MATLAB插值程序

插值程序例1：55,11)(2xxxg采用拉格朗日多项式插值：选取不同插值节点个数n+1，其中n为插值多项式的次数，当n分别取2,4,6,8,10时，绘出插值结果图形.1、Large1:functiony=lagr1(x0,y0,x)n=length(x0);m=length(x);fori=1:mz=x(i);s=0.0;fork=1:np=1.0;forj=1:nifj~=kp=p*(z-x0(j))/(x0(k)-x0(j));endends=p*y0(k)+s;endy(i)=s;end2、lch:m=101;x=-5:10/(m-1):5;y=1./(1+x.^2);z=0*x;plot(x,z,'r',x,y,'LineWidth',1.5),gtext('y=1/(1+x^2)'),pausen=3;x0=-5:10/(n-1):5;y0=1./(1+x0.^2);y1=lagr1(x0,y0,x);holdon,plot(x,y1,'b'),gtext('n=2'),pause,holdoffn=5;x0=-5:10/(n-1):5;y0=1./(1+x0.^2);y2=lagr1(x0,y0,x);holdon,plot(x,y2,'b:'),gtext('n=4'),pause,holdoffn=7;x0=-5:10/(n-1):5;y0=1./(1+x0.^2);y3=lagr1(x0,y0,x);holdon,plot(x,y3,'r'),gtext('n=6'),pause,holdoffn=9;x0=-5:10/(n-1):5;y0=1./(1+x0.^2);y4=lagr1(x0,y0,x);holdon,plot(x,y4,'r:'),gtext('n=8'),pause,holdoffn=11;x0=-5:10/(n-1):5;y0=1./(1+x0.^2);y5=lagr1(x0,y0,x);holdon,plot(x,y5,'m'),gtext('n=10')例2：55,11)(2xxxg用分段线性插值法求插值,并观察插值误差.（1）xch11:x=linspace(-6,6,100);y=1./(x.^2+1);x1=linspace(-6,6,5);y1=1./(x1.^2+1);plot(x,y,x1,y1,x1,y1,'o','LineWidth',1.5),gtext('n=4'),（2）xch12x=linspace(-6,6,100);y=1./(x.^2+1);x1=linspace(-6,6,11);y1=1./(x1.^2+1);plot(x,y,x1,y1,x1,y1,'o','LineWidth',1.5),1.在[-6,6]中平均选取5个点作插值(xch11)4.在[-6,6]中平均选取1个点作插值(xch14)2.在[-6,6]中平均选取11个点作插值(xch12)3.在[-6,6]中平均选取21个点作插值(xch13)gtext('n=10'),（3）xch13x=linspace(-6,6,100);y=1./(x.^2+1);x1=linspace(-6,6,21);y1=1./(x1.^2+1);plot(x,y,x1,y1,x1,y1,'o','LineWidth',1.5),gtext('n=20'),（4）xch14x=linspace(-6,6,100);y=1./(x.^2+1);x1=linspace(-6,6,41);y1=1./(x1.^2+1);plot(x,y,x1,y1,x1,y1,'o','LineWidth',1.5),gtext('n=40'),例2:66,11)(2xxxg用三次样条插值选取11个基点计算插值ych：x0=linspace(-5,5,11);y0=1./(1+x0.^2);x=linspace(-5,5,100);y=interp1(x0,y0,x,'spline');x1=linspace(-5,5,100);y1=1./(1+x1.^2);plot(x1,y1,'k',x0,y0,'+',x,y,'r');例3：在1-12的11小时内，每隔1小时测量一次温度，测得的温度依次为：5，8，9，15，25，29，31，30，22，25，27，24。试估计每隔1/10小时的温度值。temp:hours=1:12;temps=[589152529313022252724];h=1:0.1:12;t=interp1(hours,temps,h,'spline');plot(hours,temps,'+',h,t,hours,temps,'r:')xlabel('Hour'),ylabel('DegreesCelsius')例4：已知飞机下轮廓线上数据如下，求x每改变0.1时的y值。X035791112131415Y01.21.72.02.12.01.81.21.01.6plane:x0=[035791112131415];y0=[01.21.72.02.12.01.81.21.01.6];x=0:0.1:15;y1=lagr1(x0,y0,x);y2=interp1(x0,y0,x);y3=interp1(x0,y0,x,'spline');subplot(3,1,1)plot(x0,y0,'k+',x,y1,'r')gridtitle('lagrange')subplot(3,1,2)plot(x0,y0,'k+',x,y2,'r')gridtitle('piecewiselinear')subplot(3,1,3)plot(x0,y0,'k+',x,y3,'r')gridtitle('spline')例5：测得平板表面3*5网格点处的温度分别为：828180828479636165818484828586试作出平板表面的温度分布曲面z=f(x,y)的图形。wendu:x=1:5;y=1:3;temps=[8281808284;7963616581;8484828586];mesh(x,y,temps)pausexi=1:0.2:5;yi=1:0.2:3;zi=interp2(x,y,temps,xi',yi,'cubic');figure(2)mesh(xi,yi,zi)例6：山区地貌：在某山区测得一些地点的高程如下表。平面区域为1200=x=4000,1200=y=3600)试作出该山区的地貌图和等高线图，并对几种插值方法进行比较。XY12001600200024002800320036004000120011301250128012301040900500700160013201450142014001300700900850200013901500150014009001100106095024001500120011001350145012001150101028001500120011001550160015501380107032001500155016001550160016001600155036001480150015501510143013001200980通过此例对最近邻点插值、双线性插值方法和双三次插值方法的插值效果进行比较。moutain:x=0:400:5600;y=0:400:4800;z=[370470550600670690670620580450400300100150250;...510620730800850870850780720650500200300350320;...650760880970102010501020830900700300500550480350;...740880108011301250128012301040900500700780750650550;...830980118013201450142014001300700900850840380780750;...88010601230139015001500140090011001060950870900930950;...9101090127015001200110013501450120011501010880100010501100;...9501190137015001200110015501600155013801070900105011501200;...143014301460150015501600155016001600160015501500150015501550;...1420143014501480150015501510143013001200980850750550500;...138014101430145014701320128012001080940780620460370350;...13701390141014301440114011101050950820690540380300210;...13501370139014001410960940880800690570430290210150];figure(1);meshz(x,y,z)xlabel('X'),ylabel('Y'),zlabel('Z')xi=0:50:5600;yi=0:50:4800;figure(2)z1i=interp2(x,y,z,xi,yi','nearest');surfc(xi,yi,z1i)xlabel('X'),ylabel('Y'),zlabel('Z')figure(3)z2i=interp2(x,y,z,xi,yi');surfc(xi,yi,z2i)xlabel('X'),ylabel('Y'),zlabel('Z')figure(4)z3i=interp2(x,y,z,xi,yi','cubic');surfc(xi,yi,z3i)xlabel('X'),ylabel('Y'),zlabel('Z')figure(5)subplot(1,3,1),contour(xi,yi,z1i,10,'r');subplot(1,3,2),contour(xi,yi,z2i,10,'r');subplot(1,3,3),contour(xi,yi,z3i,10,'r');实验作业山区地貌：在某山区测得一些地点的高程如下表：(平面区域:1200=x=4000,1200=y=3600)，试作出该山区的地貌图和等高线图，并对几种插值方法进行比较。360032002800240020001600120014801500155015101430130012009801500155016001550160016001600155015001200110015501600155013801070150012001100135014501200115010101390150015001400900110010609501320145014201400130070090085011301250128012301040900500700Y/x12001600200024002800320036004000