escape}\space}%
\else
    \def\tikzexternalcheckshellescape{}%
\fi

\newif\iftikzexternal@auto@detect@jobname

\pgfqkeys{/tikz/external}{
    figure list/.is if=tikzexternal@genfigurelist,
    aux in dpth/.style={/pgf/images/aux in dpth={#1}},%
    disable dependency files/.code={%
        \let\tikzexternalfiledependsonfile@ACTIVE=\tikzexternalfiledependsonfile
    },
    % 'mode' applies only if \jobname==real job name.
    mode/.is choice,
    mode/only graphics/.code   = {%
        \def\tikzexternal@opmode{0}%
        \pgfkeysalso{/pgf/images/aux in dpth=true}%
    },
    mode/no graphics/.code     = {\def\tikzexternal@opmode{1}},
    % an alias for 'no graphics:'
    mode/only pictures/.code   = {\def\tikzexternal@opmode{1}},
    mode/graphics if exists/.code= {%
        \def\tikzexternal@opmode{2}%
        \pgfkeysalso{/pgf/images/aux in dpth=true}%
    },
    mode/list only/.code       = {\def\tikzexternal@opmode{3}\tikzexternal@genfigurelisttrue},
    mode/convert with system call/.code={%
        \def\tikzexternal@opmode{4}%
        \pgfkeysalso{/tikz/external/figure list=false,/pgf/images/aux in dpth=true}%
    },
    mode/list and make/.code   = {%
        \def\tikzexternal@opmode{5}%
        \pgfkeysalso{/tikz/external/figure list=true,/pgf/images/aux in dpth=true}%
    },
    mode=convert with system call,
    force remake/.is if=tikzexternal@force@remake,
    force remake/.default=true,
    %
    % DEPRECATED: this here will work out-of-the box (provided that
    % 'aux in dpth' is active):
    failed ref warnings for/.initial={\ref,\cite,\pageref},
    export next/.is if=tikzexternalexportnext,
    export/.is if=tikzexternal@export@enabled,
    remake next/.is if=tikzexternalremakenext,
    remake next/.default=true,
    verbose IO/.is if=tikzexternal@verboseio,
    verbose IO/.default=true,
    verbose IO=true,
    verbose optimize/.is if=tikzexternal@verbose@optimize,
    verbose up to date/.is if=tikzexternal@verboseuptodate,
    verbose/.style={
        verbose IO=#1,
        verbose optimize=#1,
        verbose up to date=#1,
    },
    shell escape/.initial=-shell-escape,
    read main aux/.is if=pgfexternalreadmainaux,
    image discarded text/.initial={%
        [[ \textsc{Image Discarded Due To} \texttt{`/tikz/external/%
                \ifcase\tikzexternal@opmode\relax
                    mode=only graphics%
                \or
                    mode=no graphics%
                \or
                    mode=graphics if exists%
                \or
                    mode=list only%
                \or
                    mode=convert with system call%
                \or
                    mode=list and make%
                \fi
        '}~]]%
        \pgfutil@ifundefined{tikzexternal@warning@at@end}{%
            \pgfutil@ifundefined{AtEndDocument}{}{%
                \AtEndDocument{%
                    \message{! Package tikz Warning: Some images are not up-to-date and need to be generated. }%
                }%
            }%
            \gdef\tikzexternal@warning@at@end{1}%
        }{}%
    },
    optimize/.is choice,
    optimize/true/.code={%
        \tikzexternal@optimizetrue
        \iftikzexternal@optimize
            \ifpgf@external@grabshipout
                % we have already started the externalization! Install
                % optimization commands to activate the new one:
                \tikzexternal@optimize@REPLACE
            \fi
        \fi
    },
    optimize/false/.code={%
        \tikzexternal@optimizefalse%
        \tikzexternal@optimize@RESTORE
    },%
    optimize=true,
    optimize away text/.code={[ \textsc{\string#1\ optimized away because it does not contribute to exported PDF}]},
    optimize/install/.code={},%
    optimize/restore/.code={},%
    % Expects two arguments, the command name and (optionally) a count
    % of expected arguments.
    % Example:
    %   'optimize command away=\includegraphics'
    %   'optimize command away={\mycommand}{3}'
    %
    % It accepts commands which have '[]' arguments and whose first
    % argument always begins with '{'.
    %
    % #1: the command name
    % #2: either empty or a number of EXPECTED arguments. It will be checked
    % for one optional argument in square brackets as well.
    optimize command away/.code 2 args={%
        \expandafter\global\expandafter\let\csname\string#1@ORIG\endcsname=#1%
        \pgfkeysalso{%
            /tikz/external/optimize/install/.append code={%
                \def#1{\tikzexternal@optimize@away@cmd{#1}{#2}}%
            },
            /tikz/external/optimize/restore/.append code={%
                \expandafter\let\expandafter#1\csname\string#1@ORIG\endcsname
            }
        }%
        \iftikzexternal@optimize
            \ifpgf@external@grabshipout
                % we have already started the externalization! Install
                % optimization commands to activate the new one:
                \tikzexternal@optimize@REPLACE
            \fi
        \fi
    },
    optimize command away=\includegraphics,
    optimize command away=\pgfincludeexternalgraphics,
    % EXPERIMENTAL (UNTESTED):
    optimize latex env away/.code={%
        \expandafter\let\expandafter\pgf@tempa\csname #1\endcsname
        \expandafter\global\expandafter\let\csname #1@ORIG\endcsname=\pgf@tempa%
        \pgfkeysalso{%
            /tikz/external/optimize/install/.append code={%
                \pgfutil@namedef{#1}{\tikzexternal@optimize@away@latex@env{#1}}%
            },
            /tikz/external/optimize/restore/.append code={%
                \pgfutil@namelet{#1}{#1@ORIG}%
            }%
        }%
    },
    only named/.is if=tikzexternal@onlynamed,
    only named/.default=true,
    figure name/.initial=\tikzexternal@realjob-figure,
    reset counter/.code={%
        \expandafter\gdef\csname c@tikzext@no@#1\endcsname{0}%
    },%
    prefix/.code={\tikzsetexternalprefix{#1}},
    up to date check/.is choice,
    up to date check/simple/.code={\def\tikzexternal@uptodate@mode{0}},
    % md5 relies on \pdfmdfivesum of pdftex. It uses 'diff' as fallback if we do not have that command.
    up to date check/md5/.code={\def\tikzexternal@uptodate@mode{1}},
    up to date check/diff/.code={\def\tikzexternal@uptodate@mode{2}},
    up to date check=md5,
}

\expandafter\def\csname tikzexternal@driver@pgfsys-luatex.def\endcsname{%
    \pgfkeyssetvalue{/tikz/external/system call}{%
        lualatex \tikzexternalcheckshellescape -halt-on-error -interaction=batchmode -jobname "\image" "\texsource"%
    }%
}%
\expandafter\def\csname tikzexternal@driver@pgfsys-pdftex.def\endcsname{%
    \pgfutil@IfUndefined{directlua}{%
        \pgfkeyssetvalue{/tikz/external/system call}{%
            pdflatex \tikzexternalcheckshellescape -halt-on-error -interaction=batchmode -jobname "\image" "\texsource"%
        }%
    }{%
        \pgfkeyssetvalue{/tikz/external/system call}{%
            lualatex \tikzexternalcheckshellescape -halt-on-error -interaction=batchmode -jobname "\image" "\texsource"%
        }%
    }%
}%
%--------------------------------------------------
% \expandafter\def\csname tikzexternal@driver@pgfsys-dvipdfm.def\endcsname{%
%     \pgfkeyssetvalue{/tikz/external/system call}{%
%         latex \tikzexternalcheckshellescape -halt-on-error -interaction=batchmode -jobname "\image" "\texsource"%
%         && dvipdfm "\image".dvi %
%     }%
% }%
%--------------------------------------------------
\expandafter\def\csname tikzexternal@driver@pgfsys-xetex.def\endcsname{%
    \pgfkeyssetvalue{/tikz/external/system call}{%
        xelatex \tikzexternalcheckshellescape -halt-on-error -interaction=batchmode -jobname "\image" "\texsource"%
    }%
}%
\expandafter\def\csname tikzexternal@driver@pgfsys-dvips.def\endcsname{%
    \pgfkeyssetvalue{/tikz/external/system call}{%
        latex \tikzexternalcheckshellescape -halt-on-error -interaction=batchmode -jobname "\image" "\texsource" %
        && dvips -o "\image".ps "\image".dvi %
    }%
}%

% Auto-select a suitable default value fo 'system call':
\pgfutil@ifundefined{tikzexternal@driver@\pgfsysdriver}{%
    % fallback. We do not know the driver here.
    \csname tikzexternal@driver@pgfsys-pdftex.def\endcsname
}{%
    \csname tikzexternal@driver@\pgfsysdriver\endcsname
}%


