

\section{The Axis-Environments}
There is an axis environment for linear scaling, two for semi-logarithmic scaling and one for double-logarithmic scaling.
\begin{environment}{{tikzpicture}\oarg{options of tikz}}
	This is the graphics environment of \Tikz. It produces a single picture and encloses also every axis.

	Instead of using the environment version, there is also a shortcut command 

	\declareandlabel{\tikz}\marg{picture content}

	which can be used alternatively.
\end{environment}

\begin{environment}{{axis}\oarg{options}}
	The axis environment for normal plots with linear axis scaling.

	The `|every linear axis|' style key can be modified with
\begin{codeexample}[code only]
\pgfplotsset{every linear axis/.append style={...}}
\end{codeexample}
to install styles specifically for linear axes. These styles can contain both \Tikz- and \PGFPlots\ options.
\end{environment}

\begin{environment}{{semilogxaxis}\oarg{options}}
The axis environment for logarithmic scaling of~$x$ and normal scaling of~$y$.
Use
\begin{codeexample}[code only]
\pgfplotsset{every semilogx axis/.append style={...}}
\end{codeexample}
to install styles specifically for the case with |xmode=log|, |ymode=normal|.

The logarithmic scaling means to apply the natural logarithm (base $e$) to each $x$ coordinate. Furthermore, ticks will be typeset as $10^{\text{\meta{exponent}}}$, see Section~\ref{sec:number:printing} for more details.
\end{environment}

\begin{environment}{{semilogyaxis}\oarg{options}}
The axis environment for normal scaling of~$x$ and logarithmic scaling of~$y$,

The style `|every semilogy axis|' will be installed for each such plot.

The same remarks as for |semilogxaxis| apply here as well.
\end{environment}

\begin{environment}{{loglogaxis}\oarg{options}}
The axis environment for logarithmic scaling of both, $x$~and~$y$ axes.
As for the other axis possibilities, there is a style `|every loglog axis|' which is installed at the environment's beginning.

The same remarks as for |semilogxaxis| apply here as well.
\end{environment}

\noindent
They are all equivalent to
\begin{codeexample}[code only]
\begin{axis}[
	xmode=log|normal,
	ymode=log|normal]
...
\end{axis}
\end{codeexample}
\noindent
with properly set variables `|xmode|' and `|ymode|' (see below).

\section{The \protect\texttt{\protect\textbackslash addplot} Command: Coordinate Input}
{
\tikzset{external/figure name/.add={}{addplot_}}%
\label{sec:addplot}%
\begin{codeexample}[]
\begin{tikzpicture}
\begin{axis}[ymin=0,ymax=1,enlargelimits=false]
\addplot
	[blue!80!black,fill=blue,fill opacity=0.5] 
coordinates
{(0,0.1)    (0.1,0.15)  (0.2,0.5)   (0.3,0.62)
 (0.4,0.56) (0.5,0.58)  (0.6,0.65)  (0.7,0.6)
 (0.8,0.58) (0.9,0.55)  (1,0.52)} 
|- (0,0) -- cycle;

\addplot
	[red,fill=red!90!black,opacity=0.5]
coordinates 
{(0,0.25)   (0.1,0.27)  (0.2,0.24)  (0.3,0.24)
 (0.4,0.26) (0.5,0.3)   (0.6,0.23)  (0.7,0.2)
 (0.8,0.15) (0.9,0.1)   (1,0.1)}
|- (0,0) -- cycle;

\addplot[green!20!black] coordinates
	{(0,0.4) (0.2,0.75) (1,0.75)};
\end{axis}
\end{tikzpicture}
\end{codeexample}

\begin{codeexample}[]
\begin{tikzpicture}
\begin{axis}
\addplot+[id=parable,domain=-5:5] 
	gnuplot{4*x**2 - 5} 
	node[pin=180:{$4x^2-5$}]{};
\end{axis}
\end{tikzpicture}
\end{codeexample}

\pgfplotsexpensiveexample
\begin{codeexample}[]
\begin{tikzpicture}
	\begin{axis}
	\addplot3[surf,domain=0:360,samples=40] 
		{sin(x)*sin(y)};	
	\end{axis}
\end{tikzpicture}
\end{codeexample}

\pgfplotsexpensiveexample
\begin{codeexample}[]
\begin{tikzpicture}
	\begin{axis}[colormap/redyellow,colorbar]
	\addplot3[surf,
		domain=0:360,samples=40] 
		{sin(x)*sin(y)};	
	\end{axis}
\end{tikzpicture}
\end{codeexample}

\pgfplotsexpensiveexample
\begin{codeexample}[]
\begin{tikzpicture}
\begin{axis}[view={60}{30}]
    \addplot3[surf,shader=flat,
		samples=20,
        domain=-1:0,y domain=0:2*pi,
        z buffer=sort]
        ({sqrt(1-x^2) * cos(deg(y))},
		 {sqrt( 1-x^2 ) * sin(deg(y))},
		 x);
\end{axis}
\end{tikzpicture}
\end{codeexample}

Inside of an axis environment, the |\addplot| command is the main user interface. It comes in two variants: |\addplot| for two--dimensional visualization and \verbpdfref{\addplot3} for three--dimensional visualization.

\begin{command}{\addplot\oarg{options} \meta{input data} \meta{trailing path commands};}
\label{cmd:pgfplots:addplot}
This is the main plotting command, available within each axis environment. It can be used one or more times within an axis to add plots to the current axis. There is also an \verbpdfref{\addplot3} command which is described in Section~\ref{sec:3d}.

It reads point coordinates from one of the available input sources specified by \meta{input data}, updates limits, remembers \meta{options} for use in a legend (if any) and applies any necessary coordinate transformations (or logarithms).

The \meta{options} can be omitted in which case the next entry from the |cycle list| will be inserted as \meta{options}. These keys characterize the plot's type like linear interpolation with |sharp plot|, |smooth| plot, constant interpolation with |const plot|, |bar| plot, |mesh| plots, |surf|ace plots or whatever and define |color|s, |mark|ers and line specifications\footnote{In version 1.2.2 and earlier, there was an explicit distinction between ``behaviour'' options like error bars, domain, number of samples etc.\ and ``style options'' like color, line width, markers etc. This distinction is obsolete now, simply collect everything into \meta{options}.}\index{Behavior Options}\index{Options!Distinction Behavior, Style Options}. Plot variants like error bars, the number of |samples| or a sample |domain| can also be configured in \meta{options}.

The \meta{input data} is one of several coordinate input tools which are described in more detail below. Finally, if |\addplot| successfully processed all coordinates from \meta{input data}, it generates \Tikz\ paths to realize the drawing operations. Any \meta{trailing path commands} are appended to the final drawing command, allowing to continue the \Tikz\ path (from the last plot coordinate).

\noindent
Some more details:
\begin{itemize}
	\item The style |/pgfplots/every axis plot| will be installed at the beginning of \meta{options}. That means you can use
\begin{codeexample}[code only]
\pgfplotsset{every axis plot/.append style={...}}
\end{codeexample}
	to add options to all your plots - maybe to set line widths to |thick|. Furthermore, if you have more than one plot inside of an axis, you can also use
\begin{codeexample}[code only]
\pgfplotsset{every axis plot no 3/.append style={...}}
\end{codeexample}
	to modify options for the plot with number~$3$ only. The first plot in an axis has number~$0$.
	\item The \meta{options} are remembered for the legend. They are available as `\declareandlabel{current plot style}' as long as the path is not yet finished or in associated error bars.
	\item See Subsection~\ref{sec:markers} for a list of available markers and line styles.
	\item For log plots, \PGFPlots\ will compute the natural logarithm $\log(\cdot)$ numerically using a floating point unit developed for this purpose\footnote{This floating point unit is available as \Tikz\ library as part of \Tikz.}. For example, the following numbers are valid input to |\addplot|.
\begin{codeexample}[]
\begin{tikzpicture}
\begin{loglogaxis}
\addplot coordinates {
	(769,   1.6227e-04)
	(1793,  4.4425e-05)
	(4097,  1.2071e-05)
	(9217,  3.2610e-06)
	(2.2e5, 2.1E-6)
	(1e6,   0.00003341)
	(2.3e7, 0.00131415)
};
\end{loglogaxis}
\end{tikzpicture}
\end{codeexample}
	You can represent arbitrarily small or very large numbers as long as its logarithm can be represented as a \TeX-length (up to about~$16384$). Of course, any coordinate~$x\le 0$ is not possible since the logarithm of a non-positive number is not defined. Such coordinates will be skipped automatically (using the initial configuration |unbounded coords=discard|).

	\item For normal (non--logarithmic) axes, \PGFPlots\ applies floating point arithmetics to support large or small numbers like 0.00000001234 or $1.234\cdot 10^{24}$. Its number range is much larger than \TeX's native support for numbers. The relative precision is between $4$ and $7$ significant decimal digits for the mantissa.
	
	As soon as the axes limits are completely known, \PGFPlots\ applies a transformation which maps these floating point numbers into \TeX-precision using transformations
		\[ T_x(x) = 10^{s_x} \cdot x - a_x
		\text{ and } T_y(y) = 10^{s_y} \cdot y - a_y 
		\text{ and (for 3D plots) } T_z(y) = 10^{s_z} \cdot z - a_z 
		\]
	with properly chosen integers $s_x, s_y, s_z \in \Z$ and shifts $a_x,a_y, a_z\in \R$. Section~\ref{sec:disabledatascaling} contains a description of |disabledatascaling| and provides more details about the transformation.
	\index{Accuracy!Floating Point in \PGFPlots}%

	\item Some of the coordinate input routines use the powerful |\pgfmathparse| feature of \pgfname\ to read their coordinates, among them |plot coordinates|, |plot expression| and |plot table|. This allows to use mathematical expressions as coordinates which will be evaluated using the floating point routines (this applies to logarithmic and linear scales).
	
	\item \PGFPlots\ automatically computes missing axis limits.
	The automatic computation of axis limits works as follows:
		\begin{enumerate}
			\item Every coordinate will be checked. Care has been taken to avoid \TeX's limited numerical capabilities.
			\item Since more than one |\addplot| command may be used inside of |\begin{axis}...\end{axis}|, all drawing commands will be postponed until |\end{axis}|.
		\end{enumerate}
\end{itemize}
\end{command}

\begin{addplot+}
Does the same like |\addplot[|\meta{options}|] ...;| except that \meta{options} are \emph{appended} to the arguments which would have been taken for |\addplot ...| (the element of the default list).

Thus, you can combine |cycle list| and \meta{options}.

\begin{codeexample}[]
\begin{tikzpicture}
\begin{axis}
\addplot {sin(deg(x))};
\end{axis}
\end{tikzpicture}

\begin{tikzpicture}
\begin{axis}
\addplot+[only marks] {sin(deg(x))};
\end{axis}
\end{tikzpicture}
\end{codeexample}

The distinction is as follows: |\addplot  ...| (without options) lets \PGFPlots\ select colors, markers and linestyles automatically (using |cycle list|). The variant |\addplot+|\oarg{option}| ...| will use the same automatically determined styles, but in addition it uses \meta{options}. Finally, |\addplot|\oarg{options} (without the |+|) uses only the manually provided \meta{options}.
\end{addplot+}

\begin{pgfplotskey}{empty line=\mchoice{auto,none,scanline,jump} (initially auto)}
	Controls how empty lines in the input coordinate stream are to be interpreted. You should ensure that you have |\pgfplotsset{compat=1.4}| or newer in your preamble and leave this key at its default |empty line=auto|.

	Empty lines can occur between the coordinates of |\addplot coordinates| or successive rows of the data file input routines |\addplot table| (and |\addplot file|).

