\chapter{Plots, Charts, \& Graphs}\label{ch:plotsandgraphs}
Throughout this chapter we will be exploring some of the different ways of displaying your data in your thesis.
Mainly this will be accomplished with the \pkg{pgfplots} package.
In the following sections, there will be a few examples of how to generate different plots.
For more information on how to create plots, \href{https://mirror.its.dal.ca/ctan/graphics/pgf/contrib/pgfplots/doc/pgfplots.pdf}{\textcolor{blue}{\underline{here}}} is the manual for \pkg{pgfplots}(the package used to generate the information for TikZ to create the plots).
For an extensive list of examples please refer to \href{https://pgfplots.sourceforge.net/gallery.html}{\textcolor{blue}{\underline{this}}}
\section{Line Plots}
A simple line plot can be effectively created using the \env{axis} environment from the \pkg{pgfplots} package in \LaTeX.
The \pkg{pgfplots} package is a powerful tool for creating high-quality plots directly within \LaTeX\ documents.
It builds upon the \pkg{TikZ} package and provides a comprehensive set of options for plotting and customizing graphs.
The following code (see \Cref{lst:line-plot}) can be used to create the figure shown in \Cref{plt:line-plot}.
\begin{figure}[htbp]
\centering
\begin{subfigure}[b]{0.45\linewidth}
\centering
\begin{lstlisting}[style=LaTeXStyle,basicstyle=\scriptsize\ttfamily,frame=single]
\begin{figure}[htbp]
\centering
\begin{tikzpicture}
\begin{axis}[
title={Simple Line Plot},
xlabel={X-axis},
ylabel={Y-axis},
]
\addplot coordinates {
(0,0)
(1,1)
(2,4)
(3,9)
(4,16)
};
\end{axis}
\end{tikzpicture}
\caption{A simple line plot.}
\label{fig:line-plot}
\end{figure}
\end{lstlisting}
\caption{}
\label{lst:line-plot}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.45\linewidth}
\centering
\begin{tikzpicture}
\begin{axis}[
width=\linewidth,
title={Simple Line Plot},
xlabel={X-axis},
ylabel={Y-axis},
]
\addplot coordinates {
(0,0)
(1,1)
(2,4)
(3,9)
(4,16)
};
\end{axis}
\end{tikzpicture}
\caption{}
\label{plt:line-plot}
\end{subfigure}
\caption[A simple line plot.]{A simple line plot (\subref{plt:line-plot}) and the code to generate the plot (\subref{lst:line-plot})}\label{fig:line-plot}
\end{figure}
Expanding on this example, we can add a second plot by adding the following code below the closing bracket and semi-colon (\texttt{\};}) of the \cmd{addplot} command:
\begin{lstlisting}[float=ht,caption=,label=lst:line-plot-2-add,style=LaTeXStyle,basicstyle=\small\ttfamily,]
\addplot coordinates {
(0,16)
(1,9)
(2,4)
(3,1)
(4,0)
};
\end{lstlisting}
This will result in the addition of the second red line shown in \Cref{fig:line-plot-2}.
\begin{figure}[htbp]
\begin{subfigure}[b]{0.45\linewidth}
\centering
\begin{lstlisting}[style=LaTeXStyle,basicstyle=\scriptsize\ttfamily,frame=single]
\begin{tikzpicture}
\begin{axis}[
title={Dual Line Plot},
xlabel={X-axis},
ylabel={Y-axis},
]
\addplot coordinates {
(0,0)
(1,1)
(2,4)
(3,9)
(4,16)
};
\addplot coordinates {
(0,16)
(1,9)
(2,4)
(3,1)
(4,0)
};
\end{axis}
\end{tikzpicture}
\end{lstlisting}
\caption{}
\label{lst:line-plot-2}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.45\linewidth}
\centering
\begin{tikzpicture}
\begin{axis}[
width=\linewidth,
title={Dual Line Plot},
xlabel={X-axis},
ylabel={Y-axis},
]
\addplot coordinates {
(0,0)
(1,1)
(2,4)
(3,9)
(4,16)
};
\addplot coordinates {
(0,16)
(1,9)
(2,4)
(3,1)
(4,0)
};
\end{axis}
\end{tikzpicture}
\caption{}
\label{plt:line-plot-2}
\end{subfigure}
\caption{A simple line plot with two sets of data.}
\label{fig:line-plot-2}
\end{figure}
\section{Customizing Plots}
This section provides some ways to increase the readability and customization of the plots we generate.
