矩阵的基本运算之数学建模实验报告.docx

1、矩阵的基本运算之数学建模实验报告%统计与数学模型分析实验中心经济数学实验与建模实验报告班级： 学号： 姓名： 实验时间 10.30 实验地点 2栋402 实验名称：矩阵的基本运算 使用软件： matlab软件 实验目的熟悉Matlab软件中关于向量、矩阵的基本运算，并会用sort命令解决有关排序的实际问题。实验内容（具体题目及程序）1.矩阵的输入方法；题目1： 已知矩阵A=的matlab输入程序：A=1,5,1,0,1;2,6,0,1,1;3,7,1,0,1;4,8,0,1,12.矩阵的合成与分解；题目2：已知矩阵A= ，求A的第一行与第一列程序：A=1,5,1,0,1;2,6,0,1,1;3

2、,7,1,0,1;4,8,0,1,1；A1=A(1,:)A2=A(:,1)3.大样本数据的排序方法；题目3：根据下表给出的我国部分城市2001年平均气温，解决以下问题： 将平均气温分别从低到高排列 我国部分城市2001年1，3，5，7，9，10，11，12月平均气温（单位摄氏度）序号城市1月3月5月7月9月10月11月12月1北京 -5.47.323.127.321.213.85.3-2.42天津 -4.97.623.027.121.214.85.3-2.53石家庄-3.510.824.128.221.815.57.3-0.94太原 -4.66.220.224.817.212.02.9-4.6

3、5呼和浩特 -9.90.718.225.016.19.3-0.7-10.56沈阳 -16.20.219.225.718.411.91.0-10.27大连 -5.63.718.224.621.315.26.9-1.98长春 -19.8-3.017.024.217.09.8-1.5-12.29哈尔滨 -22.8-4.416.524.515.88.2-2.4-13.910上海 5.911.020.829.724.920.213.77.111南京 4.010.722.730.224.018.810.84.812杭州 6.112.321.930.324.119.512.76.613合肥 3.711.72

4、3.830.624.018.311.24.414福州 12.915.623.229.126.322.917.313.615南昌 6.712.723.330.625.820.913.86.516济南 -1.59.624.627.421.016.28.4-0.517青岛 -0.46.117.825.022.117.29.11.118郑州 -1.311.623.927.621.716.59.10.719武汉 4.713.224.031.826.219.412.94.420长沙 5.412.722.930.425.019.213.24.921广州 15.419.426.528.227.825.419.

5、714.922南宁 14.418.224.927.826.123.617.313.123海口 20.022.627.828.727.926.722.219.524桂林 8.715.123.528.326.422.216.18.325重庆 8.316.122.530.724.519.715.18.626成都 7.015.122.727.620.818.813.66.827贵阳 4.912.117.423.220.616.311.34.728昆明 10.314.917.020.919.416.411.410.329拉萨 1.14.912.415.914.39.23.81.030西安 1.112.1

6、22.229.120.015.07.90.731兰州 -3.26.517.723.916.911.94.3-3.132西宁 -6.91.611.517.612.47.30.1-6.633银川 -4.74.518.924.916.311.11.9-6.934乌鲁木齐 -11.83.019.923.416.28.01.7-15.2程序：A=-5.4 -1.5 7.3 14.4 23.1 25.7 27.3 25.8 21.2 13.8 5.3 -2.4-4.9 -1.6 7.6 14.4 23.0 25.8 27.1 26.4 21.2 14.8 5.3 -2.5-3.5 0.5 10.8 15.

7、4 24.1 27.3 28.2 26.3 21.8 15.5 7.3 -0.9-4.6 -0.2 6.2 12.4 20.2 23.5 24.8 22.1 17.2 12.0 2.9 -4.6-9.9 -5.1 0.7 10.4 18.2 23.2 25.0 22.1 16.1 9.3 -0.7 -10.5-16.2 -9.1 0.2 11.8 19.2 24.1 25.7 23.7 18.4 11.9 1.0 -10.2-5.6 -2.6 3.7 10.9 18.2 23.0 24.6 24.7 21.3 15.2 6.9 -1.9-19.8 -13.9 -3.0 9.8 17.0 23.

8、0 24.2 22.2 17.0 9.8 -1.5 -12.2-22.8 -16.5 -4.4 8.6 16.5 22.8 24.5 21.7 15.8 8.2 -2.4 -13.95.9 6.8 11.0 15.2 20.8 24.2 29.7 27.0 24.9 20.2 13.7 7.14.0 5.8 10.7 15.6 22.7 24.7 30.2 26.7 24.0 18.8 10.8 4.86.1 7.1 12.3 16.0 21.9 24.4 30.3 26.4 24.1 19.5 12.7 6.63.7 5.8 11.7 16.1 23.8 25.4 30.6 26.7 24.

