用MATLAB作函數插值教材

一維插值函數：yi=interp1(x，y，xi，'method')插值方法被插值點插值節(jié)點xi處的插值結果‘nearest’

：最鄰近插值‘linear’

：線性插值；‘spline’

：三次樣條插值；‘cubic’

：立方插值。缺省時：分段線性插值。注意：所有的插值方法都要求x是單調的，并且xi不能夠超過x的范圍。用MATLAB作函數插值

例：在1-12的11小時內，每隔1小時測量一次溫度，測得的溫度依次為：5，8，9，15，25，29，31，30，22，25，27，24。試估計每隔1/10小時的溫度值。hours=1:12;temps=[589152529313022252724];h=1:0.1:12;t=interp1(hours,temps,h,'spline');(直接輸出數據將是很多的)plot(hours,temps,'+',h,t,hours,temps,'r:')%作圖xlabel('Hour'),ylabel('DegreesCelsius’)

xy機翼下輪廓線例已知飛機下輪廓線上數據如下，求x每改變0.1時的y值。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')

要求x0,y0單調；x，y可取為矩陣，或x取行向量，y取為列向量，x,y的值分別不能超出x0,y0的范圍。z=interp2(x0,y0,z0,x,y,’method’)被插值點插值方法用MATLAB作網格節(jié)點數據的插值插值節(jié)點被插值點的函數值‘nearest’

最鄰近插值‘linear’

雙線性插值‘cubic’

雙三次插值缺省時,雙線性插值例：測得平板表面3*5網格點處的溫度分別為：828180828479636165818484828586試作出平板表面的溫度分布曲面z=f(x,y)的圖形。輸入以下命令：x=1:5;y=1:3;temps=[8281808284;7963616581;8484828586];mesh(x,y,temps)2．以平滑數據,在x、y方向上每隔0.2個單位的地方進行插值.1.先在三維坐標畫出原始數據，畫出粗糙的溫度分布曲面圖.再輸入以下命令:xi=1:0.2:5;yi=1:0.2:3;zi=interp2(x,y,temps,xi,yi,'cubic');mesh(xi,yi,zi)畫出插值后的溫度分布曲面圖.ToMATLAB(wendu)

通過此例對最近鄰點插值、雙線性插值方法和雙三次插值方法的插值效果進行比較。x=0:400:5600;y=0:400:4800;z=[370470550600670690670620580450400300100150250;...510620730800850870850780720650500200300350320;...650760880970102010501020830900700300500550480350;...740880108011301250128012301040900500700780750650550;...830980118013201450142014001300700900850840380780750;...88010601230139015001500140090011001060950870900930950;...9101090127015001200110013501450120011501010880100010501100;...9501190137015001200110015501600155013801070900105011501200;...143014301460150015501600155016001600160015501500150015501550;...1420143014501480150015501510143013001200980850750550500;...138014101430145014701320128012001080940780620460370350;...13701390141014301440114011101050950820690540380300210;...13501370139014001410960940880800690570430290210150];主程序:moutain.mfigure(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');

插值函數griddata格式為:

cz

=griddata（x，y，z，cx，cy，‘method’）用MATLAB作散點數據的插值計算

要求cx取行向量，cy取為列向量。被插值點插值方法插值節(jié)點被插值點的函