matlab软件拟合与插值运算实验报告Word文档格式.docx
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MATLAB中提供了众多的数据处理命令,有插值命令,拟合命令。
1.曲线拟合
>
x=[0.5,1.0,1.5,2.0,2.5,3.0];
y=[1.75,2.45,3.81,4.80,7.00,8.60];
p=polyfit(x,y,2);
x1=0.5:
0.05:
3.0;
y1=polyval(p,x1);
plot(x,y,'
*r'
x1,y1,'
-b'
)
2.一维插值
year=[1900,1910,1920,1930,1940,1990,2000,2010];
product=[75.995,91.972,105.711,123.203,131.669,249.633,256.344,267.893];
p2005=interp1(year,product,2005)
p2005=
262.1185
y=interp1(year,product,x,'
cubic'
);
plot(year,product,'
o'
x,y)
3.二维插值
years=1950:
10:
1990;
service=10:
30;
wage=[150.697,199.592,187.625;
179.323,195.072,250.287;
203.212,179.092,322.767;
226.505,153.706,426.730;
249.636,120.281,598.243];
w=interp2(service,years,wage,15,1975)
w=
190.6288
[例1.98]
x=1:
6;
y=1:
4;
t=[12,10,11,11,13,15;
16,22,28,35,27,20;
18,21,26,32,28,25;
20,25,30,33,32,30];
subplot(1,2,1)
mesh(x,y,t)
x1=1:
0.1:
y1=1:
[x2,y2]=meshgrid(x1,y1);
t1=interp2(x,y,t,x2,y2,'
subplot(1,2,2)
mesh(x1,y1,t1)
三,练习与思考
1)已知x=[1.2,1.8,2.1,2.4,2.6,3.0,3.3],y=[4.85,5.2,5.6,6.2,6.5,7.0,7.5],求对x和y进行6阶多项式拟合的系数.
x=[1.2,1.8,2.1,2.4,2.6,3.0,3.3];
y=[4.85,5.2,5.6,6.2,6.5,7.0,7.5];
p=polyfit(x,y,6)
p=
-2.010729.0005-170.6763523.2180-878.3092763.9307-263.4667
x1=0.5:
y1=polyval(p,x1);
2)分别用2,3,4,5阶多项式来逼近[0,3]上的正弦函数sinx,并做出拟合曲线及sinx函数曲线图,了解多项式的逼近程度和有效拟合区间随多项式的阶数有何变化.
(2)
2阶:
x=0:
0.01:
3;
y=sin(x);
p=polyfit(x,y,2);
x1=0:
3阶:
p=polyfit(x,y,3);
4阶:
p=polyfit(x,y,4);
5阶:
>
p=polyfit(x,y,5);
3)已知x=[0.1,0.8,1.3,1.9,2.5,3.1],y=[1.2,1.6,2.7,2.0,1.3,0.5],用不同的方法求x=2点的插值,并分析所得结果有何不同.
x=[0.1,0.8,1.3,1.9,2.5,3.1];
y=[1.2,1.6,2.7,2.0,1.3,0.5];
p=interp1(x,y,2)
1.8833
z=interp1(x,y,2,'
z=
1.8844
四,提高内容
1.三维数据插值
[x,y,z,v]=flow(20);
[xx,yy,zz]=meshgrid(0.1:
0.25:
10,-3:
3,-3:
3);
vv=interp3(x,y,z,v,xx,yy,zz);
slice(xx,yy,zz,vv,[6,9.5],[1,2],[-2,0.2]);
shadinginterp
colormapcool
3.三次样条数据插值
x=[024561212.817.219.920];
y=exp(x).*sin(x);
xx=0:
.25:
20;
yy=spline(x,y,xx);
plot(x,y,'
xx,yy)