├── 随书光盘 ├── 程序及数据 │ ├── 16附录A │ │ ├── exA_28.m │ │ ├── exA_2.m │ │ ├── exA_9_6.m │ │ ├── exA_1_1.m │ │ ├── exA_27.m │ │ ├── exA_29_1.m │ │ ├── exA_3.m │ │ ├── exA_30.m │ │ ├── exA_13_2.m │ │ ├── exA_29_2.m │ │ ├── exA_9_3.m │ │ ├── data3.txt │ │ ├── exA_9_5.m │ │ ├── exA_33.m │ │ ├── exA_10.m │ │ ├── exA_12_2.m │ │ ├── exA_12_1.m │ │ ├── exA_16.m │ │ ├── exA_17_1.m │ │ ├── exA_18_2.m │ │ ├── exA_15.m │ │ ├── exA_18_1.m │ │ ├── exA_22.m │ │ ├── exA_25.m │ │ ├── exA_32.m │ │ ├── exA_17_2.m │ │ ├── exA_1_2.m │ │ ├── exA_6.m │ │ ├── exA_9_7.m │ │ ├── Afun1.m │ │ ├── exA_7.m │ │ ├── exA_35.m │ │ ├── exA_4.m │ │ ├── exA_9_1.m │ │ ├── exA_9_2.m │ │ ├── exA_9_4.m │ │ ├── exA_11.m │ │ ├── data1.mat │ │ ├── data5.xls │ │ ├── data6.bmp │ │ ├── data7.jpg │ │ ├── exA_14.m │ │ ├── exA_19.m │ │ ├── exA_20.m │ │ ├── exA_21.m │ │ ├── exA_23.m │ │ ├── exA_24.m │ │ ├── exA_26.m │ │ ├── exA_13_1.m │ │ ├── exA_17_3.m │ │ ├── exA_31.m │ │ ├── pinshu.txt │ │ ├── exA_8_2.m │ │ ├── exA_8_1.m │ │ ├── exA_36.m │ │ ├── exA_5.m │ │ ├── shuju.txt │ │ └── exA_34.m │ ├── 03第3章 │ │ ├── ex3_11.m │ │ ├── ex3_10.m │ │ ├── ex3_13.m │ │ ├── ex3_12.m │ │ ├── fun5.m │ │ ├── ex3_6.m │ │ ├── fun1.m │ │ ├── fun6.m │ │ ├── ex3_8_1.m │ │ ├── fun7.m │ │ ├── ex3_2.m │ │ ├── ex3_5_1.m │ │ ├── ex3_5_2.m │ │ ├── ex3_3.m │ │ ├── ex3_4.m │ │ ├── fun2.m │ │ ├── fun3.m │ │ ├── fun8.m │ │ ├── anli3_1.m │ │ ├── ex3_7_1.m │ │ ├── ex3_7_2.m │ │ ├── ex3_7_3.m │ │ ├── ex3_8_2.m │ │ ├── ex3_9_1.m │ │ ├── anli3_1.lg4 │ │ ├── ex3_14.m │ │ ├── test3.m │ │ ├── fun11.m │ │ ├── test1.m │ │ ├── test2.m │ │ ├── fun9.m │ │ ├── fun10.m │ │ ├── fun4.m │ │ └── txt1.txt │ ├── 06第6章 │ │ ├── ex6_8.m │ │ ├── ex6_2.m │ │ ├── F.m │ │ ├── dropbc.m │ │ ├── ex6_1.m │ │ ├── drop.m │ │ ├── dropinit.m │ │ ├── ex6_4.m │ │ ├── ex6_6.m │ │ ├── ex6_3.m │ │ ├── ex6_5.m │ │ ├── ex6_7.m │ │ ├── ex6_9.m │ │ ├── ex6_10.m │ │ ├── ex6_12.m │ │ ├── ex6_13.m │ │ ├── anli6_1_1.m │ │ ├── anli6_1_2.m │ │ ├── anli6_1_3.m │ │ ├── anli6_2_1.m │ │ ├── anli6_2_2.m │ │ ├── ex6_11_2.m │ │ ├── ex6_11_1.m │ │ ├── data4.txt │ │ └── example11.m │ ├── 15第15章 │ │ ├── ex15_6_2.m │ │ ├── ex15_8_1.m │ │ ├── ex15_8_2.m │ │ ├── jishu.txt │ │ ├── msdata.txt │ │ ├── yu.xls │ │ ├── ex15_1.m │ │ ├── ex15_2.m │ │ ├── ex15_3.m │ │ ├── ex15_4.m │ │ ├── ex15_5.m │ │ ├── ex15_7.m │ │ ├── ex15_9.m │ │ ├── anli15_1.m │ │ ├── anli15_2.m │ │ ├── anli15_3.m │ │ ├── anli15_4.m │ │ ├── book4.xls │ │ ├── ex15_10.m │ │ ├── ex15_11.m │ │ ├── ex15_13_1.m │ │ ├── ex15_13_2.m │ │ ├── ex15_6_1.m │ │ ├── ex15_8_3.m │ │ ├── xydata.mat │ │ ├── daodan.txt │ │ ├── jingliu.txt │ │ └── zhu.txt │ ├── 08第8章 │ │ ├── ex8_14.m │ │ ├── ranliao.txt │ │ ├── dianqi.txt │ │ ├── ex8_1.m │ │ ├── ex8_2.m │ │ ├── ex8_3.m │ │ ├── ex8_4.m │ │ ├── ex8_5.m │ │ ├── ex8_6.m │ │ ├── ex8_7.m │ │ ├── ex8_8.m │ │ ├── ex8_9.m │ │ ├── data1.xls │ │ ├── ex8_10.m │ │ ├── ex8_11.m │ │ ├── ex8_12.m │ │ ├── ex8_16.m │ │ ├── touzi.xls │ │ ├── dianqi.xls │ │ ├── ex8_15_1.m │ │ ├── ex8_15_2.m │ │ ├── fadian.xls │ │ ├── ranliao.xls │ │ ├── touzi.txt │ │ ├── jijie.txt │ │ ├── ex8_13.m │ │ ├── fadian.txt │ │ ├── water.txt │ │ └── hua.txt │ ├── 07第7章 │ │ ├── Fun.m │ │ ├── ex7_4.lg4 │ │ ├── ex7_5_1.m │ │ ├── ex7_5_2.m │ │ ├── ex7_6.lg4 │ │ ├── ex7_8.lg4 │ │ ├── ex7_10.lg4 │ │ ├── ex7_3_1.lg4 │ │ ├── ex7_3_2.lg4 │ │ ├── ex7_3_3.lg4 │ │ ├── ex7_7_1.lg4 │ │ └── ex7_7_2.lg4 │ ├── 说明.txt │ ├── 01第1章 │ │ ├── ex1_3.m │ │ ├── ex1_5.m │ │ ├── ex1_2.lg4 │ │ ├── ex1_5.lg4 │ │ ├── ex1_2.m │ │ └── anli1_1.m │ ├── 02第2章 │ │ ├── ex2_6.m │ │ ├── ex2_6.lg4 │ │ ├── ex2_7.lg4 │ │ ├── ex2_5.m │ │ ├── mengte.m │ │ └── ex2_7.m │ ├── 04第4章 │ │ ├── ex4_1.m │ │ ├── ex4_4.m │ │ ├── ex4_9.m │ │ ├── main.m │ │ ├── ex4_10.m │ │ ├── ex4_11.m │ │ ├── ex4_12.m │ │ ├── ex4_2.lg4 │ │ ├── ex4_3.lg4 │ │ ├── ex4_4.lg4 │ │ ├── myfloyd.m │ │ ├── ex4_15.lg4 │ │ ├── ex4_16.lg4 │ │ ├── ex4_17.lg4 │ │ ├── ex4_18.lg4 │ │ ├── ex4_19.lg4 │ │ ├── ex4_20.lg4 │ │ ├── ex4_21.lg4 │ │ ├── ex4_7_1.lg4 │ │ ├── ex4_7_2.lg4 │ │ ├── ex4_8_1.lg4 │ │ ├── ex4_8_2.lg4 │ │ ├── mydijkstra.m │ │ ├── anli4_1_1.lg4 │ │ ├── anli4_1_2.lg4 │ │ ├── ex4_13.m │ │ ├── ex4_5.m │ │ ├── txt1.txt │ │ ├── txt2.txt │ │ ├── ex4_6.m │ │ ├── fdata.txt │ │ ├── mydata1.txt │ │ ├── MiddleCost.txt │ │ ├── FinalResult.txt │ │ ├── Final_path.txt │ │ └── Train_path.txt │ ├── 05第5章 │ │ ├── ex5_2.m │ │ ├── ex5_3.m │ │ ├── ex5_4.m │ │ ├── ex5_8.m │ │ ├── fun1.m │ │ ├── data2.mat │ │ ├── ex5_10.m │ │ ├── ex5_12.m │ │ ├── ex5_9_1.m │ │ ├── ex5_9_2.m │ │ ├── anli5_1_1.m │ │ ├── anli5_1_2.m │ │ ├── anli5_1_3.m │ │ ├── anli5_1_4.m │ │ ├── ex5_11.m │ │ ├── ex5_6_1.m │ │ ├── ex5_6_2.m │ │ ├── ex5_5.m │ │ ├── ex5_7.m │ │ ├── data3.txt │ │ ├── data1.txt │ │ └── ex5_1.m │ ├── 09第9章 │ │ ├── ex9_1.m │ │ ├── anli9_1.m │ │ └── fenlei.txt │ ├── 12第12章 │ │ ├── ex12_1.m │ │ ├── ex12_3.m │ │ ├── ycfun1.m │ │ ├── anli12_1.m │ │ ├── anli12_2.m │ │ ├── anli12_3.m │ │ ├── ycfun2.m │ │ └── sj.txt │ ├── 11第11章 │ │ ├── ex11_1.m │ │ ├── ex11_2.m │ │ ├── pz.txt │ │ └── you.txt │ ├── 13第13章 │ │ ├── Lena.bmp │ │ ├── ex13_1.m │ │ ├── ex13_2.m │ │ ├── ex13_3.m │ │ ├── ex13_4.m │ │ ├── ex13_5.m │ │ ├── ex13_6.m │ │ ├── ex13_7.m │ │ ├── ex13_8.m │ │ ├── ex13_9.m │ │ ├── tu1.bmp │ │ ├── tu2.bmp │ │ ├── tu3.bmp │ │ ├── tu4.bmp │ │ ├── tu5.bmp │ │ ├── tu6.bmp │ │ ├── tu7.bmp │ │ ├── tu8.bmp │ │ ├── tu9.bmp │ │ ├── Lena2.bmp │ │ ├── anli13_1.m │ │ └── DCT_BASIC_FUNCTION.m │ ├── 14第14章 │ │ ├── ex14_3.m │ │ ├── ex14_5.m │ │ ├── ex14_6.m │ │ ├── ex14_7.m │ │ ├── anli14_1.m │ │ ├── book3.xls │ │ ├── ex14_1_1.m │ │ ├── ex14_1_3.m │ │ ├── ex14_4.lg4 │ │ ├── ex14_1_2.m │ │ ├── zhb.txt │ │ ├── zhaopin.txt │ │ ├── mhdata.txt │ │ └── pjsj.txt │ └── 17附录B │ │ ├── B_10.lg4 │ │ ├── B_11.lg4 │ │ ├── B_12.lg4 │ │ ├── Ldata.txt │ │ ├── exB_1.lg4 │ │ ├── exB_2.lg4 │ │ ├── exB_3.lg4 │ │ ├── exB_4.lg4 │ │ ├── exB_5.lg4 │ │ ├── exB_6.lg4 │ │ ├── exB_7.lg4 │ │ ├── exB_8.lg4 │ │ ├── exB_9.lg4 │ │ └── ydata.xls ├── 数学建模教材 │ ├── 前言.pdf │ ├── 封面.pdf │ ├── 目录.pdf │ ├── 38参考文献.pdf │ ├── 6第六章 排队论.pdf │ ├── 7第七章 对策论.pdf │ ├── 1第一章 线性规划.pdf │ ├── 2第二章 整数规划.pdf │ ├── 4第四章 动态规划.pdf │ ├── 5第五章 图与网络.pdf │ ├── 9第九章 插值与拟合.pdf │ ├── 11第十一章 方差分析.pdf │ ├── 12第十二章 回归分析.pdf │ ├── 13第十三章 微分方程建模.pdf │ ├── 14第十四章 稳定状态模型.pdf │ ├── 16第十六章 差分方程模型.pdf │ ├── 17第十七章 马氏链模型.pdf │ ├── 18第十八章 变分法模型.pdf │ ├── 19第十九章 神经网络模型.pdf │ ├── 21第二十一章 目标规划.pdf │ ├── 26第二十六章 多元分析.pdf │ ├── 28第二十八章 存贮论.pdf │ ├── 32第三十二章 作业计划.pdf │ ├── 3第三章 非线性规划.pdf │ ├── 8第八章 层次分析法.pdf │ ├── 15第十五章 常微分方程的解法.pdf │ ├── 22第二十二章 模糊数学模型.pdf │ ├── 23第二十三章 现代优化算法.pdf │ ├── 31第三十一章 支持向量机.pdf │ ├── 33附录一 Matlab入门.pdf │ ├── 10第十章 数据的统计描述和分析.pdf │ ├── 20第二十章 偏微分方程的数值解.pdf │ ├── 24第二十四章 时间序列模型.pdf │ ├── 27第二十七章 偏最小二乘回归分析.pdf │ ├── 35附录三 运筹学的LINGO软件.pdf │ ├── 25第二十五章 灰色系统理论及其应用.pdf │ ├── 29第二十九章 经济与金融中的优化问题.pdf │ ├── 37附录五 SPSS在统计分析中的应用.pdf │ ├── 30第三十章 生产与服务运作管理中的优化问题.pdf │ ├── 34附录二 Matlab在线性代数中的应用.pdf │ ├── 36附录四 Excel在统计分析与数量方法中的应用.pdf │ └── caipiao.txt └── README.md ├── 第十章 多元分析 ├── 教材、MATLAB程序和数据 │ ├── README.md │ ├── 10第10章 │ │ ├── bk.xls │ │ ├── ex10_2.m │ │ ├── ex10_5.m │ │ ├── ex10_9.m │ │ ├── tt.xls │ │ ├── tt1.xls │ │ ├── anli10_2.m │ │ ├── anli10_3.m │ │ ├── anli10_5.m │ │ ├── anli10_6.m │ │ ├── anli10_7.m │ │ ├── ex10_10.m │ │ ├── ex10_11.m │ │ ├── ex10_12.m │ │ ├── ex10_13.m │ │ ├── ex10_14.m │ │ ├── ex10_16.m │ │ ├── ex10_17.m │ │ ├── ex10_18.m │ │ ├── ex10_1_1.m │ │ ├── ex10_20.m │ │ ├── ex10_21.m │ │ ├── anli10_1_1.m │ │ ├── anli10_1_2.m │ │ ├── anli10_4_1.m │ │ ├── anli10_4_2.m │ │ ├── ex10_15_1.m │ │ ├── ex10_15_2.m │ │ ├── ex10_15_3.m │ │ ├── dy.txt │ │ ├── sn.txt │ │ ├── d.txt │ │ ├── ssgs.txt │ │ ├── y.txt │ │ ├── xf.txt │ │ ├── x.txt │ │ ├── ch.txt │ │ ├── r.txt │ │ └── sy.txt │ └── 26第二十六章 多元分析.pdf ├── 10.1 聚类分析 │ ├── 10.1聚类分析_files │ │ ├── 10.1聚类分析_13_1.png │ │ ├── 10.1聚类分析_23_1.png │ │ ├── 10.1聚类分析_28_2.png │ │ ├── 10.1聚类分析_29_2.png │ │ ├── 10.1聚类分析_33_1.png │ │ └── 10.1聚类分析_35_1.png │ ├── ch.txt │ ├── gj.txt │ └── 10.1聚类分析.md └── 10.2 主成分分析 │ ├── sn.txt │ ├── gj.txt │ ├── 10.2主成分分析.md │ └── 10.2主成分分析.ipynb └── README.md /随书光盘/程序及数据/16附录A/exA_28.m: -------------------------------------------------------------------------------- 1 | load data1 -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_2.m: -------------------------------------------------------------------------------- 1 | ezplot('tan(x)') -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_9_6.m: -------------------------------------------------------------------------------- 1 | ezsurf(@(x,y)x*y) -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_1_1.m: -------------------------------------------------------------------------------- 1 | fplot('Afun1',[-3,3]) -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_27.m: -------------------------------------------------------------------------------- 1 | save data1 a b c -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_29_1.m: -------------------------------------------------------------------------------- 1 | a=load('data2.txt'); -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_3.m: -------------------------------------------------------------------------------- 1 | ezplot('x^2+y^2/4=1') -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_30.m: -------------------------------------------------------------------------------- 1 | dlmwrite('data3.txt',b) -------------------------------------------------------------------------------- /随书光盘/程序及数据/03第3章/ex3_11.m: -------------------------------------------------------------------------------- 1 | [x,y]=fminbnd('fun6',0,5) -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_13_2.m: -------------------------------------------------------------------------------- 1 | a=[0,0.5,2,4]; da=diff(a) -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_29_2.m: -------------------------------------------------------------------------------- 1 | a=textread('data2.txt'); -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_9_3.m: -------------------------------------------------------------------------------- 1 | ezsurf(@(y,z) y.^2,50) 2 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/03第3章/ex3_10.m: -------------------------------------------------------------------------------- 1 | [x,y]=fminunc('test3',rand(2,1)) -------------------------------------------------------------------------------- /随书光盘/程序及数据/03第3章/ex3_13.m: -------------------------------------------------------------------------------- 1 | [x,y]=fminimax(@fun9,rand(2,1)) -------------------------------------------------------------------------------- /随书光盘/程序及数据/06第6章/ex6_8.m: -------------------------------------------------------------------------------- 1 | [T,Y]=ode45('F',[0 1],[0;1;-1]) -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/data3.txt: -------------------------------------------------------------------------------- 1 | 0.76393 2 | 5 3 | 5.2361 4 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_9_5.m: -------------------------------------------------------------------------------- 1 | ellipsoid(0,0,0,3,2,sqrt(6)) -------------------------------------------------------------------------------- /第十章 多元分析/教材、MATLAB程序和数据/README.md: -------------------------------------------------------------------------------- 1 | 这里是随书光盘中的教材、MATLAB程序和数据 2 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/03第3章/ex3_12.m: -------------------------------------------------------------------------------- 1 | [x,y]=fseminf(@fun7,rand(3,1),2,@fun8) -------------------------------------------------------------------------------- /随书光盘/程序及数据/03第3章/fun5.m: -------------------------------------------------------------------------------- 1 | function f=fun5(x); 2 | f=sin(x)+3; 3 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/03第3章/ex3_6.m: -------------------------------------------------------------------------------- 1 | x0=2; 2 | [x,y]=fminsearch(@fun5,x0) 3 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/03第3章/fun1.m: -------------------------------------------------------------------------------- 1 | function f=fun1(x); 2 | f=sum(x.