数值分析 Lab 2 的 C++ 程序示例

 Lab 2.  Lagrange Polynomial 

        Given a set of sample points of a certain function f , use Lagrange polynomial to approximate function values at some given points   a₁a_2 ,…,a_m                .
Input
There are several sets of inputs.  For each set:
 The 1st line contains an integer 20 >= n >=0  which is the degree of Lagrange polynomial.   n = -1 signals the end of file.
 The 2nd line contains n+1 distinct real numbers                                                                x_i  
 The 3rd line contains n+1 real numbers                                                                            f(x_i)                   .
 The last line of a test case consists of an integer m > 0 and m real numbers         a_i        .
The numbers are separated by spaces and new lines.

Output (♦represents a space)
For each ai , you are supposed to print the function value at this point in the following format:
               fprintf(outfile, "f(%6.3f)♦=♦%12.8e/n", a, f );
The outputs of two test cases must be seperated by a blank line.

Sample Input
7
0.5♦0.7♦0.9♦1.1♦1.3♦1.5♦1.7♦1.9
0.48♦0.64♦0.78♦0.89♦0.96♦1.00♦0.99♦0.95
5♦0.74♦1.6♦0.55♦1.2♦1.85
1
0.0♦1.0
0.0♦1.0
1♦0.5
–1

Sample Output
f(♦0.740) =6.68735821e–001
f(♦1.600) =1.00341309e+000
f(♦0.550) =5.26938820e–001
f(♦1.200) =9.29135742e–001
f(♦1.850) =9.52078056e–001
 
f(♦0.500) =5.00000000e–001

My answer:

 Lagrange.h

class CLagrange  
...{
private:
    double LagrangeCoe(int StepIndex,int ApproxIndex);
public:
    void Output(FILE *fp);
    unsigned char GetResult();
    void Dispose();
    unsigned char ReadNext(FILE *fp);
    CLagrange();
    virtual ~CLagrange();
private:
    double *m_pXVal;        //x values read from file(the number of x is m_ValNum)
    double *m_pYVal;        //y=f(x) values read from file( m_ValNum)
    int m_ValNum;
    

    double *m_pApproxXVal;    //x valuse will be esitmated
    double *m_pApproxYVal;    //saved the estimated f(x).
    int m_ApproxNum;        // the number of x will be esitmated

};

 Lagrange.cpp

#include "Lagrange.h"
#define DELPOINT(p)  if(p != NULL)delete p,p=NULL;
#define DELARRAYPOINT(p) if (p != NULL) delete [] p ,p=NULL;
/**///////////////////////////////////////////////////////////////////////
// Construction/Destruction
/**///////////////////////////////////////////////////////////////////////
// yxf
CLagrange::CLagrange()
...{
    m_ApproxNum=-1;
    m_pApproxXVal = NULL;
    m_pApproxYVal = NULL;

    m_pXVal = NULL;
    m_pYVal = NULL;
    m_ValNum = -1;
}

CLagrange::~CLagrange()
...{
    Dispose();
}

/**//*--------------------------------------------
return 
    0 for the end of this file
    -1 for file error
    1 for read value ok
description:
    read a group of x and f(x) from file  in.txt
    first read n degree from the first line of file(when n == -1 denoted the end of file return 0 )
    the next line has n+1 numbers which denoted as x
    the next line has n+1 numbers which denoted as f(x)
    the next line first number is how many real numbers 
    need to be estimate by lagrange algorithm. 
    then read the last number and estimated the f(x)

-----------------------------------------------*/
unsigned char  CLagrange::ReadNext(FILE *fp)
...{    
    int ret,i;
    double tmp=0;
    char c=0;
    Dispose();                            //destroy memory

    if(fp == NULL)return -1;            //file error 
    ret = fscanf(fp,"%d ",&m_ValNum);
                            
    if( ret == EOF) return -1;            //file end. but has error
    if( m_ValNum == -1 )return 0;        //file end

    m_ValNum ++;                        //degree of Lagrange polynomial + 1 is the X Value Number


    m_pXVal = new double[m_ValNum];
    m_pYVal = new double[m_ValNum ]; //allocate space
    //read x Value;
    for(i = 0; i < m_ValNum; i++)fscanf(fp,"%lf",&m_pXVal[i]);
    
    fscanf(fp,"%*[^ ] ");//go to the next line
    // read f(x)
    for(i = 0;i < m_ValNum; i++)fscanf(fp,"%lf",&m_pYVal[i]);
    
    fscanf(fp,"%*[^ ] ");//go to the next line
    fscanf(fp,"%d ",&m_ApproxNum);// read the number of the points that will be approximated.
    m_pApproxXVal = new double[m_ApproxNum];//allocate memory
    m_pApproxYVal = new double[m_ApproxNum];
    //read the points that will be approximated
    for(i = 0; i< m_ApproxNum ; i ++)fscanf(fp,"%lf",&m_pApproxXVal[i]);
    //read ok return 1
    fscanf(fp,"%*[^ ] ");//go to the next line
    return 1;

