1. Variable

声明变量并赋值即可存储变量, 默认为ans

>> a = 1
a =
    1

>> b = cos(a)
b =
    0.5403

>> e = a * b
e =
    0.5403

>> a + b
ans =
    1.5403

>> ans
ans =
    1.5403

2. Matrics and Arrays

2.1 Create Matrix and Array

  1. row vector

    >> a = [1 2 3 4]
    a =
         1     2     3     4

  2. multiple rows

    >> a = [1 2 3; 4 5 6; 7 8 10]
    a =
         1     2     3
         4     5     6
         7     8    10

  3. create matrix by function
    rand(a, b, c)的参数说明: a表示矩阵行数, b表示矩阵列数, c表示矩阵个数, 矩阵的元素范围为[0, 1]的随机数

    >> a = zeros(3)
    a =
         0     0     0
         0     0     0
         0     0     0

    >> b = ones(3)
    b =
         1     1     1
         1     1     1
         1     1     1

    >> c = rand(3,3,1)
    c =
        0.7952    0.4456    0.7547
        0.1869    0.6463    0.2760
        0.4898    0.7094    0.6797

2.2 Matrix and Array Operations

  1. Array

    >> a = [1 2 3]
    a =
         1     2     3

    >> a + 10
    ans =
        11    12    13


    >> a * 10
    ans =
        10    20    30

  2. Matrix 

    >> a = [1 2 ; 3 4]
    a =
         1     2
         3     4

    >> a + 10
    ans =
        11    12
        13    14

    >> a'       %{transpose a matrix}%
    ans =
         1     3
         2     4

    >> inv(a)   %{inverse a matrix}%
    ans =
       -2.0000    1.0000
        1.5000   -0.5000

    >> a * inv(a)
    ans =
        1.0000         0
        0.0000    1.0000

    >> a .* a   %{element-wise multiplication}%
    ans =
         1     4
         9    16

    >> a^2
    ans =
         7    10
        15    22

    >> a.^2     %{element-wise power}%
    ans =
         1     4
         9    16

2.3 Concatenation

>> a = [1 2; 3 4]
a =
     1     2
     3     4

>> A = [a, a]
A =
     1     2     1     2
     3     4     3     4

>> A = [a; a]
A =
     1     2
     3     4
     1     2
     3     4

3. Complex Numbers

>> sqrt(-1)
ans =
   0.0000 + 1.0000i

>> c = [3+4i, 4+3j; -i, 10j]
c =
   3.0000 + 4.0000i   4.0000 + 3.0000i
   0.0000 - 1.0000i   0.0000 +10.0000i

4. format

format函数用于控制输出的显示格式, 默认为short. MATLAB支持的格式有常用的以下几种:

  • short: 5位字长定点数
  • long: 15位字长定点数
  • hex: 16进制
  • compact: 压缩空格
  • rat: 分数
    >> format short
    >> a = 1.2
    a =
        1.2000


    >> format long
    >> a = 1.2
    a =
       1.200000000000000

    >> format hex
    >> a = 1.2
    a =
       3ff3333333333333

    >> format rat
    >> a = 1.2
    a =
           6/5

5. Indexing

magic(n)函数: 生成元素范围为$[1, n^2]$的矩阵, 每一行和每一列的和相同

>> A = magic(3)
A =
       8              1              6       
       3              5              7       
       4              9              2

MATLAB中的坐标必须为正整数, 越界报错

>> A(3,1)   %{get the specify row and column subscript}%
ans =
       4 

>> A(0,0)
Subscript indices must either be real positive
integers or logicals. 

>> A(4,2)
Index exceeds matrix dimensions.

也可通过元素的依次顺序获得元素(从左到右, 从上到下排序)

>> A(9)
ans =
       2

colon operator(冒号)可指定矩阵的一块区间

>> A(1:3, 2)    %{first three rows and the second column}%
ans =
       1       
       5       
       9

colon operator前后不标记start和end说明表示整个区间

>> A(2, :)      %{all second row}%
ans =
     3     5     7

通过start:step:end可生成均匀分布的vector

>> 0:2:10
ans =
     0     2     4     6     8    10

通过赋值空数组来实现删除行和列

>> X = magic(4);
>> X(:,2) = []
X =
    16     3    13
     5    10     8
     9     6    12
     4    15     1

>> X = magic(4);
>> X(2,:) = []
X =
    16     2     3    13
     9     7     6    12
     4    14    15     1

6. Workspace Variable

6.1 View the contents of workspace

whos语句可查看当前workspace下有多少个variable和其属性. clear命令可清楚当前workspace下的所有variable

>> A = magic(4);
>> B = rand(2,2,2);
>> whos
  Name      Size             Bytes  Class     Attributes
  A         4x4                128  double              
  B         2x2x2               64  double 

