Hermite插值法的方法介绍

Hermite插值法的方法介绍

相关的理论请参考相关的数值算法的书籍，我这里只给出关键的函数及主程序段，其余相关的细节就不再一一罗列了.

Hermite插值法结合了函数的导数值，使得插值的精度更为提高:

 

 

void hermite3(Type* xList,Type* yList,Type* yPList,Type x,FILE* outputFile)

{

Type h;/*The tween value*/

Type hAns;/*The return answer*/

 

assertF(xList!=NULL,"in Hermite Insert xList passed in is null/n");

assertF(yList!=NULL,"in Hermite Insert yList passed in is null/n");

assertF(yPList!=NULL,"in Hermite Insert yPList passed in is null/n");

assertF(outputFile!=NULL,"in jieXianMethod outputFile is NULL");

/*Init data*/

hAns=0;

/*Core Program*/

h=xList[1]-xList[0];

hAns+=(x-xList[1])*(x-xList[1])*(h+2*(x-xList[0]))*yList[0]/(h*h*h);

hAns+=(x-xList[0])*(x-xList[0])*(h+2*(xList[1]-x))*yList[1]/(h*h*h);

hAns+=(x-xList[1])*(x-xList[1])*(x-xList[0])*yPList[0]/(h*h);

hAns+=(x-xList[0])*(x-xList[0])*(x-xList[1])*yPList[1]/(h*h);

/*End of Core Program*/

/*Output Answer*/

printf("the answer of hermit 3 poly is:%f/n",hAns);

fprintf(outputFile,"the answer of hermit 3 poly is:%f/r/n",hAns);

}

 

#include "MyAssert.h"

#include "InsertAlgorithm.h"

#include <time.h>

#include <stdio.h>

#include <stdlib.h>

#include <string.h>

 

char *inFileName="inputData.txt";

/*

input data specification

len,

x0,x1,

y0,y1,

y0',y1',

x.

*/

 

char *outFileName="outputData.txt";

#define DEBUG 1

 

void main(int argc,char* argv[])

{

FILE *inputFile;/*input file*/

FILE *outputFile;/*output file*/

 

double startTime,endTime,tweenTime;/*time callopsed info*/

Type* xList,* yList,* yPList;

Type x;

int len;

 

/*input file open*/

if(argc>1)strcpy(inFileName,argv[1]);

assertF((inputFile=fopen(inFileName,"rb"))!=NULL,"input file error");

printf("input file open success/n");

 

/*outpout file open*/

if(argc>2)strcpy(outFileName,argv[2]);

assertF((outputFile=fopen(outFileName,"wb"))!=NULL,"output file error");

printf("output file open success/n");

 

fscanf(inputFile,"%d,",&len);

/*Memory apply*/

xList=(Type*)malloc(sizeof(Type)*len);

yList=(Type*)malloc(sizeof(Type)*len);

yPList=(Type*)malloc(sizeof(Type)*len);

/*Read info data*/

fscanf(inputFile,"%f,%f,",&xList[0],&xList[1]);

fscanf(inputFile,"%f,%f,",&yList[0],&yList[1]);

fscanf(inputFile,"%f,%f,",&yPList[0],&yPList[1]);

fscanf(inputFile,"%f,",&x);

printf("read in data info:%f,%f,%f,%f,%f,%f,%f/n",xList[0],xList[1],yList[0],yList[1],yPList[0],yPList[1],x);

 

#if DEBUG

printf("/n*******start of test program******/n");

printf("now is runnig,please wait.../n");

startTime=(double)clock()/(double)CLOCKS_PER_SEC;

/******************Core program code*************/

hermite3(xList,yList,yPList,x,outputFile);

/******************End of Core program**********/

endTime=(double)clock()/(double)CLOCKS_PER_SEC;

tweenTime=endTime-startTime;/*Get the time collapsed*/

/*Time collapsed output*/

printf("the collapsed time in this algorithm implement is:%f/n",tweenTime);

fprintf(outputFile,"the collapsed time in this algorithm implement is:%f/r/n",tweenTime);

printf("/n*******end of test program******/n");

#endif

free(yPList);

free(yList);

free(xList);

printf("program end successfully,/n you have to preess any key to clean the buffer area to output,otherwise,you wiil not get the total answer./n");

getchar();/*Screen Delay Control*/

return;

}