matlab作业Word下载.docx
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matlab作业Word下载.docx
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k-1)];
s1=sum(y1);
y2=[y(3:
s2=sum(y2);
z2=(y
(1)+y(k)+4*s1+2*s2)*0.2/3
dz2=z2-z
%梯形公式
z3=trapz(x,y)
dz3=z3-z
运行结果如下:
z=1.3749
z1=1.3749
dz1=-2.0976e-009
z2=1.3743
dz2=-5.9976e-004
z3=1.3730
dz3=-0.0019
结果分析:
用梯形公式计算的积分值,其精确程度要小于用辛普森公式算出的积分值,并且自适应辛普森公式的结果最精确。
2.下表给出的x,y数据位于机翼断面的轮廓线上,Y1和Y2分别对应轮廓的上下线,假设需要得到x坐标每改变0.1时的坐标,试完成加工所需的数据,画出曲线,求加工断面的面积。
x
9
11
12
13
14
15
Y1
1.8
2.2
2.7
3.0
3.1
2.9
2.5
2.0
1.6
Y2
1.2
1.7
2.1
1.0
程序:
%按表输入原始数据
X0=[035791112131415];
Y10=[01.82.22.73.03.12.92.52.01.6];
Y20=[01.21.72.02.12.01.81.21.01.6];
x=0:
0.1:
15;
%分段线性差值
Y11=interp1(x0,Y10,x);
Y21=interp1(x0,Y20,x);
%在Y1,Y2方向计算三次样条插值
Y12=spline(x0,Y10,x);
Y22=spline(x0,Y20,x);
[Y11'
Y12'
x'
]
[Y21'
Y22'
%画出图形
subplot(2,1,1),plot(x,Y11,x,Y21,'
:
'
),axis([01504])
title('
分段线性插值'
'
FontSize'
12)
gtext('
Y1'
)
Y2'
subplot(2,1,2),plot(x,Y12,x,Y22,'
三次样条插值'
%分段线性插值积分求面积
area1=trapz(Y11-Y21)*0.1
%三次样条差值积分求面积
area2=trapz(Y12-Y22)*0.1
运行结果:
area1=10.7500
area2=11.3444
由图形可见,三次样条插值出来的曲线要比分段线性插值更光滑,从而area2=11.3444更为准确。
附表:
ans=
000
0.06000.10890.1000
0.12000.21340.2000
0.18000.31370.3000
0.24000.40970.4000
0.30000.50180.5000
0.36000.58980.6000
0.42000.67400.7000
0.48000.75450.8000
0.54000.83140.9000
0.60000.90471.0000
0.66000.97471.1000
0.72001.04131.2000
0.78001.10471.3000
0.84001.16511.4000
0.90001.22251.5000
0.96001.27701.6000
1.02001.32871.7000
1.08001.37781.8000
1.14001.42441.9000
1.20001.46852.0000
1.26001.51042.1000
1.32001.54992.2000
1.38001.58742.3000
1.44001.62292.4000
1.50001.65652.5000
1.56001.68842.6000
1.62001.71852.7000
1.68001.74712.8000
1.74001.77422.9000
1.80001.80003.0000
1.82001.82453.1000
1.84001.84803.2000
1.86001.87043.3000
1.88001.89183.4000
1.90001.91253.5000
1.92001.93253.6000
1.94001.95193.7000
1.96001.97083.8000
1.98001.98943.9000
2.00002.00764.0000
2.02002.02584.1000
2.04002.04394.2000
2.06002.06204.3000
2.08002.08034.4000
2.10002.09894.5000
2.12002.11794.6000
2.14002.13744.7000
2.16002.15754.8000
2.18002.17844.9000
2.20002.20005.0000
2.22502.22255.1000
2.25002.24595.2000
2.27502.27005.3000
2.30002.29485.4000
2.32502.32015.5000
2.35002.34595.6000
2.37502.37205.7000
2.40002.39845.8000
2.42502.42495.9000
2.45002.45156.0000
2.47502.47816.1000
2.50002.50456.2000
2.52502.53076.3000
2.55002.55666.4000
2.57502.58216.5000
2.60002.60716.6000
2.62502.63156.7000
2.65002.65526.8000
2.67502.67806.9000
2.70002.70007.0000
2.71502.72107.1000
2.73002.74117.2000
2.74502.76027.3000
2.76002.77867.4000
2.77502.79617.5000
2.79002.81307.6000
2.80502.82917.7000