	The choice \declaretext{auto} checks if the current plot type is |mesh| or |surf|. If so, it uses |scanline|. If the current plot type is some other plot type (like a standard line plot), it uses |jump|. Note that the value \texttt{auto} for non-mesh plots results in \texttt{none} if |compat=1.3| or older is used. In other words: you have to write |\pgfplotsset{compat=1.4}| or newer to let \PGFPlots\ interpret empty lines as |jump| in standard line plots:
\begin{codeexample}[]
\begin{tikzpicture}
	\begin{axis}[tiny,
		title={Ignored: compat=1.3},
		compat=1.3]
	\addplot table {
	A B
	0 0
	1 1

	1 2
	2 2
	};
	\end{axis}
\end{tikzpicture}
\begin{tikzpicture}
	\begin{axis}[tiny,
		title={Jump: compat=1.4},
		compat=1.4]
	\addplot table {
	A B
	0 0
	1 1

	1 2
	2 2
	};
	\end{axis}
\end{tikzpicture}
\end{codeexample}

	The choice \declaretext{scanline} is only useful for |mesh| and |surf|: it is used to decode a matrix from a coordinate stream. If an empty line occurs once every $N$ data points, the ``scanline'' length is~$N$. This information, together with |mesh/ordering| and the total number of points, allows to deduce the matrix size. However, the distance between empty lines has to be consistent: if the first two empty lines have a distance of~$2$ and the next comes after~$5$, \PGFPlots\ will ignore the information and will expect explicit matrix sizes using |mesh/rows| and/or |mesh/cols|. The choice |scanline| is ignored if |mesh input=patches|. It has no effect for other plot types.

	The choice \declaretext{none} will silently discard any empty line in the input stream.

	The choice \declaretext{jump} tells \PGFPlots\ to generate a jump.
\end{pgfplotskey}

\subsection{Coordinate Lists}
\label{pgfplots:providing:input}

\begin{addplotoperation}[]{coordinates}{\marg{coordinate list}}
\label{pgfplots:addplot:coordinates}
The `|\addplot coordinates|' command is like that provided by \Tikz\ and reads its input data from a sequence of point coordinates, encapsulated in round braces.
\begin{codeexample}[]
\begin{tikzpicture}
\begin{axis}
\addplot coordinates {
	(0,0)
	(0.5,1)
	(1,2)
};
\end{axis}
\end{tikzpicture}
\end{codeexample}

	You should \empty{only} use this input format if you have short diagrams and you want to provide mathematical expressions for each of the involved coordinates. Any data plots are typically easier to handle using a table format and |\addplot table|.

The coordinates can be numbers, but they can also contain mathematical expressions like |sin(0.5)| or |\h*8| (assuming you defined |\h| somewhere). However, expressions which involve round braces need to be encapsulated in a further set of curly braces, for example |({sin(0.5)},{cos(0.1)})|.

You can also supply error coordinates (reliability bounds) if you are interested in error bars. Simply append the error coordinates with `\declareandlabel{+-} \parg{ex,ey}' (or |+- |\parg{ex,ey,ez}) to the associated coordinate:
\begin{codeexample}[]
\begin{tikzpicture}
\begin{axis}
\addplot+[error bars/.cd,x dir=both,x explicit] 
coordinates {
	(0,0)   +- (0.1,0)
	(0.5,1) +- (0.4,0.2)
	(1,2)
	(2,5)   +- (1,0.1)
};
\end{axis}
\end{tikzpicture}
\end{codeexample}
or 
\begin{codeexample}[code only]
\addplot coordinates {
	 (900,1e-6) +- (0.1,0.2)
	(2600,5e-7) +- (0.2,0.5)
	(4000,7e-8) +- (0.1,0.01)
};
\end{codeexample}
These error coordinates are only used in case of error bars, see Section~\ref{sec:errorbars}. You will also need to configure whether these values denote absolute or relative errors.

The coordinates as such can be numbers as |+5|, |-1.2345e3|, |35.0e2|, |0.00000123| or |1e2345e-8|. They are not limited to \TeX's precision.

Furthermore, |coordinates| allows to define ``meta data'' for each coordinate. The interpretation of meta data depends on the visualization technique: for scatter plots, meta data can be used to define colors or style associations for every point (see page~\pageref{pgfplots:scatterclasses} for an example). Meta data (if any) must be provided after the coordinates and after error bar bounds (if any) in square brackets:
\begin{codeexample}[]
\begin{tikzpicture}
\begin{axis}
\addplot+[scatter,scatter src=explicit] coordinates {
	 (900,1e-6) [1]
    (2600,5e-7) [2]
    (4000,7e-8) [3]
};
\end{axis}
\end{tikzpicture}
\end{codeexample}
Please refer to the documentation of |point meta| on page~\pageref{pgfplots:point:meta} for more information about per point meta data.

	The coordinate stream can contain |empty line|s to tell \PGFPlots\ that the function has jumps. To use it, simply insert an empty line (and ensure that you have |\pgfplotsset{compat=1.4}| or newer in your preamble). See the documentation of |empty line| for details.
\end{addplotoperation}

\begin{pgfplotskey}{plot coordinates/math parser=\mchoice{true,false} (initially true)}
	Allows to turn off support for mathematical expressions in every coordinate inside of |plot coordinates|. This might be necessary if coordinates are not in numerical form (or if you'd like to improve speed).

	It is necessary to disable |plot coordinates/math parser| if you use some sort of symbolic transformations (i.e. text coordinates).
\end{pgfplotskey}


\subsection{Reading Coordinates From Tables}

\begin{addplotoperation}[]{table}{\oarg{column selection}\marg{file or inline table}}
\label{pgfplots:addplot:table}
This input method is the main input format for any data--based function. It accepts either a file containing data or an inline table provided in curly braces.

Given a data file like
\begin{codeexample}[code only]
dof     L2              Lmax            maxlevel
5       8.31160034e-02  1.80007647e-01  2
17      2.54685628e-02  3.75580565e-02  3
49      7.40715288e-03  1.49212716e-02  4
129     2.10192154e-03  4.23330523e-03  5
321     5.87352989e-04  1.30668515e-03  6
769     1.62269942e-04  3.88658098e-04  7
1793    4.44248889e-05  1.12651668e-04  8
4097    1.20714122e-05  3.20339285e-05  9
9217    3.26101452e-06  8.97617707e-06  10
\end{codeexample}
one may want to plot `|dof|' versus `|L2|' or `|dof|' versus `|Lmax|'. This can be done by
\begin{codeexample}[code only]
\begin{tikzpicture}
\begin{loglogaxis}[
	xlabel=Dof,
	ylabel=$L_2$ error]
\addplot table[x=dof,y=L2] {datafile.dat};
\end{loglogaxis}
\end{tikzpicture}
\end{codeexample}
or, for the |Lmax| column, using
\begin{codeexample}[code only]
\begin{tikzpicture}
\begin{loglogaxis}[
	xlabel=Dof,
	ylabel=$L_\infty$ error]
\addplot table[x=dof,y=Lmax] {datafile.dat};
\end{loglogaxis}
\end{tikzpicture}
\end{codeexample}
It is also possible to provide the data inline, i.e.\ directly as argument in curly braces:
\begin{codeexample}[code only]
\begin{tikzpicture}
\begin{loglogaxis}[
	xlabel=Dof,
	ylabel=$L_\infty$ error]
\addplot table[x=dof,y=Lmax] {
	dof     L2              Lmax            maxlevel
	5       8.31160034e-02  1.80007647e-01  2
	17      2.54685628e-02  3.75580565e-02  3
	49      7.40715288e-03  1.49212716e-02  4
	129     2.10192154e-03  4.23330523e-03  5
	321     5.87352989e-04  1.30668515e-03  6
	769     1.62269942e-04  3.88658098e-04  7
	1793    4.44248889e-05  1.12651668e-04  8
	4097    1.20714122e-05  3.20339285e-05  9
	9217    3.26101452e-06  8.97617707e-06  10
};
\end{loglogaxis}
\end{tikzpicture}
\end{codeexample}
\noindent Inline table may be convenient together with `|\\|' and |row sep=\\|, see below for more information.

Alternatively, you can load the table \emph{once} into an internal structure and use it \emph{multiple} times\footnote{In earlier versions, there was an addition keyword `from' before the argument like \texttt{\textbackslash addplot table from \{\textbackslash loadedtable\}}. This keyword is still accepted, but no longer required.}:
\begin{codeexample}[code only]
\pgfplotstableread{datafile.dat}\loadedtable % use any custom name in place of `\loadedtable'
...
\addplot table[x=dof,y=L2] {\loadedtable};
...
\addplot table[x=dof,y=Lmax] {\loadedtable};
...
\end{codeexample}
I am not really sure how much time can be saved, but it works anyway. The |\pgfplotstableread| command is documented in all detail in the manual for \PGFPlotstable. As a rule of thumb, decide as follows:
\begin{enumerate}
	\item If tables contain few rows and many columns, the \meta{\textbackslash macro} framework will be more efficient.
	\item If tables contain more than~$200$ data points (rows), you should always use file input (and reload if necessary).
\end{enumerate}
Occasionally, it might be handy to load a table, apply manual preparation steps (for example |\pgfplotstabletranspose|) and plot the result tables afterwards.

If you do prefer to access columns by column indices instead of column names (or your tables do not have column names), you can also use
\begin{codeexample}[code only]
\addplot table[x index=2,y index=3] {datafile.dat};
\addplot table[x=dof,y index=2] {datafile.dat};
\end{codeexample}

Summary and remarks:
\begin{itemize}
	\item Use |\addplot table[||x||=|\marg{column name}|,||y||=|\marg{column name}|]| to access column names. Those names are case sensitive and need to exist.
	\item Use |\addplot table[||x index||=|\marg{column index}|,||y index||=|\marg{column index}|]| to access column indices. Indexing starts with~$0$. You may also use an index for~$x$ and a column name for~$y$.
	\item Use |\addplot table[||x expr=\coordindex,y=|\marg{column name}|]| to plot the coordinate index versus some $y$ data.
	\item Use |\addplot table[||header||=false] |\marg{file name} if your input file has no column names. Otherwise, the first non-comment line is checked for column names: if all entries are numbers, they are treated as numerical data; if one of them is not a number, all are treated as column names.
	\item It is possible to read error coordinates from tables as well. Simply add options `|x error|', `|y error|' or `|x error index|'/`|y error index|' to \meta{source columns}. See Section~\ref{sec:errorbars} for details about error bars.
	\item It is possible to read per point meta data (usable in |scatter src|, see page~\pageref{pgfplots:scatter:src}) as has been discussed for |plot coordinates| and |plot file| above. The meta data column can be provided using the |meta| key (or the |meta index| key).
	\item Use |\addplot table[|\meta{source columns}|] |\marg{\textbackslash macro} to use a pre--read table. Tables can be read using
\begin{codeexample}[code only]
\pgfplotstableread{datafile.dat}\macroname.
\end{codeexample}
		If you like, you can insert the optional keyword `|from|' before |\macroname|.

	\item The accepted input format of tables is as follows:
		\begin{itemize}
			\item Rows are separated by new line characters.

			Alternatively, you can use |row sep=\\| which enables `|\\|' as row separator. This might become necessary for inline table data, more precisely: if newline characters have been converted to white spaces by \TeX's character processing before \PGFPlots\ had a chance to see them. This happens if inline tables are provided inside of macros. Use |row sep=\\| and separate the rows by `|\\|' if you experience such problems.

			\item Columns are usually separated by white spaces (at least one tab or space).

			 If you need other column separation characters, you can use the 

			\declare{col sep}\pgfmanualpdflabel{/pgfplots/table/col sep}{}|=|\mchoice{space,tab,comma,colon,semicolon,braces,\&,ampersand} 

			option documented in all detail in the manual for \PGFPlotstable\ which is part of \PGFPlots.
			\item Any line starting with `\#' or `\%' is ignored.
			\item The first line will be checked if it contains numerical data. If there is a column in the first line which is \emph{no} number, the complete line is considered to be a header which contains column names. Otherwise it belongs to the numerical data and you need to access column indices instead of names.