\subsection{Adding a Legend}
Legends can be added to plots for better readability.
To add a legend to your plot you can use the code in \Cref{lst:legend-plot-header,lst:legend-plot-plots} to generate the plot shown in \Cref{fig:legend-plot}.
Each plot is individually added to the legend by adding a \cmd{addlegendentry}\mopt{YOUR LEGEND ENTRY HERE} command following the \cmd{addplot} command.
\note{The position of the legend can be specified by using the optional parameter \opt{legend pos=}} followed by a set of compass coordinates.
\begin{lstlisting}[float=htbp,caption=,label=lst:legend-plot-header,style=LaTeXStyle,basicstyle=\small\ttfamily,]
\begin{figure}[H]
\centering
\begin{tikzpicture}
\begin{axis}[
title={Plot with Added Legend},
xlabel={X-axis},
ylabel={Y-axis},
legend pos=north west,
]
\end{lstlisting}
\begin{lstlisting}[float=htbp,caption=,label=lst:legend-plot-plots,style=LaTeXStyle,basicstyle=\small\ttfamily,]
\addplot coordinates {
(0,0)
(1,1)
(2,4)
(3,9)
(4,16)
};
\addlegendentry{\(y = x^2\)}
\addplot coordinates {
(0,16)
(1,9)
(2,4)
(3,1)
(4,0)
};
\addlegendentry{\(y = 16 - x^2\)}
\end{axis}
\end{tikzpicture}
\caption{A customized plot with a legend.}
\label{fig:legend-plot}
\end{figure}
\end{lstlisting}
\begin{figure}[H]
\centering
\begin{tikzpicture}
\begin{axis}[
title={Plot with Added Legend},
xlabel={X-axis},
ylabel={Y-axis},
legend pos=north west,
]
\addplot coordinates {
(0,0)
(1,1)
(2,4)
(3,9)
(4,16)
};
\addlegendentry{\(y = x^2\)}
\addplot coordinates {
(0,16)
(1,9)
(2,4)
(3,1)
(4,0)
};
\addlegendentry{\(y = 16 - x^2\)}
\end{axis}
\end{tikzpicture}
\caption{A customized plot with a legend.}
\label{fig:legend-plot}
\end{figure}
\subsection{Adding Grid Lines}
To add gridlines to your plot
\begin{figure}[H]
\centering
\begin{tikzpicture}
\begin{axis}[
title={Plot with Added Gridlines},
xlabel={X-axis},
ylabel={Y-axis},
legend pos=north west,
grid=major,
]
\addplot coordinates {
(0,0)
(1,1)
(2,4)
(3,9)
(4,16)
};
\addlegendentry{\(y = x^2\)}
\addplot coordinates {
(0,16)
(1,9)
(2,4)
(3,1)
(4,0)
};
\addlegendentry{\(y = 16 - x^2\)}
\end{axis}
\end{tikzpicture}
\caption{A customized plot with added gridlines.}
\label{fig:gridlines-plot}
\end{figure}
\subsection{Changing Colors and Line Styles}
Colors and line styles can be easily modified:
\begin{figure}[H]
\centering
\begin{tikzpicture}
\begin{axis}[
title={Colored and Styled Plot},
xlabel={X-axis},
ylabel={Y-axis},
legend pos=north west,
grid=major,
]
\addplot[
color=red,
dashed
] coordinates {
(0,0)
(1,1)
(2,4)
(3,9)
(4,16)
};
\addlegendentry{\(y = x^2\)}