\def\tikzsetfigurename#1{\pgfkeyssetvalue{/tikz/external/figure name}{#1}}%
\def\tikzappendtofigurename#1{\pgfkeys{/tikz/external/figure name/.add={}{#1}}}

% This method sets the file name prefix used for every import/export.
%
% It is invoked by the '/tikz/external/prefix' key.
\def\tikzsetexternalprefix#1{\def\tikzexternal@filenameprefix{#1}}
\tikzsetexternalprefix{}

% This method initialises automatic externalization.
%
% The command does need any argument, but it has two optional ones:
%
% 1. \tikzexternalize[<options>]
%
% 2. \tikzexternalize{<real job's name>}
%
% 3. \tikzexternalize[<options>]{<real job's name>}
%
% The <real job's name> is the job's file name, without the suffix
% .tex .
% If the <real job's name> is omitted, it will be deduced
% automatically.
%
% The effect is:
% 1. automatically surround EVERY tikzpicture by \beginpgfgraphicnamed % sections.
% 2. in case that the job's real name and the current \jobname differ,
% it will process ONLY the matching tikzpicture.
\def\tikzexternalize{%
    \pgfutil@ifnextchar[{%
        \tikzexternalize@opt
    }{%
        \tikzexternalize@opt[]%
    }%
}%
\def\tikzexternalize@opt[#1]{%
    \pgfutil@ifnextchar\bgroup{%
        \tikzexternal@auto@detect@jobnamefalse
        \tikzexternalize@opt@withname[#1]%
    }{%
        \tikzexternal@auto@detect@jobnametrue
        \pgfutil@ifundefined{tikzexternalrealjob}{%
            % ok, \tikzexternalrealjob is not known.
            % Assume we are currently *not* externalizing.
            \let\tikzexternalrealjob=\jobname
        }{}%
        \def\pgf@tempa{\tikzexternalize@opt@withname[#1]}%
        \expandafter\pgf@tempa\expandafter{\tikzexternalrealjob}%
    }%
}%
\def\tikzexternalize@opt@withname[#1]#2{%
    \gdef\tikzexternalrealjob{#2}%
    \if1\tikzexternalize@hasbeencalled
    \else
        \pgfqkeys{/tikz/external}{#1}%
        \def\tikzexternal@realjob{#2}%
        \tikzexternalauxlock@init
        \pgfrealjobname{#2}%
        \def\tikzexternalize@hasbeencalled{1}%
        \tikzexternalenable
        \def\tikzexternal@determineimgextension##1:##2\relax{\gdef\tikzexternalimgextension{##1}}%
        \xdef\pgf@tempa{\pgfsys@imagesuffixlist}%
        \expandafter\tikzexternal@determineimgextension\pgf@tempa:\relax
        \pgfutil@ifundefined{includegraphics}{%
            \let\tikzexternal@orig@includegraphics=\relax
        }{%
            \let\tikzexternal@orig@includegraphics=\includegraphics
        }%
        \let\tikzexternalfiledependsonfile=\tikzexternalfiledependsonfile@ACTIVE
        \let\tikzpicturedependsonfile=\tikzpicturedependsonfile@ACTIVE
    \fi
}
\def\tikzexternalize@hasbeencalled{0}%

\def\tikzifexternalizehasbeencalled#1#2{%
    \if1\tikzexternalize@hasbeencalled
        #1%
    \else
        #2%
    \fi
}%

% If mode=`convert with system call', the boolean \ifpgfexternalreadmainaux
% will be set depending on the current lock file.
%
% The idea is as follows: Suppose
% pdflatex -shell-escape mainjob.tex
% is running.
%
% While it runs,
% a) it modifies its mainjob.aux file,
% b) it issues pdflatex -jobname mainjob-figure0 mainjob.tex .
%
% The call (b) will try to read mainjob.aux in order to resolve \ref
% commands. This may fail since the aux
% file is not complete; it may be subject to output buffering. To
% avoid such failure, a locking mechanism is established.
%
% The locking mechanisms causes (a) to write a lock command into
% mainjob.auxlock
% just before (b) is called. Then, (b) will check it. After (b) has
% completed, the lock will be reset.
%
% Thus: mode=convert with system call does NOT support \ref commands
% inside of images. You will need to call the externalization command
% manually. In this case, it should work.
%
% The lock file allows to detect automatically whether an image is created by
% 'convert with system call' or if the user issued the required command manually.
%
% @PRECONDITION : this command must be invoked AFTER
% \tikzexternal@realjob has been defined but BEFORE \pgfrealjobname is
% called.
%
% @POSTCONDITION : If \ifpgfexternalreadmainaux=\iffalse, we won't do
% anything. Otherwise, it will be changed depending for 'mode=convert
% with system call' if necessary.
\def\tikzexternalauxlock@init{%
    \if4\tikzexternal@opmode
        % mode=convert with system call
        \ifpgfexternalreadmainaux
            % ohoh. This case needs care because the main.aux might
            % not be ready at this time!
            % check.
            %
            \edef\pgf@tempa{\expandafter\string\csname\tikzexternal@realjob\endcsname}%
            \edef\pgf@tempb{\expandafter\string\csname\jobname\endcsname}%
            \ifx\pgf@tempa\pgf@tempb
                % we are *not* externalizing. Set lock into its
                % initial "unlocked" state.
                \tikzexternalauxlock@setlock{0}%
            \else
                % we are externalizing. Query the lock's value:
                \tikzexternalauxlock@getlockvalue
                \if1\tikzexternallocked
                    \pgfexternalreadmainauxfalse
                    % the main .aux file won't be read right now.
                \else
                    \pgfexternalreadmainauxtrue
                \fi
            \fi
        \else
            % NO-OP. We won't read the main aux file anyway.
            \def\tikzexternalauxlock@setlock##1{}%
        \fi
    \fi
}
% defines \tikzexternallocked to be either 0 or 1, depending on the
% lock file.
\def\tikzexternalauxlock@getlockvalue{%
    \openin\r@pgf@reada=\tikzexternal@realjob.auxlock
    \ifeof\r@pgf@reada
        % no lock file. Unlock.
        \def\tikzexternallocked{0}%
    \else
        % read first line...
        \read\r@pgf@reada to\pgf@tempa
        % ... and execute it.
        \pgf@tempa
        % it should contain a definition of \tikzexternallocked. If
        % not, lock it anyway.
        \pgfutil@ifundefined
            {tikzexternallocked}
            {\def\tikzexternallocked{1}}%
            {}%
    \fi
    \closein\r@pgf@reada
}%
\def\tikzexternalauxlock@setlock#1{%
    \immediate\openout\w@pgf@writea=\tikzexternal@realjob.auxlock
    \immediate\write\w@pgf@writea{\noexpand\def\noexpand\tikzexternallocked{#1}}%
    \immediate\closeout\w@pgf@writea
}


% this is a hook into pgfcoreexternal.code.tex:
\def\pgf@external@grab@refundefinedtrue@code{%
    \gdef\noexpand\tikzexternal@systemcall@reschedule@to@end@document{1}%
}%

% Expands to the default image extension (it is set by
% \tikzexternalize).
%
% This image extension may not resemble the correct one; you may need
% to overwrite this macro *after* \tikzexternalize in this case.
%
% The default setting uses the first registered image extension.
\def\tikzexternalimgextension{}%

% can be used to (temporarily) disable the externalization.
\def\tikzexternaldisable{%
    \tikzexternaldisable@nofading
    \pgfutil@ifundefined{tikzexternal@orig@tikzfadingfrompicture}
    {}% NOP
    {%
        \let\tikzfadingfrompicture=\tikzexternal@orig@tikzfadingfrompicture
        \let\endtikzfadingfrompicture=\tikzexternal@orig@endtikzfadingfrompicture
        \let\tikzfading=\tikzexternal@orig@tikzfading
    }%
}%
\def\tikzexternaldisable@nofading{%
    \let\tikz=\tikzexternal@origtikz
    \tikzexternal@TEXDIALECT@restore@picture
    \iftikzexternal@optimize
        \ifpgf@external@grabshipout
            \tikzexternal@optimize@RESTORE
        \fi
    \fi
}
% re-enables externalization after a \tikzexternalizedisable.
\def\tikzexternalenable{%
    \if\tikzexternalize@hasbeencalled1%
        \let\tikz=\tikzexternal@tikz@replacement
        \tikzexternal@TEXDIALECT@installreplacement@picture
        \pgfutil@ifundefined{tikzfadingfrompicture}%
        {}% no special handling for 'fading lib'
        {%
            % oh, ok -- patch fading lib!
            \pgfutil@ifundefined{tikzexternal@orig@tikzfadingfrompicture}{%
                \let\tikzexternal@orig@tikzfadingfrompicture=\tikzfadingfrompicture
                \let\tikzexternal@orig@endtikzfadingfrompicture=\endtikzfadingfrompicture
                \let\tikzexternal@orig@tikzfading=\tikzfading
            }{}%
            \def\tikzfadingfrompicture{%
                \begingroup
                \tikzexternaldisable@nofading
                \tikzexternal@orig@tikzfadingfrompicture}%
            \def\endtikzfadingfrompicture{%
                \tikzexternal@orig@endtikzfadingfrompicture
                \endgroup}%
            \def\tikzfading[##1]{%
                \begingroup
                \tikzexternaldisable@nofading
                \tikzexternal@orig@tikzfading[##1]%
                \endgroup}%
        }%
        \iftikzexternal@optimize
            \ifpgf@external@grabshipout
                \tikzexternal@optimize@REPLACE
            \fi
        \fi
    \fi
}%

