第1页 / 共528页
第2页 / 共528页
第3页 / 共528页
第4页 / 共528页
第5页 / 共528页
第6页 / 共528页
第7页 / 共528页
第8页 / 共528页
MATLAB工具箱大全，各种算法.pdf
Matlab工具箱应用 苏金明
前言
目录
第一篇 统计工具箱
第 1 章统计工具箱简介
第2 章概 率 分 布
第3 章样 本 描 述
第4 章线 性 模 型
第5 章非线性模型
第6 章假 设 检 验
第7 章分布的检验
第8 章非参数检验
第 9 章多 元 统 计
第10 章统计过程控制
第 11 章试 验 设 计
第12 章统 计 图
第13 章文件输入/输出
第 14 章统 计 演 示
第二篇优化工具箱
第 15 章优化工具箱概述
第16 章无约束最优化问题
第17 章有约束最优化问题
第 18 章二 次 规 划
第 19 章多目标规划
第20 章最大最小化
第 21 章半无限问题
第 22 章最小二乘问题
第 23 章方 程 求 解
第24 章大 型 课 题
第三篇偏微分方程数值解工具箱
第 25 章偏微分方程数值解工具箱概述
第26 章偏微分方程数值解有关函数介绍
第 27 章利用图形用户界面（GUI）求解偏微分方程的一般过程
第 28 章几种常见的偏微分方程数值求解问题
第 29 章应 用 模 式
第四篇 样条工具箱
第 30 章样条工具箱及样条曲线简介
第 31 章三次样条曲线
第 32 章分段多项式（PP）样条曲线
第 33 章 B 样条曲线
第34 章有理样条曲线
第 35 章操作器类函数
第36 章样条曲线的端点与节点处理类函数
第37 章解线性方程组类函数
第38 章样条 GUI 函数
第五篇信号处理工具箱
第 39 章采样与波形发生
第40 章模拟滤波器设计
第41 章数字滤波器设计
第42 章滤波器分析
第 43 章 随机信号的参数模型和功率谱估计
第六篇曲线拟合工具箱
第 44 章数据预处理
第 45 章曲 线 拟 合
参考 文 献
前 言
许多人很喜欢 MATLAB，觉得它是一个很不错的软件，能够给从事科学计算的同志带来
更多的便利和可能性。
MATLAB 好，首先表现在它的不断创新。MATLAB 的每次更新都能给人以惊喜，要么
是原有的功能得到扩充或提高，要么是出现新的工具箱或实用工具，要么是整体性能得到改
进。DDE、OLE、ActiveX、COM 这样一些流行或曾经流行的标准和技术，在 MATLAB 中
都被合理地吸收和利用。其次，它能满足个性化的需求。MATLAB 提供了几十个工具箱。利
用这些工具箱，可以解决不同领域的数学问题。而且，由于 MATLAB 的可扩展性，用户还
可以编写自己领域的工具箱，提高工作效率。除了工具箱以外，MATLAB 还提供了琳琅满目
的实用工具。利用它们，可以实现不同的功能。比如你用 MATLAB 开发了一套新算法，是
M 文件，但不想让别人看到源代码，想保密，于是考虑做成独立应用程序，用 mcc 来做。如
果 mcc 解决不了，就用运行时服务器。如果想把该算法集成到 VB、VC 中去，但不想重写代
码，可以用 COM 生成器把对应的 M 文件做成 COM 组件，然后集成。所以，只要你需要，
总有一款适合你。
MATLAB 是解释型语言，运行速度比较慢。但从 MATLAB 6.5 开始，它比较全面地提速
了，提速后的运行速度与向量化后的效果相当。虽然在某些情况下，仍然需要通过循环向量
化或预分配数组内存空间等技巧来加速运行。但我们仍然能看到 MATLAB 所做的努力。
MATLAB 提供了多种方法来加速运行。通过 Profiler 工具或 Profile 函数，可以获取每行代码
的运行情况，包括运行时间和调用次数等，因而知道哪些语句行花费的时间最多，可以集中
精力进行改进。
作为一个专业的科学计算软件，MATLAB 的功能首先在于应用，即应用现有函数和工具
（箱），解决具体问题。在用的过程中，用户会发现问题，并逐渐有更高的要求，比如想开发
自己的算法，开发速度更快的应用，或者想用 VC、VB 等开发更美观的界面等。所以，用而
优则开发，这是很自然的追求，也是大多数 MATLAB 学习者要走的路。
整套书共分三册，分别偏重于入门、工具箱应用和接口。第一册分计算、绘图和编程三
部分，介绍了 MATLAB 的入门知识和技巧。第二册主要介绍我们所熟悉的统计、优化、偏
微分方程数值解、样条、信号处理和曲线拟合等六个工具箱的最新版本。第三册介绍 MATLAB
与外部程序的接口，包括 MATLAB 与 FORTRAN、C、Visual Basic、Visual C++、Excel、SPSS
以及硬件等的接口技术，其中还介绍了 MATLAB 编译器、COM 生成器、Excel 生成器、运
行时服务器、报表生成器、Excel Link、ImportWizard、Profiler 等工具的用法。
应该说，除了受专业限制，有一些工具箱没有介绍以外，MATLAB 所提供的大部分功能
在这三本书中都有不同程度的阐述，只要认真阅读，终会有所收获。当你在学习的过程中，
感觉自己一天天变得更加充实，因而内心充满喜悦的时候，我们为你高兴！
·I·
关于这本书
本书比较全面地介绍了 MATLAB 的统计、优化、偏微分方程数值解、样条、信号处理
和曲线拟合等 6 个工具箱。适合于相关专业的大学生、研究生和科研工作人员阅读。
统计工具箱一篇介绍了概率分布（包括若干分布的密度函数、累加函数、参数估计、累
加函数逆函数、统计量和随机数生成等）、方差分析、假设检验、回归分析、判别分析、聚类
分析、主成分分析、试验设计、统计过程控制和数十个常用统计图形、多因子方差分析、多
元方差分析、分布检验、非参数检验、稳健性回归以及决策树、K 均值聚类和因子分析等内
容。
优化工具箱一篇结合若干实例介绍了常见的线性规划、二次规划、非线性规划、多目标
规划、最大最小化、半无限问题、最小二乘问题和方程求解以及大型优化问题的求解方法。
偏微分方程数值解工具箱一篇介绍了相关函数和图形用户界面的用法，介绍了包括结构
力学平面应力平面应变、静电学、静磁学、电磁学、热传导、发散问题等多个领域的应用模
式。
样条工具箱一篇介绍了 B 样条、三次样条、分段多项式样条以及样条的图形用户界面等。
信号处理工具箱一篇结合信号处理的算法及在工程中的运用实践，系统地介绍了
MATLAB 在信号处理中的设计技术和技巧。对模拟和数字滤波器的设计思路，滤波器的分析
和随机信号功率谱估计的实际运用等进行了详细的分析。在对函数进行分析的基础上，列举
了大量的应用设计实例,使 MATLAB 与信号处理得到有机结合。
曲线拟合工具箱一篇介绍了利用各种工具进行数据预处理、曲线拟合和残差分析的方法
和操作过程。
统计工具箱、优化工具箱和偏微分方程数值解工具箱由苏金明、张莲花负责编写，样条
工具箱由阮沈勇编写，信号处理工具箱由刘波编写，曲线拟合工具箱由王永利编写。王能峰、
钟国华、桑群芳等参与了部分内容的编写。
此外，刘宏、李攀峰等提供了帮助，苏华惠和刘玉珊做了大量的录入工作，在此一并表
示感谢！
由于能力有限，书中错误和不足之处在所难免，谨请读者批评指正！有任何问题请通过
电子邮件与我们联系：
苏金明 s_jm@263.net.cn
张莲花 zhlh@cdut.edu.cn
刘 波 sclibo@mail.sc.cninfo.net
阮沈勇 r_shenyong@yahoo.com.cn
王永利 wy_11971@tom.com
编 者
2003.9
·II·
目 录
第一篇 统计工具箱
第 1 章 统计工具箱简介 ·····································································································1
1.1 统计工具箱的内容································································································································ 1
1.2 数学符号约定 ······································································································································· 2
第 2 章 概率分布················································································································3
2.1 概率密度函数 ······································································································································· 3
2.1.1 基本数学原理 ··························································································································· 3
2.1.2 有关函数介绍 ··························································································································· 4
2.2 累加分布函数 ······································································································································· 6
2.2.1 基本数学原理 ··························································································································· 6
2.2.2 有关函数介绍 ··························································································································· 6
2.3 参数估计··············································································································································· 8
2.3.1 基本数学原理 ··························································································································· 8
2.3.2 有关函数介绍 ··························································································································· 9
2.4 逆累加分布函数 ··································································································································11
2.4.1 基本数学原理 ··························································································································11
2.4.2 有关函数介绍 ··························································································································11
2.5 随机数的生成 ······································································································································13
2.5.1 随机数生成的基本原理 ···········································································································13
2.5.2 有关函数介绍 ··························································································································14
2.6 分布函数的统计量估计·······················································································································15
第 3 章 样本描述·············································································································· 18
3.1 概述 ·····················································································································································18
3.2 描述集中趋势的统计量·······················································································································18
3.2.1 几何均值··································································································································18
3.2.2 调和均值··································································································································18
3.2.3 算术平均值 ······························································································································19
3.2.4 中值··········································································································································19
3.2.5 截尾均值··································································································································20
3.3 描述离散趋势的统计量·······················································································································20