>> clear

6.2 Save and Load

save myfile.mat
load myfile.mat

7. Text and Character

使用single quote(单引号)来包裹字符串

>> myText = 'Hello, world'
myText =
Hello, world

>> whos myText
  Name        Size            Bytes  Class    Attributes
  myText      1x12               24  char

也可用数组来连接两个或多个text

>> longText = [myText ' - ', 'otherText']
longText =
Hello, world - otherText

数字转字符用num2str或int2str, semicolon用于不显示计算结果

>> f = 71;
>> c = (f-32)/1.8;
>> tmpText = ['Temperature is ', num2str(c), 'C']
tmpText =
Temperature is 21.6667C

8. Calling Function

max()可返回vector中最大元素值

>> A = [1 2 3];
>> max(A)
ans =
     3

max()也可找出两个matrix中每个位置上最大的元素, 不同行数或不同列数的两个matrix进行max操作时报错

>> A = [1 1 6];
>> B = [3 3 3];
>> max(A, B)
ans =
     3     3     6

>> A = [0 0 0; 1 1 1; 2 2 2];
>> B = [1 1 1; 0 0 0; 3 3 3];
>> max(A, B)
ans =
     1     1     1
     1     1     1
     3     3     3

max()也可返回最大元素的位置

>> [maxA, loc] = max(A)
maxA =
     8     9     5  %{max value of each column}%
loc =
     2     2     3  %{which row of the max value in each column}%

clc命令可清空Command Window中所有输入的指令

9. 2D and 3D Plots

9.1 Line Plots

>> x = 0: pi/100: 2*pi;
>> y = sin(x);
>> plot(x, y)
>> xlabel('x')
>> ylabel('sin(x)')
>> title('Plot of the Sin Function')

sin

9.2 Different Line

MATLAB支持多种格式和颜色的线段表示, 以下是常用的几种格式:

Specifier LineStyle
'-' Solid Line
'--' Dashed Line
':' Dotted Line
'-.' Dashed-dot Line
Specifier Color Specifier Color
r Red g Green
b Blue c Cyan
m Magenta y Yellow
k Black w White

例如:

>> x = 0: pi/100: 2*pi;
>> y = sin(x);
>> plot(x, y, 'r--')

red dashed line sin

9.3 Add plots to an existing figure

hold on可在不删除之前Plot的情况下添加图像, hold off可删除之前添加的图像

x = 0: pi/100: 2*pi;
y = sin(x);
plot(x, y)
hold on
y2 = cos(x)
plot(x, y, ':')
legend('sin','cos')

sin and cos

10. Plots

三维的plot由两个变量组成, 函数可表示为 $z = f(x, y)$. 使用meshgrid创建 $(x,y)$ 的集合, 再使用surf展示

>> [x, y] = meshgrid(-2:0.2:2, -2:0.2:2);
>> z = x .* exp(-x.^2 - y.^2);
>> surf(x, y, z);

3-D Plot

11. Subplots

可使用subplot函数实现在一个window中显示多个plot. subplot(a, b, c)中a表示plot的行数, b表示plot的列数, c表示该plot在window中的位置.

>> t = 0: pi/10: 2*pi;
>> [x, y, z] = cylinder(4*cos(t));
>> subplot(2,2,1); mesh(x); title('X');
>> subplot(2,2,2); mesh(y); title('Y');
>> subplot(2,2,3); mesh(z); title('Z');
>> subplot(2,2,4); mesh(x,y,z); title('X,Y,Z');

subplots

12. Programming and Scripts

MATLAB中最简单的程序形式为script, script以**.m**为拓展名, 其中可包含MATLAB命令和函数调用.

12.1 Create a script

edit plotrand   % create a script named 'plotrand.m'

12.2 Run a script

在Editor中写入代码, 之后点击Run即可运行script

n = 50;
r = rand(n, 1); % generate 50 random data ranging from 0 to 1
plot(r)

m = mean(r);    % get the mean of random data
hold on
plot([0,n], [m,m]) % draw a mean line from 0 t0 50
hold off
title('Mean of Random Uniform Data')

subplots

12.3 Loops and Conditional Statements

使用for实现循环, 每一个for循环都需要end来结束循环

nsamples = 5;
npoints = 50;

for k = 1: nsamples     % use loop to calculate the mean of random value
    iterationString = ['Iteration #', int2str(k)];
    disp(iterationString)
    currentData = rand(npoints, 1);
    sampleMean(k) = mean(currentData)   % diplay the result of each loop
end

overallMean = mean(sampleMean)
if overallMean < 0.49
    disp('Mean is less than expected')
elseif overallMean > 0.51
    disp('Mean is greater than expected')
else
    disp('Mean is within the expected range')
end

Output:

