pgfplots1.11：LaTeX 2D/3D绘图指南

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"pgfplots1.11是LaTeX中的一个强大的2D和3D图形绘制工具包，由Christian Feuersänger开发。该版本为1.11，更新日期为2014年8月4日。pgfplots允许用户在正常或对数比例下创建高质量的函数图形，并提供了用户友好的接口。用户只需提供轴标签、图例条目以及一个或多个图的坐标，pgfplots就会自动处理轴的缩放、计算对数、设置轴刻度并绘制图形。它支持线图、散点图、阶梯图、柱状图、面积图、网状图、曲面图、补丁图、等高线图、箭流图、直方图、箱形图、极坐标图、三元图和Smith图表等多种类型的图形。这个工具包基于Till Tantau的pgf/TikZ包构建。" pgfplots是LaTeX中用于创建科学图形的重要工具，其主要特点包括： 1. **用户友好**：pgfplots提供了一个直观的接口，使得在LaTeX中绘制复杂图形变得简单。用户只需要定义数据和图形属性，如颜色、线条样式、标记等，其余工作，如坐标转换、轴标尺的设定等，都由pgfplots自动处理。 2. **图形类型丰富**：pgfplots支持多种类型的图形，包括但不限于线性图、散点图、柱状图、面积图、网状图、曲面图、补丁图、等高线图、箭流图、直方图、箱形图等，满足了科学研究和报告撰写中各种图形需求。 3. **缩放和对数处理**：pgfplots可以轻松地切换到对数尺度，这对于表示具有宽动态范围的数据特别有用。它能够自动计算合适的轴刻度，并处理对数变换。 4. **自定义能力**：pgfplots允许用户自定义图形的每一个细节，如轴标签、图例、颜色方案等，以适应不同的报告风格和需求。 5. **兼容性**：pgfplots基于pgf/TikZ，这意味着它可以无缝集成到LaTeX环境中，同时也兼容CTeX，这使得在中文环境下使用也变得可能。 6. **升级与兼容性**：pgfplots会随着新版本的发布添加新的特性，同时也会考虑到旧版本用户的兼容性问题。用户需要注意一些新旧功能的差异，以确保代码的正常运行。 7. **安装与依赖**：pgfplots的使用需要先安装LaTeX系统，以及相关的依赖包如pgf/TikZ。此外，根据版权信息，pgfplots遵循特定的开源许可证，用户在使用时应了解并遵守相应的授权条款。 pgfplots1.11版的文档详细介绍了如何使用这个工具包，包括基本组件、升级注意事项、团队成员、致谢、安装步骤和前提条件等，为用户提供了一套完整的参考指南。通过深入学习和实践，用户可以充分利用pgfplots的强大功能，提升LaTeX绘图的效率和质量。

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16 CHAPTER 3. STEP–BY–STEP TUTORIALS

(and all others referenced in this manual) are shipped with pgfplots; you can ﬁnd them in the subfolder

doc/latex/pgfplots/plotdata.

3.2.1 Getting the Data Into T

Our ﬁrst step is to get the data table into pgfplots. In addition, we want axis descriptions for the x and

y axes and a title on top of the plot.

Our ﬁrst version looks like

0 0.2 0.4 0.6 0.8 1

−4

−2

Inv. cum. normal

% Preamble: \pgfplotsset{width=7cm,compat=1.11}

%\documentclass{article}

%\usepackage{pgfplots}

%\pgfplotsset{compat=1.5}

%\begin{document}

\begin{tikzpicture}

\begin{axis}[

title=Inv. cum. normal,

xlabel={$x$},

ylabel={$y$},

]

\addplot[blue] table {invcum.dat};

\end{axis}

\end{tikzpicture}

%\end{document}

The code listing already shows a couple of important aspects:

1. As usual in L

X, you include the package using \usepackage{pgfplots}.

2. Not so common is \pgfplotsset{compat=1.5} .

A statement like this should always be used in order to (a) beneﬁt from a more-or-less recent feature

set and (b) avoid changes to your picture if you recompile it with a later version of pgfplots.

Note that pgfplots will generate some suggested value into your log ﬁle (since 1.6.1). The minimum

suggested version is \pgfplotsset{compat=1.3} as this has great eﬀect on the positioning of axis

labels.

3. pgfplots relies on Tik Z and pgf. You can say it is a “third party package” on top of TikZ/pgf.