^2)+8; 3 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/03第3章/fun6.m: -------------------------------------------------------------------------------- 1 | function f=fun6(x); 2 | f=(x-3)^2-1; 3 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_33.m: -------------------------------------------------------------------------------- 1 | b=xlsread('data5.xls','Sheet2','C3:F6') -------------------------------------------------------------------------------- /随书光盘/程序及数据/03第3章/ex3_8_1.m: -------------------------------------------------------------------------------- 1 | syms x y 2 | [x,y]=solve(x^2+y-6,y^2+x-6) 3 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/03第3章/fun7.m: -------------------------------------------------------------------------------- 1 | function f=fun7(x,s); 2 | f=sum((x-0.5).^2); 3 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_10.m: -------------------------------------------------------------------------------- 1 | [x,y,z,v] = flow; 2 | isosurface(x,y,z,v); 3 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_12_2.m: -------------------------------------------------------------------------------- 1 | syms x a 2 | b=limit((1+a/x)^x,x,inf) 3 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/06第6章/ex6_2.m: -------------------------------------------------------------------------------- 1 | y=dsolve('D3y-D2y=x','y(1)=8,Dy(1)=7,D2y(2)=4','x') -------------------------------------------------------------------------------- /随书光盘/程序及数据/15第15章/ex15_6_2.m: -------------------------------------------------------------------------------- 1 | clc, clear 2 | load xydata 3 | rstool(x123,Y) 4 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/15第15章/ex15_8_1.m: -------------------------------------------------------------------------------- 1 | x=[[1:5]',ones(5,1)];y=[11 12 13 15 16]';z=x\y -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_12_1.m: -------------------------------------------------------------------------------- 1 | syms x 2 | b=limit((sqrt(1+x^2)-1)/(1-cos(x))) 3 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_16.m: -------------------------------------------------------------------------------- 1 | syms x 2 | I=int(cos(x)*cos(2*x),-pi/2,pi/2) 3 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_17_1.m: -------------------------------------------------------------------------------- 1 | I=quadl(@(t) (t-3*t.^2+2*t.^3).^(-1/3),eps,0.5) -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_18_2.m: -------------------------------------------------------------------------------- 1 | syms n 2 | f2=1/n^2; 3 | s2=symsum(f2,n,1,inf) 4 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/06第6章/F.m: -------------------------------------------------------------------------------- 1 | function dy=F(t,y); 2 | dy=[y(2);y(3);3*y(3)+y(2)*y(1)]; 3 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/06第6章/dropbc.m: -------------------------------------------------------------------------------- 1 | function res=dropbc(ya,yb); 2 | res=[ya(1);yb(1)]; 3 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_15.m: -------------------------------------------------------------------------------- 1 | syms x 2 | I=int(1/(1+sqrt(1-x^2))); 3 | pretty(I) 4 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/03第3章/ex3_2.m: -------------------------------------------------------------------------------- 1 | [x,y]=fmincon('fun1',rand(3,1),[],[],[],[],zeros(3,1),[],'fun2') -------------------------------------------------------------------------------- /随书光盘/程序及数据/06第6章/ex6_1.m: -------------------------------------------------------------------------------- 1 | diff_equ='x^2+y+(x-2*y)*Dy=0'; 2 | dsolve(diff_equ,'x') 3 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_18_1.m: -------------------------------------------------------------------------------- 1 | syms n 2 | f1=(2*n-1)/2^n; 3 | s1=symsum(f1,n,1,inf) 4 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_22.m: -------------------------------------------------------------------------------- 1 | a=[2,4;3,-5;1,2;2,1]; 2 | b=[11;3;6;7]; 3 | solution=a\b 4 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_25.m: -------------------------------------------------------------------------------- 1 | A=[0,1,1,-1;1,0,-1,1;1,-1,0,1;-1,1,1,0]; 2 | [P,D]=eig(A) 3 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_32.m: -------------------------------------------------------------------------------- 1 | a=rand(5,10); 2 | xlswrite('data5.xls',a,'Sheet2','B2') 3 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_17_2.m: -------------------------------------------------------------------------------- 1 | I=dblquad(@(x,y)sqrt(1-x.^2-y.^2).*(x.^2+y.^2<=x),0,1,-0.5,0.5) -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_1_2.m: -------------------------------------------------------------------------------- 1 | Afun2=@(x) (x+1)*(x<1)+(1+1/x)*(x>=1); 2 | fplot(Afun2,[-3,3]) 3 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/08第8章/ex8_14.m: -------------------------------------------------------------------------------- 1 | price=[1:6]' 2 | dates=[today:today+5]' 3 | obj=fints(dates,price) 4 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/06第6章/drop.m: -------------------------------------------------------------------------------- 1 | function yprime=drop(x,y); 2 | yprime=[y(2);(y(1)-1)*(1+y(2)^2)^(3/2)]; 3 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/06第6章/dropinit.m: -------------------------------------------------------------------------------- 1 | function yinit=dropinit(x); 2 | yinit=[sqrt(1-x.^2);-x./(0.1+sqrt(1-x.^2))]; 3 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/07第7章/Fun.m: -------------------------------------------------------------------------------- 1 | function F=Fun(x); 2 | F=[-100*x(1)-90*x(2)-80*x(2)-70*x(4) 3 | 3*x(2)+2*x(4)]; 4 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_6.m: -------------------------------------------------------------------------------- 1 | [x,y]=meshgrid([-3:0.2:3]); 2 | z=(sin(x.*y)+eps)./(x.*y+eps); 3 | surf(x,y,z) 4 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_9_7.m: -------------------------------------------------------------------------------- 1 | x=@(s,t) 3*cos(s); 2 | y=@(s,t) 2*sin(s); 3 | z=@(s,t) t; 4 | ezmesh(x,y,z) 5 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/03第3章/ex3_5_1.m: -------------------------------------------------------------------------------- 1 | options = optimset('GradObj','on'); 2 | [x,y]=fminunc('fun3',rand(1,2),options) 3 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/06第6章/ex6_4.m: -------------------------------------------------------------------------------- 1 | syms t 2 | a=[2,1,3;0,2,-1;0,0,2]; 3 | x0=[1;2;1]; 4 | x=expm(a*t)*x0, pretty(x) 5 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/08第8章/ranliao.txt: -------------------------------------------------------------------------------- 1 | 24 2 | 26 3 | 27 4 | 30 5 | 32 6 | 33 7 | 36 8 | 40 9 | 41 10 | 44 11 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/15第15章/ex15_8_2.m: -------------------------------------------------------------------------------- 1 | y0=[11 12 13 15 16]'; 2 | y=y0(3:5);x=[y0(2:4),y0(1:3),ones(3,1)]; 3 | z=x\y 4 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/Afun1.m: -------------------------------------------------------------------------------- 1 | function y=Afun1(x); 2 | if x<1 3 | y=x+1; 4 | else 5 | y=1+1./x; 6 | end 7 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_7.m: -------------------------------------------------------------------------------- 1 | x=0:10:600; 2 | [X,Y,Z]=cylinder(30*exp(-x/400).*sin((x+25*pi)/100)+130); 3 | surf(X,Y,Z) 4 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/06第6章/ex6_6.m: -------------------------------------------------------------------------------- 1 | t=dsolve('Dt=10000*pi/sqrt(2*g)*(h^(3/2)-2*h^(1/2))','t(1)=0','h'); 2 | t=simple(t), pretty(t) 3 | -------------------------------------------------------------------------------- /随书光盘/数学建模教材/前言.pdf: -------------------------------------------------------------------------------- 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-------------------------------------------------------------------------------- /随书光盘/程序及数据/08第8章/dianqi.txt: -------------------------------------------------------------------------------- 1 | 50 2 | 52 3 | 47 4 | 51 5 | 49 6 | 48 7 | 51 8 | 40 9 | 48 10 | 52 11 | 51 12 | 59 13 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/15第15章/jishu.txt: -------------------------------------------------------------------------------- 1 | 0 20 40 60 80 2 | 0 1141 2019 2760 3413 3 | 100 120 140 160 184 4 | 4004 4545 5051 5525 6061 5 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_35.m: -------------------------------------------------------------------------------- 1 | a=imread('data6.bmp'); 2 | imshow(a) 3 | imwrite(a,'data7.jpg'); 4 | figure, imshow('data7.jpg') 5 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_4.m: -------------------------------------------------------------------------------- 1 | t=0:pi/50:10*pi; 2 | plot3(sin(t),cos(t),t) 3 | xlabel('sin(t)'), ylabel('cos(t)'), zlabel('t') 4 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_9_1.m: -------------------------------------------------------------------------------- 1 | x=@(s,t) 3*sec(s)*cos(t); 2 | y=@(s,t) 3*sec(s)*sin(t); 3 | z=@(s,t) 2*tan(s); 4 | ezmesh(x,y,z) 5 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_9_2.m: -------------------------------------------------------------------------------- 1 | x=@(s,t) 3*sec(s); 2 | y=@(s,t) 2*tan(s)*cos(t); 3 | z=@(s,t) 2*tan(s)*sin(t); 4 | ezmesh(x,y,z) 5 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_9_4.m: -------------------------------------------------------------------------------- 1 | x=@(s,t) 3*tan(s)*cos(t); 2 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function [c,ceq,dc,dceq]=fun11(x); 2 | c=[x(1)*x(2)-x(1)-x(2)+1.5;-x(1)*x(2)-10]; 3 | dc=[x(2)-1,-x(2);x(1)-1,-x(1)]; 4 | ceq=[];dceq=[]; 5 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/03第3章/test1.m: -------------------------------------------------------------------------------- 1 | function g=test1(x); 2 | M=50000; 3 | f=x(1)^2+x(2)^2+8; 4 | g=f-M*min(x(1),0)-M*min(x(2),0)-M*min(x(1)^2-x(2),0)+M*abs(-x(1)-x(2)^2+2); 5 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/03第3章/test2.m: -------------------------------------------------------------------------------- 1 | function g=test2(x); 2 | M=50000; 3 | f=x(1)^2+x(2)^2+8; 4 | g=f-M*sum(min([x';zeros(1,2)]))-M*min(x(1)^2-x(2),0)+M*abs(-x(1)-x(2)^2+2); 5 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/13第13章/DCT_BASIC_FUNCTION.m: 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1 | clc, clear 2 | x=unifrnd(0,12,[1,10000000]); 3 | y=unifrnd(0,9,[1,10000000]); 4 | pinshu=sum(y=3); 5 | area_appr=12*9*pinshu/10^7 6 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/08第8章/jijie.txt: -------------------------------------------------------------------------------- 1 | 137920 186742 274561 175433 2 | 142814 198423 265419 183521 3 | 131002 193987 247556 169847 4 | 157436 200144 283002 194319 5 | 149827 214301 276333 185204 6 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/14第14章/ex14_1_2.m: -------------------------------------------------------------------------------- 1 | x=[0.1 5 5000 4.7 2 | 0.2 6 6000 5.6 3 | 0.4 7 7000 6.7 4 | 0.9 10 10000 2.3 5 | 1.2 2 400 1.8]; 6 | y=zscore(x) 7 | -------------------------------------------------------------------------------- /第十章 多元分析/10.1 聚类分析/10.1聚类分析_files/10.1聚类分析_13_1.png: 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https://raw.githubusercontent.com/STL-CC/Mathematical-modeling-algorithm-and-Application/HEAD/第十章 多元分析/10.1 聚类分析/10.1聚类分析_files/10.1聚类分析_35_1.png -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_8_1.m: -------------------------------------------------------------------------------- 1 | alpha=[0:0.1:2*pi]'; beta=0:0.1:2*pi; 2 | x=4*cos(alpha)*ones(size(beta)); 3 | y=(5+4*sin(alpha))*cos(beta); 4 | z=(5+4*sin(alpha))*sin(beta); 5 | surf(x,y,z) 6 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/05第5章/ex5_6_2.m: -------------------------------------------------------------------------------- 1 | x0=[1990 1991 1992 1993 1994 1995 1996]; 2 | y0=[70 122 144 152 174 196 202]; 3 | a=polyfit(x0,y0,1) 4 | y97=polyval(a,1997) 5 | y98=polyval(a,1998) 6 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/12第12章/ycfun2.m: -------------------------------------------------------------------------------- 1 | function [f,g]=ycfun2(x); 2 | f=[x(1)+2*x(1)^2+x(2)+2*x(2)^2+x(3)-10 3 | x(1)+x(1)^2+x(2)+x(2)^2-x(3)-50 4 | 2*x(1)+x(1)^2+2*x(2)+x(3)-40]; 5 | g=x(1)^2+x(3)-2; 6 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_36.m: -------------------------------------------------------------------------------- 1 | clc, clear 2 | for i=1:10 3 | str=['jpg',int2str(i),'.jpg']; 4 | a(:,:,1)=rand(500); a(:,:,2)=rand(500)+100; a(:,:,3)=rand(500)+200; 5 | imwrite(a,str); 6 | end 7 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/03第3章/fun10.m: -------------------------------------------------------------------------------- 1 | function [f,df]=fun10(x); 2 | f=exp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+2*x(2)+1); 3 | df=[exp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+8*x(1)+6*x(2)+1);exp(x(1))*(4*x(2)+4*x(1)+2)]; 4 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/05第5章/ex5_5.m: -------------------------------------------------------------------------------- 1 | x=[19 25 31 38 44]'; 2 | y=[19.0 32.3 49.0 73.3 97.8]'; 3 | r=[ones(5,1),x.^2]; 4 | ab=r\y 5 | x0=19:0.1:44; 6 | y0=ab(1)+ab(2)*x0.^2; 7 | plot(x,y,'o',x0,y0,'r') 8 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/05第5章/ex5_7.m: -------------------------------------------------------------------------------- 1 | x=[19 25 31 38 44]'; 2 | y=[19.0 32.3 49.0 73.3 97.8]'; 3 | r=[ones(5,1),x.^2]; 4 | ab=lsqlin(r,y) 5 | x0=19:0.1:44; 6 | y0=ab(1)+ab(2)*x0.^2; 7 | plot(x,y,'o',x0,y0,'r') 8 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/08第8章/ex8_13.m: -------------------------------------------------------------------------------- 1 | clc,clear 2 | spec=garchset('R',2); 3 | y=load('mydata.txt'); 4 | [Coeff,Errors,LLF,Innovations,Sigmas,Summary]=garchfit(spec,y); 5 | Coeff 6 | [SigmaForecast,MeanForecast]=garchpred(Coeff,y,3) 7 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/03第3章/fun4.m: -------------------------------------------------------------------------------- 1 | function [f,df,d2f]=fun4(x); 2 | f=100*(x(2)-x(1)^2)^2+(1-x(1))^2; 3 | df=[-400*x(1)*(x(2)-x(1)^2)-2*(1-x(1));200*(x(2)-x(1)^2)]; 4 | d2f=[-400*x(2)+1200*x(1)^2+2,-400*x(1) 5 | -400*x(1),200]; 6 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/08第8章/fadian.txt: -------------------------------------------------------------------------------- 1 | 676 2 | 825 3 | 774 4 | 716 5 | 940 6 | 1159 7 | 1384 8 | 1524 9 | 1668 10 | 1688 11 | 1958 12 | 2031 13 | 2234 14 | 2566 15 | 2820 16 | 3006 17 | 3093 18 | 3277 19 | 3514 20 | 3770 21 | 4107 22 | -------------------------------------------------------------------------------- /第十章 多元分析/教材、MATLAB程序和数据/10第10章/dy.txt: -------------------------------------------------------------------------------- 1 | 4489 4303 4402 4350 4266 4361 2 | 4101 3800 3749 3572 3410 3234 3 | 3354 3286 3344 3278 3137 3008 4 | 2444 2587 2749 2878 2960 3049 5 | 3338 3144 2959 2791 2641 2432 6 | 1222 1196 1149 1003 959 959 7 | -------------------------------------------------------------------------------- /随书光盘/README.md: -------------------------------------------------------------------------------- 1 | 仅供学习交流，如有侵权，请联系作者删除 2 | 3 | ### 光盘使用说明 4 | 1.《数学建模算法与应用多媒体电子课件》与国防工业出版社出版的《数学建模算法与应用》教材配套使用。 5 | 2.光盘包含两部分内容，一部分为主教材的程序和数据，另一部分为本书教材的原始书稿，由于页数较多，在出版时进行了内容压缩，现放在光盘中供有兴趣的读者参考阅读。 6 | 3.光盘内的程序及数据需要Matlab 2009a以上版本和Lingo 9以上版本运行使用。 -------------------------------------------------------------------------------- /随书光盘/程序及数据/05第5章/data3.txt: -------------------------------------------------------------------------------- 1 | 1800 1900 2100 2200 2300 2400 2500 2600 2650 2700 2720 2650 2 | 32 60 75 85 90 98 100 102 108 112 115 116 3 | 2600 2500 2300 2200 2000 1850 1820 1800 1750 1500 1000 900 4 | 118 120 118 105 80 60 50 30 26 20 8 5 5 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/02第2章/mengte.m: -------------------------------------------------------------------------------- 1 | function [f,g]=mengte(x); 2 | f=x(1)^2+x(2)^2+3*x(3)^2+4*x(4)^2+2*x(5)-8*x(1)-2*x(2)-3*x(3)-... 3 | x(4)-2*x(5); 4 | g=[sum(x)-400 5 | x(1)+2*x(2)+2*x(3)+x(4)+6*x(5)-800 6 | 2*x(1)+x(2)+6*x(3)-200 7 | x(3)+x(4)+5*x(5)-200]; 8 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/06第6章/ex6_11_1.m: -------------------------------------------------------------------------------- 1 | solinit=bvpinit(linspace(-1,1,20),@dropinit); 2 | sol=bvp4c(@drop,@dropbc,solinit); 3 | fill(sol.x,sol.y(1,:),[0.7,0.7,0.7]) 4 | axis([-1,1,0,1]) 5 | xlabel('x','FontSize',12) 6 | ylabel('h','Rotation',0,'FontSize',12) 7 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_5.m: -------------------------------------------------------------------------------- 1 | x=-3:0.1:3;y=-5:0.1:5; 2 | x1=ones(size(y'))*x;y1=y'*ones(size(x)); 3 | [x2,y2]=meshgrid(x,y); 4 | z1=(sin(x1.*y1)+eps)./(x1.*y1+eps); 5 | z2=(sin(x2.*y2)+eps)./(x2.*y2+eps); 6 | subplot(1,2,1),mesh(x1,y1,z1) 7 | subplot(1,2,2),mesh(x2,y2,z2) 8 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/06第6章/data4.txt: -------------------------------------------------------------------------------- 1 | 1790 1800 1810 1820 1830 1840 1850 1860 2 | 3.9 5.3 7.2 9.6 12.9 17.1 23.2 31.4 3 | 1870 1880 1890 1900 1910 1920 1930 1940 4 | 38.6 50.2 62.9 76.0 92.0 106.5 123.2 131.7 5 | 1950 1960 1970 1980 1990 2000 6 | 150.7 179.3 204.0 226.5 251.4 281.4 7 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/02第2章/ex2_7.m: -------------------------------------------------------------------------------- 1 | c=[3 8 2 10 3;8 7 2 9 7;6 4 2 7 5 2 | 8 4 2 3 5;9 10 6 9 10]; 3 | c=c(:); 4 | a=zeros(10,25); 5 | for i=1:5 6 | a(i,(i-1)*5+1:5*i)=1; 7 | a(5+i,i:5:25)=1; 8 | end 9 | b=ones(10,1); 10 | [x,fval]=bintprog(c,[],[],a,b); 11 | x=reshape(x,[5,5]), fval 12 | -------------------------------------------------------------------------------- /第十章 多元分析/10.2 主成分分析/sn.txt: -------------------------------------------------------------------------------- 1 | 7 26 6 60 78.5 2 | 1 29 15 52 74.3 3 | 11 56 8 20 104.3 4 | 11 31 8 47 87.6 5 | 7 52 6 33 95.9 6 | 11 55 9 22 109.2 7 | 3 71 17 6 102.7 8 | 1 31 22 44 72.5 9 | 2 54 18 22 93.1 10 | 21 47 4 26 115.9 11 | 1 40 23 34 83.8 12 | 11 66 9 12 113.3 13 | 10 68 8 12 109.4 14 | -------------------------------------------------------------------------------- /第十章 多元分析/教材、MATLAB程序和数据/10第10章/sn.txt: -------------------------------------------------------------------------------- 1 | 7 26 6 60 78.5 2 | 1 29 15 52 74.3 3 | 11 56 8 20 104.3 4 | 11 31 8 47 87.6 5 | 7 52 6 33 95.9 6 | 11 55 9 22 109.2 7 | 3 71 17 6 102.7 8 | 1 31 22 44 72.5 9 | 2 54 18 22 93.1 10 | 21 47 4 26 115.9 11 | 1 40 23 34 83.8 12 | 11 66 9 12 113.3 13 | 10 68 8 12 109.4 14 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/shuju.txt: -------------------------------------------------------------------------------- 1 | 1.aggcacggaaaaacgggaataacggaggaggacttggcacggcattacacggagg 2 | 2.cggaggacaaacgggatggcggtattggaggtggcggactgttcgggga 3 | 3.gggacggatacggattctggccacggacggaaaggaggacacggcggacataca 4 | 4.atggataacggaaacaaaccagacaaacttcggtagaaatacagaagctta 5 | 5.cggctggcggacaacggactggcggattccaaaaacggaggaggcggacggaggc 6 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/04第4章/ex4_13.m: -------------------------------------------------------------------------------- 1 | clc, clear, a=zeros(9); 2 | a(1,2)=6; a(1,3)=4; a(1,4)=5; 3 | a(2,3)=3; a(2,5)=9; a(2,6)=9; 4 | a(3,4)=4; a(3,5)=6; a(3,6)=7; a(3,7)=3; 5 | a(4,7)=5; a(4,9)=2; 6 | a(5,8)=12; 7 | a(6,5)=8; a(6,8)=10; 8 | a(7,6)=4; a(7,8)=15; 9 | a(9,3)=2; 10 | b=sparse(a); 11 | [x,y,z]=graphmaxflow(b,1,8) 12 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/14第14章/zhb.txt: -------------------------------------------------------------------------------- 1 | 75.2 3.5 38.2 370.1 101.5 10.0 2 | 76.1 3.3 36.7 369.6 101.0 10.3 3 | 80.4 2.7 30.5 309.7 84.8 10.0 4 | 77.8 2.7 36.3 370.1 101.4 10.2 5 | 75.9 2.3 38.9 369.4 101.2 9.61 6 | 74.3 2.4 36.7 335.3 91.9 9.2 7 | 74.6 2.2 37.5 356.2 97.6 9.3 8 | 72.1 1.8 40.3 401.7 101.1 10.0 9 | 72.8 1.9 37.1 372.8 102.1 10.0 10 | 72.1 1.5 33.2 358.1 97.8 10.4 11 | 0.093 0.418 0.132 0.100 0.098 0.159 12 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/01第1章/anli1_1.m: -------------------------------------------------------------------------------- 1 | clc,clear 2 | a=0; 3 | hold on 4 | while a<0.05 5 | c=[-0.05,-0.27,-0.19,-0.185,-0.185]; 6 | A=[zeros(4,1),diag([0.025,0.015,0.055,0.026])]; 7 | b=a*ones(4,1); 8 | Aeq=[1,1.01,1.02,1.045,1.065]; 9 | beq=1; 10 | LB=zeros(5,1); 11 | [x,Q]=linprog(c,A,b,Aeq,beq,LB); 12 | Q=-Q; 13 | plot(a,Q,'*k'); 14 | a=a+0.001; 15 | end 16 | xlabel('a'),ylabel('Q') 17 | -------------------------------------------------------------------------------- /第十章 多元分析/教材、MATLAB程序和数据/10第10章/d.txt: -------------------------------------------------------------------------------- 1 | 0 2 | 244 0 3 | 218 350 0 4 | 284 77 369 0 5 | 197 164 347 242 0 6 | 312 444 94 463 441 0 7 | 215 221 150 236 279 245 0 8 | 469 583 251 598 598 169 380 0 9 | 166 242 116 257 269 210 55 349 0 10 | 212 53 298 72 170 392 168 531 190 0 11 | 253 325 57 340 359 143 117 264 91 273 0 12 | 270 168 284 164 277 378 143 514 173 111 256 0 13 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/14第14章/zhaopin.txt: -------------------------------------------------------------------------------- 