矩阵的基本运算之数学建模实验报告.docx
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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;4,8,0,1,1]
2.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;3,7,1,0,1;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
-5.4
7.3
23.1
27.3
21.2
13.8
5.3
-2.4
2
天津
-4.9
7.6
23.0
27.1
21.2
14.8
5.3
-2.5
3
石家庄
-3.5
10.8
24.1
28.2
21.8
15.5
7.3
-0.9
4
太原
-4.6
6.2
20.2
24.8
17.2
12.0
2.9
-4.6
5
呼和浩特
-9.9
0.7
18.2
25.0
16.1
9.3
-0.7
-10.5
6
沈阳
-16.2
0.2
19.2
25.7
18.4
11.9
1.0
-10.2
7
大连
-5.6
3.7
18.2
24.6
21.3
15.2
6.9
-1.9
8
长春
-19.8
-3.0
17.0
24.2
17.0
9.8
-1.5
-12.2
9
哈尔滨
-22.8
-4.4
16.5
24.5
15.8
8.2
-2.4
-13.9
10
上海
5.9
11.0
20.8
29.7
24.9
20.2
13.7
7.1
11
南京
4.0
10.7
22.7
30.2
24.0
18.8
10.8
4.8
12
杭州
6.1
12.3
21.9
30.3
24.1
19.5
12.7
6.6
13
合肥
3.7
11.7
23.8
30.6
24.0
18.3
11.2
4.4
14
福州
12.9
15.6
23.2
29.1
26.3
22.9
17.3
13.6
15
南昌
6.7
12.7
23.3
30.6
25.8
20.9
13.8
6.5
16
济南
-1.5
9.6
24.6
27.4
21.0
16.2
8.4
-0.5
17
青岛
-0.4
6.1
17.8
25.0
22.1
17.2
9.1
1.1
18
郑州
-1.3
11.6
23.9
27.6
21.7
16.5
9.1
0.7
19
武汉
4.7
13.2
24.0
31.8
26.2
19.4
12.9
4.4
20
长沙
5.4
12.7
22.9
30.4
25.0
19.2
13.2
4.9
21
广州
15.4
19.4
26.5
28.2
27.8
25.4
19.7
14.9
22
南宁
14.4
18.2
24.9
27.8
26.1
23.6
17.3
13.1
23
海口
20.0
22.6
27.8
28.7
27.9
26.7
22.2
19.5
24
桂林
8.7
15.1
23.5
28.3
26.4
22.2
16.1
8.3
25
重庆
8.3
16.1
22.5
30.7
24.5
19.7
15.1
8.6
26
成都
7.0
15.1
22.7
27.6
20.8
18.8
13.6
6.8
27
贵阳
4.9
12.1
17.4
23.2
20.6
16.3
11.3
4.7
28
昆明
10.3
14.9
17.0
20.9
19.4
16.4
11.4
10.3
29
拉萨
1.1
4.9
12.4
15.9
14.3
9.2
3.8
1.0
30
西安
1.1
12.1
22.2
29.1
20.0
15.0
7.9
0.7
31
兰州
-3.2
6.5
17.7
23.9
16.9
11.9
4.3
-3.1
32
西宁
-6.9
1.6
11.5
17.6
12.4
7.3
0.1
-6.6
33
银川
-4.7
4.5
18.9
24.9
16.3
11.1
1.9
-6.9
34
乌鲁木齐
-11.8
3.0
19.9
23.4
16.2
8.0
1.7
-15.2
程序:
A=[-5.4-1.57.314.423.125.727.325.821.213.85.3-2.4
-4.9-1.67.614.423.025.827.126.421.214.85.3-2.5
-3.50.510.815.424.127.328.226.321.815.57.3-0.9
-4.6-0.26.212.420.223.524.822.117.212.02.9-4.6
-9.9-5.10.710.418.223.225.022.116.19.3-0.7-10.5
-16.2-9.10.211.819.224.125.723.718.411.91.0-10.2
-5.6-2.63.710.918.223.024.624.721.315.26.9-1.9
-19.8-13.9-3.09.817.023.024.222.217.09.8-1.5-12.2
-22.8-16.5-4.48.616.522.824.521.715.88.2-2.4-13.9
5.96.811.015.220.824.229.727.024.920.213.77.1
4.05.810.715.622.724.730.226.724.018.810.84.8
6.17.112.316.021.924.430.326.424.119.512.76.6
3.75.811.716.123.825.430.626.724.018.311.24.4
12.912.915.618.223.226.829.128.826.322.917.313.6
6.78.412.717.123.325.630.627.125.820.913.86.5
-1.51.69.615.824.627.227.425.721.016.28.4-0.5
-0.42.06.111.317.821.225.025.422.117.29.11.1
-1.32.611.615.423.926.927.626.021.716.59.10.7
4.76.913.217.324.026.931.828.626.219.412.94.4
5.47.512.716.522.925.730.427.425.019.213.24.9
15.415.119.421.726.527.228.229.127.825.419.714.9
14.413.818.221.624.926.927.827.726.123.617.313.1
20.018.922.626.827.828.628.728.627.926.722.219.5
8.710.515.118.123.526.128.327.626.422.216.18.3
8.311.116.117.722.524.130.727.224.519.715.18.6
7.010.015.117.322.723.827.624.320.818.813.66.8
4.96.712.114.417.420.223.221.620.616.311.34.7
10.311.714.919.617.020.020.920.519.416.411.410.3
1.14.74.98.112.414.615.915.414.39.23.81.0
1.15.012.114.622.226.329.125.420.015.07.90.7
-3.21.16.511.417.722.223.922.416.911.94.3-3.1
-6.9-3.31.67.411.515.617.615.612.47.30.1-6.6