2.82002.84467.8000
2.83502.85957.9000
2.85002.87398.0000
2.86502.88788.1000
2.88002.90138.2000
2.89502.91448.3000
2.91002.92728.4000
2.92502.93978.5000
2.94002.95208.6000
2.95502.96418.7000
2.97002.97618.8000
2.98502.98818.9000
3.00003.00009.0000
3.00503.01199.1000
3.01003.02389.2000
3.01503.03559.3000
3.02003.04699.4000
3.02503.05789.5000
3.03003.06839.6000
3.03503.07829.7000
3.04003.08739.8000
3.04503.09569.9000
3.05003.102910.0000
3.05503.109210.1000
3.06003.114310.2000
3.06503.118110.3000
3.07003.120610.4000
3.07503.121510.5000
3.08003.120910.6000
3.08503.118510.7000
3.09003.114310.8000
3.09503.108210.9000
3.10003.100011.0000
3.08003.089711.1000
3.06003.077211.2000
3.04003.062611.3000
3.02003.045911.4000
3.00003.026911.5000
2.98003.005911.6000
2.96002.982611.7000
2.94002.957311.8000
2.92002.929711.9000
2.90002.900012.0000
2.86002.868212.1000
2.82002.834212.2000
2.78002.798412.3000
2.74002.760612.4000
2.70002.721112.5000
2.66002.679812.6000
2.62002.637012.7000
2.58002.592712.8000
2.54002.547012.9000
2.50002.500013.0000
2.45002.451813.1000
2.40002.402613.2000
2.35002.352713.3000
2.30002.302113.4000
2.25002.251313.5000
2.20002.200413.6000
2.15002.149613.7000
2.10002.099113.8000
2.05002.049113.9000
2.00002.000014.0000
1.96001.951914.1000
1.92001.904914.2000
1.88001.859414.3000
1.84001.815614.4000
1.80001.773714.5000
1.76001.733914.6000
1.72001.696314.7000
1.68001.661414.8000
1.64001.629214.9000
1.60001.600015.0000
0.04000.04990.1000
0.08000.09900.2000
0.12000.14740.3000
0.16000.19510.4000
0.20000.24210.5000
0.24000.28840.6000
0.28000.33400.7000
0.32000.37880.8000
0.36000.42300.9000
0.40000.46651.0000
0.44000.50941.1000
0.48000.55151.2000
0.52000.59301.3000
0.56000.63381.4000
0.60000.67391.5000
0.64000.71341.6000
0.68000.75231.7000
0.72000.79041.8000
0.76000.82801.9000
0.80000.86492.0000
0.84000.90122.1000
0.88000.93682.2000
0.92000.97192.3000
0.96001.00632.4000
1.00001.04012.5000
1.04001.07322.6000
1.08001.10582.7000
1.12001.13782.8000
1.16001.16922.9000
1.20001.20003.0000
1.22501.23023.1000
1.25001.25993.2000
1.27501.28893.3000
1.30001.31743.4000
1.32501.34543.5000
1.35001.37273.6000
1.37501.39953.7000
1.40001.42583.8000
1.42501.45153.9000
1.45001.47674.0000
1.47501.50144.1000
1.50001.52554.2000
1.52501.54914.3000
1.55001.57224.4000
1.57501.59474.5000
1.60001.61684.6000
1.62501.63834.7000
1.65001.65944.8000
1.67501.67994.9000
1.70001.70005.0000
1.71501.71965.1000
1.73001.73875.2000
1.74501.75735.3000
1.76001.77545.4000
1.77501.79305.5000
1.79001.81025.6000
1.80501.82695.7000
1.82001.84305.8000
1.83501.85885.9000
1.85001.87406.0000
1.86501.88876.1000
