5.1 Basic operations
5.2 Moving data around
5.3 Computing on data
5.4 Plotting data
5.5 For while if statement and functions
5.6 Vectorization
看过前两节课后，觉得matlab语言貌似和octave没差， 因此第五节学习打算利用matlab进行学习
基本操作
???怎么代码块都是一个颜色？？```matlab 识别不出来？？丑…
>> 5 + 6
ans = % matlab命令行中 ans 就是这个样子，占地方就占地方吧，不愿修改格式qaq
11
>> 3 - 2
ans =
1
>> 5 * 8
ans =
40
>> 2^6
ans =
64
>> 1 == 2 %false
ans =
0
>> 1 ~= 2 %true [注] 这里不等于写作 ~= 而不是 != (区别于其他编程语言)
ans =
1
>> 1 && 0 %AND
ans =
0
>> 1 || 0 %OR
ans =
1
>> xor(1,0)
ans =
1
变量
>> a = 3
a =
3
>> a = 3; % semicolon ";" supressing output 不输出a
>> b = 'hi';
>> c = (3 >= 1);
>> c
c =
1
>> b
b =
hi
>> a = pi;
>> a
a =
3.1416
>> disp(a) %disp
3.1416
>> disp(sprintf('2 decimals: %0.2f', a))
2 decimals: 3.14
>> disp(sprintf('6 decimals: %0.6f', a))
6 decimals: 3.141593
>> format long %format
>> a
a =
3.141592653589793
>> format short
>> a
a =
3.1416
向量和矩阵
>> A = [1 2; 3 4; 5 6]
A =
1 2
3 4
5 6
>> A = [1 2; %另一种输入矩阵A的方式
3 4;
5 6]
A =
1 2
3 4
5 6
>> v = [ 1 2 3] %行向量
v =
1 2 3
>> v = [1; 2; 3] %列向量
v =
1
2
3
>> v = 1: 0.1: 2 %从 1 到 2 步长为 0.1
v =
1.0000 1.1000 1.2000 1.3000 1.4000 1.5000 1.6000 1.7000 1.8000 1.9000 2.0000
>> v = 1 : 6
v =
1 2 3 4 5 6
>> ones (2, 3) %ones 全 1 矩阵
ans =
1 1 1
1 1 1
>> C = 2*ones(2, 3)
C =
2 2 2
2 2 2
>> w = zeros(1, 3) %zeros 全 0 矩阵
w =
0 0 0
>> w = rand(1, 3) %rand 0~1 随机数
w =
0.8147 0.9058 0.1270
>> w = rand(3, 3)
w =
0.9134 0.2785 0.9649
0.6324 0.5469 0.1576
0.0975 0.9575 0.9706
>> w = randn(1, 3) %randn 高斯随机数
w =
0.7254 -0.0631 0.7147
>> w = -6 + sqrt(10)*(randn(1, 10));
>> w
w =
-5.6077 -1.4568 -12.2009 -6.6252 -9.8195 3.1959 -3.3904 -1.6393 -9.3463 -7.4819
>> hist(w) %hist 绘w的直方图 （图在代码后给出）
>> w = -6 + sqrt(10)*(randn(1, 100));
>> hist(w)
>> w = -6 + sqrt(10)*(randn(1, 10000));
>> hist(w)
>> hist(w,50) %规定列数
>> eye(4) %eye 单位矩阵
ans =
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
>> help eye %help文档
eye Identity matrix.
eye(N) is the N-by-N identity matrix.
eye(M,N) or eye([M,N]) is an M-by-N matrix with 1's on
the diagonal and zeros elsewhere.
eye(SIZE(A)) is the same size as A.
eye with no arguments is the scalar 1.
eye(..., CLASSNAME) is a matrix with ones of class specified by
CLASSNAME on the diagonal and zeros elsewhere.
eye(..., 'like', Y) is an identity matrix with the same data type, sparsity,
and complexity (real or complex) as the numeric variable Y.
Note: The size inputs M and N should be nonnegative integers.
Negative integers are treated as 0.
