MATLAB應用教程——編程方法、科學計算與系統模擬
徐奇偉
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目錄大綱
目錄
CONTENTS
第 1 章 初識 MATLAB....................................................................................................................1
22 分鐘
1.1 MATLAB 簡介........................................................................................................................1
1.2 工作界面 ..............................................................................................................................2
1.2.1 命令行窗口 .................................................................................................................3
1.2.2 命令歷史記錄窗口........................................................................................................7
1.2.3 當前文件夾 .................................................................................................................9
1.2.4 工作區和變量編輯器.....................................................................................................9
1.3 搜索路徑 ............................................................................................................................ 12
1.3.1 路徑搜索機制 ............................................................................................................ 12
1.3.2 設置搜索路徑 ............................................................................................................ 13
1.4 M 文件 ............................................................................................................................... 14
1.4.1 M 文件編輯器 ............................................................................................................ 14
1.4.2 函數式 M 文件 ........................................................................................................... 15
1.4.3 腳本式 M 文件 ........................................................................................................... 16
1.4.4 M 文件遵循的規則...................................................................................................... 17
1.5 通用命令 ............................................................................................................................ 18
1.5.1 常用命令................................................................................................................... 18
1.5.2 編輯命令................................................................................................................... 19
1.5.3 特殊符號................................................................................................................... 19
1.5.4 數據存取................................................................................................................... 20
1.6 幫助系統 ............................................................................................................................ 22
1.6.1 使用幫助命令 ............................................................................................................ 22
1.6.2 幫助導航................................................................................................................... 24
1.6.3 示例幫助................................................................................................................... 24
1.7 初步使用 MATLAB ............................................................................................................... 25
本章小結 ................................................................................................................................... 26
本章習題 ................................................................................................................................... 26
第 2 章 基礎知識..........................................................................................................................29
30 分鐘
2.1 基本概念 ............................................................................................................................ 29
2.1.1 常量與變量 ............................................................................................................... 29
2.1.2 無窮量和非數值量...................................................................................................... 30
2.1.3 標量、向量、矩陣與數組 ............................................................................................ 31
4 MATLAB 應用教程——編程方法、科學計算與系統模擬
2.1.4 命令、函數、表達式和語句......................................................................................... 33
2.2 數據類型 ............................................................................................................................ 34
2.2.1 數據類型概述 ............................................................................................................ 34
2.2.2 整數型 ...................................................................................................................... 35
2.2.3 浮點數型................................................................................................................... 37
2.2.4 顯示格式................................................................................................................... 39
2.2.5 常用函數................................................................................................................... 39
2.3 基本運算 ............................................................................................................................ 40
2.3.1 算術運算................................................................................................................... 40
2.3.2 關系運算................................................................................................................... 42
2.3.3 邏輯運算................................................................................................................... 43
2.3.4 運算符優先級 ............................................................................................................ 46
2.3.5 常用函數................................................................................................................... 46
2.4 字符串 ............................................................................................................................... 47
2.4.1 字符串變量 ............................................................................................................... 47
2.4.2 一維字符數組 ............................................................................................................ 47
2.4.3 對字符串的操作 ......................................................................................................... 48
2.4.4 二維字符數組 ............................................................................................................ 50
本章小結 ................................................................................................................................... 52
本章習題 ................................................................................................................................... 52
第 3 章 數組.................................................................................................................................55
38 分鐘
3.1 創建數組 ............................................................................................................................ 55
3.1.1 空數組 ...................................................................................................................... 55
3.1.2 一維數組（向量）...................................................................................................... 56
3.1.3 二維數組（矩陣）...................................................................................................... 58
3.1.4 多維數組................................................................................................................... 59
3.1.5 數組拼接................................................................................................................... 60
3.1.6 復數數組................................................................................................................... 61
3.2 創建標準數組...................................................................................................................... 62
3.2.1 0-1數組.................................................................................................................... 62
3.2.2 對角數組................................................................................................................... 63
3.2.3 隨機數組................................................................................................................... 65
3.2.4 幻方數組................................................................................................................... 66
3.3 數組屬性 ............................................................................................................................ 68
3.3.1 數組維度................................................................................................................... 68
3.3.2 數組大小................................................................................................................... 68
3.3.3 數組數據類型 ............................................................................................................ 70
3.3.4 測試函數................................................................................................................... 70
3.4 數組索引與尋址................................................................................................................... 71
