// -----------------------------------------------------------------------
// Adaptive Simpson's Rule
//
double adaptiveSimpsonsAux(double (*f)(double), double a, double b, double epsilon,
double S, double fa, double fb, double fc, int bottom) {
double c = (a + b)/2, h = b - a;
double d = (a + c)/2, e = (c + b)/2;
double fd = f(d), fe = f(e);
double Sleft = (h/12)*(fa + 4*fd + fc);
double Sright = (h/12)*(fc + 4*fe + fb);
double S2 = Sleft + Sright;
if (bottom <= 0 || fabs(S2 - S) <= 15*epsilon)
return S2 + (S2 - S)/15;
return adaptiveSimpsonsAux(f, a, c, epsilon/2, Sleft, fa, fc, fd, bottom-1) +
adaptiveSimpsonsAux(f, c, b, epsilon/2, Sright, fc, fb, fe, bottom-1);
}
double adaptiveSimpsons(double (*f)(double), // ptr to function
double a, double b, // interval [a,b]
double epsilon, // error tolerance
int maxRecursionDepth) { // recursion cap
double c = (a + b)/2, h = b - a;
double fa = f(a), fb = f(b), fc = f(c);
double S = (h/6)*(fa + 4*fc + fb);
return adaptiveSimpsonsAux(f, a, b, epsilon, S, fa, fb, fc, maxRecursionDepth);
}
// an integration function for functions like: X(r) over r
// TODO: make more rebust. no infinte loops posible and such.
double NIntegration( double (*funcPtr)(double), double Start, double End)
{
double epsilon = 1.0 / PRECISION;
double Mid = (Start + End)/2, h = End - Start;
double funcStart = funcPtr(Start), funcEnd= funcPtr(End), funcMid = funcPtr(Mid);
double S = (h/6)*(funcStart + 4*funcMid + funcEnd);
return adaptiveSimpsonsAux(funcPtr, Start, End, epsilon, S, funcStart, funcEnd, funcMid, MAX_RECURSION_DEPTH);
}
/** This section of code uses the Adaptive Simpsons rule to calculate the
integral. It uses a recursive way to minimize to error.
*/
double adaptiveSimpsonsAux(double (*f)(double), double a, double b, double epsilon,
double S, double fa, double fb, double fc, int bottom)
{
double c = (a + b)/2, h = b - a;
double d = (a + c)/2, e = (c + b)/2;
double fd = f(d), fe = f(e);
double Sleft = (h/12)*(fa + 4*fd + fc);
double Sright = (h/12)*(fc + 4*fe + fb);
double S2 = Sleft + Sright;
if (S2 == NAN)
{
fprintf(stderr,"NAN detected while integrating, stopping integration");
fprintf(stderr,"Sleft = %E\n Sright = %E\n", Sleft, Sright);
return NAN;
}
if (bottom <= 0 || fabs(S2 - S) <= 15*epsilon)
return S2 + (S2 - S)/15;
return adaptiveSimpsonsAux(f, a, c, epsilon/2, Sleft, fa, fc, fd, bottom-1) +
adaptiveSimpsonsAux(f, c, b, epsilon/2, Sright, fc, fb, fe, bottom-1);
}