			\item There is future support for a second header line which must start with `|$flags |'. Currently, such a line is ignored. It may be used to provide number formatting hints like precision and number format if those tables shall be typeset using |\pgfplotstabletypeset| (see the manual for \PGFPlotstable).
			\item The accepted number format is the same as for `|plot coordinates|', see above.
			\item If you omit column selectors, the default is to plot the first column against the second. That means |plot table| does exactly the same job as |plot file| for this case.
			\item If you need unbalanced columns, simply use |nan| as ``empty cell'' placeholder. These coordinates will be skipped in plots.
			\index{Unbalanced Columns}%
			\index{table@\textcolor {gray}{\texttt {plot}}\texttt { table}!Unbalanced Columns}%
		\end{itemize}
	\item It is also possible to use \textbf{mathematical expressions} together with `|plot table|'. This is documented in all detail in Section~\ref{pgfplots:addplot:table:expr}, but the key idea is to use one of |x expr|, |y expr|, |z expr| or |meta expr| as in `|plot table[||x expr=\thisrow{maxlevel}+3,y=L2]|'.
	\item The \PGFPlotstable\ package coming with \PGFPlots\ has a the feature ``Postprocessing Data in New Columns'' (see its manual).

	This allows to compute new columns based on existing data. One of these features is |create col/linear regression| (described in Section~\ref{sec:linefitting}).

	You can invoke all the |create col/|\meta{key name} features directly in |\addplot table| using

	|\addplot table[x={create col/|\meta{key name}|=|\meta{arguments}|}]|.

	In this case, a new column will be created using the functionality of \meta{key name}. This column generation is described in all detail in \PGFPlotstable. Finally, the resulting data is available as $x$ coordinate (the same holds for |y=| or |z=|).

	One application (with several examples how to use this syntax) is line fitting with |create col/linear regression|, see Section~\ref{sec:linefitting} for details.

	\item
	The table can contain |empty line|s to tell \PGFPlots\ that the function has jumps. To use it, simply insert an empty line (and ensure that you have |\pgfplotsset{compat=1.4}| or newer in your preamble). See the documentation of |empty line| for details.
	\item Technical note: every opened file will be protocolled into your log file.

\end{itemize}

\end{addplotoperation}

\subsection*{Keys To Configure Table Input}
The following list of keys allow different methods to select input data or different input formats. Note that the common prefix `|table/|' can be omitted if these keys are set after |\addplot table|\oarg{options}. The |/pgfplots/| prefix can always be omitted when used in a \PGFPlots\ method.

\begin{pgfplotskey}{table/header=\mchoice{true,false} (initially true)}
	Allows to disable header identification for |plot table|. See above.
\end{pgfplotskey}
\begin{pgfplotsxykeylist}{table/\x=\marg{column name},
	table/\x\ index=\marg{column index}}
	These keys define the sources for |plot table|. If both column names and column indices are given, column names are preferred. Column indexing starts with~$0$. The initial setting is to use |x index=0| and |y index=1|. 

	Please note that column \emph{aliases} will be considered if unknown column names are used. Please refer to the manual of \PGFPlotstable\ which comes with this package.
\end{pgfplotsxykeylist}

\begin{pgfplotsxykeylist}{table/\x\ expr=\marg{expression}}
	These keys allow to combine the mathematical expression parser with file input. They are listed here to complete the list of table keys, but they are described in all detail in Section~\ref{pgfplots:addplot:table:expr}.

	The key idea is to provide an \meta{expression} which depends on table data (possibly on all columns in one row). Only data within the same row can be used where columns are referenced with |\thisrow|\marg{column name} or |\thisrowno|\marg{column index}. 
	
	Please refer to Section~\ref{pgfplots:addplot:table:expr} for details.
\end{pgfplotsxykeylist}


\begin{pgfplotsxykeylist}{%
	table/\x\ error=\marg{column name},
	table/\x\ error index=\marg{column index},
	table/\x\ error expr=\marg{math expression}}
	These keys define input sources for error bars with explicit error values. 
	
	The |x error| method provides an input column name (or alias), the |x error index| method provides input column \emph{indices} and |x error expr| works just as |table/x expr|: it allows arbitrary mathematical expressions which may depend on any number of table columns using |\thisrow|\marg{col name}.

	Please see Section~\ref{sec:errorbars} for details about the usage of error bars.
\end{pgfplotsxykeylist}

\begin{pgfplotsxykeylist}{%
	table/\x\ error plus=\marg{column name},
	table/\x\ error plus index=\marg{column index},
	table/\x\ error plus expr=\marg{math expression},
	table/\x\ error minus=\marg{column name},
	table/\x\ error minus index=\marg{column index},
	table/\x\ error minus expr=\marg{math expression}%
}
	These keys define input sources for error bars with \emph{asymmetric} error values, i.e.\ different values for upper and lower bounds. 
	
	They are to be used in the same way as |x error|. In fact, |x error| is just a style which sets both |x error plus| and |x error minus| to the same value.

	Please see Section~\ref{sec:errorbars} for details about the usage of error bars.
\end{pgfplotsxykeylist}

\begin{pgfplotsxykeylist}{%
	table/meta=\marg{column name},
	table/meta index=\marg{column index},
	table/meta expr=\marg{expression}}
	These keys define input sources for per point meta data. Please see page~\pageref{pgfplots:scatter:src} for details about meta data or the documentation for |plot coordinates| and |plot file| for further information.

	These keys are \emph{only} useful in conjunction with |point meta=explicit| or |point meta=explicit symbolic|. Note that 
\begin{codeexample}[code only]
\addplot[point meta=explicit] table[meta=colname] .... ;
\end{codeexample}
	is \emph{equivalent} to
\begin{codeexample}[code only]
\addplot[point meta=\thisrow{colname}] table[] .... ;
\end{codeexample}
	If the value of |point meta| is neither |explicit| nor |explicit symbolic|, the choice |table/meta| (and its friends) are ignored. 

	However, if |point meta| is one of |explicit| or |explicit symbolic|, the choice |table/meta| (or one of its friends) is mandatory. 

\end{pgfplotsxykeylist}


\begin{pgfplotskey}{table/row sep=\mchoice{newline,\string\\} (initially newline)}
	Configures the character to separate rows.

	The choice \declaretext{newline} uses the end of line as it appears in the table data (i.e.\ the input file or any inline table data).

	The choice \declaretext{\string\\} uses `|\\|' to indicate the end of a row.

	Note that \declaretext{newline} for inline table data is ``fragile'': you can't provide such data inside of \TeX\ macros (this does not apply to input files). Whenever you experience problems, proceed as follows:
	\begin{enumerate}
		\item First possibility: call |\pgfplotstableread|\marg{data}|\yourmacro| \emph{outside} of any macro declaration.
		\item Use |row sep=\\|.
	\end{enumerate}
	The same applies if you experience problems with inline data and special |col sep| choices (like |col sep=tab|).

	The reasons for such problems is that \TeX\ scans the macro bodies and replaces newlines by white spaces. It does other substitutions of this sort as well, and these substitutions can't be undone (maybe not even found).
\end{pgfplotskey}

\begin{key}{/pgfplots/table/col sep=\mchoice{space,tab,comma,semicolon,colon,braces,\&,ampersand} (initially space)}
	Allows to choose column separators for |plot table|. Please refer to the manual of \PGFPlotstable\ which comes with this package for details about |col sep|.
\end{key}
\begin{key}{/pgfplots/table/read completely=\marg{auto,true,false} (initially auto)}
	Allows to customize \verbpdfref{\addplot table}\marg{file name} such that it always reads the entire table into memory.

	This key has just one purpose, namely to create postprocessing columns on-the-fly and to plot those columns afterwards. This ``lazy evaluation'' which creates missing columns on-the-fly is documented in the \PGFPlotstable\ manual (in section ``Postprocessing Data in New Columns'').

	The initial configuration |auto| checks whether one of the keys |table/x|, |table/y|, |table/z| or |table/meta| contains a |create on use| column. If so, it enables |read completely|, otherwise it prefers to load the file in the normal way.

	\paragraph{Attention:} Usually, \verbpdfref{\addplot table} only picks required entries, requiring linear runtime complexity. As soon as |read completely| is activated, tables are loaded completely into memory. Due to datastructures issues (``macro append runtime''), the runtime complexity for |read completely| is $O(N^2)$ where $N$ is the number of rows. Thus: use this feature only for ``small'' tables\footnote{This remark might be deprecated; many of the slow routines have been optimized in the meantime to have at least pseudo-linear runtime.}.
\end{key}

\begin{key}{/pgfplots/table/ignore chars=\marg{comma-separated-list} (initially empty)}
	Allows to silently remove a set of single characters from input files. The characters are separated by commas. The documentation for this command, including cases like `|\%,\#,\ |' or binary character codes like `|\^^ff|' can be found in the manual for \PGFPlotstable.

	This setting applies to |\addplot file| as well.
\end{key}

\begin{key}{/pgfplots/table/white space chars=\marg{comma-separated-list} (initially empty)}
	Allows to define a list of single characters which are actually treated like white spaces (in addition to tabs and spaces). Please refer to the manual of \PGFPlotstable\ for details.

	This setting applies to |\addplot file| as well.
\end{key}

\begin{key}{/pgfplots/table/comment chars=\marg{comma-separated-list} (initially empty)}
	Allows to add one or more \emph{additional} comment characters. Each of these characters has a similar effect as the |#| character, i.e.\ all following characters of that particular input line are skipped.

	For example, |comment chars=!| uses `|!|' as additional comment character (which allows to parse Touchstone files).

	Please refer to the manual of \PGFPlotstable\ for details.
\end{key}

\begin{key}{/pgfplots/table/skip first n=\marg{integer} (initially 0)}
	Allows to skip the first \meta{integer} lines of an input file. The lines will not be processed.

	Please refer to the manual of \PGFPlotstable\ for details.
\end{key}

% FIXME: duplicate code in pgfplotstable.tex and pgfplots.reference.axis-addplot.tex
\begin{key}{/pgfplots/table/search path=\marg{comma-separated-list} (initially .)}
	Allows to provide a search path for input tables. This variable is evaluated whenever \PGFPlots\ attempts to read a data file. This includes both |\pgfplotstableread| and |\addplot table|; its value resembles a comma-separated list of path names. The requested file will be read from the first matching location in that list.

	Use `|.|' to search using the normal \TeX\ file searching procedure. This standard search procedure will typically use the current working directory and the environment variable |TEXINPUTS| as for any other |\input| or |\include| statements.

	An entry in \meta{comma-separated-list} can be relative to the current working directory, i.e.\ something like |search path={.,../datafiles}| is accepted.
\end{key}

% FIXME: duplicate code in pgfplotstable.tex and pgfplots.reference.axis-addplot.tex
\begin{key}{/pgfplots/table/search path/implicit .=\mchoice{true,false} (initially true)}
	\PGFPlotstable\ allows to add `|.|' to the value of |search path| implicitly as this is typically assumed in many applications of search paths.
	
	The initial configuration |search path/implicit .=true| will ensure that `|.|' is added in front of the |search path| if the user value does not contain a `|.|'.

	The value |search path/implicit .=false| will not add `|.|'.

	Keep in mind that `|.|' means ``let \TeX\ search for the file on its own''. This will typically find files in the current working directory, but it will also include processing of the environment variable |TEXINPUTS|.
\end{key}

\subsection{Computing Coordinates with Mathematical Expressions}

\begin{addplotoperation}[]{\marg{math expression}}{}
\pgfmanualpdflabel{plot expression}{}
\pgfmanualpdflabel{\textbackslash addplot expression}{}
	This input method allows to provide mathematical expressions which will be sampled. But unlike |plot gnuplot|, the expressions are evaluated using the math parser of \PGF, no external program is required.