目 錄 5
3.4.1 元素存儲次序 ............................................................................................................ 71
3.4.2 元素的下標索引 ......................................................................................................... 72
3.4.3 數組元素賦值 ............................................................................................................ 74
3.4.4 抽取法創建數組 ......................................................................................................... 75
3.5 數組操作 ............................................................................................................................ 76
3.5.1 保存和裝載 ............................................................................................................... 77
3.5.2 擴展和裁剪 ............................................................................................................... 78
3.5.3 形狀改變................................................................................................................... 84
3.5.4 數組查找................................................................................................................... 87
3.5.5 數組排序................................................................................................................... 89
3.5.6 數組運算................................................................................................................... 90
本章小結 ................................................................................................................................... 91
本章習題 ................................................................................................................................... 91
第 4 章 矩陣運算..........................................................................................................................94
40 分鐘
4.1 向量運算 ............................................................................................................................ 94
4.1.1 加減和數乘 ............................................................................................................... 94
4.1.2 點積和叉積 ............................................................................................................... 95
4.2 矩陣基本運算...................................................................................................................... 97
4.2.1 矩陣行列式的值 ......................................................................................................... 97
4.2.2 矩陣的秩................................................................................................................... 97
4.2.3 矩陣的逆與偽逆 ......................................................................................................... 98
4.2.4 矩陣算術運算 ............................................................................................................ 99
4.2.5 矩陣的乘冪 ..............................................................................................................102
4.2.6 矩陣運算函數 ...........................................................................................................103
4.3 矩陣特徵參數.....................................................................................................................105
4.3.1 範數 ........................................................................................................................105
4.3.2 條件數 .....................................................................................................................107
4.3.3 特徵值與特徵向量.....................................................................................................108
4.4 稀疏矩陣 ...........................................................................................................................111
4.4.1 稀疏矩陣存儲方式.....................................................................................................111
4.4.2 基本稀疏矩陣 ...........................................................................................................112
4.4.3 稀疏矩陣函數 ...........................................................................................................116
4.5 矩陣分解 ...........................................................................................................................118
4.5.1 Cholesky 分解............................................................................................................118
4.5.2 不完全 Cholesky 分解 .................................................................................................120
4.5.3 LU 分解 ...................................................................................................................121
4.5.4 不完全 LU 分解 .........................................................................................................122
4.5.5 QR 分解 ...................................................................................................................123
4.5.6 操作 QR 分解結果 .....................................................................................................124
6 MATLAB 應用教程——編程方法、科學計算與系統模擬
4.5.7 奇異值分解 ..............................................................................................................125
本章小結 ..................................................................................................................................126
本章習題 ..................................................................................................................................126
第 5 章 符號運算........................................................................................................................129
23 分鐘
5.1 符號對象 ...........................................................................................................................129
5.1.1 符號對象聲明函數.....................................................................................................129
5.1.2 符號表達式與符號方程 ..............................................................................................133
5.1.3 符號函數..................................................................................................................134
5.1.4 符號矩陣..................................................................................................................134
5.1.5 自變量函數 ..............................................................................................................136
5.2 符號運算函數.....................................................................................................................137
5.2.1 符號變量代換 ...........................................................................................................137
5.2.2 符號對象轉換為數值對象 ...........................................................................................138
5.2.3 符號表達式化簡 ........................................................................................................139
5.2.4 特定符號運算 ...........................................................................................................145
5.2.5 其他符號運算 ...........................................................................................................146
5.3 符號矩陣 ...........................................................................................................................147
5.3.1 元素訪問..................................................................................................................147
5.3.2 加減運算..................................................................................................................148
5.3.3 乘法運算..................................................................................................................149
5.3.4 除法運算..................................................................................................................150
5.3.5 乘方運算..................................................................................................................151
5.3.6 指數運算..................................................................................................................151
5.4 符號方程求解.....................................................................................................................151
5.4.1 代數方程求解 ...........................................................................................................152
5.4.2 微分方程求解 ...........................................................................................................154
本章小結 ..................................................................................................................................157
本章習題 ..................................................................................................................................157
第 6 章 程序設計........................................................................................................................160
21 分鐘
6.1 程序語法規則.....................................................................................................................160
6.1.1 程序設計中的變量.....................................................................................................160
6.1.2 編程方法..................................................................................................................161
6.2 程序結構 ...........................................................................................................................161