\addplot[
color=blue,
thick,
dotted
] coordinates {
(0,16)
(1,9)
(2,4)
(3,1)
(4,0)
};
\addlegendentry{\(y = 16 - x^2\)}
\end{axis}
\end{tikzpicture}
\caption{A plot with customized colors and line styles}
\label{fig:colour-plot}
\end{figure}
\section{Advanced Plot Types}
\subsection{Equations}
\begin{figure}[H]
\centering
\begin{tikzpicture}
\begin{axis}[
width=0.65\linewidth,
axis lines = left,
xlabel = \(x\),
ylabel = {\(f(x)\)},
]
\addplot[
domain=-10:10,
samples=20,
color=red,
]
{x^2 - 2*x - 1};
\addlegendentry{\(x^2 - 2x - 1\)}
\addplot[
domain=-10:10,
samples=20,
color=blue,
]
{x^2 + 2*x + 1};
\addlegendentry{\(x^2 + 2x + 1\)}
\end{axis}
\end{tikzpicture}
\caption{Plot of two parabola.}
\label{fig:equation-plot}
\end{figure}
\subsection{Scatter Plot with External Data}
\begin{figure}[H]
\centering
\begin{tikzpicture}
\begin{axis}[
width=0.65\linewidth,
enlargelimits=true,
]
\addplot+[
only marks,
scatter,
mark=*,
mark size=2.9pt
]
table[meta=ma]
{\insertdata{scattered_example.dat}};%{./99_Inclusions/Data/scattered_example.dat};
\end{axis}
\end{tikzpicture}
\caption{Example of a Scatter Plot.}
\label{fig:scatter-plot}
\end{figure}
\subsection{Bar Plot}
Bar plots are useful for categorical data.
Here’s how to create one:
\begin{figure}[H]
\centering
\begin{tikzpicture}
\begin{axis}[
ybar,
symbolic x coords={A, B, C, D, E},
xtick=data,
nodes near coords,
ymin=0,
]
\addplot coordinates {
(A,5) (B,10) (C,15) (D,20) (E,25)
};
\end{axis}
\end{tikzpicture}
\caption{A bar plot}
\label{fig:bar-plot}
\end{figure}
\begin{figure}[H]
\centering
\begin{tikzpicture}
\begin{axis}[
width=0.65\linewidth,
x tick label style={/pgf/number format/1000 sep=},
xlabel=Year,
ylabel= Population,
enlargelimits=0.15,
legend style={at={(0.5,-0.21)},
anchor=north,legend columns=-1},
ybar,
bar width=15pt,
]
\addplot
coordinates {(2012,388950) (2011,393007) (2010,398449) (2009,395972) (2008,384621)};
\addplot
coordinates {(2012,408184) (2011,408348) (2010,414870) (2009,412156) (2008,415426)};
\legend{Men,Women}
\end{axis}
\end{tikzpicture}
\caption{Example of a Bar Graph.}
\label{fig:bar-plot-2}
\end{figure}
\subsection{Pie Chart}
Pie charts are less common in \LaTeX, as well as, a lot of other media due to the pour representation of the data.
%TODO: add citation for - https://scc.ms.unimelb.edu.au/resources/data-visualisation-and-exploration/no_pie-charts
However, if you are still inclined to use them the remainder of this section will show how the package \pkg{pgf-pie} can be used to create consistent graphs that look good.
