Octave 常用命令

GNU Octave 官方文档

GNU Octave Documentation(Online)
GNU Octave Documentation(PDF)

安装额外的包

Installing and Removing Packages
Octave Forge

% 卸载包
pkg uninstall io statistics

% 从 Octave Forge 仓库直接安装包
pkg install -forge io statistics

% 从本地文件安装包
pkg install io.2.4.12.tar.gz statistics.1.4.1.tar.gz

% 从url安装包
pkg install 'http://somewebsite.org/statistics-1.4.1.tar.gz'

% 检查 Octave Forge 仓库更新所有过期的包，更新单个包使用 install 命令
pkg update

% 加载包
pkg load statistics

% 列出当前安装的包
pkg list

% 给出包的简短描述
pkg describe -verbose statistics

Package Name  | Version | Installation directory
--------------+---------+-----------------------
          io *|  2.4.12 | /Users/guoli/octave/io-2.4.12
  statistics *|   1.4.1 | /Users/guoli/octave/statistics-1.4.2

命令行常用设置

Customizing the Prompt

% 设置命令行提示符，可以将该命令添加到~/.octaverc文件中
PS('>> ')

% 显示当前环境所有变量
whos

三元操作 (ternary operation)

如果 n > 1 则返回 1，如果 n <= 1 则返回 0。此方法可用于绘制分段函数。

(n > 1) * 1

因为逻辑比较会被转换为 1 或 0，可以将逻辑比较乘以希望的输出，结果就是 0 或期望输出。

范围表达式

Ranges

% 范围表达式生成一个行向量(row vector)
1 : 2 : 5               % 1 3 5
1 : -.3 : 0             % 1 0.7 0.4 0.1
1 : 5                   % 1 2 3 4 5

索引表达式

Index Expressions

a = 1 : 5;
a(1)                    % 1
a(end)                  % 5
a(2:end)                % 2 3 4 5
a([2, end])             % 2 5
a(:)                    % change to the column-vector

% append new element to vector
a[end+1] = 6;           % works for both row- and column-vectors
a = [a 6];              % works for row-vectors
a = [a; 6];             % works for column-vectors

% delete a element
a(end) = [];

# append new element to matrix
A = eye(2);             % 2x2 identity matrix
A[end+1, :] = 3;        % get 3x2 matrix
A[end+1, :] = [4 5];    % get 4x2 matrix
A = [A; [6 7]];         % get 5x2 matrix

A = eye(2);             % 2x2 identity matrix
A[:, end+1] = 3;        % get 2x3 matrix
A[:, end+1] = [4; 5];   % get 2x4 matrix
A = [A [6; 7]];         % get 2x5 matrix

交换矩阵中的两行或两列

E = eye(5);
E([3 5], :) = E([5 3], :)   % 交换第3行和第5行
E(:, [4 5]) = E(:, [5 4])   % 交换第4列和第5列

生成随机数

% 生成一个随机数在1-10之间的2x3x4矩阵
randi(10, 2, 3, 4);

% 生成一个随机数在3-9之间的3x3方阵
randi([3,9], 3);

将向量 v 中的任意整数值转换成 one-hot 向量

v = 1:10;
E = eye(10);
E(:, v(3));

函数句柄和匿名函数

Function Handles
Anonymous Functions

命令与函数语法(MATLAB)

大专栏  Octave 常用命令x.html">Command vs. Function Syntax

绘图

Plot Annotations
Printing and Saving Plots
Axis Configuration

demo plot;
demo ('subplot', 1);
demo surf;

数据准备

x = linspace(-3,3,10);
y = linspace(-3,3,10);

% the rows of metrices X are copies of vector x,
% and the columns of metrices Y are copies of vector y.
[X Y] = meshgrid(x, y);

% below will always assert true
y' * x == X .* Y;

% function of sombrero
f = @(X,Y) sin(sqrt(X.^2+Y.^2))./(sqrt(X.^2+Y.^2))
Z = f(X, Y);

2D绘图

% produce 2-D plot
plot(x, y, 'k+', 'LineWidth', 2, 'MarkerSize', 7);

散点图

% draw a 3-D scatter plot
scatter3(X, Y, Z, 'filled');

等高线图

% create 2-D contour plot
contour(Z, 'ShowText', 'on');
colorbar;

% create 3-D contour plot
contour3(Z, 'ShowText', 'on');

3D网格图

% plot a 3-D wireframe mesh.
figure 1;
clf;
mesh(Z);

3D surface 图

% plot a 3-D surface mesh.
figure 1;
clf;
surf(Z);
shading interp;
colorbar;

% plot a function with lots of local maxima and minima.
surf(peaks);
peaks; % same as above

数轴设置

% axis configuration
axis;
axis([-3 3 -1 1], "square");    % "square", "equal", "normal"
axis("auto");                   % "auto", "manual", "tight", "image", "vis3d"
xlim;
xlim([-3 3]);
xlim("auto");

% set axis location
set(gca, 'xaxislocation', 'origin');    % {'bottom'}, 'origin', 'top'
set(gca, 'yaxislocation', 'origin');    % {'left'}, 'origin', 'right'
set(gca, 'box', 'off');

% plot annotations
title('surface of peaks');
xlabel('x axis');
ylabel('y axis');
zlabel('z axis');
legend('peaks');

保存图形

% save picture to the file
print peaks.png

3D正态分布函数

x = y = linspace (-5, 5);
[X Y] = meshgrid(x, y);
f = @(X, Y, mu, sigma) exp (-((X - mu(1)).^2 + (Y - mu(2)).^2) ./ (2 * sigma^2));
Z = f(X, Y, [0 0], 1);
surf(X, Y, Z);

分段函数

x = linspace (-3, 3);
f1 = @(x) (-x + 1).*(x < 1) + (x - 1).*(x >= 1);
f2 = @(x) (x - 1).*(x > -1);
subplot(121);
axis square;
plot(x, f1(x), 'LineWidth', 2);
subplot(122);
axis square;
plot(x, f2(x), 'LineWidth', 2);

矩阵运算

3维矩阵转置

矩阵操作

Z = reshape(1:24, 2, 3, 4);

permute(Z, [1,3,2]) % 将第2维与第3维进行转置
permute(Z, [3,2,1]) % 将第1维与第3维进行转置

线性代数

简化(行)阶梯形矩阵 (Reduced Row Echelon Form)

A = magic(3);
rref(A)