3.3.1 内四分极值 ······························································································································20
3.3.2 均值绝对差 ······························································································································20
3.3.3 极差··········································································································································21
3.3.4 方差··········································································································································21
·III·
3.3.5 标准差······································································································································22
3.4 分组数据描述 ······································································································································22
3.5 包含缺失数据的样本描述 ···················································································································23
3.6 百分位数和图形描述···························································································································23
3.7 自助统计量··········································································································································24
3.8 中心矩··················································································································································25
3.9 相关系数··············································································································································26
3.10 协方差矩阵 ········································································································································26
3.11 峰度和偏度 ········································································································································26
3.11.1 峰度········································································································································26
3.11.2 偏度········································································································································27
3.12 频数表················································································································································27
3.13 列联表················································································································································28
第 4 章 线性模型·············································································································· 29
4.1 方差分析··············································································································································29
4.1.1 单因子方差分析·······················································································································29
4.1.2 双因子方差分析·······················································································································32
4.1.3 多因素方差分析·······················································································································36
4.1.4 方差分析工具 ··························································································································39
4.2 线性回归··············································································································································40
4.2.1 基本数学原理 ··························································································································41
4.2.2 有关函数介绍 ··························································································································43
4.2.3 应用实例··································································································································47
4.2.4 岭回归······································································································································56
4.3 扩展线性模型 ······································································································································57
4.4 多项式拟合··········································································································································60
4.5 稳健回归··············································································································································61
4.6 二次响应面模型 ··································································································································63
第 5 章 非线性模型 ·········································································································· 67
5.1 非线性最小二乘 ··································································································································67
5.2 决策树··················································································································································75
第 6 章 假设检验·············································································································· 79
6.1 单个样本的 t 检验 ·······························································································································79
6.1.1 基本数学原理 ··························································································································79
6.1.2 有关函数介绍 ··························································································································79
6.1.3 应用实例··································································································································80
6.2 两个样本的 t 检验 ·······························································································································80
6.2.1 基本数学原理 ··························································································································80
6.2.2 有关函数介绍 ··························································································································81
6.2.3 应用实例··································································································································81
·IV·
6.3 z 检验···················································································································································82
第 7 章 分布的检验 ·········································································································· 84
7.1 Jarque-Bera 检验 ··································································································································84
7.1.1 基本数学原理 ··························································································································84
7.1.2 有关函数介绍 ··························································································································84
7.1.3 应用实例··································································································································85