% Sets the filename for the next tikzpicture or \tikz shortcommand.
%
% It will *only* be used for the next picture.
%
% If you don't call \tikzsetnextfilename for a picture, a file name
% will be assembled automatically.
%
% Please note that the global file prefix will be prepended anyway.
\def\tikzsetnextfilename#1{\gdef\tikzexternal@nextfile{#1}}
\tikzsetnextfilename{}


% These are few TeX dialect-specific commands which need to be overridden when used with
% something different than plain TeX:
%
% 1. this command collects a complete image into a macro, up to (but not including) the
%    final TeX-dialect specific end-image command.
%    This is really difficult for LaTeX because \end{tikzpicture} either involves dirty
%    catcode-hacks to parse the braces or an ugly loop which loops until it
%    finds \end followed by {tikzpicture}.
%
% #1: a macro which will be called with the collected environment contents.
% all following tokens: the environment contents.
\long\gdef\tikzexternal@TEXDIALECT@collectpicture#1#2\endtikzpicture{#1{#2}}
%
% 2. the following commands should expand to the TeX-dialect specific begin and end image command, i.e.
%    \tikzpicture / \endtikzpicture
%    or
%    \begin{tikzpicture} / \end{tikzpicture}
%    or
%    \starttikzpicture / \stoptikzpicture
\def\tikzexternal@TEXDIALECT@begpicture{\tikzpicture}
\def\tikzexternal@TEXDIALECT@endpicture{\endtikzpicture}%
%
% 3. This installs the replacement macros:
\def\tikzexternal@TEXDIALECT@installreplacement@picture{%
    \let\tikzpicture=\tikzexternal@tikzpicture@replacement
}%
\def\tikzexternal@TEXDIALECT@restore@picture{%
    \let\tikzpicture=\tikzexternal@origpicture
}%




\let\tikzexternal@origtikz=\tikz
\let\tikzexternal@origpicture=\tikzpicture
\let\tikzexternal@origendpicture=\endtikzpicture
\let\tikzexternal@curfilename=\relax

% Replacement for '\tikzpicture'.
%
% There are two different states in which this method is applied:
% - normal typesetting. Then, the 'mode' key controls its behavior.
% - externalize mode (i.e. jobname != real job name). Then, it will
%   externalize the picture selected by 'jobname' (and only this picture).
\def\tikzexternal@tikzpicture@replacement{%
    \leavevmode
    \global\tikzexternal@file@isuptodatetrue% may be set to false during checks.
    \tikzexternal@getnextfilename\tikzexternal@curfilename
    \ifx\tikzexternal@curfilename\pgfutil@empty
        \ifpgf@external@grabshipout
            % This picture won't be externalized.
            % But maybe we can optimize it away:
            \iftikzexternal@optimize
                % -> it won't be shipped out anyway, so save typesetting time!
                \let\tikzexternal@next=\tikzexternal@skipfigure
            \else
                % include this graphics into the output (even if
                % it will be discarded anyway).
                \let\tikzexternal@next=\tikzexternal@normalpicture@nographics
            \fi
        \else
            \let\tikzexternal@next=\tikzexternal@normalpicture@nographics
        \fi
    \else
        \ifpgf@external@grabshipout
            \tikzifexternaljobnamematches\tikzexternal@curfilename{%
                % ok, this here IS the picture for which
                % pdflatex --jobname <my name>
                % has been invoked.
                \let\tikzexternal@next=\tikzexternal@externalizefig
            }{%
                \iftikzexternal@optimize
                    % No, another picture should be exported. Simply skip this one
                    % -> it won't be shipped out anyway, so save typesetting time!
                    \let\tikzexternal@next=\tikzexternal@skipfigure
                \else
                    % include this graphics into the output (even it
                    % it will be discarded anyway).
                    \let\tikzexternal@next=\tikzexternal@normalpicture@nographics
                \fi
            }%
        \else
            \ifcase\tikzexternal@opmode\relax
                % 'mode=only graphics'
                \let\tikzexternal@next=\tikzexternal@forcegraphics
            \or
                % 'mode=no graphics'
                \let\tikzexternal@next=\tikzexternal@normalpicture@nographics
            \or
                % 'mode=graphics if exists'
                \let\tikzexternal@next=\tikzexternal@externalizefig
            \or
                % 'mode=list only'
                \let\tikzexternal@next=\tikzexternal@listmodepicture
            \or
                % 'mode=convert with system call'
                \let\tikzexternal@next=\tikzexternal@externalizefig@systemcall
            \or
                % 'mode=list and make'
                \let\tikzexternal@next=\tikzexternal@list@and@makefile@mode@picture
            \fi
        \fi
    \fi
    \tikzexternal@next
}%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Replacement for \tikz short command:
\def\tikzexternal@tikz@replacement{%
    \pgfutil@ifnextchar[{\tikzexternal@tikz@replacement@opt}{\tikzexternal@tikz@replacement@opt[]}%
}%
\def\tikzexternal@tikz@replacement@opt[#1]{%
    \pgfutil@ifnextchar\bgroup{\tikzexternal@tikz@replacement@opt@{#1}}{\tikzexternal@tikz@replacement@opt@@{#1}}%
}
\long\def\tikzexternal@tikz@replacement@opt@#1#2{%
    \tikzexternal@tikz@replacement@opt@process{#1}{#2}%
}%
\def\tikzexternal@tikz@replacement@opt@@#1{%
  \def\tikz@next{\tikzexternal@tikz@replacement@collectnormalsemicolon{#1}}%
  \ifnum\the\catcode`\;=\active\relax%
    \def\tikz@next{\tikzexternal@tikz@replacement@collectactivesemicolon{#1}}%
  \fi%
  \tikz@next}
\long\def\tikzexternal@tikz@replacement@collectnormalsemicolon#1#2;{%
    \tikzexternal@tikz@replacement@opt@process{#1}{#2;}%
}%
{
  \catcode`\;=\active
  \long\gdef\tikzexternal@tikz@replacement@collectactivesemicolon#1#2;{%
    \tikzexternal@tikz@replacement@opt@process{#1}{#2;}%
  }
}
\long\def\tikzexternal@tikz@replacement@opt@process#1#2{%
    \begingroup
    \t@tikzexternal@tmpa=\expandafter{\tikzexternal@TEXDIALECT@begpicture[#1]#2}%
    \t@tikzexternal@tmpb=\expandafter{\tikzexternal@TEXDIALECT@endpicture}%
    \xdef\pgf@tempa{\the\t@tikzexternal@tmpa\the\t@tikzexternal@tmpb}%
    \endgroup
    \pgf@tempa
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\tikzexternal@getnextfilename@advancecount{%
    \begingroup
    \c@pgf@counta=\csname c@tikzext@no@\tikzexternal@figurename\endcsname\relax
    \advance\c@pgf@counta by1
    \expandafter\xdef\csname c@tikzext@no@\tikzexternal@figurename\endcsname{\the\c@pgf@counta}%
    \endgroup
}%

% Returns the file name which will be used for the next tikzpicture (based on the currently available information only, of course).
\def\tikzexternalgetnextfilename#1{%
    \begingroup
    \let\tikzexternal@getnextfilename@advancecount\relax% NOP
    \let\tikzexternal@getnextfilename@resetglobals=\relax% NOP
    \def\tikzexternal@protocol@to@file##1{}% NOP
    \tikzexternal@getnextfilename#1%
    \pgfmath@smuggleone#1%
    \endgroup
}%

% Returns the file name of the current picture.
%
% It returns the empty string in case the command is invoked outside
% of a picture.
% #1 the macro which will contain the file name.
% @see \tikzexternalgetnextfilename
\def\tikzexternalgetcurrentfilename#1{%
    \ifx\tikzexternal@curfilename\relax
        % we are outside of a picture.
        \let#1=\pgfutil@empty
    \else
        % we are inside of a picture.
        \let#1=\tikzexternal@curfilename
    \fi
}