Consequently, we have to write each pgfplots graph into a Tik Z picture, hence the picture environ-

ment given by \begin{tikzpicture} ... \end{tikzpicture}.

4. Each axis in pgfplots is written into a separate environment. In our case, we chose \begin{axis}

... \end{axis} as this is the environment for a normal axis.

There are more axis environments (like the \begin{loglogaxis} ... \end{loglogaxis} environ-

ment for logarithmic axes).

Although pgfplots runs with default options, it accepts keys. Lots of keys. Typically, you provide

all keys which you “want to have” in square brackets “somewhere” and ignore all other keys.

Of course, the main diﬃculty is to get an overview over the available keys and to ﬁnd out how to use

them. This reference manual and especially its Section 4 has been designed for online browsing: it

contains hundreds of cross-referenced examples. Opening the manual in a pdf viewer and searching it

for keywords will hopefully jump to a good match from which you can jump to the reference section

(for example about tick labels, tick positions, plot handlers etc). It is (and will always be) the most

reliable source of detail information about all keys.

Speaking about the reference manual: note that most pdf viewers also have a function to “jump back

to the page before you clicked on a hyperlink” (for Acrobat Reader, open the menu View / Toolbars

/ More Tools and activate the “Previous View” and “Next View” buttons which are under “Page

Navigation Toolbar”).

Note that the code listing contains two sets of keys: the ﬁrst is after \begin{axis}[ .... ] and

the second right after \addplot[...]. Note furthermore that the option list after the axis has been

3.2. SOLVING A REAL USE–CASE: FUNCTION VISUALIZATION 17

indented: each option is on a separate line, and each line has a tab stop as ﬁrst character. This is a

good practice. Another good practice is to place a comma after the last option (in our case, after the

value for ylabel). This allows to add more keys easily – and you won’t forget the comma. It does

not hurt at all. The second “set” of keys after \addplot shows that indentation and trailing comma

a really just a best-practice: we simply said \addplot[blue], meaning that the plot will be placed in

blue color, without any plot mark. Of course, once another option would be added here, it would be

best to switch to indentation and trailing comma:

\addplot[

blue,

mark=*,

]

table {invcum.dat};

5. Inside of an axis, pgfplots accepts an \addplot ... ; statement (note the ﬁnal semicolon).

In our case, we use \addplot table: it loads a table from a ﬁle and plots the ﬁrst two columns.

There are, however, more input methods. The most important available inputs methods are \addplot

expression (which samples from some mathematical expression) and \addplot table (loads data

from tables), and a combination of both which is also supported by \addplot table (loads data from

tables and applies mathematical expressions). Besides those tools which rely only on builtin methods,

there is also an option to calculated data using external tools: \addplot gnuplot which uses gnuplot

as “desktop calculator” and imports numerical data, \addplot shell (which can load table data from

any system call), and the special \addplot graphics tool which loads an image together with meta

data and draws only the associated axis.

In our axis, we ﬁnd a couple of tokens: the ﬁrst is the mandatory \addplot token. It “starts” a further

plot. The second is the option list for that plot, which is delimited by square brackets (see also the

notes about best-practices above). The name “option list” indicates that this list can be empty. It

can also be omitted completely in which case pgfplots will choose an option list from its current

cycle list (more about that in a diﬀerent lecture). The next token is the keyword “table”. It tells

pgfplots that table data follows. The keyword “table” also accepts an option list (for example, to

choose columns, to deﬁne a diﬀerent col sep or row sep or to provide some math expression which

is applied to each row). More on that in a diﬀerent lecture. The next token is {invcum.dat}: an

argument in curly braces which provides the table data. This argument is interpreted by “plot table”.

Other input types would expect diﬀerent types of arguments. In our case, the curly braces contain a

ﬁle name. Plot table expects either a ﬁle name as in our case or a so-called “inline table”. An inline

table means that you would simply insert the contents of your ﬁle inside of the curly braces. In our

case, the table is too long to be inserted into the argument, so we place it into a separate ﬁle. Finally,

the last (mandatory!) token is a semicolon. It terminates the \addplot statement.

6. Axis descriptions can be added using the keys title, xlabel, ylabel as we have in our example

listing.

pgfplots accepts lots of keys — and sometimes it is the art of ﬁnding just the one that you were

looking for. Hopefully, a search through the table of contents of the reference manual and/or a keyword

search through the entire reference manual will show a hit.