6.2.1 順序結構..................................................................................................................162
6.2.2 循環結構..................................................................................................................162
6.2.3 條件結構..................................................................................................................167
6.3 控制語句 ...........................................................................................................................170
6.3.1 continue 語句.............................................................................................................170
目 錄 7
6.3.2 break 語句 ................................................................................................................171
6.3.3 keyboard 語句............................................................................................................172
6.3.4 return 語句................................................................................................................173
6.3.5 input 函數.................................................................................................................174
6.4 程序調試 ...........................................................................................................................174
6.4.1 常見的錯誤類型 ........................................................................................................175
6.4.2 直接調試法 ..............................................................................................................175
6.4.3 工具調試法 ..............................................................................................................176
6.4.4 程序調試命令 ...........................................................................................................177
6.4.5 程序調試剖析 ...........................................................................................................178
本章小結 ..................................................................................................................................181
本章習題 ..................................................................................................................................181
第 7 章 二維繪圖........................................................................................................................184
13 分鐘
7.1 數據可視化 ........................................................................................................................184
7.1.1 劃分子圖..................................................................................................................184
7.1.2 離散數據可視化 ........................................................................................................186
7.1.3 連續函數可視化 ........................................................................................................188
7.2 二維圖形繪制.....................................................................................................................189
7.2.1 二維圖形繪制步驟.....................................................................................................189
7.2.2 基本繪圖函數 ...........................................................................................................190
7.2.3 繪制函數圖 ..............................................................................................................193
7.2.4 特殊坐標圖 ..............................................................................................................197
7.2.5 專用繪圖函數 ...........................................................................................................201
7.3 圖形的修飾 ........................................................................................................................207
7.3.1 色彩、線型和點型.....................................................................................................207
7.3.2 坐標軸的調整 ...........................................................................................................208
7.3.3 刻度和柵格 ..............................................................................................................210
7.3.4 設置坐標框 ..............................................................................................................211
7.3.5 圖形標識與註釋 ........................................................................................................212
7.3.6 圖案填充..................................................................................................................215
本章小結 ..................................................................................................................................217
本章習題 ..................................................................................................................................218
第 8 章 三維繪圖........................................................................................................................222
11 分鐘
8.1 三維圖形繪制.....................................................................................................................222
8.1.1 基本繪圖步驟 ...........................................................................................................222
8.1.2 基本繪圖函數 ...........................................................................................................223
8.1.3 圖形的修飾 ..............................................................................................................226
8.2 網格與曲面圖.....................................................................................................................226
8 MATLAB 應用教程——編程方法、科學計算與系統模擬
8.2.1 生成柵格數據 ...........................................................................................................226
8.2.2 數據生成函數 ...........................................................................................................228
8.2.3 繪制網格圖 ..............................................................................................................229
8.2.4 繪制曲面圖 ..............................................................................................................231
8.2.5 繪制函數圖 ..............................................................................................................232
8.3 專用繪圖函數.....................................................................................................................234
8.3.1 序列圖 .....................................................................................................................234
8.3.2 條形圖 .....................................................................................................................235
8.3.3 餅圖 ........................................................................................................................236
8.3.4 等高線圖..................................................................................................................236
本章小結 ..................................................................................................................................237
本章習題 ..................................................................................................................................238
第 9 章 函數運用........................................................................................................................240
15 分鐘
9.1 函數文件 ...........................................................................................................................240
9.1.1 函數文件結構 ...........................................................................................................240
9.1.2 函數調用..................................................................................................................243
9.2 函數類型 ...........................................................................................................................245
9.2.1 匿名函數..................................................................................................................245
9.2.2 主函數 .....................................................................................................................246
9.2.3 嵌套函數..................................................................................................................246
9.2.4 子函數 .....................................................................................................................247
9.2.5 私有函數..................................................................................................................247
9.2.6 重載函數..................................................................................................................247
9.3 參數傳遞 ...........................................................................................................................248
9.3.1 參數傳遞概述 ...........................................................................................................248
9.3.2 輸入和輸出參數的數目 ..............................................................................................248
9.3.3 可變數目的參數傳遞..................................................................................................249
9.3.4 返回被修改的輸入參數 ..............................................................................................250
9.3.5 全局變量..................................................................................................................251