Iteration #1
sampleMean =
    0.5156

Iteration #2
sampleMean =
    0.5156    0.5385

Iteration #3
sampleMean =
    0.5156    0.5385    0.4572

Iteration #4
sampleMean =
    0.5156    0.5385    0.4572    0.5364

Iteration #5
sampleMean =
    0.5156    0.5385    0.4572    0.5364    0.5096

overallMean =
    0.5114

Mean is greater than expected

13. Help and Documentation

  1. Open the function documentation in a separate window

    doc mean

  2. View an abbreviated text version of function documentation in the Command Window

    help mean

14. Matrices and Magic Squares

14.1 Sum, Transpose and Diag

  1. sum: 求每一列的和

    >> A = magic(4)
    A =
        16     2     3    13
         5    11    10     8
         9     7     6    12
         4    14    15     1

    >> sum(A)       % compute the sum of each column
    ans =
        34    34    34    34

    >> sum(A, 2)    % compute the sum of each row
    ans =
        34
        34
        34
        34

  2. transpose: 共轭转置和非共轭转置

    1. conjugare transpose($'$) 
      A'
    2. nonconjugate transpose($.'$) 
      A.'

  3. diag: 求矩阵对角线

    >> diag(A)
    ans =
        16
        11
         6
         1

14.2 Generating Matrices

>> Z = zeros(2,4)
Z =
     0     0     0     0
     0     0     0     0

>> F = 5 * ones(3,3)
F =
     5     5     5
     5     5     5
     5     5     5

>> N = fix(10*randn(4,4))   % fix(): round number to the nearest integer
N =
     4   -11     6   -13
     9     0     5   -12
   -17    -4    -6   -11
    -1   -16     5    -1

15. Expressions

15.1 Float

Float 精确度为 16 个十进制数值, 超过16位则进行截断. float的数值范围为 $[10^{-308} - 10^{+308}]$

>> x = 12345678901234567;
>> y = 12345678901234568;
>> x == y
ans =
   1    % x == y 成立因为x和y都为 1.234567890123457e+16

15.2 Integer

Integer有不同的精度: 8bits, 32bits和64bits:

>> x = uint64(12345678901234567);
>> y = uint64(12345678901234568);
>> x == y
ans =
   0

15.3. Complex number

Complex number大小的比较根据phase angle来决定:

>> sort([3+4i, 4+3i])
ans =
   4.0000 + 3.0000i   3.0000 + 4.0000i

%{
because:
>> angle(3+4i)
ans =
    0.9273

>> angle(4+3i)
ans =
    0.6435
%}

15.4 Matrix Operators

Specifier Arithmetic Operator
+ Addition
- Subtraction
* Multiplication
/ Division
\ Left division
^ Power
' Complex conjugate transpose
() Specify evaluation order

15.5 Array Operator

Specifier Array Operator
+ Addition
- Subtraction
.* Element-by-element multiplication
./ Element-by-element division
.\ Element-by-element left division
.^ Element-by-element power
.' Unconjugated array transpose

15.6 Building Tables

>> n = (0:9)';
>> pows = [n, n.^2, 2.^n]
pows =
     0     0     1
     1     1     2
     2     4     4
     3     9     8
     4    16    16
     5    25    32
     6    36    64
     7    49   128
     8    64   256
     9    81   512

15.7 Functions

Several special functions privode values of constants

Function Constant
pi 3.14159265...
i Imaginary unit, -1
j Same as i
eps Floating-point relative precision, $\xi = 2^{-52}$
realmin Smallest floating-point number, $2^{-1023}$
realmax Largest floating-point number, $(2-\xi)2^{1023}$
Inf Infinity
NaN Not-a-number

16 Special function

16.1 isfinite()

NaN一般用来表示丢失的数据, 可用isfinite(x)来移除这些数据. isfinite()还可用于移除Inf:

>> x = [2.1 1.7 1.6 1.5 NaN 1.9 1.8 Inf];
>> x = x(isfinite(x))
x =
    2.1000    1.7000    1.6000    1.5000    1.9000    1.8000

16.2 std(), mean()

std()用于求standard deviation(标准方差), mean()用于求平均数

>> x = [1 2 3 4 5 6 7 8 9 10]
>> std(x)
ans =
    3.0277

>> mean(x)
ans =
    5.5000

16.3 isprime()

isprime()用于判断质数

>> X = magic(4);
>> X(isprime(X)) = 0    % find all prime number and set them to 0
X =
    16     0     0     0
     0     0    10     8
     9     0     6    12
     4    14    15     1

16.4 find()

find()根据条件返回一列索引的向量

>> X = magic(4)
X =
    16     2     3    13
     5    11    10     8
     9     7     6    12
     4    14    15     1

>> primes = find(isprime(X))
primes =
     2      % row 2, col 1 - 5
     5      % row 1, col 2 - 2
     6      % row 2, col 2 - 11
     7      % row 3, col 2 - 7
     9      % row 1, col 3 - 3
    13      % row 1, col 4 - 13