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\input{macro/lstMatlab.tex} % Defines the Matlab code listing style and commands.

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\input{macro/mathMacro.tex}

\input{macro/vectorMacro.tex}

\input{macro/matrixMacro.tex}

\title{Matlab Graphics}

\author{Cheng-An Yang}

\institute{UCLA HSSEAS Workshop}

\date{December 17, 2012} % Insert customized date.

\begin{document}

\frame{\titlepage}

\begin{frame}

\frametitle{Outline}

\tableofcontents[pausesections]

\end{frame}

\section{2D Plots}

\begin{frame}

\frametitle{2D Line Plot}

\begin{figure}

\begin{subfigure}[b]{0.4\textwidth}

\centering

\includegraphics[width=\textwidth]{Line_Plot_2D_2_01.png}

\caption{Stock Indices\cite{matlab_gallery} }

\end{subfigure}%

~

\begin{subfigure}[b]{0.4\textwidth}

\centering

\includegraphics[width=\textwidth]{Add_Lines_to_Plot_1_01.png}

\caption{Step Response\cite{matlab_gallery}}

\end{subfigure}

\end{figure}

\end{frame}

\begin{frame}[fragile]

\frametitle{Basic Line Plot}

\begin{block}{Syntax}

\begin{itemize}[<+->]

\item To create an empty figure, call

\begin{matlabcodebeamer}[frame=none]

figure;

\end{matlabcodebeamer}

\item To create a line plot of vector \texttt{x} versus vector \texttt{t}, use

\begin{matlabcodebeamer}[frame=none]

plot(t,x);

\end{matlabcodebeamer}

\item You can input more vector pairs like

\begin{matlabcodebeamer}[frame=none]

plot(t1,x1,t2,x2);

\end{matlabcodebeamer}

\end{itemize}

\end{block}

\end{frame}

\begin{frame}[fragile]

\frametitle{Basic Line Plot}

\begin{block}{Syntax}

\begin{itemize}[<+->]

\item Adding labels on axis

\begin{matlabcodebeamer}[frame=none]

xlabel('x label');

ylabel('y label');

\end{matlabcodebeamer}

\item Add title

\begin{matlabcodebeamer}[frame=none]

title('title for the figure');

\end{matlabcodebeamer}

\item Turn on/off the grid lines

\begin{matlabcodebeamer}[frame=none]

grid on;

grid off;

\end{matlabcodebeamer}

\item Adding legends

\begin{matlabcodebeamer}[frame=none]

legend('first','second',...);

\end{matlabcodebeamer}

\end{itemize}

\end{block}

\end{frame}

\begin{frame}[fragile]

\frametitle{Basic Line Plot}

\textbf{Exercise}

Visualizing $\sin(t)$ and $\cos(t)$ on $0 \leq t \leq 2\pi$. \pause

\begin{figure}[htb]

\centering

\includegraphics[width=6cm]{basic_plot_sine}

\end{figure}

\end{frame}

\begin{frame}[fragile]

\frametitle{Line Style}

\begin{itemize}[<+->]

\item Using the \textit{string specifier} to change the line style.

\item The \textit{string specifiers} contains

\begin{itemize}

\item Line style: \texttt{\{'-','--',':','-.','none'\}}

\item Marker symbol: \texttt{\{'+','o','*','.','x'\}} and more.

\item Color: \texttt{\{'r','g','b','w','k'\}}.

\end{itemize}

\item For example,

\begin{matlabcode}[numbers=none,frame=none]

plot(t,x,'--or');

plot(t,x,'r',t,y,'-.xk');

\end{matlabcode}

\end{itemize}

\end{frame}

\begin{frame}{Line Style}

\textbf{Exercise}

Let

\begin{equation}

\end{equation}\pause

The envelope of $x(t)$ is

\begin{equation}

\end{equation}\pause

Please duplicate the figure shown below:

\begin{figure}[htb]

\centering

\includegraphics[width=5cm]{ex_line_style}

\end{figure}

\end{frame}

\begin{frame}[fragile]

\frametitle{Plotting Complex Data}

\begin{block}{Syntax}

\begin{itemize}[<+->]

\item To plot complex array \texttt{x}, use

\begin{matlabcodebeamer}[frame=none]

plot(x);

\end{matlabcodebeamer}

\item It is equivalent to

\begin{matlabcodebeamer}[frame=none]

plot(real(x),imag(x));

\end{matlabcodebeamer}

\end{itemize}

\end{block}

\end{frame}

\begin{frame}[fragile]

\frametitle{Plotting Complex Data}

\textbf{Example}

Visualizing the distribution of the eigenvalues of the random matrix. \pause

\begin{itemize}

\item Let \texttt{H} be an $n$-by-$n$ random matrix.