% Fills #1 with a filename for the current picture.
%
% The filename will be generated automatically by appending '-figure<number>' to the real jobname.
%
% This method deals with
% - \tikzsetnextfilename
% - \tikzexternalexportnextfalse
%
% It returns #1={} if the current figure shall NOT be exported.
%
% Please note that both, \tikzsetnextfilename and \tikzexternalexportnextfalse
% affect only ONE picture. They will be reset afterwards.
\def\tikzexternal@getnextfilename#1{%
    \let#1=\pgfutil@empty
    % determine next file name:
    \iftikzexternal@export@enabled
        \iftikzexternalexportnext
            \begingroup
            \t@tikzexternal@tmpa=\expandafter{\tikzexternal@filenameprefix}%
            \ifx\tikzexternal@nextfile\pgfutil@empty
                \iftikzexternal@onlynamed
                    \xdef\pgf@tempa{}%
                \else
                    \pgfkeysgetvalue{/tikz/external/figure name}\tikzexternal@figurename
                    \pgfutil@ifundefined{c@tikzext@no@\tikzexternal@figurename}{%
                        % initialise on first usage:
                        \expandafter\gdef\csname c@tikzext@no@\tikzexternal@figurename\endcsname{0}%
                    }{}%
                    \t@tikzexternal@tmpb=\expandafter{\tikzexternal@figurename}%
                    \xdef\pgf@tempa{\the\t@tikzexternal@tmpa\the\t@tikzexternal@tmpb\csname c@tikzext@no@\tikzexternal@figurename\endcsname}%
                    % advance the counter for 'figure name':
                    \tikzexternal@getnextfilename@advancecount
                \fi
            \else
                \t@tikzexternal@tmpb=\expandafter{\tikzexternal@nextfile}%
                \xdef\pgf@tempa{\the\t@tikzexternal@tmpa\the\t@tikzexternal@tmpb}%
            \fi
            \endgroup
            \let#1=\pgf@tempa
        \fi
    \fi
    %
    \tikzexternal@getnextfilename@resetglobals%
    %
    \tikzexternal@protocol@to@file#1%
}%

\def\tikzexternal@getnextfilename@resetglobals{%
    % Reset global flags:
    \global\let\tikzexternal@nextfile=\pgfutil@empty
    \global\tikzexternalexportnexttrue
}%

% #1: the image file name which should be protocolled. (can be a
% macro)
\def\tikzexternal@protocol@to@file#1{%
    \ifpgf@external@grabshipout%
    \else
        \iftikzexternal@genfigurelist
            \edef\tikzexternal@temp{#1}%
            \ifx\tikzexternal@temp\pgfutil@empty
            \else
                \pgfutil@ifundefined{tikzexternal@listmode@openedfile}{%
                    \message{Opening '\tikzexternal@realjob.figlist' for writing.}%
                    \begingroup
                        \globaldefs=1
                        % this gets round '\outer\newwrite' in plain TeX:
                        \csname newwrite\endcsname\tikzexternal@outfile
                    \endgroup
                    \immediate\openout\tikzexternal@outfile=\tikzexternal@realjob.figlist\relax
                    \gdef\tikzexternal@listmode@openedfile{1}%
                    \if\tikzexternal@opmode5% mode='list and make'
                        \tikzexternal@list@and@make@prepare
                    \fi
                }{}%
                \iftikzexternal@verboseio
                    \pgf@typeout{Writing '#1' to '\tikzexternal@realjob.figlist'.}%
                \fi
                \immediate\write\tikzexternal@outfile{#1}%
                \if\tikzexternal@opmode5% mode='list and make'
                    \tikzexternal@list@and@make@gentarget{#1}%
                \fi
            \fi
        \fi
    \fi
}%

\def\tikzexternal@list@and@make@gentarget#1{%
    \tikzexternal@assemble@systemcall{#1}{\pgf@tempa}%
    \def\tikzexternal@tempb{\pgfutilstrreplace{^^J}{^^J\tikzexternal@TABchar}}%
    \expandafter\tikzexternal@tempb\expandafter{\pgf@tempa}%
    \let\pgf@tempa=\pgfretval
    \iftikzexternal@verboseio
        \pgf@typeout{Writing '#1' to '\tikzexternal@realjob.makefile'.}%
    \fi
    \global\tikzexternal@file@isuptodatetrue% only check for force remake:
    \tikzexternal@checkforceremake%
    \immediate\write\tikzexternal@outmakefile{#1\tikzexternalimgextension: \iftikzexternal@file@isuptodate\else FORCEREMAKE\fi}%
    \immediate\write\tikzexternal@outmakefile{\tikzexternal@TABchar\pgf@tempa}%
    \immediate\write\tikzexternal@outmakefile{}%
}

\def\tikzexternal@list@and@make@prepare{%
    \iftikzexternal@verboseio
        \pgf@typeout{Opening '\tikzexternal@realjob.makefile' for writing.}%
    \fi
    \begingroup
        % this makes \tikzexternal@outmakefile global:
        \globaldefs=1
        % this gets round '\outer\newwrite' in plain TeX:
        \csname newwrite\endcsname\tikzexternal@outmakefile
    \endgroup
    \immediate\openout\tikzexternal@outmakefile=\tikzexternal@realjob.makefile\relax
    \immediate\write\tikzexternal@outmakefile{ALL_FIGURE_NAMES=\tikzexternal@DOLLARchar(shell cat \tikzexternal@realjob.figlist)}%
    \immediate\write\tikzexternal@outmakefile{ALL_FIGURES=\tikzexternal@DOLLARchar(ALL_FIGURE_NAMES:\tikzexternal@PERCENTchar=\tikzexternal@PERCENTchar\tikzexternalimgextension)}%
    \immediate\write\tikzexternal@outmakefile{}%
    \immediate\write\tikzexternal@outmakefile{allimages: \tikzexternal@DOLLARchar(ALL_FIGURES)}%
    \immediate\write\tikzexternal@outmakefile{\tikzexternal@TABchar @echo All images exist now. Use make -B to re-generate them.}%
    \immediate\write\tikzexternal@outmakefile{}%
    \immediate\write\tikzexternal@outmakefile{FORCEREMAKE:}%
    \immediate\write\tikzexternal@outmakefile{}%
    %
    % support for .dep files and auto-dependencies:
    \immediate\write\tikzexternal@outmakefile{-include $(ALL_FIGURE_NAMES:\tikzexternal@PERCENTchar=\tikzexternal@PERCENTchar.\tikzexternaldepext)}%
    \immediate\write\tikzexternal@outmakefile{}%
    \tikzexternalmakefiledefaultdeprule
    \immediate\write\tikzexternal@outmakefile{}%
    \tikzexternal@outmakefile@pendingcommands
    \pgfutil@ifundefined{AtEndDocument}{}{%
        \AtEndDocument{\pgf@typeout{===== mode=`list and make': Use 'make -f \tikzexternal@realjob.makefile' to generate all images. Then, re-run (pdf)latex \tikzexternal@realjob. =====}}%
    }%
}%
\def\tikzexternaldepext{dep}

\def\tikzexternalmakefiledefaultdeprule{%
    \immediate\write\tikzexternal@outmakefile{\tikzexternal@PERCENTchar.\tikzexternaldepext:}%
    \immediate\write\tikzexternal@outmakefile{\tikzexternal@TABchar mkdir -p \tikzexternal@normal@dq $(dir $@)\tikzexternal@normal@dq}%
    \immediate\write\tikzexternal@outmakefile{\tikzexternal@TABchar touch \tikzexternal@normal@dq $@\tikzexternal@normal@dq\space \tikzexternal@HASHchar\space will be filled later.}%
}%

% Invokes '#1' if a makefile is to be written and '#2' if not.
\def\tikzexternalifwritesmakefile#1#2{%
    \if5\tikzexternal@opmode #1\else #2\fi
}%
\def\tikzexternal@outmakefile@pendingcommands{}%

% Will write something to the make file. If the makefile is not yet
% opened, #1 will be written as soon as it *is* opened.
\def\tikzexternalwritetomakefile#1{%
    \if\tikzexternal@opmode5% mode='list and make'
        \pgfutil@ifundefined{tikzexternal@outmakefile}{%
            \expandafter\gdef\expandafter\tikzexternal@outmakefile@pendingcommands\expandafter{%
                \tikzexternal@outmakefile@pendingcommands
                \immediate\write\tikzexternal@outmakefile{#1}%
            }%
        }{%
            \immediate\write\tikzexternal@outmakefile{#1}%
        }%
    \fi
}%

\def\tikzexternal@dep@file@name{}

% Adds a dependency for the externalized picture file name `#1',
% namely another file `#2'.
%
% #1: the fully qualified path name (without image extension) of the
% external graphics for which we are adding a dependency.
% #2: a file name. If this file gets changed, #1 shall be remade.
%
% This command will be activated as soon as \tikzexternalize has been
% called.
\def\tikzexternalfiledependsonfile@ACTIVE#1#2{%
    \begingroup
    \def\tikzpicturedependsonfile@name{#1}%
    \ifx\tikzpicturedependsonfile@name\pgfutil@empty
        % could be auto-generated: empty file name means "picture
        % won't be externalized". Skip it.
    \else
        % if we encounter any dependencies while we externalize a
        % picture, we have to write these things into the image's .dep
        % file.
        \tikzifexternalizingcurrent
            {\tikzexternalfiledependsonfile@append@to@dep@file{#1}{#2}}%
            {\tikzexternalfiledependsonfile@append@to@makefile{#1}{#2}}%
    \fi
    \endgroup
}%
\def\tikzexternalfiledependsonfile#1#2{}% NO-OP until \tikzexternalize has been called.

