实习：Matlab作业hermite插值

1、题目：利用插值实现数据的插值和分段三次小组成员:王晓波(1蔡明宇()一、程序实现意义：一般的，从各种试验得来的数据总有一定的数量，而利用插值技术能够从有限的数据中获取整体的状态。而Hermite插值不仅保证了插值函数与原函数在给定数据点处得拟合，同时保证了在相应点处导数的相同，从而在很大程度上保证了曲线的“光滑性”。因此，通过Matlab实现Hermite插值具有很普遍的意义。二、实现过程：1、Hermite插值由于并不是所有的Matlab版本都提供现有的Hermite插值函数包，故我们首先编写了实现给定五个观测点的Hermite插值的M程序，代码如下：functionf,f0=Hermite

2、1(x,y,y_1)symst;f=0.0;if(length(x)=length(y)if(length(y)=length(y_1)n=length(x);elsedisp(y和y的导数的维数不相等)；return;endelsedisp(x和y的维数不相等！);return;endfori=1:nh=1.0;a=0.0;forj=1:nif(j=i)h=h*(t-x(j)人2/(x(i)-x(j)人2);a=a+1/(x(i)-x(j);endendf=f+h*(x(i)-t)*(2*a*y(i)-y_1(i)+y(i);endf0=subs(f,t);其中为给定点横坐标数组，为给定点纵

3、坐标数组，为原函数在给定点处的导数数组。测试证明该程序可以实现，例如输入如下数组：x=1:0.2:1.8;y_1=0.50.45640.42260.39530.3727;y=11.09541.18321.26491.3416;f,f0=Hermite1(x,y,y_1)；运行结果如下：f=TOC o 1-5 h z(390625*(337232823972231*t)/35184372088832-114418258618928321/10995116277760000)*(t-1)人2*(t-7/5)人2*(t-8/5)人2*(t-9/5)人2)/36-(390625*(t-1)A2*(t-

4、6/5)A2*(t-7/5)A2*(t-9/5)A2*(2855713758717179*t)/281474976710656-384779664999124623/21990232555520000)/36+(390625*(64*t)/3-61/3)*(t-6/5)A2*(t-7/5)A2*(t-8/5)A2*(t-9/5)A2)/576+(390625*(7612884810106783*t)/18014398509481984+6660373488918492043/11258999068426240000)*(t-1)A2*(t-6/5)A2*(t-8/5)A2*(t-9/5)A2)

5、/16-(390625*(7762319875242775*t)/281474976710656-8968626627620006931/175921860444160000)*(t-1)A2*(t-6/5)A2*(t-7/5)A2*(t-8/5)A2)/576f0=1.1000利用matlab绘制图像:FigureFileEditViewInsertToolsDtEktopWindowHelpH3口匡1口1.41.351.32、程序的窗口化:利用Matlab:GUI代码如下：1.25提供的GUIDE工具以及callback函数实现相应函数的窗口化，/functionvararg?utUNTI

6、TLEDM-fileUNTITLED,bysingleton*.=untitled(varargin)”foruntitled.fig/itself,createsanewUNTITLEDorraisestheexistingH=UNTITLED_*returnsthehandleanewUNTITLEDorthehandletotheexisting1.05singleton*.UNTITLED(CALLBACK,local,hObject,eventData,handles,.)callsthe1.41111functionnamedCALLBACKi1n1UNTITLED.MWithth

7、egivenTinputarguments.%UNTITLED(Property,Valuecreatesanewun丄丄丄ledorraisestheexistingsingleton*.Startingfromtheleft,propertyvaluepairsareappliedtotheGUIbeforeuntitled_OpeningFcngetscalled.Anunrecognizedpropertynameorinvalidvaluemakespropertyapplication%stop.Allinputsarepassedtountitled_OpeningFcnviav

8、arargin.%*SeeGUIOptionsonGUIDEsToolsmenu.ChooseGUIallowsonlyoneinstancetorun(singleton)%Seealso:GUIDE,GUIDATA,GUIHANDLES%Edittheabovetexttomodifytheresponsetohelpuntitled%LastModifiedbyGUIDEv2.515-Sep-201122:24:48ifnargoutBegininitializationcode-DOgui_Singleton=1;gui_StateNOTEDIT=struct(gui_Name,gui

9、_Singleton,gui_OpeningFcn,gui_OutputFcn,gui_LayoutFcn,gui_Callback,&ischar(varargin1)mfilename,.gui_Singleton,.untitled_OpeningFcn,.untitled_OutputFcn,.,.);ifnargingui_State.gui_Callback=str2func(varargin1);endvarargout1:nargout=gui_mainfcn(gui_State,varargin:);elsegui_mainfcn(gui_State,varargin:);e

10、nd%Endinitializationcode-DONOTEDIT%-Executesjustbeforeuntitledismadevisible.functionuntitled_OpeningFcn(hObject,eventdata,handles,varargin)%Thisfunctionhasnooutputargs,seeOutputFcn.%hObjecthandletofigure%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesstructurewithhandlesanduserdata(see

11、GUIDATA)%varargincommandlineargumentstountitled(seeVARARGIN)%Choosedefaultcommandlineoutputforuntitledhandles.output=hObject;%Updatehandlesstructureguidata(hObject,handles);%UIWAITmakesuntitledwaitforuserresponse(seeUIRESUME)%uiwait(handles.figure1);%-Outputsfromthisfunctionarereturnedtothecommandli