1.88001.90306.2000
1.89501.91686.3000
1.91001.93016.4000
1.92501.94306.5000
1.94001.95536.6000
1.95501.96726.7000
1.97001.97866.8000
1.98501.98956.9000
2.00002.00007.0000
2.00502.01007.1000
2.01002.01957.2000
2.01502.02857.3000
2.02002.03707.4000
2.02502.04507.5000
2.03002.05257.6000
2.03502.05957.7000
2.04002.06607.8000
2.04502.07197.9000
2.05002.07738.0000
2.05502.08228.1000
2.06002.08658.2000
2.06502.09028.3000
2.07002.09338.4000
2.07502.09598.5000
2.08002.09798.6000
2.08502.09948.7000
2.09002.10028.8000
2.09502.10048.9000
2.10002.10009.0000
2.09502.09909.1000
2.09002.09749.2000
2.08502.09529.3000
2.08002.09259.4000
2.07502.08939.5000
2.07002.08579.6000
2.06502.08159.7000
2.06002.07709.8000
2.05502.07219.9000
2.05002.066810.0000
2.04502.061110.1000
2.04002.055210.2000
2.03502.049010.3000
2.03002.042510.4000
2.02502.035810.5000
2.02002.028910.6000
2.01502.021910.7000
2.01002.014710.8000
2.00502.007410.9000
2.00002.000011.0000
1.98001.992411.1000
1.96001.984111.2000
1.94001.974211.3000
1.92001.962111.4000
1.90001.946911.5000
1.88001.928011.6000
1.86001.904611.7000
1.84001.875911.8000
1.82001.841311.9000
1.80001.800012.0000
1.74001.751612.1000
1.68001.697012.2000
1.62001.637712.3000
1.56001.574912.4000
1.50001.509912.5000
1.44001.444212.6000
1.38001.379012.7000
1.32001.315712.8000
1.26001.255612.9000
1.20001.200013.0000
1.18001.150113.1000
1.16001.106313.2000
1.14001.068713.3000
1.12001.037713.4000
1.10001.013413.5000
1.08000.996013.6000
1.06000.985713.7000
1.04000.982813.8000
1.02000.987513.9000
1.00001.000014.0000
1.06001.020514.1000
1.12001.049214.2000
1.18001.086314.3000
1.24001.132014.4000
1.30001.186614.5000
1.36001.250314.6000
1.42001.323314.7000
1.48001.405714.8000
1.54001.497914.9000
1.60001.600015.0000
3、某海岛上有12个主要的居民点,每个居民点的位置(用平面坐标x,y表示,距离单位:
km)和居住的人数R如下表所示.现在准备在岛上建一个服务中心为居民提供各种服务,那么服务中心应该建在何处?
居民点
8
10
8.20
0.50
5.70
0.77
2.87
4.43
2.58
0.72
9.76
3.19
5.55
y
4.90
5.00
6.49
8.76
3.26
9.32
9.96
3.16
7.20
7.88
R
600
1000
800
1400
1200
700
1100
答:
此问题实际上是求所有居民到服务中心的距离之和最小时,服务中心的坐标值,故用fminunc命令求出最小值。
%建立exfun.m文件
functionr=exfun(z,x,y,R)
r=0
fori=1:
r=r+R(i)*sqrt((z
(1)-x(i))^2+(z
(2)-y(i))^2);
end
%输入程序
x=[0,8.2,0.5,5.7,0.77,2.87,4.43,2.58,0.72,9.76,3.19,5.55];
y=[0,0.5,4.9,5.0,6.49,8.76,3.26,9.32,9.96,3.16,7.2,7.88];
R=[600,1000,800,1400,1200,700,600,800,1000,1200,1000,1100];
[r,fv]=fminunc(@exfun,[0,0],[],x,y,R)
Optimizationterminated:
relativeinfinity-normofgradientlessthanoptions.TolFun.
r=3.60106.5142
fv=4.4236e+004
结果显示,当服务中心的坐标为(3.6010,6.5142)时,所有居民到服务中心的距离之和最小,为4.4236e+004。
所以服务中心应该建立在(3.6010,6.5142)的坐标上。
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