9、0 18.3 11.2 4.412.9 12.9 15.6 18.2 23.2 26.8 29.1 28.8 26.3 22.9 17.3 13.66.7 8.4 12.7 17.1 23.3 25.6 30.6 27.1 25.8 20.9 13.8 6.5-1.5 1.6 9.6 15.8 24.6 27.2 27.4 25.7 21.0 16.2 8.4 -0.5-0.4 2.0 6.1 11.3 17.8 21.2 25.0 25.4 22.1 17.2 9.1 1.1-1.3 2.6 11.6 15.4 23.9 26.9 27.6 26.0 21.7 16.5 9.1 0.74.7

10、 6.9 13.2 17.3 24.0 26.9 31.8 28.6 26.2 19.4 12.9 4.45.4 7.5 12.7 16.5 22.9 25.7 30.4 27.4 25.0 19.2 13.2 4.915.4 15.1 19.4 21.7 26.5 27.2 28.2 29.1 27.8 25.4 19.7 14.914.4 13.8 18.2 21.6 24.9 26.9 27.8 27.7 26.1 23.6 17.3 13.120.0 18.9 22.6 26.8 27.8 28.6 28.7 28.6 27.9 26.7 22.2 19.58.7 10.5 15.1

11、18.1 23.5 26.1 28.3 27.6 26.4 22.2 16.1 8.38.3 11.1 16.1 17.7 22.5 24.1 30.7 27.2 24.5 19.7 15.1 8.67.0 10.0 15.1 17.3 22.7 23.8 27.6 24.3 20.8 18.8 13.6 6.84.9 6.7 12.1 14.4 17.4 20.2 23.2 21.6 20.6 16.3 11.3 4.710.3 11.7 14.9 19.6 17.0 20.0 20.9 20.5 19.4 16.4 11.4 10.31.1 4.7 4.9 8.1 12.4 14.6 15

12、.9 15.4 14.3 9.2 3.8 1.01.1 5.0 12.1 14.6 22.2 26.3 29.1 25.4 20.0 15.0 7.9 0.7-3.2 1.1 6.5 11.4 17.7 22.2 23.9 22.4 16.9 11.9 4.3 -3.1-6.9 -3.3 1.6 7.4 11.5 15.6 17.6 15.6 12.4 7.3 0.1 -6.6-4.7 -1.5 4.5 11.3 18.9 23.2 24.9 22.7 16.3 11.1 1.9 -6.9-11.8 -8.9 3.0 9.6 19.9 23.1 23.4 23.4 16.2 8.0 1.7 -

13、15.2B=sort(A); % 此时B给出各城市从小到大的排序B,i=sort(A); % 此时i给出平均气温从小到大排列以后各城市的序号B1=sort(i) ;B1,j= sort(i); % 此时j给出各城市平均气温从小到大排序的名次矩阵C=sort(A, descend); % 此时C给出各城市平均气温从高到低的排序C,k= sort(A, descend); % 此时k给出平均气温从大到小排序的以后各城市序号C1=sort(k,descend);C1,h= sort(k); % 此时h给出各城市平均气温从大到小排序的名次矩阵m=mean(A)s=std(A)实验结果分析题目1：结果（

14、分析）：A = 1 5 1 0 1 2 6 0 1 1 3 7 1 0 1 4 8 0 1 1题目2：结果：A1 = 1 5 1 0 1 A2 = 1 2 3 4 分析：A1=A(1,:) 表示矩阵A的第一行； A2=A(:,1) 表示矩阵A的第一列；题目3：结果：A = Columns 1 through 9 -5.4000 -1.5000 7.3000 14.4000 23.1000 25.7000 27.3000 25.8000 21.2000 -4.9000 -1.6000 7.6000 14.4000 23.0000 25.8000 27.1000 26.4000 21.2000 -

15、3.5000 0.5000 10.8000 15.4000 24.1000 27.3000 28.2000 26.3000 21.8000 -4.6000 -0.2000 6.2000 12.4000 20.2000 23.5000 24.8000 22.1000 17.2000 -9.9000 -5.1000 0.7000 10.4000 18.2000 23.2000 25.0000 22.1000 16.1000 -16.2000 -9.1000 0.2000 11.8000 19.2000 24.1000 25.7000 23.7000 18.4000 -5.6000 -2.6000

16、3.7000 10.9000 18.2000 23.0000 24.6000 24.7000 21.3000 -19.8000 -13.9000 -3.0000 9.8000 17.0000 23.0000 24.2000 22.2000 17.0000 -22.8000 -16.5000 -4.4000 8.6000 16.5000 22.8000 24.5000 21.7000 15.8000 5.9000 6.8000 11.0000 15.2000 20.8000 24.2000 29.7000 27.0000 24.9000 4.0000 5.8000 10.7000 15.6000