-4.7-1.54.511.318.923.224.922.716.311.11.9-6.9
-11.8-8.93.09.619.923.123.423.416.28.01.7-15.2
]
B=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(分析):
A=
15101
26011
37101
48011
题目2:
结果:
A1=
15101
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=
Columns1through9
-5.4000-1.50007.300014.400023.100025.700027.300025.800021.2000
-4.9000-1.60007.600014.400023.000025.800027.100026.400021.2000
-3.50000.500010.800015.400024.100027.300028.200026.300021.8000
-4.6000-0.20006.200012.400020.200023.500024.800022.100017.2000
-9.9000-5.10000.700010.400018.200023.200025.000022.100016.1000
-16.2000-9.10000.200011.800019.200024.100025.700023.700018.4000
-5.6000-2.60003.700010.900018.200023.000024.600024.700021.3000
-19.8000-13.9000-3.00009.800017.000023.000024.200022.200017.0000
-22.8000-16.5000-4.40008.600016.500022.800024.500021.700015.8000
5.90006.800011.000015.200020.800024.200029.700027.000024.9000
4.00005.800010.700015.600022.700024.700030.200026.700024.0000
6.10007.100012.300016.000021.900024.400030.300026.400024.1000
3.70005.800011.700016.100023.800025.400030.600026.700024.0000
12.900012.900015.600018.200023.200026.800029.100028.800026.3000
6.70008.400012.700017.100023.300025.600030.600027.100025.8000
-1.50001.60009.600015.800024.600027.200027.400025.700021.0000
-0.40002.00006.100011.300017.800021.200025.000025.400022.1000
-1.30002.600011.600015.400023.900026.900027.600026.000021.7000
4.70006.900013.200017.300024.000026.900031.800028.600026.2000
5.40007.500012.700016.500022.900025.700030.400027.400025.0000
15.400015.100019.400021.700026.500027.200028.200029.100027.8000
14.400013.800018.200021.600024.900026.900027.800027.700026.1000
20.000018.900022.600026.800027.800028.600028.700028.600027.9000
8.700010.500015.100018.100023.500026.100028.300027.600026.4000
8.300011.100016.100017.700022.500024.100030.700027.200024.5000
7.000010.000015.100017.300022.700023.800027.600024.300020.8000
4.90006.700012.100014.400017.400020.200023.200021.600020.6000
10.300011.700014.900019.600017.000020.000020.900020.500019.4000
1.10004.70004.90008.100012.400014.600015.900015.400014.3000
1.10005.000012.100014.600022.200026.300029.100025.400020.0000
-3.20001.10006.500011.400017.700022.200023.900022.400016.9000
-6.9000-3.30001.60007.400011.500015.600017.600015.600012.4000
-4.7000-1.50004.500011.300018.900023.200024.900022.700016.3000
-11.8000-8.90003.00009.600019.900023.100023.400023.400016.2000
Columns10through12
13.80005.3000-2.4000
14.80005.3000-2.5000
15.50007.3000-0.9000
12.00002.9000-4.6000
9.3000-0.7000-10.5000
11.90001.0000-10.2000
15.20006.9000-1.9000
9.8000-1.5000-12.2000
8.2000-2.4000-13.9000
20.200013.70007.1000
18.800010.80004.8000
19.500012.70006.6000
18.300011.20004.4000
22.900017.300013.6000
20.900013.80006.5000
16.20008.4000-0.5000
17.20009.10001.1000
16.50009.10000.7000
19.400012.90004.4000
19.200013.20004.9000
25.400019.700014.9000
23.600017.300013.1000
26.700022.200019.5000
22.200016.10008.3000
19.700015.10008.6000
18.800013.60006.8000
16.300011.30004.7000
16.400011.400010.3000
9.20003.80001.0000
15.00007.90000.7000
11.90004.3000-3.1000
7.30000.1000-6.6000
11.10001.9000-6.9000
8.00001.7000-15.2000
m=
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
8.7833
14.9500
11.0000
6.0250
10.1417
7.7000
s=
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