1 | 290 0.5 0.5 0.3 0.3 2 | 288 0.5 0.3 0.5 0.15 3 | 288 0.3 0.5 0.05 0.15 4 | 285 0.5 0.3 0.3 0.3 5 | 283 0.3 0.5 0.3 0.15 6 | 283 0.3 0.05 0.5 0.3 7 | 280 0.5 0.3 0.15 0.3 8 | 280 0.3 0.5 0.5 0.15 9 | 280 0.3 0.3 0.5 0.3 10 | 280 0.05 0.3 0.5 0.15 11 | 278 0.05 0.15 0.3 0.5 12 | 277 0.5 0.3 0.15 0.5 13 | 275 0.3 0.15 0.05 0.5 14 | 275 0.05 0.3 0.5 0.3 15 | 274 0.5 0.3 0.15 0.3 16 | 273 0.3 0.5 0.3 0.15 17 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/16附录A/exA_34.m: -------------------------------------------------------------------------------- 1 | clc 2 | fid=fopen('shuju.txt','r'); 3 | i=1; 4 | while (~feof(fid)) 5 | data=fgetl(fid); 6 | a=length(find(data==97)); 7 | b=length(find(data==99)); 8 | c=length(find(data==103)); 9 | d=length(find(data==116)); 10 | e=length(find(data>=97&data<=122)); 11 | f(i,:)=[a b c d e a+b+c+d]; 12 | i=i+1; 13 | end 14 | f, he=sum(f) 15 | dlmwrite('pinshu.txt',f); dlmwrite('pinshu.txt',he,'-append'); 16 | fclose(fid); 17 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/14第14章/mhdata.txt: -------------------------------------------------------------------------------- 1 | 0.8 0.15 0.05 0 0 2 | 0.2 0.6 0.1 0.1 0 3 | 0.5 0.4 0.1 0 0 4 | 0.1 0.3 0.5 0.05 0.05 5 | 0.3 0.5 0.15 0.05 0 6 | 0.2 0.2 0.4 0.1 0.1 7 | 0.4 0.4 0.1 0.1 0 8 | 0.1 0.3 0.3 0.2 0.1 9 | 0.3 0.2 0.2 0.2 0.1 10 | 0.1 0.3 0.5 0.1 0 11 | 0.2 0.3 0.3 0.1 0.1 12 | 0.2 0.3 0.35 0.15 0 13 | 0.1 0.3 0.4 0.1 0.1 14 | 0.1 0.4 0.3 0.1 0.1 15 | 0.3 0.4 0.2 0.1 0 16 | 0.1 0.4 0.3 0.1 0.1 17 | 0.2 0.3 0.4 0.1 0 18 | 0.4 0.3 0.2 0.1 0 19 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/15第15章/daodan.txt: -------------------------------------------------------------------------------- 1 | 9.5 17675.33388 21839.81626 19851.29886 2 | 9.55 18606.75463 22807.17185 20756.90878 3 | 9.6 19575.37056 23807.47844 21700.16008 4 | 9.65 20580.73101 24840.82393 22680.74614 5 | 9.7 21622.49583 25907.33669 23698.43062 6 | 9.75 22700.42386 27007.18253 24753.04392 7 | 9.8 23814.3622 28140.56181 25844.47924 8 | 9.85 24964.23654 29307.70672 26972.68827 9 | 9.9 26150.04242 30508.87882 28137.67706 10 | 9.95 27371.83745 31744.36674 29339.50183 11 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/04第4章/ex4_5.m: -------------------------------------------------------------------------------- 1 | clc;clear; 2 | a=zeros(7); 3 | a(1,2)=50; a(1,3)=60; 4 | a(2,4)=65; a(2,5)=40; 5 | a(3,4)=52;a(3,7)=45; 6 | a(4,5)=50; a(4,6)=30;a(4,7)=42; 7 | a(5,6)=70; 8 | a=a+a';a(a==0)=inf; 9 | result=[];p=1;tb=2:length(a); 10 | while size(result,2)~=length(a)-1 11 | temp=a(p,tb);temp=temp(:); 12 | d=min(temp); 13 | [jb,kb]=find(a(p,tb)==d); 14 | j=p(jb(1));k=tb(kb(1)); 15 | result=[result,[j;k;d]];p=[p,k];tb(find(tb==k))=[]; 16 | end 17 | result 18 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/04第4章/txt1.txt: -------------------------------------------------------------------------------- 1 | 0.0000000 1.0000000 2 | 0.0000000 0.0000000 3 | 0.0000000 5.0000000 4 | 5.0000000 6.0000000 5 | 10.000000 12.000000 6 | 10.000000 10.000000 7 | 14.000000 16.000000 8 | 10.000000 10.000000 9 | 10.000000 11.000000 10 | 10.000000 16.000000 11 | 31.000000 36.000000 12 | 31.000000 31.000000 13 | 35.000000 36.000000 14 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/04第4章/txt2.txt: -------------------------------------------------------------------------------- 1 | 0.0000000 0.0000000 2 | 0.0000000 0.0000000 3 | 0.0000000 4.0000000 4 | 5.0000000 5.0000000 5 | 9.0000000 11.000000 6 | 9.0000000 9.0000000 7 | 13.000000 15.000000 8 | 9.0000000 9.0000000 9 | 9.0000000 9.0000000 10 | 9.0000000 14.000000 11 | 30.000000 34.000000 12 | 30.000000 30.000000 13 | 34.000000 34.000000 14 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/08第8章/water.txt: -------------------------------------------------------------------------------- 1 | 9.40 8.81 8.65 10.01 11.07 11.54 12.73 12.43 11.64 11.39 11.1 10.85 2 | 10.71 10.24 8.48 9.88 10.31 10.53 9.55 6.51 7.75 7.8 5.96 5.21 3 | 6.39 6.38 6.51 7.14 7.26 8.49 9.39 9.71 9.65 9.26 8.84 8.29 4 | 7.21 6.93 7.21 7.82 8.57 9.59 8.77 8.61 8.94 8.4 8.35 7.95 5 | 7.66 7.68 7.85 8.53 9.38 10.09 10.59 10.83 10.49 9.21 8.66 8.39 6 | 8.27 8.14 8.71 10.43 11.47 11.73 11.61 11.93 11.55 11.35 11.11 10.49 7 | 10.16 9.96 10.47 11.70 10.1 10.37 12.47 11.91 10.83 10.64 10.29 10.34 8 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/11第11章/pz.txt: -------------------------------------------------------------------------------- 1 | 191 36 50 5 162 60 2 | 189 37 52 2 110 60 3 | 193 38 58 12 101 101 4 | 162 35 62 12 105 37 5 | 189 35 46 13 155 58 6 | 182 36 56 4 101 42 7 | 211 38 56 8 101 38 8 | 167 34 60 6 125 40 9 | 176 31 74 15 200 40 10 | 154 33 56 17 251 250 11 | 169 34 50 17 120 38 12 | 166 33 52 13 210 115 13 | 154 34 64 14 215 105 14 | 247 46 50 1 50 50 15 | 193 36 46 6 70 31 16 | 202 37 62 12 210 120 17 | 176 37 54 4 60 25 18 | 157 32 52 11 230 80 19 | 156 33 54 15 225 73 20 | 138 33 68 2 110 43 21 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/06第6章/example11.m: -------------------------------------------------------------------------------- 1 | function sol=example11; 2 | solinit=bvpinit(linspace(-1,1,20),@dropinit); 3 | sol=bvp4c(@drop,@dropbc,solinit); 4 | fill(sol.x,sol.y(1,:),[0.7,0.7,0.7]) 5 | axis([-1,1,0,1]) 6 | xlabel('x','FontSize',12) 7 | ylabel('h','Rotation',0,'FontSize',12) 8 | 9 | function yprime=drop(x,y); 10 | yprime=[y(2);(y(1)-1)*(1+y(2)^2)^(3/2)]; 11 | 12 | function res=dropbc(ya,yb); 13 | res=[ya(1);yb(1)]; 14 | 15 | function yinit=dropinit(x); 16 | yinit=[sqrt(1-x.^2);-x./(0.1+sqrt(1-x.^2))]; 17 | 18 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/14第14章/pjsj.txt: -------------------------------------------------------------------------------- 1 | 0.71 0.49 0.41 0.51 0.46 2 | 0.40 0.49 0.44 0.57 0.50 3 | 0.55 0.56 0.48 0.53 0.49 4 | 0.62 0.93 0.38 0.53 0.47 5 | 0.45 0.42 0.41 0.54 0.47 6 | 0.36 0.37 0.46 0.54 0.48 7 | 0.55 0.68 0.42 0.54 0.46 8 | 0.62 0.90 0.38 0.56 0.46 9 | 0.61 0.99 0.33 0.57 0.43 10 | 0.71 0.93 0.35 0.66 0.44 11 | 0.59 0.69 0.36 0.57 0.48 12 | 0.41 0.47 0.40 0.54 0.48 13 | 0.26 0.29 0.43 0.57 0.48 14 | 0.14 0.16 0.43 0.55 0.47 15 | 0.12 0.13 0.45 0.59 0.54 16 | 0.22 0.25 0.44 0.58 0.52 17 | 0.71 0.49 0.41 0.51 0.46 18 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/03第3章/txt1.txt: -------------------------------------------------------------------------------- 1 | 0 5.3912 32.231 5.0918 20.963 2.2345 2 | 5.3912 0 4.804 6.6135 5.8079 3.8159 3 | 32.231 4.804 0 4.3647 22.834 2.1255 4 | 5.0918 6.6135 4.3647 0 4.5377 2.9898 5 | 20.963 5.8079 22.834 4.5377 0 2.3098 6 | 2.2345 3.8159 2.1255 2.9898 2.3098 0 7 | ~ 8 | 9 | 0 109.26 -128.25 24.18 173.07 14.475 10 | 109.26 0 -88.871 -42.244 -92.305 9 11 | -128.25 -88.871 0 12.476 -58.786 0.31081 12 | 24.18 -42.244 12.476 0 5.9692 -3.5256 13 | 173.07 -92.305 -58.786 5.9692 0 1.9144 14 | 14.475 9 0.31081 -3.5256 1.9144 0 15 | -------------------------------------------------------------------------------- /第十章 多元分析/教材、MATLAB程序和数据/10第10章/ssgs.txt: -------------------------------------------------------------------------------- 1 | 43.31 7.39 8.73 54.89 15.35 2 | 17.11 12.13 17.29 44.25 29.69 3 | 21.11 6.03 7 89.37 13.82 4 | 29.55 8.62 10.13 73 14.88 5 | 11 8.41 11.83 25.22 25.49 6 | 17.63 13.86 15.41 36.44 10.03 7 | 2.73 4.22 17.16 9.96 74.12 8 | 29.11 5.44 6.09 56.26 9.85 9 | 20.29 9.48 12.97 82.23 26.73 10 | 3.99 4.64 9.35 13.04 50.19 11 | 22.65 11.13 14.3 50.51 21.59 12 | 4.43 7.3 14.36 29.04 44.74 13 | 5.4 8.9 12.53 65.5 23.27 14 | 7.06 2.79 5.24 19.79 40.68 15 | 19.82 10.53 18.55 42.04 37.19 16 | 7.26 2.99 6.99 22.72 56.58 17 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/15第15章/jingliu.txt: -------------------------------------------------------------------------------- 1 | 15.6 5.6 3.5 25.5 22.9 2 | 27.8 4.3 1.0 7.7 23.4 3 | 35.2 3.0 38.1 3.7 36.8 4 | 10.2 3.4 3.5 7.4 22.0 5 | 29.1 33.2 1.6 24.0 6.4 6 | 10.2 11.6 2.2 26.7 29.4 7 | 35.4 4.1 1.3 7.0 26.2 8 | 8.7 3.5 7.5 5.0 20.9 9 | 25.4 0.7 22.2 35.4 26.5 10 | 15.3 6.0 2.0 17.5 37.3 11 | 25.9 1.2 9.0 3.3 22.8 12 | 64.3 3.7 4.6 4.8 19.8 13 | 55.9 2.9 0.3 5.2 19.6 14 | 19.6 10.5 10.7 10.3 28.5 15 | 35.6 2.4 6.6 24.6 22.8 16 | 10.9 9.4 0.8 7.1 18.2 17 | 24.7 8.2 7.7 14.4 23.8 18 | 22.6 11.2 9.9 18.5 17.3 19 | 21.5 2.9 1.6 4.5 21.9 20 | 54.7 3.3 3.7 11.6 32.8 21 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/04第4章/ex4_6.m: -------------------------------------------------------------------------------- 1 | clc;clear; 2 | a(1,2)=50; a(1,3)=60; a(2,4)=65; a(2,5)=40; 3 | a(3,4)=52;a(3,7)=45; a(4,5)=50; a(4,6)=30; 4 | a(4,7)=42; a(5,6)=70; 5 | [i,j,b]=find(a); 6 | data=[i';j';b'];index=data(1:2,:); 7 | loop=length(a)-1; 8 | result=[]; 9 | while length(result) STL_CC 10 | 11 | 由于作者还是大一学生，才疏学浅，难免会有错误，欢迎指正 12 | **同时作者精力有限，希望更多大佬加入此项目，一来可以提高建模水平，二来可以分享建模经验** 13 | ### 目录 14 | * 第1章 线性规划 15 | - 1.1 线性规划问题 16 | - 1.2 投资的收益和风险 17 | * 第2章 整数规划 18 | - 2.1 概论 19 | - 2.2 0-1型整数规划 20 | - 2.3 蒙特卡洛法（随机取样法） 21 | - 2.4 指派问题的计算机求解 22 | * 第3章 非线性规划 23 | - 3.1 非线性规划模型 24 | - 3.2 无约束问题的Matlab解法 25 | - 3.3 约束极值问题 26 | - 3.4 飞行管理问题 27 | * 第4章 图与网络模型及方法 28 | - 4.1 图的基本概念与数据结构 29 | - 4.2 最短路问题 30 | - 4.3 最小生成树问题 31 | - 4.4 网络最大流问题 32 | - 4.5 最小费用最大流问题 33 | - 4.6 Matlab的图论工具箱 34 | - 4.7 旅行商（TSP）问题 35 | - 4.8 计划评审方法和关键路线法 36 | - 4.9 钢管订购和运输 37 | * 第5章 插值与拟合 38 | - 5.1 插值方法 39 | - 5.2 曲线拟合的线性最小二乘法 40 | - 5.3 最小二乘优化 41 | - 5.4 曲线拟合与函数逼近 42 | - 5.5 黄河小浪底调水调沙问题 43 | * 第6章 微分方程建模 44 | - 6.1 发射卫星为什么用三级火箭 45 | - 6.2 人口模型 46 | - 6.3 Matlab求微分方程的符号解 47 | - 6.4 放射性废料的处理 48 | - 6.5 初值问题的Matlab数值解 49 | - 6.6 边值问题的Matlab数值解 50 | * 第7章 目标规划 51 | - 7.1 目标规划的数学模型 52 | - 7.2 求解目标规划的序贯算法 53 | - 7.3 多目标规划的Matlab解法 54 | - 7.4 目标规划模型的实例 55 | - 7.5 数据包络分析 56 | * 第8章 时间序列 57 | - 8.1 确定性时间序列分析方法 58 | - 8.2 平稳时间序列模型 59 | - 8.3 时间序列的Matlab相关工具箱及命令 60 | - 8.4 Arima序列与季节性序列 61 | * 第9章 支持向量机 62 | - 9.1 支持向量分类机的基本原理 63 | - 9.2 支持向量机的Matlab命令及应用例子 64 | - 9.3 乳腺癌的诊断 65 | * 第10章 多元分析 66 | - 10.1 聚类分析 67 | - 10.2 主成分分析 68 | - 10.3 因子分析 69 | - 10.4 判别分析 70 | - 10.5 典型相关分析 71 | - 10.6 对应分析 72 | - 10.7 多维标度法 73 | * 第11章 偏最小二乘回归分析 74 | - 11.1 偏最小二乘回归分析概述 75 | - 11.2 Matlab偏最小二乘回归命令Plsregress 76 | - 11.3 案例分析 77 | * 第12章 现代优化算法 78 | - 12.1 模拟退火算法 79 | - 12.2 遗传算法 80 | - 12.3 改进的遗传算法 81 | - 12.4 Matlab遗传算法工具 82 | * 第13章 数字图像处理 83 | - 13.1 数字图像概述 84 | - 13.2 亮度变换与空间滤波 85 | - 13.3 频域变换 86 | - 13.4 数字图像的水印防伪 87 | - 13.5 图像的加密和隐藏 88 | * 第14章 综合评价与决策方法 89 | - 14.1 理想解法 90 | - 14.2 模糊综合评判法 91 | - 14.3 数据包络分析法 92 | - 14.4 灰色关联分析法 93 | - 14.5 主成分分析法 94 | - 14.6 秩和比综合评价法 95 | - 14.7 案例分析 96 | * 第15章 预测方法 97 | - 15.1 微分方程模型 98 | - 15.2 灰色预测模型 99 | - 15.3 回归分析预测方法 100 | - 15.4 差分方程 101 | - 15.5 马尔可夫预测 102 | - 15.6 时间序列 103 | - 15.7 插值与拟合 104 | - 15.8 神经元网络 105 | -------------------------------------------------------------------------------- /随书光盘/程序及数据/04第4章/Final_path.txt: -------------------------------------------------------------------------------- 1 | 0 0 0 0 0 27 0 28 28 29 31 31 33 0 35 23 36 24 26 27 38 7 0 0 0 0 0 0 0 0 0 0 0 14 0 0 0 0 0 2 | 0 0 0 0 0 27 0 28 28 29 31 31 33 34 35 23 36 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-------------------------------------------------------------------------------- /第十章 多元分析/10.2 主成分分析/10.2主成分分析.md: -------------------------------------------------------------------------------- 1 | #