	Plot expression samples |x| from the interval $[a,b]$ where $a$ and $b$ are specified with the |domain| key. The number of samples can be configured with |samples=|\meta{N} as for plot gnuplot.

\begin{codeexample}[]
\begin{tikzpicture}
\begin{axis}
	\addplot {x^2 + 4};
	\addplot {-5*x^3 - x^2};
\end{axis}
\end{tikzpicture}
\end{codeexample}

Please note that \PGF's math parser is configured to use |trig format=deg|rees by default whenever trigonometric functions are involved:
\begin{codeexample}[]
\begin{tikzpicture}
\begin{axis}
	\addplot+[domain=0:360]
		{sin(x)};
\end{axis}
\end{tikzpicture}
\end{codeexample}
\noindent If you want to use radians, use 
\begin{codeexample}[]
\begin{tikzpicture}
\begin{axis}
	\addplot+[domain=-pi:pi] 
		{sin(deg(x))};
\end{axis}
\end{tikzpicture}
\end{codeexample}
\noindent to convert the radians to degrees (also see |trig format| and |trig format plots|).

The plot expression parser also accepts some more options like |samples at=|\marg{coordinate list} or |domain=|\meta{first}|:|\meta{last} which are described below.

\paragraph{Remarks}
\begin{enumerate} 
	\item What really goes on is a loop which assigns the current sample coordinate to the macro |\x|. \PGFPlots\ defines a math constant |x| which always has the same value as |\x|.

	In short: it is the same whether you write |\x| or just |x| inside of math expressions.

	The variable name can be customized using |variable=t|. Then, |t| will be the same as |\t|.
\index{x@\texttt{\textbackslash x} In Coordinate Expressions}%
%\index{y@\texttt{\textbackslash y} In Coordinate Expressions}%

	\item The complete set of math expressions can be found in the \PGF\ manual. The most important mathematical operations are
	|+|, |-|, |*|, |/|, |abs|, |round|, |floor|, |mod|, |<|, |>|, |max|, |min|, |sin|, |cos|, |tan|, |deg| (conversion from radians to degrees), |rad| (conversion from degrees to radians), |atan|, |asin|, |acos|, |cot|, |sec|, |cosec|, |exp|, |ln|, |sqrt|, the constants |pi| and |e|, |^| (power operation), |factorial|\footnote{Starting with \PGF\ versions newer than $2.00$, you can use the postfix operator \texttt{!} instead of \texttt{factorial}.}, |rand| (random between $-1$ and $1$), |rnd| (random between $0$ and $1$), number format conversions |hex|, |Hex|, |oct|, |bin| and some more. The math parser has been written by Mark Wibrow and Till Tantau~\cite{tikz}, the FPU routines have been developed as part of \PGFPlots. The documentation for both parts can be found in~\cite{tikz}.
	
	Please note, however, that trigonometric functions are defined in degrees (see |trig format|). The character `|^|' is used for exponentiation (not `|**|' as in gnuplot).

	\item If the $x$ axis is logarithmic, samples will be drawn logarithmically.

	\item Plot expression also allows to define per |point meta| data (color data) using |point meta=|\meta{math expression}.
\end{enumerate}

\paragraph{About the precision and number range:}
\index{Accuracy!High Precision for Plot Expression}%
\index{Errors!dimension too large}%
	\index{Precision}\index{Floating Point Unit} Starting with version 1.2, |plot expression| uses a floating point unit. The FPU provides the full data range of scientific computing with a relative precision between $10^{-4}$ and $10^{-6}$. The |/pgf/fpu| key provides some more details. 

	Note that \PGFPlots\ makes use of |lualatex|'s features: if you use |lualatex| instead of |pdflatex|, \PGFPlots\ will use lua's math engine which is both faster and more accurate (|compat=1.12| or higher).

\begin{codeexample}[]
\begin{tikzpicture}
	\begin{loglogaxis}[
		title={$\frac{1}{x^2}$}]
	\addplot[blue,domain=1:1e30] 
		{x^-2};
	\end{loglogaxis}
\end{tikzpicture}
\end{codeexample}

\begin{codeexample}[]
\begin{tikzpicture}
	\begin{semilogyaxis}[
		title={$e^x$ logarithmically plotted}]
	\addplot[blue,domain=1:700] 
		{exp(x)};
	\end{semilogyaxis}
\end{tikzpicture}
\end{codeexample}
\end{addplotoperation}

\begin{addplotoperation}[]{expression}{\marg{math expr}}
	The syntax

	|\addplot |\marg{math expression}|;|

	as short-hand equivalent for

	|\addplot expression |\marg{math expression}|;|
\end{addplotoperation}

\begin{addplotoperation}[]{(\meta{$x$ expression},\meta{$y$ expression})}{}
	A variant of \verbpdfref{\addplot expression} which allows to provide different coordinate expressions for the $x$ and $y$ coordinates. This can be used to generate parametrized plots.

	Please note that |\addplot (x,x^2)| is equivalent to |\addplot expression {x^2}|.

	Note further that since the complete point expression is surrounded by round braces, round braces for either \meta{$x$ expression} or \meta{$y$ expression} need special attention. You will need to introduce curly braces additionally to allow round braces:

	|\addplot (|\marg{$x$ expr}|, |\marg{$y$ expr}|, |\marg{$z$ expr}|);|
\end{addplotoperation}

\begin{pgfplotskeylist}{%
	domain=\meta{$x_1$}:\meta{$x_2$} (initially [-5:5]),%
	y domain=\meta{$y_1$}:\meta{$y_2$},
	domain y=\meta{$y_1$}:\meta{$y_2$}}
	Sets the function's domain(s) for |plot expression| and |plot gnuplot|. Two dimensional plot expressions are defined as functions $f\colon [x_1,x_2] \to \R$ and \meta{$x_1$} and \meta{$x_2$} are set with |domain|. Three dimensional plot expressions use functions $f\colon [x_1,x_2] \times [y_1,y_2] \to \R$ and \meta{$y_1$} and \meta{$y_2$} are set with |y domain|. If |y domain| is empty, $[y_1,y_2] = [x_1,x_2]$ is assumed for three dimensional plots (see page~\pageref{cmd:addplot3:expr} for details about three dimensional plot expressions).

	The keys |y domain| and |domain y| are the same.


	 The |domain| key will be ignored if |samples at| is specified; |samples at| has higher precedence.


	 Please note that |domain| is not necessarily the same as the axis limits (which are configured with the |xmin|/|xmax| options). 
	 
	 The |domain| keys are \emph{only} relevant for |gnuplot| and |plot expression|. In case you'd like to plot only a subset of other coordinate input routines, consider using the coordinate filter |restrict x to domain|.

	 \paragraph{Remark for \Tikz-users:} |/pgfplots/domain| and |/tikz/domain| are independent options. Please prefer the \PGFPlots\ variant (i.e.\ provide |domain| to an axis, |\pgfplotsset| or a plot command). Since older versions also accepted something like |\begin{tikzpicture}[domain=|$\dotsc$|]|, this syntax is also accepted as long as no \PGFPlots\ |domain| key is set.
\end{pgfplotskeylist}

\begin{pgfplotskeylist}{%
	samples=\marg{number} (initially 25),%
	samples y=\marg{number}}
	 Sets the number of sample points for |plot expression| and |plot gnuplot|. The |samples| key defines the number of samples used for line plots while the |samples y| key is used for mesh plots (three dimensional visualisation, see page~\pageref{cmd:addplot3:expr} for details). If |samples y| is not set explicitly, it uses the value of |samples|.

	 The |samples| key won't be used if |samples at| is specified; |samples at| has higher precedence.

	The same special treatment of |/tikz/samples| and |/pgfplots/samples| as for the |domain| key applies here. See above for details.
\end{pgfplotskeylist}

\begin{pgfplotskey}{samples at=\marg{coordinate list}}
	Sets the $x$ coordinates for |plot expression| explicitly. This overrides |domain| and |samples|.

	The \meta{coordinate list} is a |\foreach| expression, that means it can contain a simple list of coordinates (comma--separated), but also complex |...| expressions like\footnote{Unfortunately, the \texttt{...} is somewhat restrictive when it comes to extended accuracy. So, if you have particularly small or large numbers (or a small distance), you have to provide a comma--separated list (or use the \texttt{domain} key).}
\begin{codeexample}[code only]
\pgfplotsset{samples at={5e-5,7e-5,10e-5,12e-5}}
\pgfplotsset{samples at={-5,-4.5,...,5}}
\pgfplotsset{samples at={-5,-3,-1,-0.5,0,...,5}}
\end{codeexample}

	The same special treatment of |/tikz/samples at| and |/pgfplots/samples at| as for the |domain| key applies here. See above for details.

	\paragraph{Attention:} |samples at| overrides |domain|, even if |domain| has been set \emph{after} |samples at|! Use |samples at={}| to clear \meta{coordinate list} and re-activate |domain|.
\end{pgfplotskey}

\begin{pgfplotskeylist}{%
	variable=\marg{variable name} (initially x),%
	variable y=\marg{variable name} (initially y)}
	Defines the variables names which will be sampled in |domain| (with |variable|) and in |domain y| (with |variable y|).

	The same variables are used for parametric and for non-parametric plots. Use |variable=t| to change them if you like (for |gnuplot|, there is such a distinction; see |parametric/var 1d|).

	Technical remark: \Tikz\ also uses the |variable| key. However, it expects a \emph{macro} name, i.e.\ |\x| instead of just |x|. Both possibilities are accepted here.
\end{pgfplotskeylist}

\begin{pgfplotskey}{trig format plots=\mchoice{default,deg,rad} (initially default)}
	Allows to reconfigure the input format for trigonometric functions like |sin|, |cos|, |tan|, and their friends.

	This key reconfigures trigonometric functions inside of plot expressions, |point meta| arguments, and other items
		which are directly related to the evaluation of plot coordinates.

		Note that this does \emph{not} apply to \tikzname\ drawing instructions like |\node|, |\draw|, |\fill|, etc.

\begin{codeexample}[]
\begin{tikzpicture}
    \begin{axis}[view={60}{30},trig format plots=rad,
		title=plots in radians]
    \addplot3+[domain=0:4*pi,samples=19,samples y=0]
        ({sin(x)},
         {cos(x)},
         {2*x/(4*pi)});
	
	% drawing instructions still use PGF's default
	\node[fill=white,draw=black,anchor=center] at 
		({sin(90)},{cos(90)},1) {X};
    \end{axis}
\end{tikzpicture}
\end{codeexample}

		\paragraph{Limitations:} this feature is currently unavailable for |polaraxis| and |smithchart|. 
\end{pgfplotskey}

\begin{key}{/pgf/trig format=\mchoice{deg,red} (initially deg)}
	Allows to reconfigure the trigonometric format for \emph{all} user arguments. 

	This affects \emph{all} user arguments including |view|, \tikzname\ polar coordinates, |pin|s of |\node|s, start/end angles for edges, etc. 

	At the time of this writing, this feature is in experimental state: it can happen that it breaks \tikzname\ internals. Please handle with care and report any bugs.
	
\begin{codeexample}[]
\begin{tikzpicture}
    \begin{axis}[view={rad(60)}{rad(30)},
		trig format=rad,
		title=all in radians]
    \addplot3+[domain=0:4*pi,samples=19,samples y=0]
        ({sin(x)},
         {cos(x)},
         {2*x/(4*pi)});
	
	% drawing instructions now also use radians
	\node[fill=white,draw=black,anchor=center] at 
		({sin(pi/2)},{cos(pi/2)},1) {X};
    \end{axis}
\end{tikzpicture}
\end{codeexample}
\end{key}

\subsection{Mathematical Expressions And File Data}
\PGFPlots\ allows to combine `|plot table|' and `|plot expression|' to get both file input and modifications by means of mathematical expressions.

\begin{addplotoperation}[]{table}{\oarg{column selection and expressions}\marg{file}}
\label{pgfplots:addplot:table:expr}
	Besides the already discussed possibility to provide a column selection by means of column names (|x||=|\meta{name} or |x index||=|\meta{index}, see Section~\ref{pgfplots:addplot:table}), it is also possible to provide mathematical expressions as arguments.