}
//destroy the memory allocated by function ReadNext(FILE *fp)
void CLagrange::Dispose()
...{
    DELARRAYPOINT(m_pApproxXVal);
    DELARRAYPOINT(m_pApproxYVal);
    DELARRAYPOINT(m_pXVal);
    DELARRAYPOINT(m_pYVal);
}

unsigned char CLagrange::GetResult()
...{
    
    int i,j;
    for( i = 0; i < m_ApproxNum ; i++)
    ...{
        m_pApproxYVal[i] = 0.0;//init
        for(j = 0; j < m_ValNum ; j++)
        ...{
            //denote the formula 2.9 P26
            m_pApproxYVal[i] += (LagrangeCoe(j,i) * m_pYVal[j] );    
        }
    }
    return 1;
}
/**//*-----------------------------------------------------------
The Lagrange coefficient polynomials for degree m_ValNum-1. 
denote  the book P26 formula 2.8 
StepIndex is k   and m_pApproxXVal[ApproxIndex] is the x 
-----------------------------------------------------------*/
double CLagrange::LagrangeCoe(int StepIndex, int ApproxIndex)
...{
    double Ret=1.0,tmp=1.0;
    int i;
    for(i=0;i<m_ValNum;i++)
    ...{
        if(i!=StepIndex)tmp *= (m_pApproxXVal[ApproxIndex]-m_pXVal[i]);
    }
    for(i = 0; i < m_ValNum; i ++)
    ...{
        if( i != StepIndex) Ret *= (m_pXVal[StepIndex] - m_pXVal[i]);
    }
    return tmp / Ret;

}
/**//*------------------------------------------------------------------
print the result to the screen and in the file
----------------------------------------------------------------------*/
void CLagrange::Output(FILE *fp)
...{
    int i;

    printf(" ********************************************************************** ");
    printf("                          Read Value                                   ");
    printf("X   :");
    for(i=0 ; i < m_ValNum ; i++)printf("%6.3f ",m_pXVal[i]);
    printf(" ");
    printf("f(x):");
    for(i=0 ; i < m_ValNum ; i++)printf("%6.3f ",m_pYVal[i]);
    printf(" ");
    printf("                       Approximated Value                               ");
    for(i = 0; i < m_ApproxNum ; i ++)printf("f(%6.3f) = %12.8e ",m_pApproxXVal[i],m_pApproxYVal[i]);


    //print the result to file
    if(fp == NULL)return ;
    for(i = 0; i < m_ApproxNum ; i ++)
    fprintf(fp, "f(%6.3f) = %12.8e ", m_pApproxXVal[i],m_pApproxYVal[i] );


}

 Exe2.cpp

#include "Lagrange.h"
/**//*******************************************************
for english instruction:
http://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html
http://math.fullerton.edu/mathews/numerical/la.htm
http://private.codecogs.com/d-ox/maths/interpolation/lagrange.php
************************************************************/
#include <direct.h>

int main(int argc, char* argv[])
...{
    CLagrange lag;
    char CurDir[256];
    char InFileName[256];
    char OutFileName[256];

    // you may use ".//in.txt" for current directory file
    // i use getcwd get current directory for clearly.
    getcwd(CurDir,256);//get current directory
    sprintf(InFileName,"%s/in.txt",CurDir);
    sprintf(OutFileName,"%s/out.txt",CurDir);

    printf("Current Directory:    %s ",CurDir);
    printf("Input File name  :    %s ",InFileName);
    printf("Output File name :    %s",OutFileName);



    //open file
    FILE *fpIn= fopen(InFileName,"r");
    FILE *fpOut = fopen(OutFileName,"wb+");
    if(fpIn == NULL || fpOut == NULL)
    ...{
        printf("open file error ");
        return 0;
    }
    // ReadNext return 0 if end of file -1 if error
    while(lag.ReadNext(fpIn)>0)
    ...{
        lag.GetResult();    //get the result 
        lag.Output(fpOut);    //out put the result
        fprintf(fpOut," ");
    }
    fclose(fpIn);
    fclose(fpOut);
    printf(" ********************************************************************** ");
    
    getchar();// i am not familial with winxp .
                //in my win2000 if i don't use this  function
                // the dos windows only flashed and disappeared immediately
    return 0;
}