第十章 多元分析
2 | ##
第二节主成分分析
3 | 4 | **介绍** 5 | 这里是司守奎教授的《数学建模算法与应用》全书案例代码python实现，欢迎加入此项目将其案例代码用python实现 6 | GitHub项目地址：[Mathematical-modeling-algorithm-and-Application](https://github.com/STL-CC/Mathematical-modeling-algorithm-and-Application) 7 | CSDN专栏：[数学建模](https://blog.csdn.net/stl_cc/category_10228778.html) 8 | 知乎专栏：[数学建模算法与应用](https://zhuanlan.zhihu.com/c_1271013077337964544) 9 | **联系作者** 10 | 作者：STL_CC 11 | 邮箱：<1459078309@qq.com> 12 | 13 | 由于作者还是大一学生，才疏学浅，难免会有错误，欢迎指正 14 | 同时作者精力有限，希望更多大佬加入此项目，一来可以提高建模水平，二来可以分享建模经验 15 | 16 | ### **主成分回归分析** 17 | **例10.5** 18 | Hald水泥问题，考察含如下四种化学成分 19 | $x_1$=$3CaO.Al_2O_3$的含量（%），$x_2$=$3CaO.SiO_2$的含量（%） 20 | $x_3$=$4CaO.Al_2O_3.Fe_2O_3$的含量（%），$x_4$=$2CaO.SiO_2$的含量（%） 21 | 的某种水泥，每一克所释放出的热量（卡） y 与这四种成分含量之间的关系数据共13组，见表7，对数据实施标准化，则 X T X /12就是样本相关系数阵（见表8）。 22 | 注：表格见教材 23 | 24 | 25 | ```python 26 | import numpy as np 27 | import pandas as pd 28 | import matplotlib 29 | import matplotlib.pyplot as plt 30 | import statsmodels.api as sm 31 | from scipy.stats import zscore 32 | from sklearn.decomposition import PCA 33 | from sklearn.preprocessing import StandardScaler 34 | ``` 35 | 36 | 37 | ```python 38 | sn=pd.read_csv('sn.txt',header=None,sep=' ') 39 | m,n=sn.shape 40 | ``` 41 | 42 | 43 | ```python 44 | sn 45 | ``` 46 | 47 | 48 | 49 | 50 |
51 | 64 | 65 | 66 | 67 | 68 | 69 | 70 | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 | 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 | 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 | 101 | 102 | 103 | 104 | 105 | 106 | 107 | 108 | 109 | 110 | 111 | 112 | 113 | 114 | 115 | 116 | 117 | 118 | 119 | 120 | 121 | 122 | 123 | 124 | 125 | 126 | 127 | 128 | 129 | 130 | 131 | 132 | 133 | 134 | 135 | 136 | 137 | 138 | 139 | 140 | 141 | 142 | 143 | 144 | 145 | 146 | 147 | 148 | 149 | 150 | 151 | 152 | 153 | 154 | 155 | 156 | 157 | 158 | 159 | 160 | 161 | 162 | 163 | 164 | 165 | 166 | 167 | 168 | 169 | 170 | 171 | 172 | 173 | 174 | 175 | 176 | 177 | 178 | 179 | 180 | 181 |
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183 | 184 | 185 | 186 | 187 | ```python 188 | x0=np.array(sn.iloc[:,0:n-1]) 189 | y0=np.array(sn.iloc[:,n-1]) 190 | ``` 191 | 192 | 193 | ```python 194 | results = sm.OLS(y0, np.c_[np.ones((m,1)),x0]).fit() 195 | print(results.summary()) 196 | ``` 197 | 198 | OLS Regression Results 199 | ============================================================================== 200 | Dep. Variable: y R-squared: 0.982 201 | Model: OLS Adj. R-squared: 0.974 202 | Method: Least Squares F-statistic: 111.5 203 | Date: Fri, 31 Jul 2020 Prob (F-statistic): 4.76e-07 204 | Time: 01:16:14 Log-Likelihood: -26.918 205 | No. Observations: 13 AIC: 63.84 206 | Df Residuals: 8 BIC: 66.66 207 | Df Model: 4 208 | Covariance Type: nonrobust 209 | ============================================================================== 210 | coef std err t P>|t| [0.025 0.975] 211 | ------------------------------------------------------------------------------ 212 | const 62.4054 70.071 0.891 0.399 -99.179 223.989 213 | x1 1.5511 0.745 2.083 0.071 -0.166 3.269 214 | x2 0.5102 0.724 0.705 0.501 -1.159 2.179 215 | x3 0.1019 0.755 0.135 0.896 -1.638 1.842 216 | x4 -0.1441 0.709 -0.203 0.844 -1.779 1.491 217 | ============================================================================== 218 | Omnibus: 0.165 Durbin-Watson: 2.053 219 | Prob(Omnibus): 0.921 Jarque-Bera (JB): 0.320 220 | Skew: 0.201 Prob(JB): 0.852 221 | Kurtosis: 2.345 Cond. No. 6.06e+03 222 | ============================================================================== 223 | 224 | Warnings: 225 | [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. 226 | [2] The condition number is large, 6.06e+03. This might indicate that there are 227 | strong multicollinearity or other numerical problems. 228 | 229 | 230 | D:\Program Files\anaconda\lib\site-packages\scipy\stats\stats.py:1450: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=13 231 | "anyway, n=%i" % int(n)) 232 | 233 | 234 | 235 | ```python 236 | r=np.corrcoef(x0.T) 237 | xd=zscore(x0) 238 | yd=zscore(y0) 239 | ``` 240 | 241 | 242 | ```python 243 | pca=PCA() 244 | pca.fit(xd) 245 | ``` 246 | 247 | 248 | 249 | 250 | PCA(copy=True, iterated_power='auto', n_components=None, random_state=None, 251 | svd_solver='auto', tol=0.0, whiten=False) 252 | 253 | 254 | 255 | 256 | ```python 257 | pca.explained_variance_ratio_#计算各个变量的贡献率 258 | ``` 259 | 260 | 261 | 262 | 263 | array([5.58926009e-01, 3.94016518e-01, 4.66515373e-02, 4.05936433e-04]) 264 | 265 | 266 | 267 | 268 | ```python 269 | num=3#由于我们使用jupyter演示程序，可能不好交互式 270 | pca_=PCA(n_components=num) 271 | xd_=pca_.fit_transform(xd) 272 | ``` 273 | 274 | 275 | ```python 276 | results = sm.OLS(yd, np.c_[np.ones((m,1)),xd_]).fit() 277 | print(results.summary()) 278 | #原MATLAB程序中还做了使系数全为正的处理，在此报告中，x1为负，但是其实只要转成正的就行 279 | ``` 280 | 281 | OLS Regression Results 282 | ============================================================================== 283 | Dep. Variable: y R-squared: 0.982 284 | Model: OLS Adj. R-squared: 0.976 285 | Method: Least Squares F-statistic: 164.9 286 | Date: Fri, 31 Jul 2020 Prob (F-statistic): 3.50e-08 287 | Time: 01:16:16 Log-Likelihood: 7.7143 288 | No. Observations: 13 AIC: -7.429 289 | Df Residuals: 9 BIC: -5.169 290 | Df Model: 3 291 | Covariance Type: nonrobust 292 | ============================================================================== 293 | coef std err t P>|t| [0.025 0.975] 294 | ------------------------------------------------------------------------------ 295 | const 2.012e-16 0.045 4.52e-15 1.000 -0.101 0.101 296 | x1 -0.6570 0.030 -22.045 0.000 -0.724 -0.590 297 | x2 0.0083 0.035 0.234 0.820 -0.072 0.089 298 | x3 0.3028 0.103 2.935 0.017 0.069 0.536 299 | ============================================================================== 300 | Omnibus: 0.246 Durbin-Watson: 1.943 301 | Prob(Omnibus): 0.884 Jarque-Bera (JB): 0.416 302 | Skew: 0.162 Prob(JB): 0.812 303 | Kurtosis: 2.186 Cond. No. 3.46 304 | ============================================================================== 305 | 306 | Warnings: 307 | [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. 308 | 309 | 310 | D:\Program Files\anaconda\lib\site-packages\scipy\stats\stats.py:1450: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=13 311 | "anyway, n=%i" % int(n)) 312 | 313 | 314 | 315 | ```python 316 | xback=np.dot(xd_,pca.components_[:3]) 317 | ``` 318 | 319 | 320 | ```python 321 | results = sm.OLS(yd, np.c_[np.ones((m,1)),xback]).fit() 322 | print(results.summary()) 323 | ``` 324 | 325 | OLS Regression Results 326 | ============================================================================== 327 | Dep. Variable: y R-squared: 0.982 328 | Model: OLS Adj. R-squared: 0.976 329 | Method: Least Squares F-statistic: 164.9 330 | Date: Fri, 31 Jul 2020 Prob (F-statistic): 3.50e-08 331 | Time: 01:16:23 Log-Likelihood: 7.7143 332 | No. Observations: 13 AIC: -7.429 333 | Df Residuals: 9 BIC: -5.169 334 | Df Model: 3 335 | Covariance Type: nonrobust 336 | ============================================================================== 337 | coef std err t P>|t| [0.025 0.975] 338 | ------------------------------------------------------------------------------ 339 | const 2.012e-16 0.045 4.52e-15 1.000 -0.101 0.101 340 | x1 0.5130 0.073 6.992 0.000 0.347 0.679 341 | x2 0.2787 0.039 7.078 0.000 0.190 0.368 342 | x3 -0.0608 0.070 -0.866 0.409 -0.220 0.098 343 | x4 -0.4229 0.030 -13.871 0.000 -0.492 -0.354 344 | ============================================================================== 345 | Omnibus: 0.246 Durbin-Watson: 1.943 346 | Prob(Omnibus): 0.884 Jarque-Bera (JB): 0.416 347 | Skew: 0.162 Prob(JB): 0.812 348 | Kurtosis: 2.186 Cond. No. 8.35e+15 349 | ============================================================================== 350 | 351 | Warnings: 352 | [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. 353 | [2] The smallest eigenvalue is 4.17e-31. This might indicate that there are 354 | strong multicollinearity problems or that the design matrix is singular. 355 | 356 | 357 | **说明** 358 | 1.在教材原来的matlab程序中，OLS普通最小二乘法系数他是用朴素的方法计算出来的，在本文中，借助python强大的拓展能力，笔者使用了statsmodel统计模型库中的OLS模型进行建模。它不仅能够返回相关系数，更重要的是他可以返回与之相关的各项参数并生成报表。 359 | 2.在matlab中，相关系数矩阵计算使用的corrcoef列指标是变量，然而np.corrcoef行指标是向量，所以要先转置。 360 | 3.PCA模型在python的sklearn机器学习库中，相比比较裸的MATLAB工具，它提供了更多强大的功能，可以去sklearn文档探索更多，这里写法会和MATLAB写法有所不同。 361 | 4.协方差矩阵和相关系数矩阵易混： 362 | * 相关系数矩阵:相当于消除量纲的表示变量间相关性的一个矩阵 363 | * 协方差矩阵:它是没有消除量纲的表示变量间相关性的矩阵 364 | * r=COV(x,y)/D(x)D(y) 365 | 366 | **参考文献** 367 | 1.[python中使用多个模块使用普通最小二乘法回归](https://www.jianshu.com/p/ded62d82a787) 368 | 2.[最小二乘法原理](https://blog.csdn.net/m0_38075425/article/details/90738415) 369 | 3.[机器学习中的降维算法](https://blog.csdn.net/github_38486975/article/details/88384884) 370 | 4.[浅谈方差、协方差矩阵、相关系数矩阵](https://blog.csdn.net/scpcmoon/article/details/80549059) 371 | 5.[用scikit-learn学习主成分分析(PCA)](https://www.cnblogs.com/pinard/p/6243025.html) 372 | 6.[sklearn中PCA官方文档](https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html#sklearn.decomposition.PCA) 373 | 7.[使用sklearn进行对数据标准化、归一化以及将数据还原的方法](https://www.jb51.net/article/143571.htm) 374 | 375 | ### **案例研究** 376 | **主成分分析案例－我国各地区普通高等教育发展水平综合评价** 377 | 主成分分析试图在力保数据信息丢失最少的原则下，对多变量的截面数据表进行最佳综合简化，也就是说，对高维变量空间进行降维处理。本案例运用主成分分析方法综合评价我国各地区普通高等教育的发展水平。 378 | 具体资料见教材，部分数据将在程序中给出 379 | 380 | 381 | ```python 382 | import numpy as np 383 | import pandas as pd 384 | import matplotlib 385 | import matplotlib.pyplot as plt 386 | import statsmodels.api as sm 387 | from scipy.stats import zscore 388 | from sklearn.decomposition import PCA 389 | from sklearn.preprocessing import StandardScaler 390 | ``` 391 | 392 | 393 | ```python 394 | gj=pd.read_csv('gj.txt',header=None,sep=' ') 395 | gj=zscore(gj) 396 | r=np.corrcoef(gj.T) 397 | ``` 398 | 399 | 400 | ```python 401 | pca=PCA() 402 | pca.fit(gj) 403 | pca.explained_variance_ratio_#计算各个变量的得分 404 | ``` 405 | 406 | 407 | 408 | 409 | array([7.50215857e-01, 1.57698725e-01, 5.36213464e-02, 2.06379017e-02, 410 | 1.45001273e-02, 2.21867124e-03, 7.12026644e-04, 2.65835385e-04, 411 | 7.25914518e-05, 5.69183083e-05]) 412 | 413 | 414 | 415 | 416 | ```python 417 | 418 | ``` 419 | -------------------------------------------------------------------------------- /第十章 多元分析/10.2 主成分分析/10.2主成分分析.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "markdown", 5 | "metadata": {}, 6 | "source": [ 7 | "#
第十章 多元分析
\n", 8 | "##
第二节主成分分析