	Mathematical expressions are specified with |x expr||=|\meta{expression} inside of \meta{column selection and expressions}. They can depend on zero, one or more columns of the input file. A column is referenced using the special command `|\thisrow|\marg{column name}' within \meta{expression} (or |\thisrowno|\meta{column index}).

\pgfplotstableset{begin table={\begin{tabular}[b]}}
\begin{codeexample}[vbox]
\pgfplotstabletypeset[columns={maxlevel,L2}]{plotdata/newexperiment1.dat}

\begin{tikzpicture}
	\begin{semilogyaxis}[
		xlabel=\texttt{maxlevel}$ + 10$
	]
	\addplot table
		[x expr=\thisrow{maxlevel}+10, y=L2] 
		{plotdata/newexperiment1.dat};
	\end{semilogyaxis}
\end{tikzpicture}
\end{codeexample}

	Besides |x expr|, there are keys |y expr|, |z expr| and |meta expr| where the latter allows to provide point meta data (which is used as |scatter src| or color data for surface plots etc.).

	Inside of \meta{expression}, the following macros can be used to access numerical data cells inside of the input file:

	\begin{command}{\thisrow\marg{column name}}
		Yields the value of the column designated by \meta{column name}. There is no limit on the number of columns which can be part of a mathematical expression, but only values inside of the currently processed \emph{table row} can be used.
		
		It is possible to provide column aliases for \meta{column name} as described in the manual of \PGFPlotstable. 

		The argument \meta{column name} has to denote either an existing column or one for which a column alias exists (see the manual of \PGFPlotstable). If it can't be resolved, the math parser yields an ``Unknown function'' error message.
	\end{command}
	\begin{command}{\thisrowno\marg{column index}}
		Similar to |\thisrow|, this command yields the value of the column with index \meta{column index} (starting with $0$). 
	\end{command}
	\begin{command}{\coordindex}
		Yields the current index of the table row (starting with $0$). This does \emph{not} count header or comment lines.		
	\end{command}
	\begin{command}{\lineno}
		Yields the current line number (starting with $0$). This does also count header and comment lines.
	\end{command}

	If |x index|, |x| and |x expr| (or the corresponding keys for |y|, |z| or |meta|) are combined, this is how they interact:
	\begin{enumerate}
		\item Column access via |x| has higher precedence than index access via |x index|.
		\item Even if |x expr| is provided, the values of |x index| and |x| are still checked. Any value found using column name access or column index access is made available as |\columnx| (or |\columny|, |\columnz|, |\columnmeta|, resp.). However, the result of |x expr| is used as plot coordinate.

		This allows to access the cell values identified by |x| or |x index| using the ``pointer'' |\columnx|. I am not sure if this yields any advantage, but it is possible nevertheless. If in doubt, prefer using |\thisrow|\marg{column name}.
	\end{enumerate}

	\paragraph{Attention:} If your table has less than two rows, you may need to set |x index={},y index={}| explicitly. This is a consequence of the fact that column name/index access is still applied even if an expression is provided.
\end{addplotoperation}

\subsection{Computing Coordinates with Mathematical Expressions (gnuplot)}

\begin{addplotoperation}[]{gnuplot}{\oarg{further options}\marg{gnuplot code}}
In contrast to |plot expression|, the |plot gnuplot| command\footnote{Note that \texttt{plot gnuplot} is actually a re-implementation of the |plot function| method known from \PGF. It also invokes \PGF\ basic layer commands.} employs the external program |gnuplot| to compute coordinates. The resulting coordinates are written to a text file which will be plotted with |plot file|. \PGF\ checks whether coordinates need to be re-generated and calls |gnuplot| whenever necessary (this is usually the case if you change the number of samples, the argument to |plot gnuplot| or the plotted domain\footnote{Please note that \PGFPlots\ produces slightly different files than \Tikz\ when used with \texttt{plot gnuplot} (it configures high precision output). You should use different \texttt{id} for \PGFPlots\ and \Tikz\ to avoid conflicts in such a case.}).

The differences between |plot expression| and |plot gnuplot| are:
\begin{itemize}
	\item |plot expression| does not require any external programs and requires no additional command line options.
	\item |plot expression| does not produce a lot of temporary files.
	\item |plot gnuplot| uses radians for trigonometric functions while |plot expression| has degrees (unless \pgfname\ is configured for |trig format=rad|).
	\item |plot gnuplot| is faster than |pdflatex|. Using |lualatex| and |compat=1.12| (or higher) can reach a similar speed.
	\item |plot gnuplot| has a larger mathematical library.
	\item |plot gnuplot| has a higher accuracy. Note that |lualatex| and |compat=1.12| (or higher) come with the same precision.
\end{itemize}

Since system calls are a potential danger, they need to be enabled explicitly using command line options, for example
\begin{codeexample}[code only]
pdflatex -shell-escape filename.tex.
\end{codeexample}
Sometimes it is called |shell-escape| or |enable-write18|. Sometimes one needs two hyphens -- that all depends on your \TeX\ distribution.
\begin{codeexample}[]
\begin{tikzpicture}
\begin{axis}
\addplot 
	gnuplot[id=sin]{sin(x)};
\end{axis}
\end{tikzpicture}
\end{codeexample}

\begin{codeexample}[]
\begin{tikzpicture}
\begin{semilogyaxis}
\addplot gnuplot
	[id=exp,domain=0:10]{exp(x)};
\end{semilogyaxis}
\end{tikzpicture}
\end{codeexample}

The \meta{options} determine the appearance of the plotted function; these parameters also affect the legend. There is also a set of options which are specific to the gnuplot interface. These options are described in all detail in \cite[section~18.6]{tikz}. A short summary is shown below.


Some remarks:
\begin{itemize}
	\item The independent variable for one-dimensional plots can be changed with the |variable| option, just as for |plot expression|. Similarly, the second variable for two dimensional plots can be changed with |variable y|.

	For |parametric| plots, the variable names need to be adjusted with |parametric/var 1d| and |parametric/var 2d| (since gnuplot uses |t| and |u,v| as initial values for |parametric| plots).
	\item 
Please note that |plot gnuplot| does not allow separate per point meta data (color data for each coordinate). You can, however, use |point meta=f(x)| or |point meta=x|.

	\item The generated output file name can be customized with |id|, see below.
\end{itemize}

Please refer to \cite[section~18.6]{tikz} for more details about |plot function| and the |gnuplot| interaction.

\end{addplotoperation}

\begin{addplotoperation}[]{function}{\marg{gnuplot code}}
	Use

	|\addplot function |\marg{gnuplot code}|;|

	as alias for

	|\addplot gnuplot |\marg{gnuplot code}|;|
\end{addplotoperation}

\begin{pgfplotskey}{translate gnuplot=\mchoice{true,false} (initially true)}
	Enables or disables automatic translation of the exponentiation operator `|^|' to `|**|'. 

	This features allows to use |^| in |plot gnuplot| instead of gnuplot's |**|.
\end{pgfplotskey}

\begin{pgfplotskey}{parametric=\mchoice{true,false} (initially false)}
	Set this to |true| if you'd like to use parametric plots with |gnuplot|. Parametric plots use a comma separated list of expressions to make up $x(t),\, y(t)$ for a line plot or $x(u,v), \, y(u,v)\, z(u,v)$ for a mesh plot (refer to the gnuplot manual for more information about its input methods for parametric plots).
\end{pgfplotskey}

\begin{pgfplotskeylist}{%
	parametric/var 1d=\marg{variable name} (initially t),%
	parametric/var 2d=\marg{variable name,variable name} (initially {u,v})%
	}
	Allows to change the dummy variables used by |parametric| |gnuplot| plots. The initial setting is the one of |gnuplot|: to use the dummy varialbe `|t|' for parametric line plots and `|u,v|' for parametric mesh plots. 

	These keys are quite the same as |variable| and |variable y|, only for parametric plots. If you like to change variables for non-parametric plots, use |variable| and/or |variable y|.

	In case you don't want the distinction between parametric and non-parametric plots, use 
	
	|\pgfplotsset{parametric/var 1d=,parametric/var 2d=}|.

\end{pgfplotskeylist}

\begin{key}{/tikz/id=\marg{unique string identifier}}
	 A unique identifier for the current plot. It is used to generate temporary filenames for |gnuplot| output.
\end{key}

\begin{key}{/tikz/prefix=\marg{file name prefix}}
	 A common path prefix for temporary filenames (see \cite[section~18.6]{tikz} for details).
\end{key}

\begin{key}{/tikz/raw gnuplot}
	 Disables the use of |samples| and |domain|.
\end{key}

\subsection{Computing Coordinates with External Programs (shell)}

\begin{addplotoperation}[]{shell}{\oarg{further options}\marg{shell commands}}
{\small \emph{An extension by Stefan Tibus}}

In contrast to |plot gnuplot|, the |plot shell| command allows execution of arbitrary shell commands to compute coordinates. The resulting coordinates are written to a text file which will be plotted with |plot file|. \PGF\ checks whether coordinates need to be re-generated and executes the \meta{shell commands} whenever necessary.

Since system calls are a potential danger, they need to be enabled explicitly using command line options, for example
\begin{codeexample}[code only]
pdflatex -shell-escape filename.tex.
\end{codeexample}
Sometimes it is called |shell-escape| or |enable-write18|. Sometimes one needs two slashes -- that all depends on your \TeX\ distribution.
\begin{codeexample}[]
\begin{tikzpicture}
\begin{axis}
\addplot
	shell[prefix=pgfshell_,id=cos]{awk 'BEGIN{
		pi=3.14159; N=10;
		for(i=0;i<=N;i++) print i,cos(i/N*pi);}'};
\end{axis}
\end{tikzpicture}
\end{codeexample}

\begin{codeexample}[]
\begin{tikzpicture}
\begin{axis}
\addplot+[prefix=pgfshell_,id=replot]
	shell{cat pgfshell_cos.out};
	% just reprint the result from above
\end{axis}
\end{tikzpicture}
\end{codeexample}

The \meta{options} determine the appearance of the plotted function; these parameters also affect the legend. There is also a set of options which are specific to the gnuplot and the shell interface. These options are described in all detail in \cite[section~19.6]{tikz}. A short summary is shown below.
\end{addplotoperation}

\begin{key}{/tikz/id=\marg{unique string identifier}}
	 A unique identifier for the current plot. It is used to generate temporary filenames for |shell| output.
\end{key}

\begin{key}{/tikz/prefix=\marg{file name prefix}}
	 A common path prefix for temporary filenames (see \cite[section~19.6]{tikz} for details).
\end{key}

\subsection{Using External Graphics as Plot Sources}
{
\pgfkeys{/pdflinks/search key prefixes in/.add={/pgfplots/plot graphics/,}{}}

\begin{addplotoperation}[]{graphics}{\marg{file name}}
	This plot type allows to extend the plotting capabilities of \PGFPlots\ beyond its own limitations. The idea is to generate the graphics as such (for example, a contour plot, a complicated shaded surface\footnote{See also Section~\ref{sec:pgfplots:surfplots} for an overview of \PGFPlots\ methods to draw shaded surfaces.} or a large point cluster) with an external program like Matlab (\textregistered) or |gnuplot|. The graphics, however, should \emph{not} contain an axis or descriptions. Then, we use |\includegraphics| and a \PGFPlots\ axis which fits exactly on top of the imported graphics.