\begin{figure}[H]
\centering
\begin{tikzpicture}
\pie[
radius=2,
text=legend,
]{
20/A, 30/B, 10/C, 25/D, 15/E
}
\end{tikzpicture}
\caption{A basic pie chart.}
\label{fig:pie-chart}
\end{figure}
\begin{figure}[H]
\centering
\begin{tikzpicture}
\pie[
radius=2,
text=legend,
explode={0, 0, 0, 0, 0.2},
]{
20/A, 30/B, 10/C, 25/D, 15/E
}
\end{tikzpicture}
\caption{A pie chart with an ``Exploded'' slice.}
\label{fig:pie-chart-2}
\end{figure}
\begin{figure}[H]
\centering
\begin{tikzpicture}
\pie[
square,
text=legend,
]{
20/A, 30/B, 10/C, 25/D, 15/E
}
\end{tikzpicture}
\caption{A ``square'' pie chart.}
\label{fig:pie-chart-3}
\end{figure}
\subsection{3D Plot}
3D plots can be created for more complex data visualization:
\begin{figure}[H]
\centering
\begin{tikzpicture}
\begin{axis}[
view={60}{30},
xlabel={X-axis},
ylabel={Y-axis},
zlabel={Z-axis},
]
\addplot3[surf] {
x^2 - y^2
};
\end{axis}
\end{tikzpicture}
\caption{A 3D surface plot}
\label{fig:3d-plot}
\end{figure}
\begin{figure}[H]
\centering
\begin{tikzpicture}
\begin{axis}[
width=0.65\linewidth,
title=Example using the mesh parameter,
hide axis,
colormap/cool,
]
\addplot3[
mesh,
samples=25,
domain=-8:8,
]
{sin(deg(sqrt(x^2+y^2)))/sqrt(x^2+y^2)};
\addlegendentry{\(\frac{sin(r)}{r}\)}
\end{axis}
\end{tikzpicture}
\caption{Example of a 3D Plot}
\label{fig:3d-plot-2}
\end{figure}
\subsection{Polar Plot}
Polar plots are useful for circular data:
\begin{figure}[H]
\centering
\begin{tikzpicture}
\begin{polaraxis}[
title={Polar Plot},
xlabel={Radius},
ylabel={Angle (degrees)},
]
\addplot coordinates {
(0,1) (30,2) (60,3) (90,4)
(120,5) (150,6) (180,7)
};
\end{polaraxis}
\end{tikzpicture}
\caption{A polar plot}
\label{fig:polar-plot}
\end{figure}
\subsection{Box Plot}
Box plots are used to visualize the distribution of data:
\begin{figure}[H]
\centering
\begin{tikzpicture}
\begin{axis}[
boxplot/draw direction=y,
x axis line style = {opacity=0},
axis x line* = bottom,
axis y line = left,
ymajorgrids,
ymin=0,
ymax=10,
enlarge y limits,
xticklabel style = {align=center, font=\small, rotate=60},
xtick = {1,2,3,4},
xticklabels = {Apples, Oranges, Bananas, Grapes},
]
\addplot+[
boxplot prepared={
median=5,
upper quartile=6,
lower quartile=4,
upper whisker=7,
lower whisker=3
},
fill=red,
draw=black
] coordinates {};
\addplot+[
boxplot prepared={
median=4,
upper quartile=5,
lower quartile=2,
upper whisker=8,
lower whisker=1
},
fill=orange,
draw=black
] coordinates {};
\addplot+[
boxplot prepared={
median=6,
upper quartile=6.5,
lower quartile=2,
upper whisker=7,
lower whisker=1.5
},
fill=yellow,
draw=black
] coordinates {};
\addplot+[
boxplot prepared={
median=3,
upper quartile=4,
lower quartile=2.5,
upper whisker=9,
lower whisker=2
},
fill=green,
draw=black
] coordinates {};
\end{axis}
\end{tikzpicture}
\caption{A box plot}
\label{fig:box-plot}
\end{figure}
\section{Conclusion}
The \pkg{pgfplots} package is an incredibly versatile tool for creating a wide range of plots and graphs in \LaTeX.
This chapter has provided examples of various plot types and customization options, showcasing the power and flexibility of \pkg{pgfplots}.
By leveraging these capabilities, you can create high-quality, publication-ready figures for your thesis.