" 9 | ] 10 | }, 11 | { 12 | "cell_type": "markdown", 13 | "metadata": {}, 14 | "source": [ 15 | "**介绍** \n", 16 | "这里是司守奎教授的《数学建模算法与应用》全书案例代码python实现，欢迎加入此项目将其案例代码用python实现 \n", 17 | "GitHub项目地址：[Mathematical-modeling-algorithm-and-Application](https://github.com/STL-CC/Mathematical-modeling-algorithm-and-Application) \n", 18 | "CSDN专栏：[数学建模](https://blog.csdn.net/stl_cc/category_10228778.html) \n", 19 | "知乎专栏：[数学建模算法与应用](https://zhuanlan.zhihu.com/c_1271013077337964544) \n", 20 | "**联系作者** \n", 21 | "作者：STL_CC \n", 22 | "邮箱：<1459078309@qq.com> \n", 23 | "\n", 24 | "由于作者还是大一学生，才疏学浅，难免会有错误，欢迎指正 \n", 25 | "同时作者精力有限，希望更多大佬加入此项目，一来可以提高建模水平，二来可以分享建模经验" 26 | ] 27 | }, 28 | { 29 | "cell_type": "markdown", 30 | "metadata": {}, 31 | "source": [ 32 | "### **主成分回归分析**\n", 33 | "**例10.5** \n", 34 | "Hald水泥问题，考察含如下四种化学成分 \n", 35 | "$x_1$=$3CaO.Al_2O_3$的含量（%），$x_2$=$3CaO.SiO_2$的含量（%） \n", 36 | "$x_3$=$4CaO.Al_2O_3.Fe_2O_3$的含量（%），$x_4$=$2CaO.SiO_2$的含量（%） \n", 37 | "的某种水泥，每一克所释放出的热量（卡） y 与这四种成分含量之间的关系数据共13组，见表7，对数据实施标准化，则 X T X /12就是样本相关系数阵（见表8）。 \n", 38 | "注：表格见教材" 39 | ] 40 | }, 41 | { 42 | "cell_type": "code", 43 | "execution_count": 1, 44 | "metadata": {}, 45 | "outputs": [], 46 | "source": [ 47 | "import numpy as np\n", 48 | "import pandas as pd\n", 49 | "import matplotlib\n", 50 | "import matplotlib.pyplot as plt\n", 51 | "import statsmodels.api as sm\n", 52 | "from scipy.stats import zscore\n", 53 | "from sklearn.decomposition import PCA\n", 54 | "from sklearn.preprocessing import StandardScaler" 55 | ] 56 | }, 57 | { 58 | "cell_type": "code", 59 | "execution_count": 2, 60 | "metadata": {}, 61 | "outputs": [], 62 | "source": [ 63 | "sn=pd.read_csv('sn.txt',header=None,sep='\t')\n", 64 | "m,n=sn.shape" 65 | ] 66 | }, 67 | { 68 | "cell_type": "code", 69 | "execution_count": 3, 70 | "metadata": {}, 71 | "outputs": [ 72 | { 73 | "data": { 74 | "text/html": [ 75 | "
\n", 76 | "\n", 89 | "\n", 90 | " \n", 91 | " \n", 92 | " \n", 93 | " \n", 94 | " \n", 95 | " \n", 96 | " \n", 97 | " \n", 98 | " \n", 99 | " \n", 100 | " \n", 101 | " \n", 102 | " \n", 103 | " \n", 104 | " \n", 105 | " \n", 106 | " \n", 107 | " \n", 108 | " \n", 109 | " \n", 110 | " \n", 111 | " \n", 112 | " \n", 113 | " \n", 114 | " \n", 115 | " \n", 116 | " \n", 117 | " \n", 118 | " \n", 119 | " \n", 120 | " \n", 121 | " \n", 122 | " \n", 123 | " \n", 124 | " \n", 125 | " \n", 126 | " \n", 127 | " \n", 128 | " \n", 129 | " \n", 130 | " \n", 131 | " \n", 132 | " \n", 133 | " \n", 134 | " \n", 135 | " \n", 136 | " \n", 137 | " \n", 138 | " \n", 139 | " \n", 140 | " \n", 141 | " \n", 142 | " \n", 143 | " \n", 144 | " \n", 145 | " \n", 146 | " \n", 147 | " \n", 148 | " \n", 149 | " \n", 150 | " \n", 151 | " \n", 152 | " \n", 153 | " \n", 154 | " \n", 155 | " \n", 156 | " \n", 157 | " \n", 158 | " \n", 159 | " \n", 160 | " \n", 161 | " \n", 162 | " \n", 163 | " \n", 164 | " \n", 165 | " \n", 166 | " \n", 167 | " \n", 168 | " \n", 169 | " \n", 170 | " \n", 171 | " \n", 172 | " \n", 173 | " \n", 174 | " \n", 175 | " \n", 176 | " \n", 177 | " \n", 178 | " \n", 179 | " \n", 180 | " \n", 181 | " \n", 182 | " \n", 183 | " \n", 184 | " \n", 185 | " \n", 186 | " \n", 187 | " \n", 188 | " \n", 189 | " \n", 190 | " \n", 191 | " \n", 192 | " \n", 193 | " \n", 194 | " \n", 195 | " \n", 196 | " \n", 197 | " \n", 198 | " \n", 199 | " \n", 200 | " \n", 201 | " \n", 202 | " \n", 203 | " \n", 204 | " \n", 205 | " \n", 206 | "
01234
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\n", 207 | "
" 208 | ], 209 | "text/plain": [ 210 | " 0 1 2 3 4\n", 211 | "0 7 26 6 60 78.5\n", 212 | "1 1 29 15 52 74.3\n", 213 | "2 11 56 8 20 104.3\n", 214 | "3 11 31 8 47 87.6\n", 215 | "4 7 52 6 33 95.9\n", 216 | "5 11 55 9 22 109.2\n", 217 | "6 3 71 17 6 102.7\n", 218 | "7 1 31 22 44 72.5\n", 219 | "8 2 54 18 22 93.1\n", 220 | "9 21 47 4 26 115.9\n", 221 | "10 1 40 23 34 83.8\n", 222 | "11 11 66 9 12 113.3\n", 223 | "12 10 68 8 12 109.4" 224 | ] 225 | }, 226 | "execution_count": 3, 227 | "metadata": {}, 228 | "output_type": "execute_result" 229 | } 230 | ], 231 | "source": [ 232 | "sn" 233 | ] 234 | }, 235 | { 236 | "cell_type": "code", 237 | "execution_count": 4, 238 | "metadata": {}, 239 | "outputs": [], 240 | "source": [ 241 | "x0=np.array(sn.iloc[:,0:n-1])\n", 242 | "y0=np.array(sn.iloc[:,n-1])" 243 | ] 244 | }, 245 | { 246 | "cell_type": "code", 247 | "execution_count": 5, 248 | "metadata": {}, 249 | "outputs": [ 250 | { 251 | "name": "stdout", 252 | "output_type": "stream", 253 | "text": [ 254 | " OLS Regression Results \n", 255 | "==============================================================================\n", 256 | "Dep. Variable: y R-squared: 0.982\n", 257 | "Model: OLS Adj. R-squared: 0.974\n", 258 | "Method: Least Squares F-statistic: 111.5\n", 259 | "Date: Fri, 31 Jul 2020 Prob (F-statistic): 4.76e-07\n", 260 | "Time: 01:24:42 Log-Likelihood: -26.918\n", 261 | "No. Observations: 13 AIC: 63.84\n", 262 | "Df Residuals: 8 BIC: 66.66\n", 263 | "Df Model: 4 \n", 264 | "Covariance Type: nonrobust \n", 265 | "==============================================================================\n", 266 | " coef std err t P>|t| [0.025 0.975]\n", 267 | "------------------------------------------------------------------------------\n", 268 | "const 62.4054 70.071 0.891 0.399 -99.179 223.989\n", 269 | "x1 1.5511 0.745 2.083 0.071 -0.166 3.269\n", 270 | "x2 0.5102 0.724 0.705 0.501 -1.159 2.179\n", 271 | "x3 0.1019 0.755 0.135 0.896 -1.638 1.842\n", 272 | "x4 -0.1441 0.709 -0.203 0.844 -1.779 1.491\n", 273 | "==============================================================================\n", 274 | "Omnibus: 0.165 Durbin-Watson: 2.053\n", 275 | "Prob(Omnibus): 0.921 Jarque-Bera (JB): 0.320\n", 276 | "Skew: 0.201 Prob(JB): 0.852\n", 277 | "Kurtosis: 2.345 Cond. No. 6.06e+03\n", 278 | "==============================================================================\n", 279 | "\n", 280 | "Warnings:\n", 281 | "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", 282 | "[2] The condition number is large, 6.06e+03. This might indicate that there are\n", 283 | "strong multicollinearity or other numerical problems.\n" 284 | ] 285 | }, 286 | { 287 | "name": "stderr", 288 | "output_type": "stream", 289 | "text": [ 290 | "D:\\Program Files\\anaconda\\lib\\site-packages\\scipy\\stats\\stats.py:1450: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=13\n", 291 | " \"anyway, n=%i\" % int(n))\n" 292 | ] 293 | } 294 | ], 295 | "source": [ 296 | "results = sm.OLS(y0, np.c_[np.ones((m,1)),x0]).fit()\n", 297 | "print(results.summary())" 298 | ] 299 | }, 300 | { 301 | "cell_type": "code", 302 | "execution_count": 6, 303 | "metadata": {}, 304 | "outputs": [], 305 | "source": [ 306 | "r=np.corrcoef(x0.T)\n", 307 | "xd=zscore(x0)\n", 308 | "yd=zscore(y0)" 309 | ] 310 | }, 311 | { 312 | "cell_type": "code", 313 | "execution_count": 7, 314 | "metadata": {}, 315 | "outputs": [ 316 | { 317 | "data": { 318 | "text/plain": [ 319 | "PCA(copy=True, iterated_power='auto', n_components=None, random_state=None,\n", 320 | " svd_solver='auto', tol=0.0, whiten=False)" 321 | ] 322 | }, 323 | "execution_count": 7, 324 | "metadata": {}, 325 | "output_type": "execute_result" 326 | } 327 | ], 328 | "source": [ 329 | "pca=PCA()\n", 330 | "pca.fit(xd)" 331 | ] 332 | }, 333 | { 334 | "cell_type": "code", 335 | "execution_count": 8, 336 | "metadata": {}, 337 | "outputs": [ 338 | { 339 | "data": { 340 | "text/plain": [ 341 | "array([5.58926009e-01, 3.94016518e-01, 4.66515373e-02, 4.05936433e-04])" 342 | ] 343 | }, 344 | "execution_count": 8, 345 | "metadata": {}, 346 | "output_type": "execute_result" 347 | } 348 | ], 349 | "source": [ 350 | "pca.explained_variance_ratio_#计算各个变量的贡献率" 351 | ] 352 | }, 353 | { 354 | "cell_type": "code", 355 | "execution_count": 9, 356 | "metadata": {}, 357 | "outputs": [], 358 | "source": [ 359 | "num=3#由于我们使用jupyter演示程序，可能不好交互式\n", 360 | "pca_=PCA(n_components=num)\n", 361 | "xd_=pca_.fit_transform(xd)" 362 | ] 363 | }, 364 | { 365 | "cell_type": "code", 366 | "execution_count": 10, 367 | "metadata": {}, 368 | "outputs": [ 369 | { 370 | "name": "stdout", 371 | "output_type": "stream", 372 | "text": [ 373 | " OLS Regression Results \n", 374 | "==============================================================================\n", 375 | "Dep. Variable: y R-squared: 0.982\n", 376 | "Model: OLS Adj. R-squared: 0.976\n", 377 | "Method: Least Squares F-statistic: 164.9\n", 378 | "Date: Fri, 31 Jul 2020 Prob (F-statistic): 3.50e-08\n", 379 | "Time: 01:24:42 Log-Likelihood: 7.7143\n", 380 | "No. Observations: 13 AIC: -7.429\n", 381 | "Df Residuals: 9 BIC: -5.169\n", 382 | "Df Model: 3 \n", 383 | "Covariance Type: nonrobust \n", 384 | "==============================================================================\n", 385 | " coef std err t P>|t| [0.025 0.975]\n", 386 | "------------------------------------------------------------------------------\n", 387 | "const 2.012e-16 0.045 4.52e-15 1.000 -0.101 0.101\n", 388 | "x1 -0.6570 0.030 -22.045 0.000 -0.724 -0.590\n", 389 | "x2 0.0083 0.035 0.234 0.820 -0.072 0.089\n", 390 | "x3 0.3028 0.103 2.935 0.017 0.069 0.536\n", 391 | "==============================================================================\n", 392 | "Omnibus: 0.246 Durbin-Watson: 1.943\n", 393 | "Prob(Omnibus): 0.884 Jarque-Bera (JB): 0.416\n", 394 | "Skew: 0.162 Prob(JB): 0.812\n", 395 | "Kurtosis: 2.186 Cond. No. 3.46\n", 396 | "==============================================================================\n", 397 | "\n", 398 | "Warnings:\n", 399 | "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n" 400 | ] 401 | }, 402 | { 403 | "name": "stderr", 404 | "output_type": "stream", 405 | "text": [ 406 | "D:\\Program Files\\anaconda\\lib\\site-packages\\scipy\\stats\\stats.py:1450: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=13\n", 407 | " \"anyway, n=%i\" % int(n))\n" 408 | ] 409 | } 410 | ], 411 | "source": [ 412 | "results = sm.OLS(yd, np.c_[np.ones((m,1)),xd_]).fit()\n", 413 | "print(results.summary())\n", 414 | "#原MATLAB程序中还做了使系数全为正的处理，在此报告中，x1为负，但是其实只要转成正的就行" 415 | ] 416 | }, 417 | { 418 | "cell_type": "code", 419 | "execution_count": 11, 420 | "metadata": {}, 421 | "outputs": [], 422 | "source": [ 423 | "xback=np.dot(xd_,pca.components_[:3])" 424 | ] 425 | }, 426 | { 427 | "cell_type": "code", 428 | "execution_count": 12, 429 | "metadata": {}, 430 | "outputs": [ 431 | { 432 | "name": "stdout", 433 | "output_type": "stream", 434 | "text": [ 435 | " OLS Regression Results \n", 436 | "==============================================================================\n", 437 | "Dep. Variable: y R-squared: 0.982\n", 438 | "Model: OLS Adj. R-squared: 0.976\n", 439 | "Method: Least Squares F-statistic: 164.9\n", 440 | "Date: Fri, 31 Jul 2020 Prob (F-statistic): 3.50e-08\n", 441 | "Time: 01:24:43 Log-Likelihood: 7.7143\n", 442 | "No. Observations: 13 AIC: -7.429\n", 443 | "Df Residuals: 9 BIC: -5.169\n", 444 | "Df Model: 3 \n", 445 | "Covariance Type: nonrobust \n", 446 | "==============================================================================\n", 447 | " coef std err t P>|t| [0.025 0.975]\n", 448 | "------------------------------------------------------------------------------\n", 449 | "const 2.012e-16 0.045 4.52e-15 1.000 -0.101 0.101\n", 450 | "x1 0.5130 0.073 6.992 0.000 0.347 0.679\n", 451 | "x2 0.2787 0.039 7.078 0.000 0.190 0.368\n", 452 | "x3 -0.0608 0.070 -0.866 0.409 -0.220 0.098\n", 453 | "x4 -0.4229 0.030 -13.871 0.000 -0.492 -0.354\n", 454 | "==============================================================================\n", 455 | "Omnibus: 0.246 Durbin-Watson: 1.943\n", 456 | "Prob(Omnibus): 0.884 Jarque-Bera (JB): 0.416\n", 457 | "Skew: 0.162 Prob(JB): 0.812\n", 458 | "Kurtosis: 2.186 Cond. No. 8.35e+15\n", 459 | "==============================================================================\n", 460 | "\n", 461 | "Warnings:\n", 462 | "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", 463 | "[2] The smallest eigenvalue is 4.17e-31. This might indicate that there are\n", 464 | "strong multicollinearity problems or that the design matrix is singular.