Example:
x = eye(2,3,'int8');
See also speye, ones, zeros, rand, randn.
eye 的参考页
名为 eye 的其他函数
>>
w = -6 + sqrt(10)*(randn(1, 10));
w = -6 + sqrt(10)*(randn(1, 100));
w = -6 + sqrt(10)*(randn(1, 10000));
>> clear %清除工作区中所有变量
>> A = [1 2;3 4; 5 6]
A =
1 2
3 4
5 6
>> size(A) %size 矩阵 A 大小
ans =
3 2
>> sz = size(A)
sz =
3 2
>> size(sz)
ans =
1 2
>> size(A, 1) %A矩阵的第一维度的大小 即矩阵行数
ans =
3
>> size(A, 2) %A矩阵的第二维度的大小 即矩阵列数
ans =
2
>> v = [1 2 3 4]
v =
1 2 3 4
>> length(v) %最大维度的大小
ans =
4
>> length(A) %但一般 length 多用于求向量长度
ans =
3
>> length([1; 2; 3; 4; 5])
ans =
5
>> pwd %pwd 当前路径
ans =
C:\Users\asus\Documents\MATLAB
>> cd 'C:\Users\asus\Desktop' %cd 修改路径(到桌面Desktop)
>> ls %ls 当前路径下文档
2020winter Sublime Text 3.lnk lab01.zip
Adobe Dreamweaver CC 2018.lnk Typora.lnk
>> load featureX.dat
>> load priceY.dat
>> load('featureX.dat')
>> who %列出所有变量
您的变量为: %汉化了的matlab
A ans featureX priceY sz v
>> whos %列出所有变量详细信息
Name Size Bytes Class Attributes
A 3x2 48 double
ans 1x30 60 char
featureX 19x2 304 double
priceY 19x1 152 double
sz 1x2 16 double
v 1x4 32 double
>> featureX
featureX =
2104 3
1400 3
2400 3
1416 2
3000 4
1985 4
1534 3
1427 3
1330 3
1494 3
1940 4
2000 3
1890 3
4478 5
1238 3
2300 4
1320 2
1236 3
2609 4
>> size(featureX)
ans =
19 2
>> size(priceY)
ans =
19 1
>> clear featureX %清除某一变量
>> whos
Name Size Bytes Class Attributes
A 3x2 48 double
ans 1x2 16 double
priceY 19x1 152 double
sz 1x2 16 double
v 1x4 32 double
>> v = priceY(1:10) %取priceY前十列
v =
3399
3299
3609
2320
5399
2999
3149
1989
2120
2425
>> who
您的变量为:
A ans priceY sz v
>> whos
Name Size Bytes Class Attributes
A 3x2 48 double
ans 1x2 16 double
priceY 19x1 152 double
sz 1x2 16 double
v 10x1 80 double
>> save hello.mat v; %save 存储文件
>> clear
>> load hello.mat
>> whos
Name Size Bytes Class Attributes
v 10x1 80 double
>> v
v =
3399
3299
3609
2320
5399
2999
3149
1989
2120
2425
>> save hello.txt v -ascii %save as text(ASCII)
hello.txt
索引
>> A = [1 2; 3 4; 5 6]
A =
1 2
3 4
5 6
>> A(3, 2) %index
ans =
6
>> A(2,:) % ":" means every element along that row/column
ans =
3 4
>> A(:,2)
ans =
2
4
6
>> A([1 3], :) %第一行和第三行
ans =
1 2
5 6
>> A(:,2) = [10; 11; 12] %替换列
A =
1 10
3 11
5 12
>> A = [A, [100; 101; 102]] %append another column vector to the right
A =
1 10 100
3 11 101
5 12 102
>> A(:) %把A的所有元素放入一个列向量
ans =
1
3
5
10
11
12
100
101
102
>> A = [1 2; 3 4; 5 6]
A =
1 2
3 4
5 6
>> B = [11 12; 13 14; 15 16]
B =
11 12
13 14
15 16
>> C = [A B] %左右重组
C =
1 2 11 12
3 4 13 14
5 6 15 16
>> C = [A; B] %上下重组
C =
1 2
3 4
5 6
11 12
13 14
15 16
>> size(C)
ans =
6 2
>> A = [1 2; 3 4; 5 6]
A =
1 2
3 4
5 6
>> B = [11 12; 13 14; 15 16]
B =
11 12
13 14
15 16
