// Recursive Romberg, level 1 : Trapezodial, level >= 1
double Romberg(fp f, double a, double b, int n, int level){
if (level == 1){
return Trapezodial(f, a, b, n);
}
else {
return ((Romberg(f,a,b,2 * n,level - 1) - pow(4,-(level-1)) * Romberg(f,a,b,n,level-1)) /
(1 - pow(4, -(level-1))) );
}
}
inline double Integral(double a, double b, double (*f)(double x, double y, double z), double eps, double l, double t)
{
const double pi(acos(-1.0f));
int n;
double R, p, res;
n = (int)(floor)(b * t * 0.50 / pi);
p = 2.0 * pi / t;
res = b - (double)n * p;
if (n)
R = Romberg (a, p, f0, eps/(double)n, l, t);
R = R * (double)n + Romberg( 0.0, res, f0, eps, l, t );
return R/100.0;
}
double Integral(double a, double b, double (*f)(double x, double y, double z),
double eps, double l, double t)
{
//count cycles
double T = 2.0 * PI / t;
int count_T = (int)(b / T);
double remain = b - (double)count_T * T;
double length_T = Romberg(0.0, T, f0, eps, l, t);
double length_r = Romberg(0.0, remain, f0, eps, l, t);
double result = (length_T * count_T + length_r) / 100.0;
return result;
}
int main() {
double a, b;
printf("请输入积分上下限！\n 下限a = ");
scanf ("%lf", &a);
getchar();
printf(" 上限b = ");
scanf ("%lf", &b);
getchar();
printf("\n龙贝格法求积分结果为: %lf\n", Romberg(a, b));
system("pause");
return 0;
}
//积分计算
ErrNo Calculus::GetStart_I(int iSelectIndex)
{
ErrNo err;
int iLength;
ChangeVariableSymbol(TEXT('x')); //使用默认的变量符号
//获取函数表达式
if(! (iLength = Edit_GetText(GetDlgItem(hDlg,EditControlID[0]),expression,MAXINPUT)))
{
MessageBox(hDlg,TEXT("未输入表达式"),TEXT("错误"),MB_ICONERROR);
return NO_DATA_INPUT;
}
iLength = lstrlen(expression);
for(int i=0;i<=iLength;i++)
{
exp_store[i] = expression[i];
}
//获取区间大小
if(err = GetLine_Double(GetDlgItem(hDlg,EditControlID[1]),&left_interval))
{
ErrorReport(hDlg,err);
return err;
}
if(err = GetLine_Double(GetDlgItem(hDlg,EditControlID[2]),&right_interval))
{
ErrorReport(hDlg,err);
return err;
}
if(iSelectIndex == GAUSS_LEGENDRE_INDEX || iSelectIndex == GAUSS_CHEBYSHEV_INDEX)
{
if(fabs(left_interval+1)>eps || fabs(right_interval-1)>eps)
{
MessageBox(hDlg,TEXT("区间输入错误，应输入范围[-1,1]"),TEXT("错误"),MB_ICONERROR);
return NOT_MATCH;
}
}
//获取计算精度
if(err = GetLine_Double(GetDlgItem(hDlg,EditControlID[3]),&precision))
{
if(iSelectIndex == GAUSS_LEGENDRE_INDEX || iSelectIndex == GAUSS_CHEBYSHEV_INDEX)
;
else
{
ErrorReport(hDlg,err);
return err;
}
}
precision_a = precision;
switch(iSelectIndex)
{
case ROMBERG_INDEX:
err = Romberg(expression,precision,left_interval,right_interval,result,precision_a,times);
break;
case GAUSS_LEGENDRE_INDEX:
err = Gauss_Legendre(expression,result);
break;
case GAUSS_CHEBYSHEV_INDEX:
err = Gauss_Chebyshev(expression,result);
break;
}
OutputResult_I(iSelectIndex,err);
return 0;
}