\item Let \texttt{x} be its eigenvalues.

\end{itemize}

\begin{figure}[htb]

\centering

\includegraphics[width=5cm]{random_matrix_eigenvalue}

\end{figure}

\end{frame}

\begin{frame}[fragile]

\frametitle{Plotting Matrix Data}

\begin{block}{Syntax}

\begin{itemize}[<+->]

\item By default \tttbf{plot}\texttt{(Y)} will plot each column of \texttt{Y}.

\item When specifying the \texttt{x} vector,

\begin{matlabcodebeamer}[frame=none]

plot(x,Y);

\end{matlabcodebeamer}

will try to match the dimension of \texttt{x} and \texttt{Y}.

\end{itemize}

\end{block}

\end{frame}

\begin{frame}[fragile]

\frametitle{Plotting Matrix Data}

\textbf{Example}

Plot \texttt{y = randn(5,3)} with and without \texttt{x = 1:3}.\pause

\setcounter{subfigure}{0}

\begin{figure}

\begin{subfigure}[b]{0.3\textwidth}

\centering

\includegraphics[width=\textwidth]{plot_matrix_data1}

\caption{Without \texttt{x}.}

\end{subfigure}%

~\pause

\begin{subfigure}[b]{0.3\textwidth}

\centering

\includegraphics[width=\textwidth]{plot_matrix_data2}

\caption{With \texttt{x}.}

\end{subfigure}

\end{figure}

\end{frame}

\begin{frame}[fragile]

\frametitle{Plotting Multiple Lines On the Same Axes}

\begin{itemize}[<+->]

\item If you call \tttbf{plot} twice, the first plot will be erased.

\item To retain current graph when adding new graph, tell Matlab to

\begin{matlabcode}[frame=none]

hold on;

\end{matlabcode}

\item If you want different lines to have different color, use

\begin{matlabcode}[frame=none]

hold all;

\end{matlabcode}

\item The default is

\begin{matlabcode}[frame=none]

hold off;

\end{matlabcode}

\end{itemize}

\end{frame}

\begin{frame}[fragile]

\frametitle{Plotting Multiple Lines On the Same Axes}

\textbf{Exercise}

In our first sine wave example, we use

\begin{matlabcode}[frame=none]

plot(t,x,t,y)

\end{matlabcode}\pause

Now try

\begin{matlabcode}[frame=none]

plot(t,x);

hold all;

plot(t,y);

\end{matlabcode}

Change \texttt{'all'} to \texttt{'on'} and \texttt{'off'}.

\end{frame}

\begin{frame}{Hierarchy of The Graphic Objects}

A Matlab plot is composed of (at least) three objects:

\setcounter{subfigure}{0}

\begin{figure}

\begin{subfigure}[b]{0.3\textwidth}

\centering

\includegraphics[width=\textwidth]{figure_window.png}

\caption{Figure window.}

\end{subfigure}%

~\pause

\begin{subfigure}[b]{0.3\textwidth}

\centering

\includegraphics[width=\textwidth]{empty_axis.png}

\caption{Axis object.}

\end{subfigure}

~\pause

\begin{subfigure}[b]{0.3\textwidth}

\centering

\includegraphics[width=\textwidth]{lineseries_object.png}

\caption{Line series object.}

\end{subfigure}

\end{figure}

\end{frame}

\begin{frame}[fragile]

\frametitle{Hierarchy of The Graphic Objects}

\begin{itemize}[<+->]

\item Each object has a unique identifier, called the \textbf{handle}.

\item You can ask Matlab to get and set the properties of the object with its handle.