% sub-routine of \tikzexternalfiledependsonfile which appends stuff to
% the pictures .dep file.
%
% The file #1.dep is generated during the externalization of #1. If
% you change and/or overwrite it in any other context, its information
% might get lost (because #1 won't be regenerated).
%
% Consequently, this here has to be called if and only if #1 is about
% to be externalized.
\def\tikzexternalfiledependsonfile@append@to@dep@file#1#2{%
    % write every dependency which is defined *INSIDE* of the current
    % picture into the .dep file of the current picture:
    \tikzexternalgetcurrentfilename\tikzpicturedependsonfile@name
    \edef\tikzpicturedependsonfile@name{\tikzpicturedependsonfile@name.\tikzexternaldepext}%
    %\edef\tikzpicturedependsonfile@name{#1.\tikzexternaldepext}%
    \ifx\tikzexternal@dep@file@name\tikzpicturedependsonfile@name
        % file is open and ready.
    \else
        % create new output file.
        \pgfutil@ifundefined{tikzexternal@dep@file}{%
            \begingroup
                % this makes \tikzexternal@dep@file global:
                \globaldefs=1
                % this gets round '\outer\newwrite' in plain TeX:
                \csname newwrite\endcsname\tikzexternal@dep@file
            \endgroup
        }{}%
        \ifx\tikzexternal@dep@file@name\pgfutil@empty
        \else
            % it is already open. Close it.
            \immediate\closeout\tikzexternal@dep@file
        \fi
        \global\let\tikzexternal@dep@file@name=\tikzpicturedependsonfile@name
        \immediate\openout\tikzexternal@dep@file=\tikzexternal@dep@file@name\relax
    \fi
    \immediate\write\tikzexternal@dep@file{#1\tikzexternalimgextension: #2}%
}

% sub-routine of \tikzexternalfiledependsonfile which appends stuff to
% the makefile of the current \jobname .
%
% This is used for dependencies which are recomputed by every run of
% tex; we must not write them into #1.dep (for reasons explained in
% the documentation of
% \tikzexternalfiledependsonfile@append@to@dep@file)
\def\tikzexternalfiledependsonfile@append@to@makefile#1#2{%
    \edef\tikzexternal@temp{#1\tikzexternalimgextension: #2}%
    \expandafter\tikzexternalwritetomakefile\expandafter{\tikzexternal@temp}%
}

% Adds a dependency for the NEXT picture which is about to be
% externalized. If we are currently inside of a picture, the
% dependency is added for this current picture.
%
% #1: a file name. If this file gets changed, the tikzpicture's
% externalized graphics shall be remade.
%
% This command will be activated as soon as \tikzexternalize has been
% called.
\def\tikzpicturedependsonfile@ACTIVE#1{%
    \begingroup
    \tikzexternalgetcurrentfilename\tikzpicturedependsonfile@name
    \ifx\tikzpicturedependsonfile@name\pgfutil@empty
        \tikzexternalgetnextfilename\tikzpicturedependsonfile@name
    \fi
    \expandafter\tikzexternalfiledependsonfile\expandafter{\tikzpicturedependsonfile@name}{#1}%
    \endgroup
}%
\def\tikzpicturedependsonfile#1{}% NO-OP until \tikzexternalize has been called.


% This command is invoked
%  if and only if ( (grab mode && --jobname matches) || 'mode=graphics if exists' )
%
% It converts the current tikzpicture into an image in grab mode
% or processes the 'graphics if exist' mode.
\def\tikzexternal@externalizefig{%
    \ifpgf@external@grabshipout%
        % In this case, we already KNOW that the filename matches.
        \expandafter\tikzexternal@externalizefig@GRAB%
    \else
        \expandafter\tikzexternal@externalizefig@mode@graphics@if@exists
    \fi%
}
\def\tikzexternal@externalizefig@mode@graphics@if@exists{%
    % check if there is already a file.
    % In that case, use it. If not, typeset the picture normally.
    \gdef\pgf@filename{}%
    \xdef\pgf@tempa{\noexpand\pgf@findfile\pgfsys@imagesuffixlist:+{\tikzexternal@curfilename}}%
    \pgf@tempa
    \ifx\pgf@filename\pgfutil@empty%
        % Note: since we have no 'GRAB' mode, we do not have to deal with optimization.
        % there is no graphics.
        \expandafter\tikzexternal@normalpicture@nographics
    \else
        \expandafter\tikzexternal@forcegraphics
    \fi
}%


% Used by the optimization code.
% It will be called if GRAB mode is on.
% See the 'optimize command away' key.
\def\tikzexternal@optimize@away@cmd#1#2{%
    \pgfutil@ifnextchar[{%
        \tikzexternal@optimize@away@cmd@{#1}{#2}%
    }{%
        \tikzexternal@optimize@away@cmd@{#1}{#2}[]%
    }%
}%
\def\tikzexternal@optimize@away@cmd@#1#2[#3]{%
    \def\tikz@temp{#2}%
    \ifx\tikz@temp\pgfutil@empty
        \def\tikz@temp{\tikzexternal@optimize@away@cmd@auto{#1}{#3}}%
    \else
        \ifcase#2\relax
            \def\tikzexternal@optimize@away@cmd@manual{%
                \tikzexternal@optimize@away@cmd@@@{#1}{#3}{}%
            }%
        \or
            \def\tikzexternal@optimize@away@cmd@manual##1{%
                \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}}%
            }%
        \or
            \def\tikzexternal@optimize@away@cmd@manual##1##2{%
                \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}}%
            }%
        \or
            \def\tikzexternal@optimize@away@cmd@manual##1##2##3{%
                \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}{##3}}%
            }%
        \or
            \def\tikzexternal@optimize@away@cmd@manual##1##2##3##4{%
                \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}{##3}{##4}}%
            }%
        \or
            \def\tikzexternal@optimize@away@cmd@manual##1##2##3##4##5{%
                \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}{##3}{##4}{##5}}%
            }%
        \or
            \def\tikzexternal@optimize@away@cmd@manual##1##2##3##4##5##6{%
                \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}{##3}{##4}{##5}{##6}}%
            }%
        \or
            \def\tikzexternal@optimize@away@cmd@manual##1##2##3##4##5##6##7{%
                \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}{##3}{##4}{##5}{##6}{##7}}%
            }%
        \or
            \def\tikzexternal@optimize@away@cmd@manual##1##2##3##4##5##6##7##8{%
                \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}{##3}{##4}{##5}{##6}{##7}{##8}}%
            }%
        \or
            \def\tikzexternal@optimize@away@cmd@manual##1##2##3##4##5##6##7##8##9{%
                \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}{##3}{##4}{##5}{##6}{##7}{##8}{##9}}%
            }%
        \fi
        \def\tikz@temp{\tikzexternal@optimize@away@cmd@manual}%
    \fi
    \tikz@temp
}%
\def\tikzexternal@optimize@away@cmd@auto#1#2{%
    \pgfutil@ifnextchar\bgroup{%
        \tikzexternal@optimize@away@cmd@auto@{#1}{#2}%
    }{%
        \tikzexternal@optimize@away@cmd@auto@{#1}{#2}{<no argument in curly braces>}% give empty argument.
    }
}%

\def\tikzexternal@optimize@away@cmd@auto@#1#2#3{%
    \tikzexternal@optimize@away@cmd@@@{#1}{#2}{{#3}}% <-- provide braces
}%
\def\tikzexternal@optimize@away@cmd@@@#1#2#3{%
    \begingroup
    \toks0={#1[#2]#3}%
    \iftikzexternal@verbose@optimize
        \pgf@typeout{The command '\the\toks0' has been optimized away. Use '/tikz/external/optimize=false' to disable this.}%
    \fi
    \endgroup
    \begingroup
    \pgfkeysvalueof{/tikz/external/optimize away text/.@cmd}#1\pgfeov%
    \endgroup
}%

\def\tikzexternal@optimize@away@latex@env#1{%
    \def\tikzexternal@optimize@away@latex@env@{#1}%
    \begingroup
        \def\tikzexternal@laTeX@collect@until@end@tikzpicturetikzpicturestring{#1}%
        \tikzexternal@TEXDIALECT@collectpicture\tikzexternal@optimize@away@latex@env@close
}%
\long\def\tikzexternal@optimize@away@latex@env@close#1{%
    \iftikzexternal@verbose@optimize
        \pgf@typeout{The complete contents of \string\begin{tikzexternal@optimize@away@latex@env@} up to the next \end{tikzexternal@optimize@away@latex@env@} has been optimized away because it does not contribute to the exported PDF. Use '/tikz/external/optimize=false' to disable this.}%
    \fi
    \endgroup
    % we still need to invoke \end{<name>} in latex because \begin{<name>}
    % starts a local group - that must be closed properly. Make sure then \end<name> does nothing:
    \expandafter\let\csname end\tikzexternal@optimize@away@latex@env@\endcsname=\relax
    \expandafter\end\expandafter{\tikzexternal@optimize@away@latex@env@}%
}%