>> C = [1 1; 2 2]
C =
1 1
2 2
>> A*C
ans =
5 5
11 11
17 17
>> A .* B %A,B相对应的元素相乘 .一般表示元素之间的运算
ans =
11 24
39 56
75 96
>> A
A =
1 2
3 4
5 6
>> A .^ 2 %这里^ 与 2 之间要加空格！
ans =
1 4
9 16
25 36
>> v = [1; 2; 3]
v =
1
2
3
>> 1 ./ v
ans =
1.0000
0.5000
0.3333
>> 1 ./ A
ans =
1.0000 0.5000
0.3333 0.2500
0.2000 0.1667
>> log(v)
ans =
0
0.6931
1.0986
>> exp(v)
ans =
2.7183
7.3891
20.0855
>> abs(v)
ans =
1
2
3
>> abs([-1; -1; -3])
ans =
1
1
3
>> -v
ans =
-1
-2
-3
>> v + ones(length(v),1) %对v中每个元素加一
ans =
2
3
4
>> v + 1 %对v中每个元素加一的另一种方法
ans =
2
3
4
>> A' %转置
ans =
1 3 5
2 4 6
>> (A')'
ans =
1 2
3 4
5 6
>> a = [1 15 2 0.5]
a =
1.0000 15.0000 2.0000 0.5000
>> val = max(a) %A中元素最大值
val =
15
>> [val, ind] = max(a) %ind=index 索引 最大值元素的位置
val =
15
ind =
2
>> max(A) %A的每一列的最大值
ans =
5 6
>> a < 3 %a的每一个元素与3进行比较
ans =
1 0 1 1
>> a
a =
1.0000 15.0000 2.0000 0.5000
>> find(a < 3) %返回值为其索引值
ans =
1 3 4
>> A = magic(3) % magic矩阵 每行每列元素的和都是同一个数
A =
8 1 6
3 5 7
4 9 2
>> [r, c] = find( A >= 7) %r=row c=column
r =
1
3
2
c =
1
2
3
>> a
a =
1.0000 15.0000 2.0000 0.5000
>> sum(a)
ans =
18.5000
>> prod(a) %四个元素乘积
ans =
15
>> floor(a)
ans =
1 15 2 0
>> ceil(a)
ans =
1 15 2 1
>> ceiling(a)
未定义函数或变量 'ceiling'。
%Andrew Ng老师说ceiling=ceil 但在matlab中没有这个命令 可能仅适用于octave
>> rand(3) %3*3随机矩阵
ans =
0.0581 0.1216 0.3025
0.3230 0.7500 0.6023
0.8535 0.4727 0.2124
>> max(rand(3),rand(3)) %由两个3*3矩阵中对应较大元素组成的
ans =
0.6958 0.7344 0.7514
0.8546 0.9334 0.9937
0.3971 0.8652 0.4279
>> A
A =
8 1 6
3 5 7
4 9 2
>> max(A,[],1) %A矩阵每一列最大值
ans =
8 9 7
>> max(A,[],2) %A矩阵每一行最大值 max默认求每一列最大值
ans =
8
7
9
>> max(max(A)) %求A中最大元素
ans =
9
>> A(:)
ans =
8
3
4
1
5
9
6
7
2
>> max(A(:)) %求A中最大元素另一种方法
ans =
9
>> A = magic(9)
A =
47 58 69 80 1 12 23 34 45
57 68 79 9 11 22 33 44 46
67 78 8 10 21 32 43 54 56
77 7 18 20 31 42 53 55 66
6 17 19 30 41 52 63 65 76
16 27 29 40 51 62 64 75 5
26 28 39 50 61 72 74 4 15
36 38 49 60 71 73 3 14 25
37 48 59 70 81 2 13 24 35
>> sum(A,1) %取A的每一列相加
ans =
369 369 369 369 369 369 369 369 369
>> sum(A,2) %取A的每一行相加
ans =
369
369
369
369
369
369
369
369
369
>> eye(9)
ans =
1 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0
0 0 0 0 1 0 0 0 0
0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 1 0 0
0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 1
>> A .* eye(9)
ans =
47 0 0 0 0 0 0 0 0
0 68 0 0 0 0 0 0 0
0 0 8 0 0 0 0 0 0
0 0 0 20 0 0 0 0 0
0 0 0 0 41 0 0 0 0
0 0 0 0 0 62 0 0 0
0 0 0 0 0 0 74 0 0
0 0 0 0 0 0 0 14 0
0 0 0 0 0 0 0 0 35
>> sum(sum(A .* eye(9))) %对角线之和
ans =
369
>> sum(sum(A .*flipud(eye(9)))) %flipud矩阵垂直翻转 对另一条对角线求和
ans =
369
>> A = magic(3)
A =
8 1 6
3 5 7
4 9 2
>> pinv(A) %INVERSE 求A的逆
ans =