	Of course, one could do this manually by providing proper scales and such. The operation |plot graphics| is intended so simplify this process. However the \emph{main difficulty} is to get images with correct bounding box. Typically, you will have to adjust bounding boxes manually.

	Let's start with an example: Suppose we use, for example, matlab to generate a surface plot like
\begin{codeexample}[code only]
[X,Y] = meshgrid( linspace(-3,3,500) );
surf( X,Y, exp(-(X - Y).^2 - X.^2 ) );
shading flat; view(0,90); axis off; 
print -dpng external1
\end{codeexample}
	\noindent which is then found in |external1.png|. The |surf| command of Matlab generates the surface, the following commands disable the axis descriptions, initialise the desired view and export it. Viewing the image in any image tool, we see a lot of white space around the surface -- Matlab has a particular weakness in producing tight bounding boxes, as far as I know. Well, no problem: use your favorite image editor and crop the image (most image editors can do this automatically). We could use the free ImageMagick command
	
	|convert -trim external1.png external1.png|

	to get a tight bounding box. Then, we use

\begin{codeexample}[]
\begin{tikzpicture}
	\begin{axis}[enlargelimits=false,axis on top]
		\addplot graphics
			[xmin=-3,xmax=3,ymin=-3,ymax=3] 
			{external1};
	\end{axis}
\end{tikzpicture}
\end{codeexample}
\noindent to load the graphics\footnote{Please note that I don't have a Matlab license, so I used \texttt{gnuplot} to produce an equivalent replacement graphics.} just as if we would have drawn it with \PGFPlots. The |axis on top| simply tells \PGFPlots\ to draw the axis on top of any plots (see its description).

Please note that \PGFPlots\ offers support for smaller surface plots as well which might be an option -- unless the number of samples is too large. See Section~\ref{sec:pgfplots:surfplots} for details.

\noindent However, external programs have the following advantages here: they are faster, allow more complexity and provide real $z$ buffering which is currently only simulated by \PGFPlots. Thus, it may help to consider |plot graphics| for complicated surface plots.

Our first test was successful -- and not difficult at all because graphics programs can automatically compute the bounding box. There are a couple of free tools available which can compute tight bounding boxes for |.eps| or |.pdf| graphics:
\begin{enumerate}
	\item The free vector graphics program |inkscape| can help here. Its feature ``File $\gg$ Document Properties: Fit page to selection'' computes a tight bounding box around every picture element. 

	However, some images may contain a rectangular path which is as large as the bounding box (Matlab (\textregistered) computes such |.eps| images). In this case, use the ``Ungroup'' method (context menu of |inkscape|) as often as necessary and remove such a path.

	Finally, save as |.eps|.

	However, |inkscape| appears to have problems with postscript fonts -- it substitutes them. This doesn't pose problems in this application because fonts shouldn't be part of such images -- the descriptions will be drawn by \PGFPlots.

	\item The tool |pdfcrop| removes surrounding whitespace in |.pdf| images and produces quite good bounding boxes.
\end{enumerate}

\subsubsection{Adjusting bounding boxes manually}
In case you don't have tools at hand to provide correct bounding boxes, you can still use \TeX\ to set the bounding box manually. Some viewers like |gv| provide access to low--level image coordinates. The idea is to determine the number of units which need to be removed and communicate these units to |\includegraphics|.

I am aware of the following methods to determine bounding boxes manually:
\begin{description}
	\item[inkscape] I am pretty sure that |inkscape| can do it.
	\item[gv] The ghost script viewer |gv| always shows the postscript units under the mouse cursor.
	\item[gimp] The graphics program |gimp| usually shows the cursor position in pixels, but it can be configured to display postscript points  (|pt|) instead.
\end{description}

Let's follow this approach in a further example. 

	We use |gnuplot| to draw a (relatively stupid) example data set. The gnuplot script
\begin{codeexample}[code only]
set samples 30000
set parametric
unset border
unset xtics
unset ytics
set output "external2.eps"
set terminal postscript eps color
plot [t=0:1] rand(0),rand(0) with dots notitle lw 5
\end{codeexample}
\noindent generates |external2.eps| with a uniform random sample of size $30000$. As before, we import this scatter plot into \PGFPlots\ using |plot graphics|. Again, the bounding box is too large, so we need to adjust it (|gnuplot| can do this automatically, but we do it anyway to explain the mechanisms):

Using |gv|, I determined that the bounding box needs to be shifted |12| units to the left and |9| down. Furthermore, the right end is |12| units too far off and the top area has about |8| units space wasted. This can be provided to the |trim| option of |\includegraphics|, and we use |clip| to clip the rest away: 
\begin{codeexample}[]
\begin{tikzpicture}
	\begin{axis}[axis on top,title=Graphics Import]
		\addplot graphics
			[xmin=0,xmax=1,ymin=0,ymax=1,
			% trim=left bottom right top
			includegraphics={trim=12 9 12 8,clip}]
			{external2};
		\addplot coordinates {(0,0) (1,1)};
	\end{axis}
\end{tikzpicture}
\end{codeexample}

	So, |plot graphics| takes a graphics file along with options which can be passed to |\includegraphics|. Furthermore, it provides the information how to embed the graphics into an axis. The axis can contain any other |\addplot| command as well and will be resized properly.


\subsubsection{Details about \texttt{plot graphics}:}
	The loaded graphics file is drawn with
	
	|\node[/pgfplots/plot graphics/node] {\includegraphics[|\meta{options}|]|\marg{file name}|};|

	where the |node| style is a configurable style. The node is placed at the coordinate designated by |xmin|, |ymin|. 
	
	The \meta{options} are any arguments provided to the |includegraphics| key (see below) and |width| and |height| determined such that the graphics fits exactly into the rectangle denoted by the |xmin|, |ymin| and |xmax|, |ymax| coordinates.

	The scaling will thus ignore the aspect ratio of the external image and prefer the one used by \PGFPlots. You will need to provide |width| and |height| to the \PGFPlots\ axis to change its scaling. Use the |scale only axis| key in such a case.

\subsubsection{Legends in \texttt{plot graphics}:} A legend for |plot graphics| uses the current plot handler and the current plot |mark|:
\begin{codeexample}[]
\begin{tikzpicture}
\begin{axis}[axis on top,title=Graphics Import]
	% provide options for the legend:
    \addplot[red,only marks,mark=*,mark size=1pt]
	graphics
        [xmin=0,xmax=1,ymin=0,ymax=1,
        % trim=left bottom right top
        includegraphics={trim=12 9 12 8,clip}]
        {external2};

    \addplot coordinates {(0,0) (1,1)};

	\legend{Scatter,Line}
\end{axis}
\end{tikzpicture}
\end{codeexample}

\end{addplotoperation}

\subsection{Keys To Configure Plot Graphics}
The following list of keys configure |\addplot graphics|. Note that the common prefix `|plot graphics/|' can be omitted if these keys are set after |\addplot graphics|\oarg{options}. The |/pgfplots/| prefix can always be omitted when used in a \PGFPlots\ method.

\begin{pgfplotsxykeylist}{
	plot graphics/\x min=\marg{coordinate},
	plot graphics/\x max=\marg{coordinate}}
	These keys are required for |plot graphics| and provide information about the external data range. The graphics will be squeezed between these coordinates. The arguments are axis coordinates; they are only useful if you provide each of them.

	Alternatively, you can also use the |plot graphics/points| feature to provide the external data range, see below.
\end{pgfplotsxykeylist}

\begin{pgfplotskey}{plot graphics/points=\marg{list of coordinates} (initially empty)}
	This key also allows to provide the external data range. It constitutes an alternative to |plot graphics/xmin| (and its variants): simply provide at least two coordinates in \meta{list of coordinates}. Their bounding box is used to determine the external data range, and the graphics is squeezed between these coordinates. 

	The example from above can be written equivalently as
\begin{codeexample}[]
\begin{tikzpicture}
	\begin{axis}[axis on top,title=Graphics Import]
		\addplot graphics
			% instead of the min/max things:
			[points={(0,1) (1,0)},
			% trim=left bottom right top
			includegraphics={trim=12 9 12 8,clip}]
			{external2};
		\addplot coordinates {(0,0) (1,1)};
	\end{axis}
\end{tikzpicture}
\end{codeexample}
	\noindent The \meta{list of coordinates} is a sequence of the form |(x,y)| for two--dimensional plots and \texttt{(x,y,z)} for three--dimensional ones, the ordering is irrelevant. The single elements are separated by white space.
	
	It is possible to mix |plot graphics/xmin| and variants with |plot graphics/points|.

	The |plot graphics/points| key has further functionality for inclusion of three--dimensional graphics which is discussed at the end of this section (on page~\pageref{sec:plotgraphics3d}). Here is a short reference on the accepted syntax for three--dimensional plot graphics: in addition to the |(x,y,z)| syntax, you can provide arguments of the form |(x,y,z) => (X,Y)|. Here, the first (three--dimensional) coordinate is a logical coordinate and the second (two--dimensional) coordinate denotes the coordinates of the very same point, but inside of the included image (relative to the lower left corner of the image). Applications and examples for this syntax can be found in the section for three--dimensional plot graphics (see page~\pageref{sec:plotgraphics3d}).
\end{pgfplotskey}

\begin{pgfplotskey}{plot graphics/includegraphics=\marg{options}}
	A list of options which will be passed as--is to |\includegraphics|. Interesting options include the \declareandlabel{trim}|=|\meta{left} \meta{bottom} \meta{right} \meta{top} key which reduces the bounding box and \pgfmanualpdflabel{/pgfplots/plot graphics/clip}{\declaretext{clip}} which discards everything outside of the bounding box. The scaling options won't have any effect, they will be overwritten by \PGFPlots.
\end{pgfplotskey}
\begin{pgfplotskey}{plot graphics/includegraphics cmd=\marg{\textbackslash macro} (initially \textbackslash includegraphics)}
	Allows to use a different graphics routine. A possible choice could be |\pgfimage|. The macro should accept the |width| and |height| arguments (in brackets) and the file name as first argument.
\end{pgfplotskey}
\begin{stylekey}{/pgfplots/plot graphics/node}
	A predefined style used for the \Tikz\ node containing the graphics. The predefined value is
\begin{codeexample}[code only]
\pgfplotsset{
	plot graphics/node/.style={
		transform shape,
		inner sep=0pt,
		outer sep=0pt,
		every node/.style={},
		anchor=south west,
		at={(0pt,0pt)},
		rectangle
	}
}
\end{codeexample}
\end{stylekey}

\begin{pgfplotskey}{plot graphics}
	This key belongs to the public low--level plotting interface. You won't need it in most cases.

	This key is similar to |sharp plot| or |smooth| or |const plot|: it installs a low--level plot--handler which expects exactly two points: the lower left corner and the upper right one. The graphics will be drawn between them. The graphics file name is expected as value of the |/pgfplots/plot graphics/src| key. The other keys described above need to be set correctly (excluding the limits, these are ignored at this level of abstraction). This key can be used independently of an axis.
\end{pgfplotskey}

\begin{pgfplotskey}{plot graphics/lowlevel draw=\marg{width}\marg{height}}
	A low--level interface for |plot graphics| which actually invokes |\includegraphics|. But there is no magic involved: the command is simply expected to draw a box of dimensions \meta{width} $\times$ \meta{height}. The coordinate system has already been shifted correctly.

	The initial configuration is

	|\includegraphics[|\meta{value of ``{\normalfont\texttt{plot graphics/includegraphics}}''}|,width=#1,height=#2]|

	\hspace{10pt}\marg{value of ``{\normalfont\texttt{plot graphics/src}}''}.

