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MATLAB工具箱大全,各种算法
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MATLAB工具箱大全,各种算法,遗传算法、神经网络、传统算法实现及应用,非常全面,绝对非常好的资源
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·I·
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!
·II·
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 阮沈勇 r_shenyong@yahoo.com.cn
张莲花 zhlh@cdut.edu.cn 王永利 wy_11971@tom.com
刘 波 sclibo@mail.sc.cninfo.net
编 者
2003.9
·III·
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
·IV·
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
·V·
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
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