\item To get the handle of the current figure, type

\begin{matlabcode}[frame=none]

h_fig = gcf;

\end{matlabcode}

\item To get the handle of the current axis, type

\begin{matlabcode}[frame=none]

h_ax = gca;

\end{matlabcode}

\item To get the handle of the line series, use

\begin{matlabcode}[frame=none]

h = plot(t,x);

\end{matlabcode}

\end{itemize}

\end{frame}

\begin{frame}[fragile]

\frametitle{Set and Get}

\begin{itemize}

\item Get the value of the property:

\begin{matlabcode}[frame=none]

value = get(h,'PropertyName');

\end{matlabcode}

\item Set using property-value pair:

\begin{matlabcode}[frame=none]

set(h,'PropertyName',value);

\end{matlabcode}

\end{itemize}

Complicated? Let's try an example.

\end{frame}

\begin{frame}[fragile]

\frametitle{Set and Get}

\textbf{Example}

Plot $\sin(t)$ and $\cos(t)$. Change the line width and fine-tune the axis.

\setcounter{subfigure}{0}

\begin{figure}

\centering

\includegraphics[width=6cm]{set_axis_lineseries}

\end{figure}

\end{frame}

\begin{frame}[fragile]

\frametitle{Linear and Log Scale}

\begin{itemize}[<+->]

\item By default \tttbf{plot} use linear scale on both axis.

\item Replace \tttbf{plot} by

\begin{itemize}

\item \tttbf{semilogx}

\item \tttbf{semilogy}

\item \tttbf{loglog}

\end{itemize}

\item Equivalently, use

\begin{matlabcode}[numbers=none,frame=none]

set(gca, 'XScale', 'log');

\end{matlabcode}

and/or

\begin{matlabcode}[numbers=none,frame=none]

set(gca, 'YScale', 'log');

\end{matlabcode}

\end{itemize}

\end{frame}

\begin{frame}[fragile]

\frametitle{Linear and Log Scale}

\textbf{Example}

The transfer function of a second order system has the form

where $\zeta$ is the damping ratio and $\omega_n$ is the natural frequency.

The frequecny response of a system is characterized by

\begin{itemize}

\item The magnitude $|H(\jmath \omega)|$

\item The phase $\angle H(\jmath \omega)$

\end{itemize}

In this example, we will plot the frequency response of $H(s)$.

\end{frame}

\begin{frame}[fragile]

\frametitle{Linear and Log Scale}

\setcounter{subfigure}{0}

\begin{figure}

\centering

\includegraphics[width=6cm]{log_scale}

\caption{Frequency response of $H(s)$.}

\end{figure}

\end{frame}

\begin{frame}[fragile]

\frametitle{Subplot}

\begin{block}{Syntax}

\begin{matlabcodebeamer}[frame=none]

subplot(m,n,1);

plot(t,x);

\end{matlabcodebeamer}

Will create a $m$-by-$n$ subplot and place the plot of \texttt{x} versus \texttt{t} at location 1.

\end{block}

\end{frame}

\begin{frame}[fragile]

\frametitle{Subplot}

\textbf{Example}

Create 25 subplots of sine wave with increasing frequency.

\setcounter{subfigure}{0}

\begin{figure}

\centering

\includegraphics[width=6cm]{subplot_sine}

\end{figure}

\end{frame}

\section{GUI and More 2D Plots}

\begin{frame}[fragile]

\frametitle{Adding Annotations}

\begin{block}{Syntax}

If you want to put \texttt{'some text'} at location \texttt{(x,y)}, type

\begin{matlabcodebeamer}[numbers=none,frame=none]

text(x,y,'some text');

\end{matlabcodebeamer}

\end{block}

\end{frame}

\begin{frame}[fragile]

\frametitle{Adding Annotations}

\textbf{Example}

\setcounter{subfigure}{0}

\begin{figure}

\centering

\includegraphics[width=6cm]{set_axis_lineseries_text}

\end{figure}

\end{frame}

\begin{frame}[fragile]

\frametitle{Adding Annotations}

\begin{itemize}[<+->]

\item It's a pain to calculate the coordinates, is there any easier way?

\item Luckily, Matlab provides a useful function

\begin{matlabcode}[numbers=none,frame=none]

gtext('some text');

\end{matlabcode}

\item Click on the figure to place the text.

