/*Romberg Algorithm 寮鍙戣?newplan寮鍙戞棩鏈?08.05.07 *//*=======================================*//*INCLUDES*/ #include <cstdlib>#include <iostream>#include <cmath>/*=======================================*//*MACROS USED IN THIS FILE*/#define MAX 20 #define PRECISION 0.000008/*=======================================*//*DECLARE NAMES IN STL NAMESAPCE */using std::cout;using std::endl;/*=======================================*//*CLASS FUNC (FUNCTION OBJECT): THE ORIGINAL FUNCTION WE WANT TO INTEGRAL*/class func{ public: func(double x=1.0):exp(x){} double operator()(const double& dnum)const{return pow(dnum,exp);} private: double exp; };/*=======================================*//*CLASS ECHELONFUNC (FUNCTION OBJECT)姊艦娉曠殑閫掓帹鍏紡*/class echelonFunc{ public: echelonFunc(double begining,double ending,func & myfunc); double operator()(); private: double h; int n; double T; func myfunc; double begining; double ending ; };/*=======================================*/echelonFunc::echelonFunc(double begining,double ending,func & myfunc) { this->begining=begining; this->ending=ending; this->h=ending-begining; this->n=0; this->T=0; this->myfunc=myfunc;//FUCNTION }/*------------------------------*//* INCREASE FUNCTION 閫掓帹鍑芥暟*/double echelonFunc::operator()() { if(this->n==0) { this->T=h*0.5*(myfunc(this->begining)+myfunc(this->ending)); this->n=1; return this->T; } double len=0.5*h; double sum=0; int k=0; for(k=0;k<this->n;k++) { sum+=myfunc(len); len=len+h; } this->T=0.5*this->T+0.5*h*sum; this->h/=2; this->n*=2; return this->T; }/*=======================================*//*THE MAIN CLASS IN THIS PROGRAM*/ class Romberg{ public: Romberg(double begining,double ending,double exp); ~Romberg(); private: void RombergCPU();/*THE MOST IMPORTANT FUNCTION IN THIS PROGRAM*/ echelonFunc *echol; double T[MAX][MAX];/*STO THE ROMBERG TABLE*/ };/*------------------------------*/Romberg::Romberg(double begining ,double ending ,double paraexp){ func myfunc(paraexp); echol = new echelonFunc(begining,ending,myfunc); RombergCPU();}/*------------------------------*/Romberg::~Romberg(){ delete echol;}/*------------------------------*/void Romberg::RombergCPU(){ clock_t Start; //TIME STARAT clock_t End; //TIME END double *p[MAX];//WE USE THIS POINTER ARRAY TO ACCELERATE ALGOTITHM double **q; int i,j; Start = clock();//TIME START FROM HERE for(i = 0,q = p; q < p+MAX; q++,i++) *q= &T[i][0]; double a,b,pows; cout<<"-----------------------Romberg Algorithm---------------------"<<endl; *p[0]=(*echol)(); cout<<" "<<*p[0]<<endl; p[0]++; do{ *p[0]=(*echol)(); cout<<" "<<*p[0]; p[0]++; for(i=1;;i++) { pows=pow(4.0,double(i)); a=pows/(pows-1); b=1/(pows-1); *p[i]=a*(*(p[i-1]-1))-b*(*(p[i-1]-2));//ROMBERG ALGORITHM cout<<" "<<*p[i]; if(p[i]==&T[i][0]) { p[i]++; break; } p[i]++; } cout<<endl;//fabs(T[i][0]-T[i-1][0]) }while(fabs(T[i][0]-T[i-1][0])>PRECISION); End = clock();//TIME END HERE cout<<"-------------------------------------------------------------"<< endl<<" TIME SPEND:"<<(double)(End-Start)/CLOCKS_PER_SEC<<endl; } /*=======================================*//*MAIN FUNCTION*/int main(int argc, char *argv[]){ Romberg romberg(0,1,1.5);//ROMBERG API :BEGIN(0) END(1) EXP(1.5) system("PAUSE"); return EXIT_SUCCESS;}
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