7.2 单样本的 Kolmogorov-Smirnov 检验···································································································85
7.2.1 基本数学原理 ··························································································································85
7.2.2 有关函数介绍 ··························································································································86
7.2.3 应用实例··································································································································86
7.3 两个样本的 Kolmogorov-Smirnov 检验·······························································································88
7.3.1 基本数学原理 ··························································································································88
7.3.2 有关函数介绍 ··························································································································89
7.3.3 应用实例··································································································································89
7.4 Lilliefors 检验 ······································································································································91
7.4.1 基本数学原理 ··························································································································91
7.4.2 有关函数介绍 ··························································································································91
7.4.3 应用举例··································································································································91
第 8 章 非参数检验 ·········································································································· 94
8.1 Kruskal-Wallis 检验······························································································································94
8.1.1 基本数学原理 ··························································································································94
8.1.2 有关函数介绍 ··························································································································94
8.1.3 应用实例··································································································································95
8.2 Friedman 检验······································································································································96
8.2.1 基本数学原理 ··························································································································96
8.2.2 有关函数介绍 ··························································································································96
8.2.3 应用实例··································································································································97
8.3 秩和检验··············································································································································98
8.3.1 基本数学原理 ··························································································································98
8.3.2 有关函数介绍 ··························································································································98
8.3.3 应用举例··································································································································98
8.4 符号秩检验··········································································································································99
8.4.1 基本数学原理 ··························································································································99
8.4.2 关函数介绍 ······························································································································99
8.4.3 应用实例··································································································································99
8.5 符号检验············································································································································100
8.5.1 基本数学原理 ························································································································100
8.5.2 有关函数介绍 ························································································································100
8.5.3 应用实例································································································································101
第 9 章 多元统计·············································································································102
·V·
9.1 判别分析············································································································································102
9.1.1 基本数学原理 ························································································································102
9.1.2 有关函数介绍 ························································································································103
9.1.3 应用综合实例 ························································································································104
9.2 系统聚类分析 ····································································································································105
9.2.1 基本数学原理 ························································································································105
9.2.2 有关函数介绍 ························································································································107
9.2.3 应用综合实例 ························································································································113
9.3 K 均值聚类 ········································································································································122
9.4 主成分分析········································································································································125
9.4.1 有关函数介绍 ························································································································125
9.4.2 应用综合实例 ························································································································127
9.5 因子分析············································································································································135
9.6 多元方差分析 ····································································································································139
9.6.1 单因素多元方差分析·············································································································139
9.6.2 分组聚类································································································································142
9.6.3 多元比较································································································································143