17、 22.7000 24.7000 30.2000 26.7000 24.0000 6.1000 7.1000 12.3000 16.0000 21.9000 24.4000 30.3000 26.4000 24.1000 3.7000 5.8000 11.7000 16.1000 23.8000 25.4000 30.6000 26.7000 24.0000 12.9000 12.9000 15.6000 18.2000 23.2000 26.8000 29.1000 28.8000 26.3000 6.7000 8.4000 12.7000 17.1000 23.3000 25.6000 3

18、0.6000 27.1000 25.8000 -1.5000 1.6000 9.6000 15.8000 24.6000 27.2000 27.4000 25.7000 21.0000 -0.4000 2.0000 6.1000 11.3000 17.8000 21.2000 25.0000 25.4000 22.1000 -1.3000 2.6000 11.6000 15.4000 23.9000 26.9000 27.6000 26.0000 21.7000 4.7000 6.9000 13.2000 17.3000 24.0000 26.9000 31.8000 28.6000 26.2

19、000 5.4000 7.5000 12.7000 16.5000 22.9000 25.7000 30.4000 27.4000 25.0000 15.4000 15.1000 19.4000 21.7000 26.5000 27.2000 28.2000 29.1000 27.8000 14.4000 13.8000 18.2000 21.6000 24.9000 26.9000 27.8000 27.7000 26.1000 20.0000 18.9000 22.6000 26.8000 27.8000 28.6000 28.7000 28.6000 27.9000 8.7000 10.

20、5000 15.1000 18.1000 23.5000 26.1000 28.3000 27.6000 26.4000 8.3000 11.1000 16.1000 17.7000 22.5000 24.1000 30.7000 27.2000 24.5000 7.0000 10.0000 15.1000 17.3000 22.7000 23.8000 27.6000 24.3000 20.8000 4.9000 6.7000 12.1000 14.4000 17.4000 20.2000 23.2000 21.6000 20.6000 10.3000 11.7000 14.9000 19.

21、6000 17.0000 20.0000 20.9000 20.5000 19.4000 1.1000 4.7000 4.9000 8.1000 12.4000 14.6000 15.9000 15.4000 14.3000 1.1000 5.0000 12.1000 14.6000 22.2000 26.3000 29.1000 25.4000 20.0000 -3.2000 1.1000 6.5000 11.4000 17.7000 22.2000 23.9000 22.4000 16.9000 -6.9000 -3.3000 1.6000 7.4000 11.5000 15.6000 1

22、7.6000 15.6000 12.4000 -4.7000 -1.5000 4.5000 11.3000 18.9000 23.2000 24.9000 22.7000 16.3000 -11.8000 -8.9000 3.0000 9.6000 19.9000 23.1000 23.4000 23.4000 16.2000 Columns 10 through 12 13.8000 5.3000 -2.4000 14.8000 5.3000 -2.5000 15.5000 7.3000 -0.9000 12.0000 2.9000 -4.6000 9.3000 -0.7000 -10.50

23、00 11.9000 1.0000 -10.2000 15.2000 6.9000 -1.9000 9.8000 -1.5000 -12.2000 8.2000 -2.4000 -13.9000 20.2000 13.7000 7.1000 18.8000 10.8000 4.8000 19.5000 12.7000 6.6000 18.3000 11.2000 4.4000 22.9000 17.3000 13.6000 20.9000 13.8000 6.5000 16.2000 8.4000 -0.5000 17.2000 9.1000 1.1000 16.5000 9.1000 0.7

24、000 19.4000 12.9000 4.4000 19.2000 13.2000 4.9000 25.4000 19.7000 14.9000 23.6000 17.3000 13.1000 26.7000 22.2000 19.5000 22.2000 16.1000 8.3000 19.7000 15.1000 8.6000 18.8000 13.6000 6.8000 16.3000 11.3000 4.7000 16.4000 11.4000 10.3000 9.2000 3.8000 1.0000 15.0000 7.9000 0.7000 11.9000 4.3000 -3.1

25、000 7.3000 0.1000 -6.6000 11.1000 1.9000 -6.9000 8.0000 1.7000 -15.2000m = 12.8833 13.0500 14.4000 10.9917 8.2333 8.3750 11.5333 6.0500 4.8417 17.2083 16.5667 17.2833 16.8083 20.6333 18.2083 14.6250 13.1583 15.0583 18.0250 17.5667 22.5333 21.2833 24.8583 19.2417 18.8000 17.3167 14.4500 16.0333 8.783

26、3 14.9500 11.0000 6.0250 10.1417 7.7000s = 11.9813 11.9730 11.5231 10.8575 12.9984 14.7700 11.2244 15.6195 16.4681 8.3942 9.2120 8.3463 9.3892 6.2645 8.5002 10.9146 9.5159 10.5233 9.6380 8.8811 5.4909 5.6621 3.9058 7.4631 7.2802 6.9358 6.5538 4.1753 5.6296 9.8542 9.8446 8.8398 11.3174 14.1204 分析：见程序里具体说明 成绩