\end{itemize}

\end{frame}

\begin{frame}[fragile]

\frametitle{GUI}

It's about time to talk about the Graphical User Interface (GUI).

Pros:

\begin{itemize}

\item Easy to use.

\item No need to remember many commands.

\end{itemize}

Cons:

\begin{itemize}

\item Less flexible.

\item Can not batch process.

\end{itemize}

\begin{block}{Go with GUI if}

\begin{itemize}

\item There are only a few figures to edit.

\item No need to edit them in the future.

\end{itemize}

Otherwise using commands will be more efficient.

\end{block}

\end{frame}

\begin{frame}[fragile]

\frametitle{Saving and Exporting}

Some tips about exporting figures:

\begin{itemize}[<+->]

\item Try to save to vector format.

\item Use `copy figure' on Windows.

\item Keep a \texttt{.fig} copy so you can edit it later.

\end{itemize}

\end{frame}

\begin{frame}[fragile]

\frametitle{Histogram}

\begin{block}{Syntax}

\begin{itemize}[<+->]

\item Create a histogram of data vector \texttt{x}

\begin{matlabcodebeamer}[numbers=none,frame=none]

hist(x);

\end{matlabcodebeamer}

\end{itemize}

\end{block}

\end{frame}

\begin{frame}[fragile]

\frametitle{Histogram}

\textbf{Example}

Linear Congruential Generator (LCG)

\begin{itemize}[<+->]

\item LCG is a popular (and old) Pseudo-Random Numbers Generator.

\item Simple and efficient to compute.

\item Well understood.

\item Poor choice of parameters lead to bad performance.

\end{itemize}

\begin{block}{LCG}

\begin{equation}

\end{equation}

\begin{itemize}

\item $m > 0$: the modulus

\item $a > 0$: the multiplier

\item $b \geq 0$: the increment

\item $x_0$: the seed

\end{itemize}

\end{block}

\end{frame}

\begin{frame}[fragile]

\frametitle{Histogram}

\textbf{Exercise}

Use

\begin{itemize}

\item $a = 3$

\item $b = 0$

\item $m = 31$

\item $x_0 = 1$

\end{itemize}

Generate $100$ samples to find its distribution.

\setcounter{subfigure}{0}

\begin{figure}

\centering

\includegraphics[width=5cm]{lcg_histogram}

\end{figure}

\end{frame}

\begin{frame}[fragile]

\frametitle{Bar Chart}

\begin{block}{Syntax}

\begin{itemize}[<+->]

\item Create a bar chart

\begin{matlabcodebeamer}[numbers=none,frame=none]

bar(Y);

\end{matlabcodebeamer}

Each column of \texttt{Y} will have the same color and rows are grouped together.

\item It is equivalent to

\begin{matlabcodebeamer}[numbers=none,frame=none]

bar(Y,'grouped');

\end{matlabcodebeamer}

Try \texttt{'stacked'} instead of \texttt{'grouped'}.

\end{itemize}

\end{block}

\end{frame}

\begin{frame}[fragile]

\frametitle{Bar Chart}

\textbf{Example}

\setcounter{subfigure}{0}

\begin{figure}

\centering

\includegraphics[width=6cm]{bar_chart}

\end{figure}

\end{frame}

\begin{frame}[fragile]

\frametitle{Area Plot}

\begin{block}{Syntax}

\begin{itemize}

\item Stacks each data series and fill the underlying area with different colors

\begin{matlabcodebeamer}[numbers=none,frame=none]

area(X,Y);

\end{matlabcodebeamer}

\end{itemize}

\end{block}

\end{frame}

\begin{frame}[fragile]

\frametitle{Area Plot}

\textbf{Example}

\setcounter{subfigure}{0}

\begin{figure}

\centering

\includegraphics[width=6cm]{area_plot}

\end{figure}

\end{frame}

\begin{frame}[fragile]

\frametitle{Stem Plot}

Stem plot is useful for visualizing discrete time data.

\begin{block}{Syntax}

\begin{itemize}

\item Use exactly like the \tttbf{plot} function

\begin{matlabcodebeamer}[numbers=none,frame=none]

stem(t,x);

\end{matlabcodebeamer}

\end{itemize}

\end{block}

\end{frame}

\begin{frame}[fragile]

\frametitle{Stem Plot}

\textbf{Example}

\setcounter{subfigure}{0}

\begin{figure}

\centering

\includegraphics[width=6cm]{stem_sine}

\end{figure}

\end{frame}

\begin{frame}[fragile]

\frametitle{Polar Plot}

\begin{itemize}[<+->]

\item Sometimes it is easier to express coordinate in the polar form.