第 10 章 统计过程控制····································································································147
10.1 过程控制图 ······································································································································147
10.1.1 基本原理······························································································································147
10.1.2 有关函数介绍 ······················································································································147
10.2 过程性能图 ······································································································································151
第 11 章 试验设计···········································································································154
11.1 完全析因设计 ··································································································································154
11.1.1 基本原理 ······························································································································154
11.1.2 有关函数介绍·······················································································································155
11.2 不完全析因设计·······························································································································155
11.2.1 基本数学原理·······················································································································155
11.2.2 有关函数介绍·······················································································································156
11.2.3 应用实例 ······························································································································156
11.3 响应面设计 ······································································································································158
11.4 D-优化设计 ······································································································································159
11.4.1 基本数学原理·······················································································································159
11.4.2 有关函数介绍·······················································································································159
11.4.3 综合实例 ······························································································································163
第 12 章 统计图 ··············································································································165
12.1 箱形图··············································································································································165
12.2 经验累加分布函数图·······················································································································166
12.3 误差条图··········································································································································167
12.4 函数交互等值线图···························································································································168
·VI·
12.5 交互画线··········································································································································169
12.6 交互点标注 ······································································································································170
12.7 散点矩阵图 ······································································································································170
12.8 散点图··············································································································································172
12.9 添加最小二乘拟合线·······················································································································173
12.10 正态概率图 ····································································································································174
12.11 帕累托图 ········································································································································174
12.12 q-q 图 ·············································································································································175
12.13 回归个案次序图·····························································································································177
12.14 参考多项式曲线·····························································································································177
12.15 添加参考线 ····································································································································178
12.16 交互插值等值线图·························································································································179
12.17 威布尔图········································································································································179
第 13 章 文件输入/输出···································································································181
13.1 文件输入··········································································································································181
13.2 文件输出··········································································································································182
第 14 章 统计演示···········································································································184
14.1 交互式方差分析工具·······················································································································184
14.2 交互式经验分布函数工具 ···············································································································185
14.3 一般线性模型演示···························································································································186
14.4 稳健回归与最小二乘拟合比较工具 ································································································186
14.5 多项式拟合工具·······························································································································187
14.6 随机数生成工具·······························································································································188
第二篇 优化工具箱
第 15 章 优化工具箱概述 ································································································190
15.1 优化工具箱中的函数·······················································································································190
15.2 优化函数的变量·······························································································································191
15.3 参数设置··········································································································································194
15.4 模型输入时需要注意的问题············································································································195
15.5 @（函数句柄）函数 ·······················································································································196
