[Andrew Ng machine learning notes] Chapter V Octave Tutorial

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Chapter V Octave Tutorial

5.1 Basic Operations

In Octave, we can use the PS1 ( '>>') command to change the command prompt. % Followed by a comment .

>>a = 3; %分号的作用是在敲下回车后可以阻止打印输出
>>a = pi;
>>disp(a)
3.1416
>>disp(sprintf('2 decimals:%0.2f'),a) %这里的格式化输出有点类似C语言
2 decimals:3.14
>>disp(sprintf('6 decimals:%0.6f'),a)
6 decimals:3.141593
>>A = [12; 34; 56] %分号的作用是矩阵换行到下一行
A = 
    1 2
    3 4
    5 6
>>v = 1: 0.1: 2 %v从1开始，步长为0.1，一直增加到2
v = 
	1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
>>v = 1: 6 %没有规定步长时默认为1
v = 
	1 2 3 4 5 6
>>ones(2, 3) %用来生成一个维度为2×3的所有元素都为1的矩阵
ans = 
	1 1 1
	1 1 1
>>c = 2 * ones(2, 3)
c = 
	2 2 2
	2 2 2
>>w = zeros(2, 3) %用来生成一个2×3的零矩阵
w = 
	0 0 0
>>w = randn(1, 3) %得到一个维度为1×3的随机矩阵，随机值介于0到1之间
w = 
	0.91744 0.14359 0.84860
>>w = -6 + sqrt(10)*(randn(1, 10000))；
>>hist(w) %绘制出变量w的直方图

>>hist(w, 50) %绘制出变量w的有50个竖条的直方图

>>eye(4) %生成一个4×4的单位矩阵
ans = 
Diagonal Matrix
	1 0 0 0
	0 1 0 0
	0 0 1 0
	0 0 0 1
>>help eye %可以使用help指令查看eye中的一些操作

5.2 Mobile data

If you have a machine learning problem, you how to load data into Octave * in?

>>A = [12; 34; 56];
>>size(A) %返回矩阵的维度，所返回的是一个维度为1×2的矩阵
ans = 3
>>length(A) %返回矩阵A最大维度的大小，一般对向量使用
ans = 3
>>pwd %显示当前路径
>>load featuresX.dat %加载当前路径下的文件featuresX.dat
>>load priceY.dat
>>who %能显示出现在octave中所有的变量

>>featuresX %显示featuresX中的数据
>>whos %显示更加详细的变量信息

>>clear %删除变量指令
>>v = priceY(1: 10) %将向量Y中的前10个元素赋给v
>>save hello.mat v; %将变量v保存为一个名为hello.mat的文件，其中数据为二进制格式
>>save hello.txt v -ascii %将变量v保存为一个名为hello的txt文件，数据用ASCII码编码
>>A(3, 2) %索引A矩阵的第3行第2列的元素
ans = 6
>>A(2, :) %冒号在这里代表所在行/列的所有元素
ans = 3 4
>>A(:, 2)
ans = 
	2
	4
	6
>>A([1, 3], :) %A中第一索引为1和3的所有元素
ans = 
	1 2
	5 6
>>A(:, 2) = [10; 11; 12]
ans = 
	1 10
	3 11
	5 12
>>A = [A, [100, 101, 102]] %在A矩阵的右侧新添一列
A = 
	1 10 100
	3 11 101
	5 12 102
>>A(:) %将A矩阵中的所有元素放到一个向量中
ans = 
	1
	3
	5
	11
	12
	13
	100
	101
	102
>>A = [1 2; 3 4; 5 6];
>>B = [11 12; 13 14; 15 16];
>>C = [A B] %将B矩阵接在A矩阵右侧
C = 
	1 2 11 12
	3 4 13 14
	5 6 15 16
>>C = [A; B] %将B矩阵接在A矩阵的下面
C = 
	1 2
	3 4
	5 6
	11 12
	13 14
	15 16

5.3 calculate data

>>A = [1 2; 3 4; 5 6];
>>B = [11 12; 13 14; 15 16];
>>C = [1 1; 2 2];
>>V = [1; 2; 3];
>>A * C
ans = 
	5 5
	11 11
	17 17
>>A .* B %点乘，A与B中对应元素相乘
ans = 
	11 24
	39 59
	75 96
>>A ./ V %点除，可以用此命令取倒数
ans = 
	1.00000
	0.50000
	0.33333
>>log(v) %对V中所有元素取对数
>>exp(v) %以e为底，以V中元素为指数的幂运算
>>abs(v) %求V中所有元素的绝对值
>>V + ones(length(v), 1) %对V中每个元素都加1
>>A` %求A矩阵的转置
>>a = [1 15 2 0.5];
>>val = max(a); %返回a中最大的元素
>>[val, ind] = max(a) %val是a中最大的元素，ind是a中该元素的索引
val = 15
ind = 2
>>max(A) %得到A矩阵中每一列的最大值
ans = 5 6
>>a < 3 %a中每一个元素与3比较，返回一个布尔值
ans = 1 0 1 1
>>find(a < 3) %找到a中所有小于3的元素并返回它们的索引
ans = 1 3 4
>>A = magic(3) %生成幻方，常用这个函数便捷的生成一个3×3的矩阵
A = 
	8 1 6
	3 5 7
	4 9 2
>>[r, c] = find(A >= 7) %找出A中大于等于7的元素，r，c分别表示它们的所在行、列
r = 
	1
	3
	2
c = 
	1
	2
	3
>>sum(a) %求和函数
>>prod(a) %求积函数
>>floor(a) %向下取整
>>ceil(a) %向上取整
>>max(A, [], 1) %得到A中每一列的最大值，1表示从A的第一维度去取值
ans = 8 9 7
>>max(A, [], 2) %得到每一行的最大值
ans = 
	8
	7
	9
>>max(max(A)) %求A矩阵中的最大值
ans = 9
>>A = magic(9);
>>sum(sum(A .* eye(9))) %求A的对角线元素之和
>>sum(sum(A .* flipud(eye(9)))) %flipud表示使矩阵垂直翻转，可以用来求矩阵A的副对角线之和
>>pinv(A) %求逆