\n" 465 | ] 466 | } 467 | ], 468 | "source": [ 469 | "results = sm.OLS(yd, np.c_[np.ones((m,1)),xback]).fit()\n", 470 | "print(results.summary())" 471 | ] 472 | }, 473 | { 474 | "cell_type": "markdown", 475 | "metadata": {}, 476 | "source": [ 477 | "**说明** \n", 478 | "1.在教材原来的matlab程序中，OLS普通最小二乘法系数他是用朴素的方法计算出来的，在本文中，借助python强大的拓展能力，笔者使用了statsmodel统计模型库中的OLS模型进行建模。它不仅能够返回相关系数，更重要的是他可以返回与之相关的各项参数并生成报表。 \n", 479 | "2.在matlab中，相关系数矩阵计算使用的corrcoef列指标是变量，然而np.corrcoef行指标是向量，所以要先转置。 \n", 480 | "3.PCA模型在python的sklearn机器学习库中，相比比较裸的MATLAB工具，它提供了更多强大的功能，可以去sklearn文档探索更多，这里写法会和MATLAB写法有所不同。\n", 481 | "4.协方差矩阵和相关系数矩阵易混：\n", 482 | "* 相关系数矩阵:相当于消除量纲的表示变量间相关性的一个矩阵\n", 483 | "* 协方差矩阵:它是没有消除量纲的表示变量间相关性的矩阵 \n", 484 | "* r=COV(x,y)/D(x)D(y)\n", 485 | "\n", 486 | "**参考文献** \n", 487 | "1.[python中使用多个模块使用普通最小二乘法回归](https://www.jianshu.com/p/ded62d82a787) \n", 488 | "2.[最小二乘法原理](https://blog.csdn.net/m0_38075425/article/details/90738415) \n", 489 | "3.[机器学习中的降维算法](https://blog.csdn.net/github_38486975/article/details/88384884) \n", 490 | "4.[浅谈方差、协方差矩阵、相关系数矩阵](https://blog.csdn.net/scpcmoon/article/details/80549059) \n", 491 | "5.[用scikit-learn学习主成分分析(PCA)](https://www.cnblogs.com/pinard/p/6243025.html) \n", 492 | "6.[sklearn中PCA官方文档](https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html#sklearn.decomposition.PCA) \n", 493 | "7.[使用sklearn进行对数据标准化、归一化以及将数据还原的方法](https://www.jb51.net/article/143571.htm)" 494 | ] 495 | }, 496 | { 497 | "cell_type": "markdown", 498 | "metadata": {}, 499 | "source": [ 500 | "### **案例研究** \n", 501 | "**主成分分析案例－我国各地区普通高等教育发展水平综合评价** \n", 502 | "主成分分析试图在力保数据信息丢失最少的原则下，对多变量的截面数据表进行最佳综合简化，也就是说，对高维变量空间进行降维处理。本案例运用主成分分析方法综合评价我国各地区普通高等教育的发展水平。 \n", 503 | "具体资料见教材，部分数据将在程序中给出" 504 | ] 505 | }, 506 | { 507 | "cell_type": "code", 508 | "execution_count": 13, 509 | "metadata": {}, 510 | "outputs": [], 511 | "source": [ 512 | "import numpy as np\n", 513 | "import pandas as pd\n", 514 | "import matplotlib\n", 515 | "import matplotlib.pyplot as plt\n", 516 | "import statsmodels.api as sm\n", 517 | "from scipy.stats import zscore\n", 518 | "from sklearn.decomposition import PCA\n", 519 | "from sklearn.preprocessing import StandardScaler" 520 | ] 521 | }, 522 | { 523 | "cell_type": "code", 524 | "execution_count": 14, 525 | "metadata": {}, 526 | "outputs": [], 527 | "source": [ 528 | "gj=pd.read_csv('gj.txt',header=None,sep='\t')\n", 529 | "gj=zscore(gj)\n", 530 | "r=np.corrcoef(gj.T)" 531 | ] 532 | }, 533 | { 534 | "cell_type": "code", 535 | "execution_count": 15, 536 | "metadata": {}, 537 | "outputs": [ 538 | { 539 | "data": { 540 | "text/plain": [ 541 | "array([7.50215857e-01, 1.57698725e-01, 5.36213464e-02, 2.06379017e-02,\n", 542 | " 1.45001273e-02, 2.21867124e-03, 7.12026644e-04, 2.65835385e-04,\n", 543 | " 7.25914518e-05, 5.69183083e-05])" 544 | ] 545 | }, 546 | "execution_count": 15, 547 | "metadata": {}, 548 | "output_type": "execute_result" 549 | } 550 | ], 551 | "source": [ 552 | "pca=PCA()\n", 553 | "pca.fit(gj)\n", 554 | "pca.explained_variance_ratio_#计算各个变量的得分" 555 | ] 556 | } 557 | ], 558 | "metadata": { 559 | "kernelspec": { 560 | "display_name": "Python 3", 561 | "language": "python", 562 | "name": "python3" 563 | }, 564 | "language_info": { 565 | "codemirror_mode": { 566 | "name": "ipython", 567 | "version": 3 568 | }, 569 | "file_extension": ".py", 570 | "mimetype": "text/x-python", 571 | "name": "python", 572 | "nbconvert_exporter": "python", 573 | "pygments_lexer": "ipython3", 574 | "version": "3.7.4" 575 | } 576 | }, 577 | "nbformat": 4, 578 | "nbformat_minor": 4 579 | } 580 | -------------------------------------------------------------------------------- /第十章 多元分析/10.1 聚类分析/10.1聚类分析.md: -------------------------------------------------------------------------------- 1 | #
第十章 多元分析
2 | ##
第一节 聚类分析
3 | 4 | **介绍** 5 | 这里是司守奎教授的《数学建模算法与应用》全书案例代码python实现，欢迎加入此项目将其案例代码用python实现 6 | GitHub项目地址：[Mathematical-modeling-algorithm-and-Application](https://github.com/STL-CC/Mathematical-modeling-algorithm-and-Application) 7 | CSDN专栏：[数学建模](https://blog.csdn.net/stl_cc/category_10228778.html) 8 | 知乎专栏：[数学建模算法与应用](https://zhuanlan.zhihu.com/c_1271013077337964544) 9 | **联系作者** 10 | 作者：STL_CC 11 | 邮箱：<1459078309@qq.com> 12 | 13 | 由于作者还是大一学生，才疏学浅，难免会有错误，欢迎指正 14 | 同时作者精力有限，希望更多大佬加入此项目，一来可以提高建模水平，二来可以分享建模经验 15 | 16 | ### **系统聚类法** 17 | **例10.1** 18 | 设有5个销售员$w_1$,$w_2$,$w_3$,$w_4$,$w_5$,他们的销售业绩由二维变量($v_1$,$v_2$)描述,见表1 销售员业绩表 19 | 20 | | 销售员 | $v_1$(销售量)百件 |$v_2$(回收款项)万元| 21 | | :----: | :----: |:----:| 22 | | $w_1$ | 1 |0| 23 | | $w_2$ | 1 |1| 24 | | $w_3$ | 3 |2| 25 | | $w_4$ | 4 |3| 26 | | $w_5$ |2 |5| 27 | 28 | **方法一** 系统聚类法中的最长距离法 29 | 30 | 31 | ```python 32 | import numpy as np 33 | import numpy.matlib 34 | import pandas as pd 35 | import matplotlib 36 | import matplotlib.pyplot as plt 37 | from scipy.spatial.distance import pdist,squareform 38 | from scipy.cluster.hierarchy import dendrogram, linkage,fcluster 39 | ``` 40 | 41 | 42 | ```python 43 | a = np.array([[1,0],[1,1],[3,2],[4,3],[2,5]]) 44 | (m,n)=a.shape 45 | d = np.zeros((m,m)) 46 | ``` 47 | 48 | 49 | ```python 50 | for i in range(m): 51 | for j in range(i+1,m): 52 | d[i,j]=sum(map(abs,(a[i,:]-a[j,:]))) 53 | ``` 54 | 55 | 56 | ```python 57 | nd=d.ravel()[np.flatnonzero(d)] 58 | nd=np.unique(nd) 59 | ``` 60 | 61 | 62 | ```python 63 | l=len(nd) 64 | for i in range(0,l): 65 | nd_min=min(nd) 66 | (row,col)=np.where(d==nd_min) 67 | tm=np.union1d(row,col) 68 | print('第{:d}次合成,平台高度为{}时的分类结果为:{}'.format(i+1,nd_min,tm)) 69 | nd=np.delete(nd,np.where(nd==min(nd))) 70 | if(not len(nd)): 71 | break 72 | ``` 73 | 74 | 第1次合成,平台高度为1.0时的分类结果为:[0 1] 75 | 第2次合成,平台高度为2.0时的分类结果为:[2 3] 76 | 第3次合成,平台高度为3.0时的分类结果为:[1 2] 77 | 第4次合成,平台高度为4.0时的分类结果为:[0 2 3 4] 78 | 第5次合成,平台高度为5.0时的分类结果为:[1 3 4] 79 | 第6次合成,平台高度为6.0时的分类结果为:[0 3 4] 80 | 81 | 82 | **方法二** 使用python的scipy库 83 | 84 | 85 | ```python 86 | import numpy as np 87 | import pandas as pd 88 | import matplotlib 89 | import matplotlib.pyplot as plt 90 | from scipy.spatial.distance import pdist,squareform 91 | from scipy.cluster.hierarchy import dendrogram, linkage,fcluster 92 | ``` 93 | 94 | 95 | ```python 96 | a = np.array([[1,0],[1,1],[3,2],[4,3],[2,5]]) 97 | y=pdist(a,'cityblock') 98 | yc=squareform(y) 99 | ``` 100 | 101 | 102 | ```python 103 | z=linkage(y) 104 | dendrogram(z) 105 | ``` 106 | 107 | 108 | 109 | 110 | {'icoord': [[5.0, 5.0, 15.0, 15.0], 111 | [35.0, 35.0, 45.0, 45.0], 112 | [25.0, 25.0, 40.0, 40.0], 113 | [10.0, 10.0, 32.5, 32.5]], 114 | 'dcoord': [[0.0, 1.0, 1.0, 0.0], 115 | [0.0, 2.0, 2.0, 0.0], 116 | [0.0, 4.0, 4.0, 2.0], 117 | [1.0, 6.0, 6.0, 4.0]], 118 | 'ivl': ['0', '1', '4', '2', '3'], 119 | 'leaves': [0, 1, 4, 2, 3], 120 | 'color_list': ['g', 'r', 'r', 'b']} 121 | 122 | 123 | 124 | 125 | ![png](10.1%E8%81%9A%E7%B1%BB%E5%88%86%E6%9E%90_files/10.1%E8%81%9A%E7%B1%BB%E5%88%86%E6%9E%90_13_1.png) 126 | 127 | 128 | 129 | ```python 130 | T = fcluster(z,3,'maxclust') 131 | ``` 132 | 133 | 134 | ```python 135 | for i in range(1,3+1): 136 | tm=np.where(T==i) 137 | print('第{}类的有'.format(i),tm) 138 | ``` 139 | 140 | 第1类的有 (array([0, 1], dtype=int64),) 141 | 第2类的有 (array([2, 3], dtype=int64),) 142 | 第3类的有 (array([4], dtype=int64),) 143 | 144 | 145 | ### **变量聚类法** 146 | **例10.2** 服装标准制定中的变量聚类法。 147 | 在服装标准制定中，对某地成年女子的各部位尺寸进行了统计，通过14个部位的测量资料，获得各因素之间的相关系数表（见表5）。 148 | 注：具体资料见教材，部分数据将在程序中给出 149 | 150 | 151 | ```python 152 | import numpy as np 153 | import pandas as pd 154 | import matplotlib 155 | import matplotlib.pyplot as plt 156 | from scipy.spatial.distance import pdist,squareform 157 | from scipy.cluster.hierarchy import dendrogram, linkage,fcluster 158 | ``` 159 | 160 | 161 | ```python 162 | a=pd.read_csv('ch.txt',header=None,sep=' ') 163 | ``` 164 | 165 | 166 | ```python 167 | a 168 | ``` 169 | 170 | 171 | 172 | 173 |
174 | 187 | 188 | 189 | 190 | 191 | 192 | 193 | 194 | 195 | 196 | 197 | 198 | 199 | 200 | 201 | 202 | 203 | 204 | 205 | 206 | 207 | 208 | 209 | 210 | 211 | 212 | 213 | 214 | 215 | 216 | 217 | 218 | 219 | 220 | 221 | 222 | 223 | 224 | 225 | 226 | 227 | 228 | 229 | 230 | 231 | 232 | 233 | 234 | 235 | 236 | 237 | 238 | 239 | 240 | 241 | 242 | 243 | 244 | 245 | 246 | 247 | 248 | 249 | 250 | 251 | 252 | 253 | 254 | 255 | 256 | 257 | 258 | 259 | 260 | 261 | 262 | 263 | 264 | 265 | 266 | 267 | 268 | 269 | 270 | 271 | 272 | 273 | 274 | 275 | 276 | 277 | 278 | 279 | 280 | 281 | 282 | 283 | 284 | 285 | 286 | 287 | 288 | 289 | 290 | 291 | 292 | 293 | 294 | 295 | 296 | 297 | 298 | 299 | 300 | 301 | 302 | 303 | 304 | 305 | 306 | 307 | 308 | 309 | 310 | 311 | 312 | 313 | 314 | 315 | 316 | 317 | 318 | 319 | 320 | 321 | 322 | 323 | 324 | 325 | 326 | 327 | 328 | 329 | 330 | 331 | 332 | 333 | 334 | 335 | 336 | 337 | 338 | 339 | 340 | 341 | 342 | 343 | 344 | 345 | 346 | 347 | 348 | 349 | 350 | 351 | 352 | 353 | 354 | 355 | 356 | 357 | 358 | 359 | 360 | 361 | 362 | 363 | 364 | 365 | 366 | 367 | 368 | 369 | 370 | 371 | 372 | 373 | 374 | 375 | 376 | 377 | 378 | 379 | 380 | 381 | 382 | 383 | 384 | 385 | 386 | 387 | 388 | 389 | 390 | 391 | 392 | 393 | 394 | 395 | 396 | 397 | 398 | 399 | 400 | 401 | 402 | 403 | 404 | 405 | 406 | 407 | 408 | 409 | 410 | 411 | 412 | 413 | 414 | 415 | 416 | 417 | 418 | 419 | 420 | 421 | 422 | 423 | 424 | 425 | 426 | 427 | 428 | 429 | 430 | 431 | 432 | 433 | 434 | 435 | 436 | 437 | 438 | 439 | 440 | 441 | 442 | 443 | 444 | 445 | 446 | 447 |
012345678910111213
01.000NaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaN
10.3661.000NaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaN
20.2420.2331.000NaNNaNNaNNaNNaNNaNNaNNaNNaNNaNNaN
30.2800.1940.5901.000NaNNaNNaNNaNNaNNaNNaNNaNNaNNaN
40.3600.3240.4760.4351.000NaNNaNNaNNaNNaNNaNNaNNaNNaN
50.2820.2620.4830.4700.4521.000NaNNaNNaNNaNNaNNaNNaNNaN
60.2450.2650.5400.4780.5350.6631.000NaNNaNNaNNaNNaNNaNNaN
70.4480.3450.4520.4040.4310.3220.2661.000NaNNaNNaNNaNNaNNaN
80.4860.3670.3650.3570.4290.2830.2870.8201.000NaNNaNNaNNaNNaN
90.6480.6620.2160.0320.4290.2830.2630.5270.5471.000NaNNaNNaNNaN
100.6890.6710.2430.3130.4300.3020.2940.5200.5580.9571.000NaNNaNNaN
110.4860.6360.1740.2430.3750.2960.2550.4030.4170.8570.8521.000NaNNaN
120.1330.1530.7320.4770.3390.3920.4460.2660.2410.0540.0990.0551.000NaN
130.3760.2520.6760.5810.4410.4470.4400.4240.3720.3630.3760.3210.6271.0
448 |