\def\tikzexternal@optimize@REPLACE{%
    \pgfkeysvalueof{/tikz/external/optimize/install/.@cmd}\pgfeov
}%

\def\tikzexternal@optimize@RESTORE{%
    \pgfkeysvalueof{/tikz/external/optimize/restore/.@cmd}\pgfeov
}%

% Closes one 'tikzpicture' environment. This is only used for LaTeX,
% because the '\end{tikzpicture}' command would raise an exception otherwise.
% It does *not* call \endtikzpicture.
\def\tikzexternal@closeenvironments{%
    \let\endtikzpicture=\relax
    \tikzexternal@TEXDIALECT@endpicture
    \let\endtikzpicture=\tikzexternal@origendpicture
    \let\tikzexternal@curfilename=\relax
}

% Throws a tikzpicture away - without further notice.
% Used if we are currently converting *another* picture. No need to waste time
% with expensive pictures if they are not shipped out anyway.
%
% See the 'optimize' key to disable this.
\def\tikzexternal@skipfigure{%
    \tikzexternal@TEXDIALECT@collectpicture\tikzexternal@skipfigure@@
}
\long\def\tikzexternal@skipfigure@@#1{%
    \iftikzexternal@verbose@optimize
        \pgf@typeout{A tikzpicture has been optimized away. Use '/tikz/external/optimize=false' to disable this.}%
    \fi
    \tikzexternal@closeenvironments
    \pgfkeysvalueof{/tikz/external/optimize away text/.@cmd}tikzpicture\pgfeov%
}

% Processes tikzpicture normally; without any externalization.
%
% We need to do further work here to deal with NESTED tikzpicture environments
% because all of them shall also be typeset normally.
%
% Idea:
% 1. restore the original \tikzpicture macro
% 2. install the replacement \tikzpicture in \end{tikzpicture}.
% and keep track of nesting.
%
% FIXME: could it be possible that nested tikzpictures use other code anyway?
\def\tikzexternal@normalpicture@nographics{%
    \tikzexternal@nestedflagfalse
    \let\tikzpicture=\tikzexternal@normalpicture@begreplace
    \let\endtikzpicture=\tikzexternal@normalpicture@endreplace
    \tikzpicture
}
\def\tikzexternal@normalpicture@begreplace{%
    \begingroup
    \tikzexternal@nestedflagtrue
    \tikzexternal@origpicture
}
\def\tikzexternal@normalpicture@endreplace{%
    \tikzexternal@origendpicture
    \endgroup
    \iftikzexternal@nestedflag
    \else
        \let\tikzpicture=\tikzexternal@tikzpicture@replacement
        \let\endtikzpicture=\tikzexternal@origendpicture
    \fi
}%

% Assumes there is an image on disk and reads it. The tikzpicture is thrown away.
\def\tikzexternal@forcegraphics{%
    \tikzexternal@TEXDIALECT@collectpicture\tikzexternal@forcegraphics@@
}
\long\def\tikzexternal@forcegraphics@@#1{\tikzexternal@forcegraphics@@@}%
\def\tikzexternal@forcegraphics@@@{%
    \if5\tikzexternal@opmode
        \let\tikz@refundefinedtrue@@=\G@refundefinedtrue
        \gdef\G@refundefinedtrue{%
            \tikz@refundefinedtrue@@
            \tikzexternal@forceremake@undefined@reference@handler
        }%
    \fi
    \expandafter\pgfincludeexternalgraphics\expandafter{\tikzexternal@curfilename}%
    \if5\tikzexternal@opmode
        \global\let\G@refundefinedtrue=\tikz@refundefinedtrue@@
    \fi
    \tikzexternal@closeenvironments
}

\def\tikzexternal@forceremake@undefined@reference@handler{%
    \pgf@typeout{===== 'mode=list and make': encountered undefined reference in current picture. Adding dependency to FORCEREMAKE. Rerun make to update the picture.' ========^^J}%
    \tikzpicturedependsonfile{FORCEREMAKE}%
}%

% Simply replaces the complete picture by some placeholder text.
% It is used by 'mode=list only' to reduce runtime.
\def\tikzexternal@listmodepicture{%
    \tikzexternal@TEXDIALECT@collectpicture\tikzexternal@listmodepicture@@
}
\long\def\tikzexternal@listmodepicture@@#1{\tikzexternal@listmodepicture@@@}
\def\tikzexternal@listmodepicture@@@{%
    \pgfkeysvalueof{/tikz/external/image discarded text}%
    \tikzexternal@closeenvironments
}

% check if there is already a file.
% In that case, use it. If not, skip it.
\def\tikzexternal@list@and@makefile@mode@picture{%
    \tikzexternal@TEXDIALECT@collectpicture\tikzexternal@list@and@makefile@mode@picture@
}%
\long\def\tikzexternal@list@and@makefile@mode@picture@#1{%
    %
    \tikzexternal@check@uptodate@mode{#1}%
    %
    \gdef\pgf@filename{}%
    \xdef\pgf@tempa{\noexpand\pgf@findfile\pgfsys@imagesuffixlist:+{\tikzexternal@curfilename}}%
    \pgf@tempa
    \ifx\pgf@filename\pgfutil@empty%
        % Note: since we have no 'GRAB' mode, we do not have to deal with optimization.
        % there is no graphics.
        \expandafter\tikzexternal@listmodepicture@@@
    \else
        \expandafter\tikzexternal@forcegraphics@@@
    \fi
}%

\def\tikzexternal@externalizefig@before@grab{%
    \pgfutil@IfUndefined{TP@holdbox}{%
    }{%
        % \usepackage[absolute]{textpos}
        % populates this box -- and would inject unwanted material into our images. Reset it:
        \global\setbox\TP@holdbox\vbox{}%
    }%
}%

\def\tikzexternal@externalizefig@GRAB{%
    \ifpgf@external@grabshipout
        \iftikzexternal@optimize
            \tikzexternal@optimize@RESTORE
        \fi
        \tikzexternal@externalizefig@before@grab
    \fi
    \def\tikzpicture{%
        \def\tikzpicture{% make sure that nested \tikzpicture are processed normally.
            \begingroup
            \def\endtikzpicture{%
                \tikzexternal@origendpicture
                \endgroup
            }%
            \tikzexternal@origpicture
        }%
        \pgf@external@grab{\tikzexternal@curfilename}%
        \tikzexternal@origpicture
    }%
    \def\endtikzpicture{%
        \tikzexternal@origendpicture
        \pgf@externalend
        %
        \tikzexternal@ensure@nonempty@floats
        %
        \let\tikzpicture=\tikzexternal@tikzpicture@replacement
        \let\endtikzpicture=\tikzexternal@origendpicture
        \iftikzexternal@optimize
            \ifpgf@external@grabshipout
                \tikzexternal@optimize@REPLACE
            \fi
        \fi
    }%
    \tikzpicture
}%

% If a sequence of floats containing JUST tikzpictures is
% externalized, this results in EMPTY floats. Empty floats, in turn,
% can confuse latex; it thinks it did something wrong.
%
% Solution: Avoid empty floats by writing junk into it.
%
% Note that this method is only invoked if \ifpgf@external@grabshipout
% is true and if the text is OUTSIDE of the original shipout routine.
% In other words: this text is being thrown away.
%
% see
% http://tex.stackexchange.com/questions/54625/why-is-fixltx2e-incompatible-with-tikzexternalize
\def\tikzexternal@ensure@nonempty@floats{%
    tikzexternal: picture has been externalized. This text is required to avoid empty floats.
}%

% 1. Discards the current picture in this document.
% 2. Checks whether an image exists already. If that is the case: acquire it.
% 3. If no image exists: call '/tikz/external/system call'. This will
%    process \tikzexternal@externalizefig.
% 4. Assert that finally an image exists and use it.
\def\tikzexternal@externalizefig@systemcall{%
    \tikzexternal@TEXDIALECT@collectpicture\tikzexternal@externalizefig@systemcall@@
}

{
\catcode`\"=12
\catcode`\'=12
\catcode`\;=12
\catcode`\&=12
\catcode`\-=12
\xdef\tikzexternal@normal@dq{"}
\xdef\tikzexternal@normal@sq{'}
\xdef\tikzexternal@normal@semic{;}
\xdef\tikzexternal@normal@and{&}
\xdef\tikzexternal@normal@dash{-}
\catcode`\"=13
\catcode`\'=13
\catcode`\;=13
\catcode`\&=13
\catcode`\-=13
\gdef\tikzexternal@activate@normal@dq{\let"=\tikzexternal@normal@dq}
\gdef\tikzexternal@activate@normal@sq{\let'=\tikzexternal@normal@sq}
\gdef\tikzexternal@activate@normal@semic{\let;=\tikzexternal@normal@semic}
\gdef\tikzexternal@activate@normal@and{\let&=\tikzexternal@normal@and}
\gdef\tikzexternal@activate@normal@dash{\let-=\tikzexternal@normal@dash}
\catcode`\|=0
\catcode`\\=12
|xdef|tikzexternal@normal@backslash{\}%
}
{
\catcode`\^^I=12
\catcode`\$=12
\catcode`\%=12
\catcode`\#=12
\gdef\tikzexternal@HASHchar{#}
\gdef\tikzexternal@TABchar{^^I}\gdef\tikzexternal@PERCENTchar{%}\xdef\tikzexternal@DOLLARchar{$}}