0.1472 -0.1444 0.0639
-0.0611 0.0222 0.1056
-0.0194 0.1889 -0.1028
>> temp = pinv(A)
temp =
0.1472 -0.1444 0.0639
-0.0611 0.0222 0.1056
-0.0194 0.1889 -0.1028
>> temp * A
ans =
1.0000 0.0000 -0.0000
-0.0000 1.0000 0.0000
0.0000 -0.0000 1.0000
可视化
>> t = [0: 0.01: 0.98];
>> y1 = sin(2 * pi * 4 * t);
>> plot(t, y1);
>> y2 = cos(2 * pi * 4 * t);
>> plot(t, y2);
>> plot(t, y1);
>> hold on; %在同一个图绘制两条曲线
>> plot(t, y2); %plot(t, y2, 'r') 红色线
>> xlabel('time')
>> ylabel('value')
>> legend('sin','cos')
>> title('mt plot')
>> print -dpng 'myPlot.png' %保存到本地
>> close %关闭图像
>> figure(1);plot(t, y1);
>> figure(2);plot(t, y2); %两个图像
>> subplot(1, 2, 1); %Divides plot a 1*2 grid, access first element 将图像分成1*2的网格，现在使用第一个格子
>> plot(t, y1);
>> subplot(1, 2, 2);
>> plot(t, y2);
>> axis([0.5 1 -1 1]) %改变x轴和y轴
>> clf; %清除一个图像
>> A = magic(5)
A =
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9
>> imagesc(A) %可视化一个矩阵 不同的颜色对应不同的值
>> imagesc(A), colorbar, colormap gray;
>> imagesc(magic(15)), colorbar, colormap gray;
控制语句
>> v = zeros(10, 1)
v =
0
0
0
0
0
0
0
0
0
0
>> for i = 1 : 10, %这里空格没有意义， 只是为了让结构更加明显
v(i) = 2^i; % for
end;
>> v
v =
2
4
8
16
32
64
128
256
512
1024
>> indices = 1 : 10;
>> indices
indices =
1 2 3 4 5 6 7 8 9 10
>> for i = indices,
disp(i);
end;
1
2
3
4
5
6
7
8
9
10
>> v
v =
2
4
8
16
32
64
128
256
512
1024
>> i = 1;
>> while i <= 5, %while
v(i) = 100;
i = i + 1;
end;
>> v
v =
100
100
100
100
100
64
128
256
512
1024
>> i = 1;
>> while true,
v(i) = 999;
i = i + 1;
if i == 6,
break; %break
end;
end;
>> v
v =
999
999
999
999
999
64
128
256
512
1024
函数
>> pwd
ans =
C:\Users\asus\Documents\MATLAB
>> cd 'C:\Users\asus\Desktop'
%在桌面上事先建立一个suqareThisNumber.m文档， 用写字板打开后是一个函数
%function y = suqareThisNumber(x)
%y = x^2;
%这里推荐用写字板而不是记事本打开文件
>> squareThisNumber(5)
ans =
25
>> addpath('C:\Users\asus\Desktop') %不必修改路径， 而是将路径添加到搜索路径中
>> cd 'C:\'
>> squareThisNumber(5)
ans =
25
>> pwd
ans =
C:\
>> %返回多个值
%建立一个文件在桌面 squareAndCubeThisNumber.m 内容如下
%function [y1, y2] = squareAndCubeThisNumber(x)
%y1 = x^2;
%y2 = x^3;
>> [a, b] = squareAndCubeThisNumber(5);
>> a
a =
25
>> b
b =
125
Cost function
%costFunction.m
function J = costFunctionJ(X, y, theta)
%X is the "design matrix" containing our training examples.
%y is the class labels
m = size(X, 1); %Number of training examples.
predictions = X*theta; %Predictions of hypothesis on all m examples.
sqrErrors = (predictions - y) .^ 2; %square errors.
J = 1/(2*m) * sum(sqrErrors);
>> X = [1 1; 1 2; 1 3]
X =
1 1
1 2
1 3
>> y = [1; 2; 3]
y =
1
2
3
>> theta = [0; 1];
>> j = costFunction(X, y, theta)
j =
0
>> theta = [0; 0];
>> j = costFunction(X, y, theta)
j =
2.3333
向量化