	Thus, you can tweak |plot graphics| to place any \TeX\ box of the desired dimensions into an axis between the provided minimum and maximum coordinates. It is not necessary to make use of the graphics file name or the options in the `|includegraphics|' key if you overwrite this lowlevel interface with

	|plot graphics/lowlevel draw/.code 2 args=|\marg{code which depends on \texttt{\#1} and \texttt{\#2}}.
\end{pgfplotskey}
	
\subsection*{Support for External Three-Dimensional Graphics}
\label{sec:plotgraphics3d}
\PGFPlots\ offers several visualization techniques for three dimensional graphics. Nevertheless, complex visualizations or specialized applications are beyond the scope of \PGFPlots\ and you might want to use other tools to generate such figures. 

The |plot graphics| tool of \PGFPlots\ allows to include three--dimensional external graphics: it generates a three--dimensional axis on its own. The idea is to provide a graphics (without descriptions) and use \PGFPlots\ to overlay a three--dimensional axis automatically. This allows to maintain document consistency (making it unnecessary to use different programs within the same document). 

You are probably wondering how this is possible. Well, it needs more user input than two--dimensional external graphics. The cost to include external three dimensional images into \PGFPlots\ is essentially control of a graphics program like |gimp|: you need to identify the 3D coordinates of a couple of points in your image. \PGFPlots\ will then squeeze the graphics correctly, and it reconfigures the axis to ensure a correct display of the result.

\paragraph{Matlab versus other tools:} Although this section is based on Matlab images, the technique to import three--dimensional graphics is independent of Matlab. Thus, if you have a different tool, you need to read all that follows. However, users of Matlab \emph{can use a simplified export mechanism} which has been contributed by J\"urnjakob Dugge. Please skip to section~\ref{sec:plotgraphics3d:matlabscript} on page~\pageref{sec:plotgraphics3d:matlabscript} if you use Matlab to generate the graphics files (although you may want to take a brief look at the examples on the following pages to learn about flexibility or legends).

Let's start with two examples. Suppose you generate a surface plot with Matlab and want to include it in \PGFPlots. We have the matlab script
\begin{codeexample}[code only]
[x,y]=meshgrid(linspace(0,1,120));
surf(x,y,sin(8*pi*x).* exp(-20*(y-0.5).^2) + exp(-(x-0.5).^2*30 - (y-0.25).^2 - (x-0.5).*(y-0.25)))
xlabel('x'), ylabel('y')
axis off
print -dpng plotgraphics3dsurf
\end{codeexample}
\noindent which generates the figure in question. 

After automatically computing a tight bounding box for |plotgraphics3dsurf.png| (I used |gimp|'s Image$\gg$Autocrop feature), and making the background color transparent (|gimp|: select the outer white space with the magic wand, then use\footnote{I have a german version, I am not sure if the translation is correct.} Layer$\gg$Transparency$\gg$Color to Transparency) we get:

{\setlength{\fboxsep}{0pt}%
\centering
\fbox{\includegraphics[width=6cm]{plotdata/plotgraphics3dsurf.png}}%

}%

The key idea is now to identify several points in the image, and assign \emph{both} their logical three--dimensional coordinates \emph{and} the corresponding two--dimensional canvas coordinates in image coordinates. How? Well, the three--dimensional coordinates are known to Matlab, it can display them for you if you click somewhere into the image, compare Figure~\ref{fig:plotgraphics3d} (left).

\begin{figure}
\noindent
\hbox to \linewidth{\hfill
	\includegraphics{plotdata/plotgraphics3dsurfmatlab.png}%
	\hfill
	\begin{minipage}[b][4cm][c]{2.6cm}%
	\includegraphics[width=\linewidth]{plotdata/plotgraphics_gimpmeasure.png}%
	\end{minipage}
	\hfill
}%


\caption{Using Matlab to extract image coordinates (left) and Gimp to measure distances (right).}
\label{fig:plotgraphics3d}
\end{figure}

The two--dimensional canvas coordinates need work; they need to be provided relative to the \emph{lower left corner} of the image. I used |gimp| and activated ``Points'' as units (lower left corner). The lower left corner now displays the image coordinates in |pt| which is compatible with \PGFPlots. An alternative to pointing onto coordinates is a measurement tool; compare Figure~\ref{fig:plotgraphics3d} (right) for the ``Measure'' tool in |gimp| which allows to compute the length of a line (in our case, the length of the lower left corner to the point of interest).

I selected four points in the graphics and noted their 2d image coordinates and their 3d logical coordinates as follows:
\begin{codeexample}[]
\begin{tikzpicture}
\begin{axis}[
	grid=both,minor tick num=1,
	xlabel=$x$,ylabel=$y$,
	]
\addplot3 graphics[
	points={% important
		(0,1,0) => (0,207-112) 
		(1,0,0) => (446,207-133)
		(0.5546,0.5042,1.825) => (236,207)
		(0,0,0) => (194,207-202)
	}] {plotdata/plotgraphics3dsurf.png};
\end{axis}
\end{tikzpicture}
\end{codeexample}
Here, the |points| key gets our collected coordinates as argument. It accepts a sequence of maps of the form \meta{3d logical coordinate} | => | \meta{2d canvas coordinate}. In our case, |(0,1,0)| has been found in the |.png| file at |(0,207-112)|. Note that I introduced the difference since |gimp| counts from the upper left, but \PGFPlots\ counts from the lower left. 

Once these four point coordinates are gathered, we find Matlab's surface plot in a \PGFPlots\ axis. You can modify any appearance options, including different axis limits or further |\addplot| commands:
\begin{codeexample}[]
\begin{tikzpicture}
\begin{axis}[
	xmax=1.5,% extra limits
	grid=both,minor tick num=1,
	xlabel=$x$,ylabel=$y$,
	]
\addplot3[surf] % 'surf' is only used for the legend.
	graphics[
		points={
			(0,1,0) => (0,207-112) 
			(1,0,0) => (446,207-133)
			(0.5546,0.5042,1.825) => (236,207)
			(0,0,0) => (194,207-202)
	}] 
	{plotdata/plotgraphics3dsurf.png};
\addlegendentry{Graphics}

\addplot3+[only marks] coordinates {
	(0,1,0) (1,0,0) 
	(0.5546,0.5042,1.825) (0,0,0)
};
\addlegendentry{Scatter}
\end{axis}
\end{tikzpicture}
\end{codeexample}
\noindent \PGFPlots\ uses the four input points to compute appropriate |x|, |y| and |z| unit vectors (and the origin in graphics coordinates). These four vectors (with two components each) can be computed as a result of a linear system of size $8\times 8$, that is why you need to provide four input points (each has two coordinates). \PGFPlots\ computes the unit vectors of the imported graphics, and afterwards it rescales the result such that it fits into the specified |width| and |height|. This rescaling respects the |unit vector ratio| (more precisely, it uses |scale mode=scale uniformly| instead of |scale mode=stretch to fill|). Consequently, the freedom to change the view of a three--dimensional axis which contains a projected graphics is considerably smaller than before. Surprisingly, you can still change axis limits and |width| and |height| -- \PGFPlots\ will take care of a correct display of your imported graphics. Since version~1.6, you can also change |zmin| and/or |zmax| -- \PGFPlots\ will respect your changes as good as it can.

Here is a further example. Suppose we are given the three--dimensional visualization

{\setlength{\fboxsep}{0pt}%
\centering
\fbox{\includegraphics[width=6cm]{plotdata/risingdrop3d}}%

}%

It has been generated by matlab (I only added transparency to the background with |gimp|). Besides advanced visualization techniques, it uses |axis equal|, i.e.\ |unit vector ratio=1 1 1|. As before, we need to identify four points, each with its 3d logical coordinates (from matlab) and the associated 2d canvas coordinates relative to the lower left corner of the graphics (note that there is a lot of white space around the graphics). Here is the output of \PGFPlots\ when you import the resulting graphics:

\begin{codeexample}[]
\begin{tikzpicture}
\begin{axis}[
	grid=both,minor tick num=1,
	xlabel=$x$,ylabel=$y$,
	title={\centering
	  Geometry provided by Sven Gro\ss, Bonn\\
	  \url{http://www.igpm.rwth-aachen.de/DROPS}\\},
	title style={text width=6cm,font=\tiny},
]
	\addplot3 graphics[
		points={
			(-0.002625,0.002625,0) => (140,234)
			(0,0.00263,0.00263)    => (230,364)
			(0,-0.00263,-0.00263)  => (366,81)
			(0,-0.00263,0.00263)   => (366,276)
			(0.002625,0.002625,0.002625)
		}
	]
	{plotdata/risingdrop3d.png};
\end{axis}
\end{tikzpicture}
\end{codeexample}
\noindent Note that I provided \emph{five} three--dimensional coordinates here, but the last entry has no |=>| mapping to two--dimensional canvas coordinates. Thus, it is only used to update the bounding box (see the reference manual for the |points| key for details).

The example above leads to a relatively small image and much ``empty space''. This is due to the |scale mode=scale uniformly| implementation of \PGFPlots: it decided that the best way is to enlarge the involved axis limits. Here, ``best way'' means to satisfy |width|/|height| constraints combined with minimally enlarged (never shrinked) axis limits. The remaining degrees of freedom are |width|, |height|, and the axis limits. In our case, changing the ratio between |width| and |height| improves the display:

\begin{codeexample}[]
\begin{tikzpicture}
\begin{axis}[
	height=8cm,width=7cm,% improve scaling manually
	grid=both,minor tick num=1,
	xlabel=$x$,ylabel=$y$,
	title={\centering
	  Geometry provided by Sven Gro\ss, Bonn\\
	  \url{http://www.igpm.rwth-aachen.de/DROPS}\\},
	title style={text width=6cm,font=\tiny},
]
	\addplot3 graphics[
		points={
			(-0.002625,0.002625,0) => (140,234)
			(0,0.00263,0.00263)    => (230,364)
			(0,-0.00263,-0.00263)  => (366,81)
			(0,-0.00263,0.00263)   => (366,276)
			(0.002625,0.002625,0.002625)
		}
	]
	{plotdata/risingdrop3d.png};
\end{axis}
\end{tikzpicture}
\end{codeexample}
\noindent What happens is that \PGFPlots\ selects a \emph{single} scaling factor which is applied to all units as they have been deduced from the |points| key. This ensures that the imported graphics fits correctly into the axis. In addition, \PGFPlots\ does its best to satisfy the remaining constraints. 

The complete description of how \PGFPlots\ scales the axis can be found in the documentation for |scale mode=scale uniformly|. Here is just a brief summary: \PGFPlots\ assumes that the prescribed |width| and |height| have to be satisfied. To this end, it rescales the projected unit vectors (i.e.\ the space which is taken up for each unit in $x$, $y$, and $z$) and it can modify the axis limits. In the default configuration |scale uniformly strategy=auto|, \PGFPlots\ will \emph{never} shrink axis limits.  

\paragraph{Compatibility remark:} Note that the scaling capabilities have been improved for \PGFPlots\ version~1.6. In previous versions, only |scale uniformly strategy=change vertical limits| was available which lead to clipped axes. In short: please consider writing |\pgfplotsset{compat=1.6}| or newer into your document to benefit from the improved scaling. If you have |\pgfplotsset{compat=1.5}| or older, the outcome for |\addplot3 graphics| will be different.

