MATLAB（Matrix Laboratory，矩阵实验室）是由美国The MathWorks公司出品的商业数学软件。MATLAB是一种用于算法开发、数据可视化、数据分析以及数值计算的高级技术计算语言和交互式环境。除矩阵运算、绘制函数/数据图像等常用功能外，MATLAB还可用来创建用户界面，以及调用其它语言（包括C、C++、Java、Python、FORTRAN）编写的程序。
MATLAB主要用于数值运算，但利用为数众多的附加工具箱，它也适合不同领域的应用，例如控制系统设计与分析、影像处理、深度学习、信号处理与通讯、金融建模和分析等。另外还有配套软件包Simulink提供可视化开发环境，常用于系统模拟、动态/嵌入式系统开发等方面。
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1.1.1 Example
a) Create a matrix of zeros with 2 rows and 4 columns.
b) Create the row vector of odd numbers through 21,
$$
\begin{array}{rlllllllllll}
\mathrm{L}= & & & & & & & & & & & \
1 & 3 & 5 & 7 & 9 & 11 & 13 & 15 & 17 & 19 & 21
\end{array}
$$
Use the colon operator.
c) Find the sum S of vector L’s elements.
d) Form the matrix
$$
\begin{aligned}
& \mathrm{A}= \
& \begin{array}{lll}
2 & 3 & 2 \
1 & 0 & 1
\end{array} \
&
\end{aligned}
$$
Solution:
a)
$$
\begin{aligned}
& \gg \mathrm{A}=\operatorname{zeros}(2,4) \
& \mathrm{A}= \
& \begin{array}{llll}
0 & 0 & 0 & 0 \
0 & 0 & 0 & 0
\end{array} \
&
\end{aligned}
$$
b)
$$
\begin{array}{lllllllllllll}
\gg & \mathrm{L}= & : & 2 & : & 21 \
\mathrm{~L}= & 1 & 3 & 5 & 7 & 9 & 11 & 13 & 15 & 17 & 19 & 21
\end{array}
$$
c)
$$
\begin{aligned}
& \gg \mathrm{S}=\operatorname{sum}(\mathrm{L}) \
& \mathrm{S}= \
& 121
\end{aligned}
$$
d)
$$
\begin{aligned}
& \gg A=[2,3,2 ; 1001] \
& \mathrm{A}= \
& \begin{array}{lll}
2 & 3 & 2 \
1 & 0 & 1
\end{array} \
&
\end{aligned}
$$
a) Create two different vectors of the same length and add them.
b) Now subtract them.
c) Perform element-by-element multiplication on them.
d) Perform element-by-element division on them.
e) Raise one of the vectors to the second power.
f) Create a $3 \times 3$ matrix and display the first row of and the second column on the screen.
a)
$$
\gg \mathrm{a}=\left[\begin{array}{ll}
2, & 1,3
\end{array}\right] ; \mathrm{b}=\left[\begin{array}{lll}
4 & 2 & 1
\end{array}\right] ; \mathrm{c}=\mathrm{a}+\mathrm{b}
$$
$$
c=
$$
$$
\begin{array}{llll}
6 & 3 & 4
\end{array}
$$
b)
$$
\begin{aligned}
& \gg c=a-b \
& \mathrm{c}= \
& \begin{array}{lll}
-2 & -1 & 2
\end{array} \
&
\end{aligned}
$$
c)
$$
\begin{aligned}
& \gg c=a, * b \
& \mathrm{c}= \
& \begin{array}{lll}
8 & 2 & 3
\end{array} \
&
\end{aligned}
$$
d)
$$
\begin{aligned}
& \gg c=a . / b \
& c= \
& 0.5000 \quad 0.5000 \quad 3.0000
\end{aligned}
$$
e)
$$
\gg c=a .-2
$$
$$
c=
$$
$$
\begin{array}{lll}
4 & 1 & 9
\end{array}
$$
f) $\gg d=\left[\begin{array}{lllllllll}1 & 2 & 3 ; & 2 & 3 & 4 ; & 4 & 5 & 6\end{array}\right]$; $d(1,:)$, $d(:, 2)$
$$
\text { ans }=
$$
$$
\begin{array}{lll}
1 & 2 & 3
\end{array}
$$
Let us plot projectile trajectories using equations for ideal projectile motion:
$$
\begin{aligned}
& y(t)=y_0-\frac{1}{2} g t^2+\left(v_0 \sin \left(\theta_0\right)\right) t, \
& x(t)=x_0+\left(v_0 \cos \left(\theta_0\right)\right) t,
\end{aligned}
$$
where $y(t)$ is the vertical distance and $x(t)$ is the horizontal distance traveled by the projectile in metres, $g$ is the acceleration due to Earth’s gravity $=9.8 \mathrm{~m} / \mathrm{s}^2$ and $t$ is time in seconds. Let us assume that the initial velocity of the projectile $v_0=50.75 \mathrm{~m} / \mathrm{s}$ and the projectile’s launching angle $\theta_0=\frac{5 \pi}{12}$ radians. The initial vertical and horizontal positions of the projectile are given by $y_0=0 \mathrm{~m}$ and $x_0=0 \mathrm{~m}$. Let us now plot $\mathrm{y}$ vs. $\mathrm{t}$ and $\mathrm{x}$ vs. $\mathrm{t}$ in two separate graphs with the vector: $t=0: 0.1: 10$ representing time in seconds. Give appropriate titles to the graphs and label the axes. Make sure the grid lines are visible.
We first plot $x$ and $y$ in separate figures:
$\gg \mathrm{t}=0: 0.1: 10$;
$\gg \mathrm{g}=9.8$
$\gg \mathrm{v} 0=50.75$;
$\gg$ thetao $=5 * \mathrm{pi} / 12$;
$\gg \mathrm{y} 0=0$
$\gg \mathrm{x} 0=0$
$\gg \mathrm{y}=\mathrm{y} 0-0.5 * \mathrm{~g} * \mathrm{t} \cdot{ }^{\wedge} 2+\mathrm{v} 0 * \sin ($ theta 0$) . * \mathrm{t}$;
$\gg \mathrm{x}=\mathrm{x} 0+\mathrm{v} 0 * \cos (\operatorname{theta} 0) . * \mathrm{t}$;
$\gg$
$\gg$ figure;
$\gg \operatorname{plot}(t, x)$;
$\gg$ title(‘ $x(t)$ vs. $\left.t^{\prime}\right)$;
$\gg x$ label (‘Time (s)’);
$\gg$ ylabel (‘Horizontal Distance (m)’);
grid on;
$\gg$
$\gg$ figure;
$\gg \operatorname{plot}(\mathrm{t}, \mathrm{y})$;
$\gg$ title(‘y(t) vs. $\left.t^{\prime}\right)$;
$\gg$ xlabel (‘Time (s)’);
$\gg$ ylabel (‘Altitude (m)’);
$\gg$ grid on;
