Matlab求解插值問題

Matlab求解插值問題在應(yīng)用領(lǐng)域中，由有限個已知數(shù)據(jù)點(diǎn)，構(gòu)造一個解析表達(dá)式，由此計算數(shù)據(jù)點(diǎn)之間的函數(shù)值，稱之為插值。實例：海底探測問題某公司用聲納對海底進(jìn)行測試，在5X5海里的坐標(biāo)點(diǎn)上測得海底深度的值,希望通過這些有限的數(shù)據(jù)了解更多處的海底情況。并繪出較細(xì)致的海底曲面圖。1、一元插值一元插值是對一元數(shù)據(jù)點(diǎn)（比,片）進(jìn)行插值。線性插值：由已知數(shù)據(jù)點(diǎn)連成一條折線，認(rèn)為相臨兩個數(shù)據(jù)點(diǎn)之間的函數(shù)值就在這兩點(diǎn)之間的連線上。一般來說，數(shù)據(jù)點(diǎn)數(shù)越多，線性插值就越精確。調(diào)用格式：yi=interpl（x，y，xi，，linear，）%線性插值zi=interp1（x,y,xi,'spline'）%三次樣條插值wi=interp1（x，y，xi，'cubic'）%三次多項式插值說明：yi、zi、wi為對應(yīng)xi的不同類型的插值。x、y為已知數(shù)據(jù)點(diǎn)。例：已知數(shù)據(jù)：x0.1.2.3.4.5.6.7.8.91y.3.511.41.61.9.6.4.81.52求當(dāng)xi=0.25時的yi的值。程序：x=0:.1:1;y=[.3.511.41.61.6.4.81.52];yi0=interp1(x,y,0.025,'linear')xi=0:.02:1;yi=interp1(x,y,xi,'linear');zi=interp1(x,y,xi,'spline');wi=interp1(x,y,xi,'cubic');plot(x,y,'o',xi,yi,'r+',xi,zi,'g*',xi,wi,'k.-')legend('原始點(diǎn)’，’線性點(diǎn)’，’三次樣條'，’三次多項式')結(jié)果：yiO=0.3500FileEditToolsfindowHelp要得到給定的幾個點(diǎn)的對應(yīng)函數(shù)值，可用：xi=[0.25000.35000.4500]yi=interp1(x,y,xi,'spline')結(jié)果：yi=1.20881.58021.34542、二元插值二元插值與一元插值的基本思想一致，對原始數(shù)據(jù)點(diǎn)(x,y,z)構(gòu)造見上面函數(shù)求出插值點(diǎn)數(shù)據(jù)(xi,yi,zi)。單調(diào)節(jié)點(diǎn)插值函數(shù)，即x,y向量是單調(diào)的。調(diào)用格式1：zi=interp2(x,y,z,xi,yi,'linear')‘liner'是雙線性插值(缺省)調(diào)用格式2：zi=interp2(x,y,z,xi,yi,'nearest')'nearest'是最近鄰域插值調(diào)用格式3：zi=interp2(x,y,z,xi,yi,'spline')‘spline'是三次樣條插值說明：這里x和y是兩個獨(dú)立的向量，它們必須是單調(diào)的。z是矩陣，是由x和y確定的點(diǎn)上的值。z和x,y之間的關(guān)系是z(i,:)=f(x,y(i))，z(:,j)=f(x(j),y)即：當(dāng)x變化時，z的第i行與y的第i個元素相關(guān)，當(dāng)y變化時z的第j列與x的第j個元素相關(guān)。如果沒有對x,y賦值，則默認(rèn)x=1:n,y=l:m。n和m分別是矩陣z的行數(shù)和列數(shù)。例2：已知某處山區(qū)地形選點(diǎn)測量坐標(biāo)數(shù)據(jù)為：x=0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5y=0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.56

程序：x=0:.5:5;y=0:.5:6;z=[8990878592919693908782929698999591898684828496989592808182898282程序：x=0:.5:5;y=0:.5:6;z=[8990878592919693908782929698999591898684828496989592808182898282889285879885899492939496979885858182848681989088858483818595969392898686999697959392958987969395808081999897888582918684868384828590969583889284818193958487z=8990878592919693908782929698999591898684828496989592908885848381858081828995969392898686828587989996978885828382858994959392918684888892939495898786838192929697989693958482818485858182808081859093958486819899989796958487808185828384879095868880828184858683828180828788899899979698949287808185828384879095868880828184858683828180828788899899979698949287];mesh(x,y,z)%繪原始數(shù)據(jù)圖xi=linspace(0,5,50);%加密橫坐標(biāo)數(shù)據(jù)到50個yi=linspace(0,6,80);%加密縱坐標(biāo)數(shù)據(jù)到60個[xii,yii]=meshgrid(xi,yi);%生成網(wǎng)格數(shù)據(jù)zii=interp2(x,y,z,xii,yii,'cubic');%插值mesh(xii,yii,zii)%加密后的地貌圖holdon%保持圖形[xx,yy]=meshgrid(x,y);%生成網(wǎng)格數(shù)據(jù)plot3(xx,yy,z+0.1,'ob') %原始數(shù)據(jù)用'O'繪出3、二元非等距插值調(diào)用格式：zi二griddata(x,y,z,xi,yi,'指定插值方法')插值方法有：linear %線性插值 (默認(rèn))bilinear % 雙線性插值cubic % 三次插值bicubic%雙三次插值nearest%最近鄰域插值例3：用隨機(jī)數(shù)據(jù)生成地貌圖再進(jìn)行插值程序：x=rand(100,1)*4-2;y=rand(100,1)*4