插值及matlab处理.doc

插值：例1编写程序如下：clearx0=0,3,5,7,9,11,12,13,14,15;y0=0,1.2,1.7,2.0,2.1,2.0,1.8,1.2,1.0,1.6;x=13:0.1:15;y1=lagrange(x0,y0,x);y2=interp1(x0,y0,x);y3=interp1(x0,y0,x,spline);pp1=csape(x0,y0);y4=ppval(pp1,x);pp2=csape(x0,y0,not-a-knot);y5=ppval(pp2,x);fprintf(比较不同插值结果下的边界值的差别:n)fprintf(x,y1,y2,y3,y4,y5n)xianshi=x,y1,y2,y3,y4,y5;fprintf(%ft%ft%ft%ft%ft%fn,xianshi)subplot(2,2,1),plot(x0,y0,*r,x,y1),title(lagrange)subplot(2,2,2),plot(x0,y0,*b,x,y2),title(linear)subplot(2,2,3),plot(x0,y0,*y,x,y3),title(spline)subplot(2,2,4),plot(x0,y0,*g,x,y4),title(spline csape1)subplot(2,2,4),plot(x0,y0,*c,x,y5),title(spline csape2)dyx0=ppval(fnder(pp1),x0(1) %求x=0处的导数ytemp=y3(13:15);index=find(ytemp=min(ytemp);xymin=x(13+index),ytemp(index)function y=lagrange(x0,y0,x);n=length(x0);m=length(x);for i=1:m z=x(i); s=0.0; for k=1:n p=1.0; for j=1:n if j=k p=p*(z-x0(j)/(x0(k)-x0(j); end end s=p*y0(k)+s; end y(i)=s;end比较不同插值结果下的边界值的差别:x, y1, y2 y3, y4, y513.0000001.2000001.2000001.2000001.2000001.20000013.1000001.1398561.1800001.1500901.1506011.15009013.2000001.0848011.1600001.1062571.1073611.10625713.3000001.0363881.1400001.0687141.0704191.06871413.4000000.9961671.1200001.0376751.0399161.03767513.5000000.9656441.1000001.0133551.0159941.01335513.6000000.9462201.0800000.9959660.9987910.99596613.7000000.9391291.0600000.9857220.9884500.98572213.8000000.9453611.0400000.9828380.9851110.98283813.9000000.9655751.0200000.9875260.9889140.98752614.0000001.0000001.0000001.0000001.0000001.00000014.1000001.0483241.0600001.0204741.0185671.02047414.2000001.1095681.1200001.0491621.0450441.04916214.3000001.1819451.1800001.0862781.0799181.08627814.4000001.2627041.2400001.1320341.1236751.13203414.5000001.3479551.3000001.1866451.1768011.18664514.6000001.4324811.3600001.2503251.2397831.25032514.7000001.5095221.4200001.3232861.3131081.32328614.8000001.5705451.4800001.4057431.3972611.40574314.9000001.6049911.5400001.4979101.4927301.49791015.0000001.6000001.6000001.6000001.6000001.600000dyx0 = 0.5007xymin =14.3000 1.0492二维插网格节点一）：另一组数据：原始数据例2已知某处山区地形选点测量坐标数据为：海拔高度数据为： Xy 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5089908785929196939087820.500092969899959189868482841.000096989592908885848381851.500080818289959693928986862.00082858798999697888582832.500082858994959392918684883.000088929394958987868381923.500092969798969395848281844.000085858182808081859093954.500084868198999897969584875.000080818582838487909586885.500080828184858683828180826.00008788899899979698949287程序：x=0:0.5:5;y=0:0.5:6;z=89 90 87 85 92 91 96 93 90 87 82 92 96 98 99 95 91 89 86 84 82 84 96 98 95 92 90 88 85 84 83 81 85 80 81 82 89 95 96 93 92 89 86 86 82 85 87 98 99 96 97 88 85 82 83 82 85 89 94 95 93 92 91 86 84 88 88 92 93 94 95 89 87 86 83 81 92 92 96 97 98 96 93 95 84 82 81 84 85 85 81 82 80 80 81 85 90 93 95 84 86 81 98 99 98 97 96 95 84 87 80 81 85 82 83 84 87 90 95 86 88 80 82 81 84 85 86 83 82 81 80 82 87 88 89 98 99 97 96 98 94 92 87;mesh(x,y,z) %绘原始数据图xi=linspace(0,5,50); %加密横坐标数据到50个yi=linspace(0,6,80); %加密纵坐标数据到60个xii,yii=meshgrid(xi,yi); %生成网格数据zii=interp2(x,y,z,xii,yii,cubic); %插值mesh(xii,yii,zii) %加密后的地貌图hold on % 保持图形xx,yy=meshgrid(x,y); %生成网格数据plot3(xx,yy,z+0.1,ob) %原始数据用O绘出sandian散点插值：程序：clearx=129,140,103.5,88,185.5,195,105,157.5,107.5,77,81,162,162,117.5;y=7.5,141.5,23,147,22.5,137.5,85.5,-6.5,-81,3,56.5,-66.5,84,-33.5;z=-4,-8,-6,-8