3.2.2 Fine–Tuning of the First Picture

While looking at the result of Section 3.2.1, we decide that we want to change something. First, we decide

that the open ends on the left and on the right are disturbing (perhaps we have a strange taste – or perhaps

we know in advance that the underlying function is not limited to any interval). Anyway, we would like to

show it only in the y interval from −3 to +3.

We can do so as follows:

18 CHAPTER 3. STEP–BY–STEP TUTORIALS

0 0.2 0.4 0.6 0.8 1

−2

Inv. cum. normal

% Preamble: \pgfplotsset{width=7cm,compat=1.11}

\begin{tikzpicture}

\begin{axis}[

title=Inv. cum. normal,

xlabel={$x$},

ylabel={$y$},

ymin=-3, ymax=3,

minor y tick num=1,

]

\addplot[blue] table {invcum.dat};

\end{axis}

\end{tikzpicture}

We added three more options to the option list of the axis. The ﬁrst pair is ymin=-3 and ymax=3. Note

that we have placed them on the same line although we said the each should be on a separate line. Line

breaks are really optional; and in this case, the two options appear to belong together. They deﬁne the

display limits. Display limits deﬁne the “window” of the axis. Note that any \addplot statements might

have more data (as in our case). They would still generate graphics for their complete set of data points!

The keys ymin,ymax,xmin,xmax control only the visible part, i.e. the axis range. Everything else is clipped

away (by default). The third new option is minor y tick num=1 which allows to customize minor ticks.

Note that minor ticks are only displayed if the major ticks have the same distance as in our example.

Note that we could also have modiﬁed the width and/or height of the ﬁgure (the keys have these

names). We could also have used one of the predeﬁned styles like tiny or small in order to modify not

just the graphics, but also use diﬀerent fonts for the descriptions. We could also have chosen to adjust the

unspeciﬁed limits: either by ﬁxing them explicitly (as we did for y above) or by modifying the enlargelimits

key (for example using enlargelimits=false).

We are now satisﬁed with the ﬁrst picture and we would like to add the second one.

3.2.3 Adding the Second Picture with a Diﬀerent Plot

As motivated, our goal is to have two separate axes placed side–by–side. The second axis should show

a function given as math expression. More precisely, we want to show the density function of a normal

distribution here (which is just a special math expression).

We simply start a new tikzpicture and insert a new axis environment (perhaps by copy-pasting our

existing one). The \addplot command is diﬀerent, though:

−2 0 2

·10

−3

100

200

300

400

% Preamble: \pgfplotsset{width=7cm,compat=1.11}

\begin{tikzpicture}

\begin{axis}[

]

% density of Normal distribution:

\addplot[

red,

domain=-3e-3:3e-3,

samples=201,

]

{exp(-x^2 / (2e-3^2)) / (1e-3 * sqrt(2*pi))};

\end{axis}

\end{tikzpicture}

We see that it has an axis environment with an empty option list. This is quite acceptable: after all, it

is to be expected that we will add options eventually. Even if we don’t: it does not hurt. Then, we ﬁnd the

expected \addplot statement. As already explained, \addplot statements initiate a new plot. It is followed

by an (optional) option list, then by some keyword which identiﬁes the way input coordinates are provided,

then arguments, and ﬁnally a semicolon. In our case, we ﬁnd an option list which results in a red plot.

The two keys domain and samples control how our math expression is to be evaluated: domain deﬁnes the

sampling interval in the form a:b and samples=N expects the number of samples inserted into the sampling

3.2. SOLVING A REAL USE–CASE: FUNCTION VISUALIZATION 19

interval. Note that domain merely controls which samples are taken; it is independent of the displayed axis

range (and both can diﬀer signiﬁcantly). If the keyword deﬁning how coordinates are provided is missing,

pgfplots assumes that the next argument is a math expression. Consequently, the ﬁrst token after the

option list is a math expression in curly braces. We entered the density function of a normal distribution

here (compare Wikipedia).

Note that the axis has an axis multiplier: the x tick labels have been chosen to be −2, 0, and 2 and an

extra x tick scale label of the form ‘·10

−3

’. These tick scale labels are quite convenient are are automatically

deduced from the input data. We will see an example with the eﬀects of scaled x ticks=false at the end

of this tutorial.