5.4 Data Draw

>>t = [0: 0.01: 0.98];
>>y1 = sin(2 * pi * 4 * t);
>>plot(t, y1) %横轴是变量t，纵轴是变量y1的正弦函数 

>>hold on %在已有的图像上绘制新的图像
>>y2 = cos(2 * pi * 4 * t);
>>plot(t, y2); %横轴是变量t，纵轴是变量y2的余弦函数 
>>xlabel('time');
>>ylabel('value') %给x轴y轴打上标签

>>title('my plot'); %给图像加标题
>>legend('sin', 'cos'); %给图像加图例
>>print –dpng 'myplot.png' %保存图像为png格式

>>subplot(1, 2, 1); %将图像分为一个1*2的格子，也就是前两个参数，然后它使用第一个格子，也就是最后一个参数1的意思
>>axis([0.5, 1, -1, 1]) %改变x轴，y轴的刻度

>>A = magic(5);
>>imagesc(A) %绘制一个5×5的矩阵，由彩色格图构成，不同颜色对用不同的值，用于可视化矩阵

>>imagesc(A), colorbar, colormap gray %生成一个灰度分布图，并在右边加入一个颜色条

5.5 Control statements: for, while, if the statement

>>v = zeros(10, 1);
>>for i = 1 : 10,
>	v(i) = 2^i;
>end; %循环结束必须加end;
v = 
	2
	4
	8
	16
	32
	64
	128
	256
	512
	1024
>>i = 1;
>>while i <= 5,
>	v(i) = 100;
>	i = i + 1;
>end; %v的前5位被赋值为100
>>i = 1;
while true,
>	v(i) = 999
>	i = i + 1
>	if i == 6,
>		break;
>	end;
>end; %999覆盖了v的前5个元素
>>v(1) = 2;
>>if v(1) ==1,
>	disp('The value is one');
>elseif v(1) == 2,
>	disp('The value is two');
>else
>	disp('The value is not one or two');
>end;
The value is two

Define a function in Octave, you need to create a file with your function name to name, then end with the suffix .m .

The first line of code to tell Octave we want a return value, and store it in the variable y. In addition, this function has one argument x.

Before calling the function, first check the path with the pwd command , you must call in order to function in the current path.

>>squareThisNumber(5)
ans = 25
>>addpath('C:\users\JermaineZ\Desktop') %使用这条命令添加参数中的路径到octave的搜索路径

octave function and other programming language barrier, there are two possible return values .

>>[a, b]squareAndCubeThisNumber(5)
a = 25
b = 125

Next we want to write a function to compute unreasonable $\theta$ values corresponding to the cost function $J$。

5.6 vectorization

The data to quantify the operation, make your code more simple and efficient . Let's look at an example. Assume functions $h_\theta(x)=\sum_{i=0}^n \theta_jx_j$. To calculate $h_\theta(x)$ , and requires, but a different way of thinking,can $h_\theta(x)$ as $\theta^tx$, i.e., the inner product of two vectors, which would make the code more compact and efficient. The following is a comparison of the two cases the code.

So, instead of writing a for loop, it is better to write only one line of code. Same, to quantify ideas can be applied in different programming languages.

The cost function, how do we decline to quantify gradients of it? Let's look at the gradient descent update rule:

we can be seen as the gradient descent update rule $\theta:=\theta-\alpha\delta$ , and where $\delta=\frac{1}{m}\sum_{i=1}^m(h_\theta(x^{(i)})-y^{(i)})x^{(i)}$。

In the new update rule, $\theta$ is a $n+1$ dimensional vector, $\alpha$ is a real number, $\delta$ is a $n+1$ vector dimension. Its essence is to do vector subtraction.

We look $\delta$ content. For each $\delta$ corresponding $h_\theta(x^{(i)})-y^{(i)}$ is a real number, $x^{(i)}$ is a $n+1$ -dimensional vector. Its essential feature vector is multiplied with a real number $x$ , so $\delta$ essence is a vector.

Here I will Andrew Ng teacher courseware posted here, in order to deepen understanding.

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