第 16 章 无约束最优化问题·····························································································197
16.1 单变量最小化 ··································································································································197
16.1.1 基本数学原理 ······················································································································197
16.1.2 有关函数介绍 ······················································································································198
16.2 无约束非线性规划问题 ···················································································································200
16.2.1 基本数学原理 ······················································································································200
16.2.2 有关函数介绍 ······················································································································202
第 17 章 有约束最优化问题·····························································································207
17.1 线性规划··········································································································································207
·VII·
17.1.1 基本数学原理 ······················································································································207
17.1.2 有关函数介绍 ······················································································································208
17.1.3 应用实例······························································································································209
17.2 有约束非线性最优化问题 ···············································································································216
17.2.1 基本数学原理 ······················································································································216
17.2.2 有关函数介绍 ······················································································································218
17.2.3 应用实例······························································································································221
第 18 章 二次规划···········································································································225
18.1 基本数学原理 ··································································································································225
18.2 有关函数介绍 ··································································································································225
18.3 应用实例··········································································································································226
第 19 章 多目标规划 ·······································································································228
19.1 算法··················································································································································228
19.2 有关函数介绍 ··································································································································229
19.3 应用实例··········································································································································231
第 20 章 最大最小化 ·······································································································235
20.1 算法··················································································································································235
20.2 有关函数介绍 ··································································································································235
20.3 应用实例··········································································································································236
第 21 章 半无限问题 ·······································································································238
21.1 基本数学原理 ··································································································································238
21.2 有关函数介绍 ··································································································································238
21.3 应用实例··········································································································································240
第 22 章 最小二乘问题····································································································244
22.1 算法··················································································································································244
22.2 线性最小二乘问题···························································································································245
22.3 非负线性最小二乘解问题 ···············································································································245
22.3.1 基本数学原理 ······················································································································245
22.3.2 有关函数介绍 ······················································································································246
22.3.3 应用实例······························································································································246
22.4 有约束线性最小二乘问题 ···············································································································247
22.4.1 基本数学原理 ······················································································································247
22.4.2 有关函数介绍 ······················································································································247
22.4.3 应用实例······························································································································248
22.5 非线性最小二乘问题·······················································································································249
22.5.1 基本数学原理 ······················································································································249
22.5.2 有关函数介绍 ······················································································································250
22.5.3 应用实例······························································································································251
22.6 非线性曲线拟合问题·······················································································································252
22.6.1 基本数学原理 ························································································································252
·VIII·
相关推荐
2023年江西萍乡中考道德与法治真题及答案.doc
2012年重庆南川中考生物真题及答案.doc
2013年江西师范大学地理学综合及文艺理论基础考研真题.doc
2020年四川甘孜小升初语文真题及答案I卷.doc
2020年注册岩土工程师专业基础考试真题及答案.doc
2023-2024学年福建省厦门市九年级上学期数学月考试题及答案.doc
2021-2022学年辽宁省沈阳市大东区九年级上学期语文期末试题及答案.doc
2022-2023学年北京东城区初三第一学期物理期末试卷及答案.doc
2018上半年江西教师资格初中地理学科知识与教学能力真题及答案.doc
2012年河北国家公务员申论考试真题及答案-省级.doc
2020-2021学年江苏省扬州市江都区邵樊片九年级上学期数学第一次质量检测试题及答案.doc
2022下半年黑龙江教师资格证中学综合素质真题及答案.doc