We consider a third example which has been generated by the Matlab code
\begin{codeexample}[code only]
clear all
close all
seed = sum(clock)
rand('seed',seed);
X = rand(10,10,10);
data = smooth3(X,'box',5);
p1 = patch(isosurface(data,.5), ...
   'FaceColor','blue','EdgeColor','none');
p2 = patch(isocaps(data,.5), ...
    'FaceColor','interp','EdgeColor','none');
isonormals(data,p1)
daspect([1 2 2])
view(3); axis vis3d tight
camlight; lighting phong
% print -dpng plotgraphics3withaxis
axis off
print -dpng plotgraphics3
save  plotgraphics3.seed seed -ASCII % to reproduce the result
\end{codeexample}
\noindent I only added background transparency with |gimp| and got the following graphics:

{\setlength{\fboxsep}{0pt}%
\centering
\fbox{\includegraphics[width=6cm]{plotdata/plotgraphics3.png}}%

}%

We proceed as before and collect four points, each with 3d logical coordinates (by clicking into the matlab figure) and their associated 2d canvas (graphics) coordinates using the measure tool of gimp. The result is shown in the code example below.
\begin{codeexample}[]
\begin{tikzpicture}
\begin{axis}[
	grid=both,minor tick num=1,
	xlabel=$x$,ylabel=$y$,
	3d box,
]
	\addplot3 graphics[
		points={
			(1,1,1)    => (205,48)
			(10,1,10)  => (503,324)
			(1,1,4.044)=> (206,102)
			(10,10,10) => (390,398)
		}
	]
	{plotdata/plotgraphics3.png};
\end{axis}
\end{tikzpicture}
\end{codeexample}
\noindent Note that it has non-standard data aspect ratio which is respected by \PGFPlots\ automatically.


\subsection*{External Three-Dimensional Graphics and Matlab}

\textit{An extension by J\"urnjakob Dugge}
\vskip\baselineskip

\noindent
\label{sec:plotgraphics3d:matlabscript}
The procedure to map three--dimensional logical coordinates to two--dimensional canvas coordinates is tedious.

J\"urnjakob Dugge contributed a script which does most of the logic and your work is reduced to a copy--paste job. With his permission, I post the contribution here. 

The idea is to start a simple script which \emph{records} mappings for any coordinates which have been clicked by the user. It works as follows:

\begin{enumerate}
	\item Create the Matlab plot, say, using
\begin{codeexample}[code only]
hist3(randn(10000,2)) % some random data
set(get(gca,'child'),'FaceColor','interp','CDataMode','auto'); % colors
% make sure the "print" paper format is the same as the screen paper format:
set(gcf,'PaperPositionMode','auto') 
\end{codeexample}

	\item Save the following code as |pgfplotscsconversion.m|:
\begin{codeexample}[code only]
function pgfplotscsconversion

% Hook into the Data Cursor "click" event
h = datacursormode(gcf);
set(h,'UpdateFcn',@myupdatefcn,'SnapToDataVertex','off');
datacursormode on

% select four points in plot using mouse

% The function that gets called on each Data Cursor click
function [txt] = myupdatefcn(obj,event_obj)

% Get the screen resolution, in dots per inch
dpi = get(0,'ScreenPixelsPerInch');

% Get the click position in pixels, relative to the lower left of the
% screen
screen_location=get(0,'PointerLocation');

% Get the position of the plot window, relative to the lower left of
% the screen
figurePos = get(gcf,'Position');

% Get the data coordinates of the cursor
pos = get(event_obj,'Position');

% Format the data and figure coordinates. The factor "72.27/dpi" is
% necessary to convert from pixels to TeX points (72.27 poins per inch)
display(['(',num2str(pos(1)),',',num2str(pos(2)),',',num2str(pos(3)),') => (', ...
   num2str((screen_location(1)-figurePos(1))*72.27/dpi),',', ...
   num2str((screen_location(2)-figurePos(2))*72.27/dpi),')'])

% Format the tooltip display
txt = {['X: ',num2str(pos(1))],['Y: ',num2str(pos(2))],['Z: ',num2str(pos(3))]};
\end{codeexample}
	
	Run |pgfplotscsconversion|, click on four points in your plot. Preferably select non-colinear points near the edges of the plot. Copy and paste the four lines that were written to the Matlab command window.

	Make sure that the first two points have different $X$ and $Y$ values on screen (i.e.\ image canvas coordinates).
	\item Export the plot as an image
\begin{codeexample}[code only]
axis off
print -dpng matlabout -r400 % PNG called "matlabout.png" with 400 dpi resolution
\end{codeexample}

If you want to export vectors graphics, you should note that |pdf| output of Matlab is clumsy. It might be best to export to |eps| first, followed by a conversion from |eps| to |pdf|.

\emph{If} you really want to use |pdf| output of Matlab, you may need to set the paper size to match the figure size by yourself, since the PDF driver does not automatically adjust the size:

\begin{codeexample}[code only]
% It might be better to use print -depsc  followed by epstopdf. 
% Use this if you (really) want to use print -dpdf:
currentScreenUnits=get(gcf,'Units')     % Get current screen units
currentPaperUnits=get(gcf,'PaperUnits') % Get current paper units
set(gcf,'Units',currentPaperUnits)      % Set screen units to paper units
plotPosition=get(gcf,'Position')        % Get the figure position and size
set(gcf,'PaperSize',plotPosition(3:4))  % Set the paper size to the figure size
set(gcf,'Units',currentScreenUnits)     % Restore the screen units

print -dpdf matlabout      % PDF called "matlabout.pdf"
\end{codeexample}
\item Include the image in your \PGFPlots\ axis. If you selected points on the plot corners, your |xmin|, |xmax|, |ymin| and |ymax| should be set automatically, otherwise you may want to provide those yourself. Also, adjustments of |width| and |height| might be of interest to get the right vertical placement of the plot. Consider changing |zmin| and/or |zmax| to fit your needs (preferrably only one of them; otherwise \PGFPlots\ may be unable to fix the |height|).
\end{enumerate}

This contribution is from

\noindent
\url{http://tex.stackexchange.com/questions/52987/3-dimensional-histogram-in-pgfplots} .



\subsection*{Summary: External Three-Dimensional Graphics}
As has been shown in the previous sections, \verbpdfref{\addplot3} |graphics| allows to include three-dimensional graphics and \PGFPlots\ overlays a flexible axis with all its power. The cost to do so is
\begin{enumerate}
	\item collect both logical three--dimensional coordinates \emph{and} image--internal two--dimensional coordinates for \emph{four points} of your graphics.

	In Matlab, this can be simplified by the tool mentioned on page~\pageref{sec:plotgraphics3d:matlabscript}.

	\item If your axes form a right--handed--coordinate system, that is all. If not, also add |x dir=reverse| for any reversed axes.
\end{enumerate}

\noindent
Consider the following list of you encounter problems while working with \verbpdfref{\addplot3} |graphics|:
\begin{itemize}
	\item It must be possible to deduce the origin and the three (two--dimensional) unit vectors from the four provide |points|; otherwise the algorithm will fail. 
	
	The algorithm should detect any deficiancies. However, if you encounter strange ``Dimension too large'' messages here, you can try other arguments in |points|. Take a look into your log file, it will probably indicate the source of problems (or use the |debug| key).

	\item Ensure that the external graphics has an orthogonal axis. In fact, the axis may be skewed (just like a \PGFPlots\ axis can be created by means of custom |x|, |y|, and |z| vectors). However, the external image must not have perspective projection as this is unsupported by \PGFPlots. The |points| command needs to receive four points which belong to linearly independent position vectors. 

	\item \PGFPlots\ uses the first two points to squeeze the graphics into the desired coordinates (which implies that they should not have the same canvas $X$ or $Y$ coordinates). It verifies that the remaining |points| arguments are projected correctly.
	\item The resulting scaling by means of |scale mode=scale uniformly| will try to satisfy all scaling constraints. You can change these constraints by modifying |width|, |height|, |xmin|, |xmax|, |ymin|, |ymax|, |zmin|, |zmax| and/or any combination of these parameters. See also |unit rescale keep size| which controls the flexibility of limit changes. There is also a key |scale uniformly strategy| which allows to select a different scaling strategy.
	 
	\item The image should have a ``right--handed--coordinate system'': you should be able to take your right hand, point your thumb in direction of the $x$ axis, your first finger in direction of~$y$, and your second finger in direction of the $z$~axis. If that is impossible, once of your axes is reversed and you need to communicate that to \PGFPlots\ explicitly by means of the |x dir=reverse| key (and its variants).

	\item Note that this feature has been verified with standard cartesian axes only.

	\item There is a |debug| key to investigate what the algorithm is doing:
\begin{pgfplotskey}{plot graphics/debug=\mchoice{true,false,visual} (initially false)}
	If you provide |\addplot3 graphics[debug,points={...}]|, \PGFPlots\ will provide debug information onto your terminal and into the logfile. It will also generate extra files containing the determined unit vectors and the linear system used to derive them (one such file for every |\addplot3 graphics| statement, the filename will be the graphics file name and |.dat| appended).

	Without the |debug| key, only the log file will contain brief information what \PGFPlots\ is doing behind the scenes. 

	The choice \declaretext{true} activates log messages. The choice \declaretext{visual} activates log messages \emph{and} places some filled circles at the provided |points|. The choice \declaretext{false} disables all |debug| features.
\end{pgfplotskey}
\end{itemize}
}

\subsection{Reading Coordinates From Files}

\begin{addplotoperation}[]{file}{\marg{name}}
\label{pgfplots:addplot:file}
\paragraph{Deprecation note:} If you have data files, you should generally use |\addplot table|. The input type |\addplot file| is almost the same, but considerably less powerful. It is only kept for backwards compatibility.


The |\addplot file| input mechanism is similar to the \Tikz-command `|plot file|'. It is to be used like
\begin{codeexample}[code only]
\addplot file {datafile.dat};
\end{codeexample}
where \meta{name} is a text file with at least two columns which will be used as $x$ and $y$ coordinates. Lines starting with `|%|' or `|#|' are ignored. Such files are often generated by \textsc{gnuplot}:
\begin{codeexample}[code only]
#Curve 0, 20 points
#x y type
0.00000 0.00000 i
0.52632 0.50235 i
1.05263 0.86873 i
1.57895 0.99997 i
...
9.47368 -0.04889 i
10.00000 -0.54402 i
\end{codeexample}
This listing has been copied from~\cite[section~16.4]{tikz}.

Plot file accepts one optional argument,

\begin{codeexample}[code only]
\addplot file[skip first] {datafile.dat};
\end{codeexample}

\noindent
which allows to skip over a non-comment header line. This allows to read the same input files as |plot table| by skipping over column names. Please note that comment lines do not count as lines here.

The input method |plot file| can also read meta data for every coordinate. As already explained for |plot coordinates| (see above), meta data can be used to change colors or other style parameters for every marker separately. Now, if |point meta| is set to |explicit| or to |explicit symbolic| and the input method is |plot file|, one further element will be read from disk -- for every line. Meta data is always the last element which is read. See page~\pageref{pgfplots:scatter:src} for information and examples about per point meta data and page~\pageref{pgfplots:scatterclasses} for an application example using |scatter/classes|.


Plot file is very similar to |plot table|: you can achieve the same effect with
\begin{codeexample}[code only]
\addplot table[x index=0,y index=1,header=false] {datafile.dat};
\end{codeexample}
\noindent Due to its simplicity, |plot file| is slightly faster while |plot table| allows higher flexibility.

Technical note: every opened file will be protocolled into your log file.

	The file can contain |empty line|s to tell \PGFPlots\ that the function has jumps. To use it, simply insert an empty line (and ensure that you have |\pgfplotsset{compat=1.4}| or newer in your preamble). See the documentation of |empty line| for details.
\end{addplotoperation}

\begin{pgfplotskeylist}{%
	plot file/skip first=\mchoice{true,false} (initially false),%
	plot file/ignore first=\mchoice{true,false} (initially false)}
	The two keys can be provided as arguments to |\addplot file[|\meta{options}|] |\marg{filename}|;| to skip the first non-comment entry in the file. They are equivalent.
	If you provide them in this context, the prefix |/pgfplots/plot file| can be omitted.
\end{pgfplotskeylist}
}%