% Creates the '/tikz/external/system call' command as string and
% returns it into the (global!) macro #2.
% #1: the image file name (as returned by
% \tikzexternalgetnextfilename)
% #2: the global return value macro
%
\def\tikzexternal@assemble@systemcall#1#2{%
    \begingroup
        \def\image{#1}%
        \iftikzexternal@auto@detect@jobname
            \edef\texsource{\string\def\string\tikzexternalrealjob{\tikzexternal@realjob}\string\input{\tikzexternal@realjob}}%
        \else
            \let\texsource=\tikzexternal@realjob
        \fi
        \ifnum\the\catcode`\"=13 \tikzexternal@activate@normal@dq\fi
        \ifnum\the\catcode`\'=13 \tikzexternal@activate@normal@sq\fi
        \ifnum\the\catcode`\;=13 \tikzexternal@activate@normal@semic\fi
        \ifnum\the\catcode`\-=13 \tikzexternal@activate@normal@dash\fi
        \let\\=\tikzexternal@normal@backslash
        \xdef#2{\pgfkeysvalueof{/tikz/external/system call}}%
    \endgroup
}%
\long\def\tikzexternal@externalizefig@systemcall@@#1{%
    \tikzexternal@externalizefig@systemcall@uptodatecheck{#1}%
    \tikzexternal@assemble@systemcall{\tikzexternal@curfilename}{\pgf@tempa}%
    \global\let\tikzexternal@cursyscall=\pgf@tempa
    \gdef\tikzexternal@typeset@picture@on@failure{1}%
    \iftikzexternal@file@isuptodate
        \iftikzexternal@verboseio
            \pgf@typeout{===== Image '\tikzexternal@curfilename' is up-to-date. ======}%
        \fi
        \let\pgf@filename=\tikzexternal@curfilename
    \else
        \begingroup
        % no such image. Generate it!
        %
        \tikzexternalauxlock@setlock1%
        \tikzexternal@externalizefig@systemcall@call{\tikzexternal@cursyscall}%
        \tikzexternalauxlock@setlock0%
        \expandafter\tikzexternal@externalizefig@systemcall@assertsuccess\expandafter{\tikzexternal@cursyscall}%
        \pgfmath@smuggleone\pgf@filename
        \endgroup
    \fi
    \ifx\pgf@filename\pgfutil@empty
        \if1\tikzexternal@typeset@picture@on@failure
            % error recovery: something did not work! Try to load it
            % anyway. Perhaps it was just that shell-escape wasn't
            % enabled.
            \begingroup
            \toks0={%
                \tikzexternaldisable
            }%
            % FIXME : THIS WILL FAIL IF THERE IS '##' INSIDE OF '#1'!
            % for example something like /.style={#1} in the picture environment *will* fail.
            \toks1={%
                \tikzpicture
                #1%
            }%
            \toks2={%
                \tikzexternal@TEXDIALECT@endpicture
                \tikzexternalenable
            }%
            \xdef\tikzexternal@externalizefig@systemcall@next{%
                \the\toks0
                %  try reading them again as if they were in the input file.
                \noexpand\scantokens{\the\toks1 }%
                \the\toks2
            }%
            \endgroup
        \else
            % Ah -- this picture failed, but the failure has already
            % been handled somehow. Do not typeset it again!
            %
            % A use-case is that the picture has been rescheduled for
            % \end{document}.
            \gdef\tikzexternal@externalizefig@systemcall@next{\tikzexternal@closeenvironments}%
        \fi
    \else
        % ok, take the image!
        \gdef\tikzexternal@systemcall@reschedule@to@end@document{0}%
        \expandafter\pgfincludeexternalgraphics\expandafter{\tikzexternal@curfilename}%
        \if1\tikzexternal@systemcall@reschedule@to@end@document
            \pgfutil@IfUndefined{AtVeryEndDocument}{%
            }{%
                \pgf@typeout{===== The previous system call resulted in undefined references inside of the output file. Rescheduling it for \string\end{document}. ========}%
                \expandafter\tikzexternal@externalizefig@systemcall@reschedule\expandafter{\tikzexternal@cursyscall}%
            }%
        \fi
        \gdef\tikzexternal@externalizefig@systemcall@next{\tikzexternal@closeenvironments}%
    \fi
    \tikzexternal@externalizefig@systemcall@next
}%

\def\tikzexternal@externalizefig@systemcall@call#1{%
    \iftikzexternal@verboseio
        \pgf@typeout{===== 'mode=convert with system call': Invoking '#1' ========}%
    \fi
    \pgfutil@shellescape{#1}%
}%

% Sets \iftikzexternal@file@isuptodate to false if one of the "force
% remake" things is active.
\def\tikzexternal@checkforceremake{%
    \iftikzexternal@force@remake
        \global\tikzexternal@file@isuptodatefalse
    \else
        \iftikzexternalremakenext
            \global\tikzexternal@file@isuptodatefalse
            \global\tikzexternalremakenextfalse
        \fi
    \fi
}

\pgfutil@IfUndefined{pdfmdfivesum}{%
}{%
    % predefine to this value. This does only make sense for pdftex.
    % note that the latex library for 'external' loads \usepackage{pdftexcmds} which \let's this to \pdf@mdfivesum:
    \let\tikzexternal@mdfivesum=\pdfmdfivesum
}%

\long\def\tikzexternal@computemdfivesum#1{%
    \t@tikzexternal@tmpb={#1}%
    \edef\tikzexternal@temp{\the\t@tikzexternal@tmpb}%
    % \meaning results in a string of catcode 12 - which is expandable.
    \edef\pgfretval{\tikzexternal@mdfivesum{\meaning\tikzexternal@temp}}%
}
\long\def\tikzexternal@computemdfivesum@diff@fallback#1{%
    \t@tikzexternal@tmpb={#1}%
    \edef\tikzexternal@temp{\the\t@tikzexternal@tmpb}%
    % \meaning results in a string of catcode 12 - which is expandable.
    \edef\pgfretval{\meaning\tikzexternal@temp}%
}

% Will be set dynamically, depending on 'up to date check'.
%
% It expands to code such that \tikzexternallastkey contains the
% serialized version of '#1'.
%
% It is used as argument for \write{..}
%
% #1 the hash key to serialize.
% \def\tikzexternal@hashfct@serialize
\long\def\tikzexternal@hashfct@serialize@std#1{%
    \noexpand\def\noexpand\tikzexternallastkey{#1}%
}%

% serializes using temporary token registers. Necessary if #1 contains
% executable code.
\long\def\tikzexternal@hashfct@serialize@tok#1{%
    \noexpand\begingroup
        % in order to allow '#' inside of the body, we have to use token registers:
        \noexpand\toks0={#1}%
        \noexpand\xdef\noexpand\tikzexternallastkey{\noexpand\the\noexpand\toks0 }%
    \noexpand\endgroup
}%

\def\tikzexternal@check@uptodate@ext{.md5}

\def\tikzexternal@check@uptodate@mode@warn@fallback{%
    \message{Package tikz Warning: The key 'up to date check=md5' is impossible, there is no macro to compute MD5. Falling back to 'up to date check=diff'.}%
    %
    % warn only once:
    \global\let\tikzexternal@check@uptodate@mode@warn@fallback=\relax
}%