Inside of the math expression, you can use a lot of math functions like exp, sin, cos, sqrt, you

can use exponents using the a^b syntax, and the sampling variable is x by default. Note, however,

that trigonometric functions operate on degrees by default! If you need to sample the sinus func-

tion, you can use \addplot[domain=0:360] {sin(x)};. This is quite uncommon. You can also use

\addplot[domain=0:2*pi] {sin(deg(x)};. This samples radians (which is more common). But since

the math parser expects degrees, we have to convert x to degrees ﬁrst using the deg() function. See also

trig format plots=rad. The math parser is written in T

X(it does not need any third-party tool). It

supports the full range of a double precision number, even though the accuracy is about that of a single

precision number. This is typically more than suﬃcient to sample any function accurately. If you ever en-

counter diﬃculties with precision, you can still resort to \addplot gnuplot in order to invoke the external

tool gnuplot as “coordinate calculator”.

The experienced reader might wonder about constant math expressions domain=-3e-3:3e-3, 2e-3^2,

and 1e-3 rather than some variable name like “mu” or ‘sigma’. This is actually a matter of taste: both is

supported and we will switch to variable names in the next listing.

The main part of our step here is still to be done: we wanted to place two ﬁgures side–by–side. This can

be done as follows:

0 0.2 0.4 0.6 0.8 1

−2

Inv. cum. normal

−2 0 2

·10

−3

200

400

20 CHAPTER 3. STEP–BY–STEP TUTORIALS

% Preamble: \pgfplotsset{width=7cm,compat=1.11}

\begin{tikzpicture}

\begin{axis}[

title=Inv. cum. normal,

xlabel={$x$},

ylabel={$y$},

ymin=-3, ymax=3,

minor y tick num=1,

]

\addplot[blue] table {invcum.dat};

\end{axis}

\end{tikzpicture}% - avoid white space

\hskip 10pt % insert a non-breaking space of specified width.

\begin{tikzpicture}

\begin{axis}[

]

% density of Normal distribution:

\newcommand\MU{0}

\newcommand\SIGMA{1e-3}

\addplot[

red,

domain=-3*\SIGMA:3*\SIGMA,

samples=201,

]

{exp(-(x-\MU)^2 / 2 / \SIGMA^2) / (\SIGMA * sqrt(2*pi))};

\end{axis}

\end{tikzpicture}

The listing above shows the two separate picture environments: the ﬁrst is simply taken as-is from the

previous step and the second is new. Note that both are simply placed adjacent to each other: we only

inserted comment signs to separate them. This approach to place graphics side–by–side is common in T

it works for \includegraphics in the same way. You could, for example, write

\includegraphics{image1}%

\hskip 10pt % insert a non-breaking space of specified width.

\includegraphics{image2}

to place two graphics next to each other. This here is just the same (except that our graphics occupy

more code in the .tex ﬁle).

Note that there is also a comment sign after \end{tikzpicture}. This is not just a best-practice: it

is necessary to suppress spurious spaces! In T

X, every newline character is automatically converted to a

white space (unless you have an empty line, of course). In our case, we want no white spaces.

In our second picture, we see the eﬀects of switch our math expression to constant deﬁnitions as promised

earlier. The interesting part starts with two constants which are deﬁned by means of two \newcommand s:

we deﬁne \MU to be 0 and \SIGMA to be 1e-3. This is one way to deﬁne constants (note that such a

deﬁnition of constants should probably introduce round braces if numbers are negative, i.e. something like

\newcommand\negative{(-4)}).

3.2.4 Fixing the Vertical Alignment and Adjusting Tick Label Positions

Note that even though our individual pictures look quite good, the combination of both is not properly

aligned. The experienced reader identiﬁes the weak point immediately: the bounding box of the two images

diﬀers, and they are aligned at their baseline (which is the bottom edge of the picture). In particular,

the xlabel=$x$ of the left picture and the automatically inserted scaling label \cdot 10^{-3} of the right

picture cause an unwanted vertical shift. We want to ﬁx that in the next step.

Besides the bad alignment, we ﬁnd it a little bit misleading that the axis descriptions of the second

picture are between both pictures. We would like to move them to the right.

Let us present the result ﬁrst:

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pgfplots1.11：LaTeX 2D/3D绘图指南

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