\item Let $(x,y)$ be the coordinates in the Cartesian coordinate system, its corresponding polar coordinates is given by

\begin{align}

\end{align}

\end{itemize}

\begin{block}{Syntax}

\begin{itemize}

\item Plot \texttt{r} versus \texttt{theta} in the polar coordinate

\begin{matlabcodebeamer}[numbers=none,frame=none]

polar(theta,r);

\end{matlabcodebeamer}

\end{itemize}

\end{block}

\end{frame}

\begin{frame}[fragile]

\frametitle{Polar Plot}

\textbf{Example}

The butterfly fly curve, discovered by Temple H. Fay, is generated by the equations

\begin{equation}

\end{equation}\pause

\setcounter{subfigure}{0}

\begin{figure}

\centering

\includegraphics[width=5cm]{polar_butterfly_curve}

\end{figure}

\end{frame}

\begin{frame}[fragile]

\frametitle{Scatter Plot}

Scatter plot is used to visualize the distribution of two dimensional data.

\begin{block}{Syntax}

\begin{itemize}

\item to generate the scatter plot for the data vector \texttt{X} and \texttt{Y}

\begin{matlabcodebeamer}[numbers=none,frame=none,backgroundcolor=\color{blockbody}]

scatter(X,Y)

\end{matlabcodebeamer}

\end{itemize}

\end{block}

\end{frame}

\begin{frame}[fragile]

\frametitle{Scatter Plot}

\textbf{Example} Linear Fitting

\begin{itemize}[<+->]

\item Suppose we are given a data set \texttt{x} and \texttt{y}.

\item It is assumed that $y = ax + b + \mbox{noise}$.

\item Find the best linear fit $\hat{y} = \hat{a} x + \hat{b}$.

\end{itemize}

\setcounter{subfigure}{0}

\begin{figure}

\centering

\includegraphics[width=6cm]{scatter_linear_fitting}

\end{figure}

\end{frame}

\begin{frame}[fragile]

\frametitle{Contour Plot}

\begin{block}{Syntax}

\begin{itemize}[<+->]

\item The basic syntax is

\begin{matlabcodebeamer}[numbers=none,frame=none]

contour(Z);

\end{matlabcodebeamer}

\item You can specify the number of contour level

\begin{matlabcodebeamer}[numbers=none,frame=none]

contour(Z, n_level);

\end{matlabcodebeamer}

\end{itemize}

\end{block}

\end{frame}

\begin{frame}[fragile]

\frametitle{Contour Plot}

\textbf{Example} Visualizing \texttt{peaks}

The Matlab function \texttt{peaks} is defined as

\begin{equation}

\end{equation}\pause

\setcounter{subfigure}{0}

\begin{figure}

\centering

\includegraphics[width=6cm]{contour_peaks}

\end{figure}

\end{frame}

\begin{frame}[fragile]

\frametitle{Animation}

The simplest way to generate animation in Matlab is use the template

\begin{matlabcode}[numbers=none,frame=none]

figure;

% Prevent Matlab reseting your view angle.

hold on;

for I=1:N

% Update your data here.

plot(t,x); % Draw new frame.

pause(0.1); % Pause for 0.1 seconds.

end

\end{matlabcode}

\end{frame}

\section{3D Plots}

\begin{frame}[fragile]

\frametitle{3D Plot}

\begin{figure}

\begin{subfigure}[b]{0.4\textwidth}

\centering

\includegraphics[width=\textwidth]{Streamline_01.png}

\caption{Stream lines\cite{matlab_gallery} }

\end{subfigure}%

~

\begin{subfigure}[b]{0.4\textwidth}

\centering

\includegraphics[width=\textwidth]{Wind_01.png}

\caption{Wind Field\cite{matlab_gallery}}

\end{subfigure}

\end{figure}

\end{frame}

\begin{frame}[fragile]

\frametitle{3D Line Plot}

\begin{block}{Syntax}

\begin{itemize}

\item Plot lines in 3D

\begin{matlabcodebeamer}[numbers=none,frame=none]

plot3(x,y,z);

\end{matlabcodebeamer}

\end{itemize}

\end{block}

\end{frame}

\begin{frame}[fragile]

\frametitle{3D Line Plot}

\textbf{Example} 3D Brownian Motion:

the position $\vx_n$ of a Brownian particle at time $n$ is given by

\begin{equation}

\end{equation}

where $\vv$ is a standard normal random vector.