本章小結 ..................................................................................................................................251
本章習題 ..................................................................................................................................252
第 10 章 Simulink 系統模擬 .......................................................................................................254
16 分鐘
10.1 基本介紹..........................................................................................................................254
10.1.1 運行 Simulink ..........................................................................................................254
10.1.2 初識模塊庫.............................................................................................................255
10.1.3 打開系統模型..........................................................................................................256
10.1.4 保存系統模型..........................................................................................................256
10.1.5 打印模型框圖並生成報告..........................................................................................256
目 錄 9
10.1.6 常用鼠標和鍵盤操作 ................................................................................................257
10.1.7 環境設置 ................................................................................................................258
10.1.8 模擬基本步驟..........................................................................................................259
10.1.9 系統封裝 ................................................................................................................261
10.2 模塊庫介紹 ......................................................................................................................262
10.2.1 信號源模塊庫..........................................................................................................262
10.2.2 信號輸出模塊庫 ......................................................................................................263
10.2.3 表格模塊庫.............................................................................................................264
10.2.4 數學運算模塊庫 ......................................................................................................265
10.2.5 連續模塊庫.............................................................................................................266
10.2.6 非線性模塊庫..........................................................................................................268
10.2.7 離散模塊庫.............................................................................................................269
10.2.8 信號路由模塊庫 ......................................................................................................270
10.3 模塊操作..........................................................................................................................271
10.3.1 Simulink 模塊類型 ....................................................................................................271
10.3.2 模塊的創建.............................................................................................................272
10.3.3 模塊的連接.............................................................................................................273
10.3.4 模塊參數設置..........................................................................................................276
10.4 系統模擬..........................................................................................................................276
10.4.1 設置模擬參數..........................................................................................................277
10.4.2 啟動模擬 ................................................................................................................278
10.4.3 模擬結果分析..........................................................................................................278
10.4.4 簡單系統的模擬分析 ................................................................................................279
本章小結 ..................................................................................................................................283
本章習題 ..................................................................................................................................283
第 11 章 數據分析與優化求解....................................................................................................286
21 分鐘
11.1 多項式計算 ......................................................................................................................286
11.1.1 四則運算 ................................................................................................................286
11.1.2 多項式導函數..........................................................................................................287
11.1.3 多項式導函數求值 ...................................................................................................288
11.2 數據插值..........................................................................................................................289
11.2.1 一維插值 ................................................................................................................289
11.2.2 二維插值 ................................................................................................................291
11.2.3 三維插值 ................................................................................................................293
11.2.4 多維插值 ................................................................................................................294
11.2.5 樣條插值 ................................................................................................................295
11.3 曲線擬合..........................................................................................................................296
11.3.1 多項式擬合.............................................................................................................296
11.3.2 曲線擬合工具..........................................................................................................297
10 MATLAB 應用教程——編程方法、科學計算與系統模擬
11.4 優化問題..........................................................................................................................300
11.4.1 創建優化變量..........................................................................................................301
11.4.2 創建方程問題..........................................................................................................301
11.4.3 創建優化問題..........................................................................................................302
11.4.4 問題求解 ................................................................................................................304
本章小結 ..................................................................................................................................309
本章習題 ..................................................................................................................................309
第 12 章 輸入與輸出 ..................................................................................................................313
17 分鐘
12.1 文件打開與關閉 ................................................................................................................313
12.1.1 打開文件 ................................................................................................................313
12.1.2 關閉文件 ................................................................................................................314
12.2 文件讀寫..........................................................................................................................315
12.2.1 讀取二進制文件 ......................................................................................................315
12.2.2 寫入二進制文件 ......................................................................................................317
12.2.3 寫入文本文件..........................................................................................................318
12.2.4 讀取文本文件..........................................................................................................319
12.2.5 文件格式化與二進制輸入/輸出 ..................................................................................321
12.3 文件位置控制 ...................................................................................................................323
12.3.1 檢測函數 ................................................................................................................323
12.3.2 錯誤提示 ................................................................................................................324
12.3.3 判斷數據位置..........................................................................................................325
12.3.4 指針位置設定..........................................................................................................325
本章小結 ..................................................................................................................................326
本章習題 ..................................................................................................................................326
參考文獻 ......................................................................................................................................330
