[MITOPENCOURSEWARE] 6.094 Introduction to Programming in MATLAB

Introduction to MATLAB

Lecture 1 Variables, Scripts, and Operations

• Matlab Basic

  • MATLAB can be thought of as a super-powerful graphing calculator
  • In addition it is a programming language

• 一些命令

  • 帮助命令

    • help [ ]
    • doc [ ] 更详细的帮助

  • 注释 %

    第一行注释为脚本的帮助文档

  • 新建脚本 edit

    edit [ ].m

  • 输出字符串disp

    注意字符串使用单引号

  • 保存变量到文件中save

    save myFile a b

    • saves variables a and b to the file myfile.mat
    • myfile.mat file is saved in the current directory

  • 移除当前环境中变量 clear

  • 加载文件中变量load

  • 清理命令窗口clc

• 变量

  • 创建和修改的变量会一直保存在工作区
  • Matlab is a weekly typed language. 不需要初始化变量
  • 变量命名：首位必须是字母；以字母、数字、下划线_ 组成
  • 大小写敏感
  • Built-in variables. Don’t use these names!
    • i and j can be used to indicate complex numbers
    • pi has the value 3.1415926…
    • ans stores the last unassigned value (like on a calculator)
    • Inf and -Inf are positive and negative infinity
    • NaN represents ‘Not a Number’

• 若不想显示输出，则在句末加上;

• 数组[ ]

  Two types of arrays

  1. matrix of numbers (either double or complex)
  2. cell array of objects (more advanced data structure)
  • 行向量：在[ ] 中使用逗号或空格分隔值
  • 列向量：在[ ]中使用;分隔
  • size( )显示矩阵大小
  • length( )得到矩阵长度
    
  • Initialize a vector of ones, zeros, or random numbers
    » o=ones(1,10)
    row vector with 10 elements, all 1
    » z=zeros(23,1)
    column vector with 23 elements, all 0
    » r=rand(1,45)
    row vector with 45 elements (uniform [0,1])
    » n=nan(1,69)
    row vector of NaNs (useful for representing uninitialized variables)
    
  • To initialize a linear vector of values use linspace
    » a=linspace(0,10,5)
    starts at 0, ends at 10 (inclusive), 5 values
    Can also use colon operator (:)
    » b=0:2:10
    starts at 0, increments by 2, and ends at or before 10
    increment can be decimal or negative
    » c=1:5
    if increment isn’t specified, default is 1
  • To initialize logarithmically spaced values use logspace
    similar to linspace, but generate logarithmically spaced vectors
  • Vector Indexing
    • Matlab 索引从0开始
    • The index argument can be a vector
    • 使用max和min得到最大/小值和索引号
    • 使用find特殊值或一定范围内的索引号
    • To convert between subscripts and indices, use ind2sub, and sub2ind.

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Homework 1

• 科学技术法使用e表示
• 虚数可以直接使用虚数单位i,j 表示也可以使用复数函数complex( )
• 以e为底数，使用exp( )
• 产生从a到b之间的随机数r=a+(b-a)*rand(m,n)
• 数除矩阵要在除号前面加点.，平方也是
• 取平均值使用mean，可选择行或列

// 不保证没错
a = 10;
b = 2.5e23;
c = 2+3i;
d = exp((j*2*pi)/3);
 
aVec = [3.14 15 9 26];
bVec = [2.71;8;28;182];
cVec = 5:-0.2:-5;
dVec = logspace(0,1,100);
eVec = ['Hello'];
 
aMat = ones(9) * 2;
bMat = diag([1 2 3 4 5 4 3 2 1]);
cMat = reshape(1:100,[10 10]);
dMat = NaN(3,4);
eMat = [13 -1 5;-22 10 -87];
fMat = floor(rand(5,3)*6-3);
 
x = 1 / (1 + exp(-(a - 15)/6));
y = (sqrt(a) + b^(1/21))^pi;
z = log(real((c + d) * (c - d)) * sin(a * pi / 3))/(c * conj(c));
 
xVec = (1 / (sqrt(2 * pi * 2.5^2))) * exp(-power(cVec,2) / (2 * 2.5 * 2.5));
yVec = sqrt(power((aVec)',2) + power(bVec,2));
zVec = log10(1 ./ dVec);
 
xMat = (aVec * bVec) * aMat.^2;
yMat = bVec * aVec;
zMat = det(cMat) * (aMat * bMat)';
 
cSum = sum(cMat);
eMean = mean(eMat,2);
eMat = [1 1 1;eMat(2,:)];
cSub = cMat(2:9,2:9);
lin = 1:20;lin(2:2:20) = -lin(2:2:20);
r = rand(1,5);r(find(r<0.5)) = 0;

• 构造正余弦曲线使用函数linspace

t = linspace(0,2*pi,100);
plot(t,sin(t));
hold on;
plot(t,cos(t),'r--');
xlabel('Time(x)');
ylabel('Function value');
title('Sin and Cos functions');
legend('Sin','Cos');
xlim([0 2*pi]);
ylim([-1.4 1.4]);