\setcounter{subfigure}{0}

\begin{figure}

\centering

\includegraphics[width=6cm]{plot3D_brownian_motion}

\end{figure}

\end{frame}

\begin{frame}[fragile]

\frametitle{3D Line Plot}

\textbf{Example} Lorenz Attractor

Lorenz system is a simplified model for atmospheric convection, it is modeled by the ordinary differential equations

\begin{align}

\end{align}

where $x$, $y$ and $z$ are the coordinate of the state, $t$ represents time, $\rho$, $\sigma$ and $\beta$ are parameters.

\end{frame}

\begin{frame}[fragile]

\frametitle{3D Line Plot}

\textbf{Example} Lorenz Attractor

\setcounter{subfigure}{0}

\begin{figure}

\centering

\includegraphics[width=6cm]{lorenz_attractor}

\end{figure}

\end{frame}

\begin{frame}[fragile]

\frametitle{Mesh Plot}

Mesh plot is used to visualize 2D scalar fields.

\begin{block}{Syntax}

\begin{itemize}

\item Plot \texttt{Z} as a function of \texttt{X} and \texttt{Y}

\begin{matlabcodebeamer}[numbers=none,frame=none]

mesh(X,Y,Z);

\end{matlabcodebeamer}

\end{itemize}

\end{block}

\end{frame}

\begin{frame}[fragile]

\frametitle{Mesh Plot}

\textbf{Example} 3D Sinc function

The 3D sinc function is defined as

\begin{equation}

\end{equation}\pause

\setcounter{subfigure}{0}

\begin{figure}

\centering

\includegraphics[width=6cm]{mesh_3D_sinc}

\end{figure}

\end{frame}

\begin{frame}[fragile]

\frametitle{Surface Plot}

Surface plot is mesh plot plus patches.

\begin{block}{Syntax}

\begin{itemize}

\item Plot \texttt{Z} as a function of \texttt{X} and \texttt{Y}

\begin{matlabcodebeamer}[numbers=none,frame=none]

surf(X,Y,Z);

\end{matlabcodebeamer}

\end{itemize}

\end{block}

\end{frame}

\begin{frame}[fragile]

\frametitle{Surface Plot}

\textbf{Example} 3D Sinc function

\setcounter{subfigure}{0}

\begin{figure}

\centering

\includegraphics[width=6cm]{surf_3D_sinc}

\end{figure}

\end{frame}

\begin{frame}[fragile]

\frametitle{Surface Plot}

\textbf{Example} 2D Wave Equation

The wave equation is a partial differential equation

\begin{equation}\label{eq:wave_eq}

\end{equation}\pause

\begin{itemize}

\item $c$ is the wave speed

\item $b$ is the damping coefficient

\item $\Delta$ is Laplacian, defined as

\begin{equation}

\end{equation}

\end{itemize}

We use the Finite Difference Method (FDM) to approximate

\begin{equation}

\end{equation}

\end{frame}

\begin{frame}[fragile]

\frametitle{Surface Plot}

\textbf{Example} 2D Wave Equation

\setcounter{subfigure}{0}

\begin{figure}

\centering

\includegraphics[width=6cm]{wave_fdm}

\end{figure}

\end{frame}

\begin{frame}[fragile]

\frametitle{2D Vector Field}

\begin{block}{Syntax}

\begin{itemize}

\item Plot the vector field \texttt{Zx} and \texttt{Zy} as a function of \texttt{X} and \texttt{Y}

\begin{matlabcodebeamer}[numbers=none,frame=none]

quiver(X,Y,Zx,Zy);

\end{matlabcodebeamer}

\end{itemize}

\end{block}

\end{frame}

\begin{frame}[fragile]

\frametitle{2D Vector Field}