% assigns the boolean \iftikzexternal@file@isuptodate
\long\def\tikzexternal@check@uptodate@mode#1{%
    \if1\tikzexternal@uptodate@mode
        % up to date check=md5:
        % check if we CAN compute MD5 sums:
        \pgfutil@IfUndefined{tikzexternal@mdfivesum}{%
            % we cannot compute md5 sums - fallback to diff.
            \tikzexternal@check@uptodate@mode@warn@fallback
            \def\tikzexternal@uptodate@mode{2}%
        }{}%
    \fi
    %
    \ifcase\tikzexternal@uptodate@mode
        % up to date check=simple
        % nothing to do -- file existence is checked anyway.
        \let\tikzexternal@hashfct=\pgfutil@empty
        \let\tikzexternal@hashfct@serialize=\pgfutil@empty
    \or
        % up to date check=md5
        \let\tikzexternal@hashfct=\tikzexternal@computemdfivesum
        \let\tikzexternal@hashfct@serialize=\tikzexternal@hashfct@serialize@std
    \or
        \let\tikzexternal@hashfct=\tikzexternal@computemdfivesum@diff@fallback
        \let\tikzexternal@hashfct@serialize=\tikzexternal@hashfct@serialize@tok
    \fi
    \ifx\tikzexternal@hashfct\pgfutil@empty
    \else
        \tikzpicturedependsonfile{\tikzexternal@curfilename\tikzexternal@check@uptodate@ext}%
        \tikzexternal@hashfct{#1}%
        \let\tikzexternal@lastkey@new=\pgfretval
        \begingroup
        % no '@' token in this macro: avoid messing up the catcodes in input files:
        \global\let\tikzexternallastkey=\pgfutil@empty
        \openin\r@pgf@reada=\tikzexternal@curfilename\tikzexternal@check@uptodate@ext\relax %
        \ifeof\r@pgf@reada
        \else
            % read first line...
            \endlinechar=-1 % older versions did not have a '%' at the end-of-line. Avoid spurious spaces.
            \read\r@pgf@reada to\pgf@tempa
            % ... and execute it.
            \pgf@tempa
            % it should contain a definition of \tikzexternallastkey.
        \fi
        \closein\r@pgf@reada
        %
        \let\tikzexternal@lastkey=\tikzexternallastkey
        \pgfmath@smuggleone\tikzexternal@lastkey
        \endgroup
        % normalize catcodes. Unfortunately, they cannot be expected to be the same.
        % \meaning will use catcode 12 for each token:
        \edef\tikzexternal@lastkey@normalized{\meaning\tikzexternal@lastkey}%
        \edef\tikzexternal@lastkey@new@normalized{\meaning\tikzexternal@lastkey@new}%
        \iftikzexternal@verboseuptodate
            \pgf@typeout{Up-to-date check of \tikzexternal@curfilename: new \tikzexternal@lastkey@new@normalized; old \tikzexternal@lastkey@normalized.^^J}%
        \fi
        \ifx\tikzexternal@lastkey@normalized\tikzexternal@lastkey@new@normalized
            \tikzexternal@file@isuptodatetrue
        \else
            \tikzexternal@file@isuptodatefalse
            \immediate\openout\w@pgf@writea=\tikzexternal@curfilename\tikzexternal@check@uptodate@ext\relax%
            \immediate\write\w@pgf@writea{\tikzexternal@hashfct@serialize{\tikzexternal@lastkey@new}\tikzexternal@PERCENTchar}%
            \immediate\closeout\w@pgf@writea
        \fi
    \fi
}

% Checks whether the current picture needs to be externalized.
%
% This is the case if
% a) there is no external image yet,
% b) the picture has been invalidated manually.
%
% It returns \iftikzexternal@file@isuptodate accordingly.
% #1: the picture-content
\long\def\tikzexternal@externalizefig@systemcall@uptodatecheck#1{%
    \tikzexternal@check@uptodate@mode{#1}%
    \tikzexternal@checkforceremake
    \iftikzexternal@file@isuptodate
        % check if there is already a file.
        % In that case, use it. If that is not the case, generate it and include it afterwards.
        \gdef\pgf@filename{}%
        \xdef\pgf@tempa{\noexpand\pgf@findfile\pgfsys@imagesuffixlist:+{\tikzexternal@curfilename}}%
        \pgf@tempa
        \ifx\pgf@filename\pgfutil@empty%
            \global\tikzexternal@file@isuptodatefalse
        \fi
    \fi
}%

% \pgf@filename will be empty if the assertion failed.
\def\tikzexternal@externalizefig@systemcall@assertsuccess#1{%
    % check if there is a file now and raise an error message if not.
    \gdef\pgf@filename{}%
    \xdef\pgf@tempa{\noexpand\pgf@findfile\pgfsys@imagesuffixlist:+{\tikzexternal@curfilename}}%
    \pgf@tempa
    \ifx\pgf@filename\pgfutil@empty%
        \tikzexternal@externalizefig@systemcall@handleexception{#1}%
    \fi
}%
\def\tikzexternal@externalizefig@systemcall@handleexception@msg#1{%
    \tikzerror{Sorry, the system call '#1' did NOT result in a usable output file '\tikzexternal@curfilename' (expected one of \pgfsys@imagesuffixlist). Please verify that you have enabled system calls. For pdflatex, this is 'pdflatex -shell-escape'. Sometimes it is also named 'write 18' or something like that. Or maybe the command simply failed? Error messages can be found in '\tikzexternal@curfilename.log'. If you continue now, I'll try to typeset the picture}{}%
}
\def\tikzexternal@externalizefig@systemcall@handleexception@retry@later#1{%
    \gdef\tikzexternal@systemcall@reschedule@to@end@document{0}%
    \expandafter\pgfexternalreaddpth\expandafter{\tikzexternal@curfilename}%
    \if1\tikzexternal@systemcall@reschedule@to@end@document
        \pgfutil@IfUndefined{AtVeryEndDocument}{%
            \tikzexternal@externalizefig@systemcall@handleexception@msg{#1}%
        }{%
            \pgf@typeout{===== The last system call resulted in an EMPTY output file. Maybe it is part of \string\ref. Rescheduling it for \string\end{document}. ========}%
            \gdef\tikzexternal@typeset@picture@on@failure{0}%
            \tikzexternal@externalizefig@systemcall@reschedule{#1}%
        }%
    \else
        \tikzexternal@externalizefig@systemcall@handleexception@msg{#1}%
    \fi
}

% reschedules the externalization of the current file to
% \AtVeryEndDocument.
%
% This hook allows to execute code AFTER the main .aux file is
% finished; it will even re-read the main aux file.
\def\tikzexternal@externalizefig@systemcall@reschedule#1{%
    \t@tikzexternal@tmpb={%
        \global\let\tikzexternal@externalizefig@systemcall@handleexception=\tikzexternal@externalizefig@systemcall@handleexception@msg%
        % ... no auxlocks!
        \tikzexternal@externalizefig@systemcall@call{#1}%
        \tikzexternal@externalizefig@systemcall@assertsuccess{#1}%
    }%
    \xdef\pgfutil@tempa{%
        \noexpand\def\noexpand\tikzexternal@curfilename{\tikzexternal@curfilename}%
        \the\t@tikzexternal@tmpb
    }%
    \expandafter\AtVeryEndDocument\expandafter{\pgfutil@tempa}%
    \gdef\tikzexternal@has@rescheduled@something{1}%
}%
\let\tikzexternal@externalizefig@systemcall@handleexception=\tikzexternal@externalizefig@systemcall@handleexception@retry@later%

\def\tikzexternal@has@rescheduled@something{0}%
\pgfutil@IfUndefined{AtVeryEndDocument}{}{%
    \AtVeryEndDocument{%
        \if1\tikzexternal@has@rescheduled@something
            \pgf@typeout{===== tikzexternal: \string\end{document} reached. Working on rescheduled images to resolve references... ========}%
        \fi
    }%
}

% Overwrite error message of pgf.
% This happens if the generated image was empty, i.e. if there was no \shipout.
\def\pgfexternal@error@no@shipout{%
    \begingroup
        \begingroup
        % overwrite .dpth file in order to flag the file as "need to be scheduled
        % for \AtVeryEndDocument" :
        \immediate\openout\pgf@plotwrite=\pgfactualjobname.dpth
        \let\w@pgfexternal@auxout=\pgf@plotwrite
        \pgfexternalstorecommand@isexporting{\gdef\noexpand\tikzexternal@systemcall@reschedule@to@end@document{1}}%
        \immediate\closeout\pgf@plotwrite
        \endgroup
    \tikzexternal@assemble@systemcall{\pgfactualjobname}{\pgf@tempa}%
    \toks0=\expandafter{\pgf@tempa}%
    \tikzerror{Sorry, image externalization failed: the resulting image was EMPTY. I tried to externalize '\pgfactualjobname', but it seems there is no such image in the document!?
 \if\tikzexternal@opmode4 ^^J
\space\space You are currently using 'mode=convert with system call'. This problem can happen if the image (or one of the images preceding it) was declared inside of a \string\label{} (i.e. in the .aux file): 'convert with system call' has no access to the main aux file.^^J
\space\space Possible solutions in this case:^^J
\space\space (a) Try using 'mode=list and make',^^J
\space\space (b) Issue the externalization command '\the\toks0' *manually* (also check the preceding externalized images, perhaps the file name sequence is not correct).^^J
\space\space Repeat: the resulting image was EMPTY, your attention is required
\else
    \if\tikzexternal@opmode5 ^^J
\space\space You are currently using 'mode=list and make'. Possible solutions:^^J
\space\space (a) Try to delete `\tikzexternal@realjob.makefile'. Perhaps it is not up-to-date.^^J
\space\space (b) Perhaps pictures are declared inside of \string\label{} and the .aux file is not up-to-date. Re-run latex, perhaps re-generate the graphics as well.^^J
\space\space Repeat: the resulting image was EMPTY, your attention is required
    \fi
\fi}%
    \endgroup
}%