449 | 450 | 451 | 452 | 453 | ```python 454 | d=1-abs(a) 455 | ``` 456 | 457 | 458 | ```python 459 | for i in range(len(d)): 460 | for j in range(i+1,len(d)): 461 | d.iloc[i,j]=d.iloc[j,i] 462 | ``` 463 | 464 | 465 | ```python 466 | z=linkage(d,'complete') 467 | y=fcluster(z,2,'maxclust') 468 | ``` 469 | 470 | D:\Program Files\anaconda\lib\site-packages\ipykernel_launcher.py:1: ClusterWarning: scipy.cluster: The symmetric non-negative hollow observation matrix looks suspiciously like an uncondensed distance matrix 471 | """Entry point for launching an IPython kernel. 472 | 473 | 474 | 475 | ```python 476 | dendrogram(z) 477 | ``` 478 | 479 | 480 | 481 | 482 | {'icoord': [[25.0, 25.0, 35.0, 35.0], 483 | [15.0, 15.0, 30.0, 30.0], 484 | [5.0, 5.0, 22.5, 22.5], 485 | [55.0, 55.0, 65.0, 65.0], 486 | [45.0, 45.0, 60.0, 60.0], 487 | [13.75, 13.75, 52.5, 52.5], 488 | [85.0, 85.0, 95.0, 95.0], 489 | [75.0, 75.0, 90.0, 90.0], 490 | [125.0, 125.0, 135.0, 135.0], 491 | [115.0, 115.0, 130.0, 130.0], 492 | [105.0, 105.0, 122.5, 122.5], 493 | [82.5, 82.5, 113.75, 113.75], 494 | [33.125, 33.125, 98.125, 98.125]], 495 | 'dcoord': [[0.0, 0.29809729955167313, 0.29809729955167313, 0.0], 496 | [0.0, 0.4028870809544531, 0.4028870809544531, 0.29809729955167313], 497 | [0.0, 0.7535436284648688, 0.7535436284648688, 0.4028870809544531], 498 | [0.0, 0.28955310393777517, 0.28955310393777517, 0.0], 499 | [0.0, 0.9263082640244553, 0.9263082640244553, 0.28955310393777517], 500 | [0.7535436284648688, 501 | 1.158768311613672, 502 | 1.158768311613672, 503 | 0.9263082640244553], 504 | [0.0, 0.49697082409332655, 0.49697082409332655, 0.0], 505 | [0.0, 0.8415325305655154, 0.8415325305655154, 0.49697082409332655], 506 | [0.0, 0.5600321419347287, 0.5600321419347287, 0.0], 507 | [0.0, 0.7182241989796779, 0.7182241989796779, 0.5600321419347287], 508 | [0.0, 0.850338756026091, 0.850338756026091, 0.7182241989796779], 509 | [0.8415325305655154, 510 | 1.2178604189314965, 511 | 1.2178604189314965, 512 | 0.850338756026091], 513 | [1.158768311613672, 514 | 2.1077737070188536, 515 | 2.1077737070188536, 516 | 1.2178604189314965]], 517 | 'ivl': ['1', 518 | '11', 519 | '9', 520 | '10', 521 | '0', 522 | '7', 523 | '8', 524 | '4', 525 | '5', 526 | '6', 527 | '12', 528 | '3', 529 | '2', 530 | '13'], 531 | 'leaves': [1, 11, 9, 10, 0, 7, 8, 4, 5, 6, 12, 3, 2, 13], 532 | 'color_list': ['g', 533 | 'g', 534 | 'g', 535 | 'g', 536 | 'g', 537 | 'g', 538 | 'r', 539 | 'r', 540 | 'r', 541 | 'r', 542 | 'r', 543 | 'r', 544 | 'b']} 545 | 546 | 547 | 548 | 549 | ![png](10.1%E8%81%9A%E7%B1%BB%E5%88%86%E6%9E%90_files/10.1%E8%81%9A%E7%B1%BB%E5%88%86%E6%9E%90_23_1.png) 550 | 551 | 552 | **说明** 553 | 1.在教材原来的matlab程序的数据预处理中，原始数据被去掉了0，向量长度不一。然而这样长度不一的向量是不能在python中被处理的。笔者将其转换为了一个对称矩阵再行操作，更能适应python操作。 554 | 2.在matlab中，相关系数矩阵计算使用的corrcoef列指标是变量，然而np.corrcoef行指标是向量，所以要先转置 555 | **参考文献** 556 | 1.[python中scipy库实现计算各种距离](https://blog.csdn.net/Jiajikang_jjk/article/details/83474446) 557 | 2.[Python之向量（Vector）距离矩阵计算](https://zhuanlan.zhihu.com/p/77034615) 558 | 3.[scipy.spatial.distance.pdist官方文档](https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.distance.pdist.html) 559 | 4.[使用Python进行层次聚类（一）——基本使用+主成分分析绘图观察结果+绘制热图](https://blog.csdn.net/qq_19528953/article/details/79133889) 560 | 5.[python的scipy层次聚类参数详解](https://blog.csdn.net/enigma_tong/article/details/79081449) 561 | 6.[皮尔逊积矩相关系数--NumPy--corrcoef()](https://blog.csdn.net/weixin_38287297/article/details/81501529) 562 | 563 | ### **案例研究** 564 | **聚类分析案例—我国各地区普通高等教育发展状况分析** 565 | 具体资料见教材，部分数据将在程序中给出 566 | 567 | **R型聚类分析** 568 | 569 | 570 | ```python 571 | import numpy as np 572 | import pandas as pd 573 | import matplotlib 574 | import matplotlib.pyplot as plt 575 | from scipy.spatial.distance import pdist,squareform 576 | from scipy.cluster.hierarchy import dendrogram, linkage,fcluster 577 | ``` 578 | 579 | 580 | ```python 581 | gj=pd.read_csv('gj.txt',header=None,sep=' ').T 582 | ``` 583 | 584 | 585 | ```python 586 | r=np.corrcoef(gj) 587 | d=1-r 588 | d=d.T 589 | z=linkage(d,'average') 590 | dendrogram(z) 591 | ``` 592 | 593 | D:\Program Files\anaconda\lib\site-packages\ipykernel_launcher.py:4: ClusterWarning: scipy.cluster: The symmetric non-negative hollow observation matrix looks suspiciously like an uncondensed distance matrix 594 | after removing the cwd from sys.path. 595 | 596 | 597 | 598 | 599 | 600 | {'icoord': [[5.0, 5.0, 15.0, 15.0], 601 | [55.0, 55.0, 65.0, 65.0], 602 | [85.0, 85.0, 95.0, 95.0], 603 | [75.0, 75.0, 90.0, 90.0], 604 | [60.0, 60.0, 82.5, 82.5], 605 | [45.0, 45.0, 71.25, 71.25], 606 | [35.0, 35.0, 58.125, 58.125], 607 | [25.0, 25.0, 46.5625, 46.5625], 608 | [10.0, 10.0, 35.78125, 35.78125]], 609 | 'dcoord': [[0.0, 0.8525484864006131, 0.8525484864006131, 0.0], 610 | [0.0, 0.024863305626884467, 0.024863305626884467, 0.0], 611 | [0.0, 0.02757546216575882, 0.02757546216575882, 0.0], 612 | [0.0, 0.04009972160627508, 0.04009972160627508, 0.02757546216575882], 613 | [0.024863305626884467, 614 | 0.14222971620143948, 615 | 0.14222971620143948, 616 | 0.04009972160627508], 617 | [0.0, 0.3129510501346711, 0.3129510501346711, 0.14222971620143948], 618 | [0.0, 0.4732207840475411, 0.4732207840475411, 0.3129510501346711], 619 | [0.0, 1.0379457746449512, 1.0379457746449512, 0.4732207840475411], 620 | [0.8525484864006131, 621 | 1.7688040008982475, 622 | 1.7688040008982475, 623 | 1.0379457746449512]], 624 | 'ivl': ['6', '7', '9', '8', '0', '4', '5', '1', '2', '3'], 625 | 'leaves': [6, 7, 9, 8, 0, 4, 5, 1, 2, 3], 626 | 'color_list': ['g', 'r', 'r', 'r', 'r', 'r', 'r', 'r', 'b']} 627 | 628 | 629 | 630 | 631 | ![png](10.1%E8%81%9A%E7%B1%BB%E5%88%86%E6%9E%90_files/10.1%E8%81%9A%E7%B1%BB%E5%88%86%E6%9E%90_29_2.png) 632 | 633 | 634 | 635 | ```python 636 | T=fcluster(z,6,'maxclust') 637 | ``` 638 | 639 | 640 | ```python 641 | for i in range(1,6+1): 642 | tm=np.where(T==i) 643 | print('第{}类的有'.format(i),tm) 644 | ``` 645 | 646 | 第1类的有 (array([ 1, 2, 5, 6, 9, 14, 16, 20, 22, 27, 28], dtype=int64),) 647 | 第2类的有 (array([11, 17, 19], dtype=int64),) 648 | 第3类的有 (array([ 3, 4, 7, 8, 10, 12, 13, 15, 18, 23, 25, 26], dtype=int64),) 649 | 第4类的有 (array([ 0, 29], dtype=int64),) 650 | 第5类的有 (array([24], dtype=int64),) 651 | 第6类的有 (array([21], dtype=int64),) 652 | 653 | 654 | **Q型聚类分析** 655 | 656 | 657 | ```python 658 | import numpy as np 659 | import pandas as pd 660 | import matplotlib 661 | import matplotlib.pyplot as plt 662 | from scipy.spatial.distance import pdist,squareform 663 | from scipy.cluster.hierarchy import dendrogram, linkage,fcluster 664 | from scipy.stats import zscore 665 | ``` 666 | 667 | 668 | ```python 669 | gj=pd.read_csv('gj.txt',header=None,sep=' ') 670 | gj.drop([2,3,4,5],axis=1,inplace=True) 671 | gj=zscore(gj) 672 | ``` 673 | 674 | 675 | ```python 676 | y=pdist(gj) 677 | z=linkage(y,'average') 678 | dendrogram(z) 679 | ``` 680 | 681 | 682 | 683 | 684 | {'icoord': [[25.0, 25.0, 35.0, 35.0], 685 | [55.0, 55.0, 65.0, 65.0], 686 | [45.0, 45.0, 60.0, 60.0], 687 | [115.0, 115.0, 125.0, 125.0], 688 | [105.0, 105.0, 120.0, 120.0], 689 | [95.0, 95.0, 112.5, 112.5], 690 | [135.0, 135.0, 145.0, 145.0], 691 | [175.0, 175.0, 185.0, 185.0], 692 | [165.0, 165.0, 180.0, 180.0], 693 | [155.0, 155.0, 172.5, 172.5], 694 | [140.0, 140.0, 163.75, 163.75], 695 | [205.0, 205.0, 215.0, 215.0], 696 | [195.0, 195.0, 210.0, 210.0], 697 | [151.875, 151.875, 202.5, 202.5], 698 | [103.75, 103.75, 177.1875, 177.1875], 699 | [245.0, 245.0, 255.0, 255.0], 700 | [235.0, 235.0, 250.0, 250.0], 701 | [225.0, 225.0, 242.5, 242.5], 702 | [285.0, 285.0, 295.0, 295.0], 703 | [275.0, 275.0, 290.0, 290.0], 704 | [265.0, 265.0, 282.5, 282.5], 705 | [233.75, 233.75, 273.75, 273.75], 706 | [140.46875, 140.46875, 253.75, 253.75], 707 | [85.0, 85.0, 197.109375, 197.109375], 708 | [75.0, 75.0, 141.0546875, 141.0546875], 709 | [52.5, 52.5, 108.02734375, 108.02734375], 710 | [30.0, 30.0, 80.263671875, 80.263671875], 711 | [15.0, 15.0, 55.1318359375, 55.1318359375], 712 | [5.0, 5.0, 35.06591796875, 35.06591796875]], 713 | 'dcoord': [[0.0, 2.165069616081611, 2.165069616081611, 0.0], 714 | [0.0, 1.2583609996700658, 1.2583609996700658, 0.0], 715 | [0.0, 1.8417771551214015, 1.8417771551214015, 1.2583609996700658], 716 | [0.0, 0.5102264872107092, 0.5102264872107092, 0.0], 717 | [0.0, 0.6832038743184952, 0.6832038743184952, 0.5102264872107092], 718 | [0.0, 1.0534720455396414, 1.0534720455396414, 0.6832038743184952], 719 | [0.0, 0.5781192315086323, 0.5781192315086323, 0.0], 720 | [0.0, 0.39279767533924836, 0.39279767533924836, 0.0], 721 | [0.0, 0.6920728341799272, 0.6920728341799272, 0.39279767533924836], 722 | [0.0, 0.8587702247881565, 0.8587702247881565, 0.6920728341799272], 723 | [0.5781192315086323, 724 | 0.951351143405573, 725 | 0.951351143405573, 726 | 0.8587702247881565], 727 | [0.0, 0.5422575852550412, 0.5422575852550412, 0.0], 728 | [0.0, 0.9931260197301512, 0.9931260197301512, 0.5422575852550412], 729 | [0.951351143405573, 730 | 1.1337053131831187, 731 | 1.1337053131831187, 732 | 0.9931260197301512], 733 | [1.0534720455396414, 734 | 1.3091848224406866, 735 | 1.3091848224406866, 736 | 1.1337053131831187], 737 | [0.0, 0.7003307018910611, 0.7003307018910611, 0.0], 738 | [0.0, 0.8455264592324916, 0.8455264592324916, 0.7003307018910611], 739 | [0.0, 1.183614496022609, 1.183614496022609, 0.8455264592324916], 740 | [0.0, 0.7408663414479949, 0.7408663414479949, 0.0], 741 | [0.0, 0.7928025480682006, 0.7928025480682006, 0.7408663414479949], 742 | [0.0, 1.43244903784588, 1.43244903784588, 0.7928025480682006], 743 | [1.183614496022609, 744 | 1.4564970761510314, 745 | 1.4564970761510314, 746 | 1.43244903784588], 747 | [1.3091848224406866, 748 | 1.7995913531962198, 749 | 1.7995913531962198, 750 | 1.4564970761510314], 751 | [0.0, 2.389167635724778, 2.389167635724778, 1.7995913531962198], 752 | [0.0, 2.4533056587669138, 2.4533056587669138, 2.389167635724778], 753 | [1.8417771551214015, 754 | 2.801906683718659, 755 | 2.801906683718659, 756 | 2.4533056587669138], 757 | [2.165069616081611, 4.23103702123038, 4.23103702123038, 2.801906683718659], 758 | [0.0, 5.540472787063805, 5.540472787063805, 4.23103702123038], 759 | [0.0, 8.531300289191663, 8.531300289191663, 5.540472787063805]], 760 | 'ivl': ['0', 761 | '24', 762 | '1', 763 | '2', 764 | '29', 765 | '27', 766 | '28', 767 | '3', 768 | '9', 769 | '20', 770 | '16', 771 | '14', 772 | '22', 773 | '13', 774 | '19', 775 | '21', 776 | '26', 777 | '18', 778 | '25', 779 | '17', 780 | '15', 781 | '23', 782 | '5', 783 | '6', 784 | '4', 785 | '7', 786 | '12', 787 | '10', 788 | '8', 789 | '11'], 790 | 'leaves': [0, 791 | 24, 792 | 1, 793 | 2, 794 | 29, 795 | 27, 796 | 28, 797 | 3, 798 | 9, 799 | 20, 800 | 16, 801 | 14, 802 | 22, 803 | 13, 804 | 19, 805 | 21, 806 | 26, 807 | 18, 808 | 25, 809 | 17, 810 | 15, 811 | 23, 812 | 5, 813 | 6, 814 | 4, 815 | 7, 816 | 12, 817 | 10, 818 | 8, 819 | 11], 820 | 'color_list': ['g', 821 | 'g', 822 | 'g', 823 | 'g', 824 | 'g', 825 | 'g', 826 | 'g', 827 | 'g', 828 | 'g', 829 | 'g', 830 | 'g', 831 | 'g', 832 | 'g', 833 | 'g', 834 | 'g', 835 | 'g', 836 | 'g', 837 | 'g', 838 | 'g', 839 | 'g', 840 | 'g', 841 | 'g', 842 | 'g', 843 | 'g', 844 | 'g', 845 | 'g', 846 | 'g', 847 | 'g', 848 | 'b']} 849 | 850 | 851 | 852 | 853 | ![png](10.1%E8%81%9A%E7%B1%BB%E5%88%86%E6%9E%90_files/10.1%E8%81%9A%E7%B1%BB%E5%88%86%E6%9E%90_35_1.png) 854 | 855 | 856 | 857 | ```python 858 | for k in range(3,6): 859 | print('划分成{}类的结果如下'.format(k)) 860 | T=fcluster(z,k,'maxclust') 861 | for i in range(1,k+1): 862 | tm=np.where(T==i) 863 | print('第{}类的有{}'.format(i,tm)) 864 | ``` 865 | 866 | 划分成3类的结果如下 867 | 第1类的有(array([ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 868 | 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29], dtype=int64),) 869 | 第2类的有(array([24], dtype=int64),) 870 | 第3类的有(array([0], dtype=int64),) 871 | 划分成4类的结果如下 872 | 第1类的有(array([1, 2], dtype=int64),) 873 | 第2类的有(array([ 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 874 | 20, 21, 22, 23, 25, 26, 27, 28, 29], dtype=int64),) 875 | 第3类的有(array([24], dtype=int64),) 876 | 第4类的有(array([0], dtype=int64),) 877 | 划分成5类的结果如下 878 | 第1类的有(array([1, 2], dtype=int64),) 879 | 第2类的有(array([27, 28, 29], dtype=int64),) 880 | 第3类的有(array([ 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 881 | 20, 21, 22, 23, 25, 26], dtype=int64),) 882 | 第4类的有(array([24], dtype=int64),) 883 | 第5类的有(array([0], dtype=int64),) 884 | 885 | 886 | 887 | ```python 888 | 889 | ``` 890 | --------------------------------------------------------------------------------