12、ne.functionvarargout=untitled_OutputFcn(hObject,eventdata,handles)%varargoutcellarrayforreturningoutputargs(seeVARARGOUT);%hObjecthandletofigure%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesstructurewithhandlesanduserdata(seeGUIDATA)%Getdefaultcommandlineoutputfromhandlesstructurevar

13、argout1=handles.output;functionedit1_Callback(hObject,eventdata,handles)%hObjecthandletoedit1(seeGCBO)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesstructurewithhandlesanduserdata(seeGUIDATA)%Hints:get(hObject,String)returnscontentsofedit1astext%str2double(get(hObject,String)returnsc

14、ontentsofedit1asadoubleguidata(hObject,handles);%-Executesduringobjectcreation,aftersettingallproperties.functionedit1_CreateFcn(hObject,eventdata,handles)%hObjecthandletoedit1(seeGCBO)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesempty-handlesnotcreateduntilafterallCreateFcnscalled%

15、Hint:editcontrolsusuallyhaveawhitebackgroundonWindows.%SeeISPCandCOMPUTER.ifispc&isequal(get(hObject,BackgroundColor),get(0,defaultUicontrolBackgroundColor)set(hObject,BackgroundColor,white);endfunctionedit2_Callback(hObject,eventdata,handles)%hObjecthandletoedit2(seeGCBO)%eventdatareserved-tobedefi

16、nedinafutureversionofMATLAB%handlesstructurewithhandlesanduserdata(seeGUIDATA)%Hints:get(hObject,String)returnscontentsofedit2astext%str2double(get(hObject,String)returnscontentsofedit2asadoubleguidata(hObject,handles);%-Executesduringobjectcreation,aftersettingallproperties.functionedit2_CreateFcn(

17、hObject,eventdata,handles)%hObjecthandletoedit2(seeGCBO)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesempty-handlesnotcreateduntilafterallCreateFcnscalled%Hint:editcontrolsusuallyhaveawhitebackgroundonWindows.%SeeISPCandCOMPUTER.ifispc&isequal(get(hObject,BackgroundColor),get(0,defau

18、ltUicontrolBackgroundColor)set(hObject,BackgroundColor,white);endfunctionedit3_Callback(hObject,eventdata,handles)%hObjecthandletoedit3(seeGCBO)%eventdatareservedtobedefinedinafutureversionofMATLAB%handlesstructurewithhandlesanduserdata(seeGUIDATA)%Hints:get(hObject,String)returnscontentsofedit3aste

19、xt%str2double(get(hObject,String)returnscontentsofedit3asadoubleguidata(hObject,handles);%-Executesduringobjectcreation,aftersettingallproperties.functionedit3_CreateFcn(hObject,eventdata,handles)%hObjecthandletoedit3(seeGCBO)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesempty-handle

20、snotcreateduntilafterallCreateFcnscalled%Hint:editcontrolsusuallyhaveawhitebackgroundonWindows.%SeeISPCandCOMPUTER.ifispc&isequal(get(hObject,BackgroundColor),get(0,defaultUicontrolBackgroundColor)set(hObject,BackgroundColor,white);endfunctionedit4_Callback(hObject,eventdata,handles)%hObjecthandleto

21、edit4(seeGCBO)%eventdatareservedtobedefinedinafutureversionofMATLAB%eventdatareservedtobedefinedinafutureversionofMATLAB%handlesstructurewithhandlesanduserdata(seeGUIDATA)%handlesstructurewithhandlesanduserdata(seeGUIDATA)%Hints:get(hObject,String)returnscontentsofedit4astext%str2double(get(hObject,

22、String)returnscontentsofedit4asadouble%-Executesduringobjectcreation,aftersettingallproperties.functionedit4_CreateFcn(hObject,eventdata,handles)%hObjecthandletoedit4(seeGCBO)%eventdatareserved-tobedefinedinafutureversionofMATLAB%handlesempty-handlesnotcreateduntilafterallCreateFcnscalled%Hint:editc

23、ontrolsusuallyhaveawhitebackgroundonWindows.%SeeISPCandCOMPUTER.ifispc&isequal(get(hObject,BackgroundColor),get(0,defaultUicontrolBackgroundColor)set(hObject,BackgroundColor,white);end%-Executesonbuttonpressinpushbutton1.functionpushbutton1_Callback(hObject,eventdata,handles)%hObjecthandletopushbutt

24、on1(seeGCBO)x=str2num(get(handles.edit1,string);y=str2num(get(handles.edit2,string);y_1=str2num(get(handles.edit3,string);x0=str2num(get(handles.edit5,string);symst;f=0.0;if(length(x)=length(y)if(length(y)=length(y_1)n=length(x);elsedisp(yfyp亘卩吻总亘(总？2工卩总)；return;endelsedisp(xfy卩亘f总卩总：)；return;endfor

25、i=1:nh=1.0;a=0.0;forj=1:nif(j=i)h=h*(t-x(j)八2/(x(i)-x(j)八2);a=a+1/(x(i)-x(j);endendf=f+h*(x(i)-t)*(2*a*y(i)-y_1(i)+y(i);endf0=subs(f,t,x0);plot(handles.poltarea,x,y,*);functionedit5_Callback(hObject,eventdata,handles)%hObjecthandletoedit5(seeGCBO)%eventdatareservedtobedefinedinafutureversionofMATLAB%handlesstructurewithhandlesanduserdata(seeGUIDATA)%Hints:get(hObject,String)returnscontentsofedit5astext%str2double(get(hObject,String)returnscontentsofedit