int main(){
double result, teto,base, real;
double tol = 0.5e-5;
teto = 1+tol; //100% + tol
base = 1-tol; //100% - tol
result = AdaptiveSimpson(0,4,first,tol);
real = 2.0;
printf("[%s] the result was: %0.15f\n",((result<real*teto)&&(result>real*base))?"Success":"Fail",result );
result = AdaptiveSimpson(1,3,second,tol);
real = 6.9986217091241;
printf("[%s] the result was: %0.15f\n",((result<real*teto)&&(result>real*base))?"Success":"Fail",result );
result = AdaptiveSimpson(0,M_PI,third,tol);
real = 5.8696044010894;
printf("[%s] the result was: %0.15f\n",((result<real*teto)&&(result>real*base))?"Success":"Fail",result );
return 0;
}
/// Nested adaptive Simpson integration over a 2D rectangle
Float AdaptiveSimpson2D(const std::function<Float(Float, Float)>& f, Float x0,
Float y0, Float x1, Float y1, Float eps = 1e-6f,
int depth = 6) {
/* Lambda function that integrates over the X axis */
auto integrate = [&](Float y) {
return AdaptiveSimpson(std::bind(f, std::placeholders::_1, y), x0, x1,
eps, depth);
};
Float value = AdaptiveSimpson(integrate, y0, y1, eps, depth);
return value;
}
double AdaptiveSimpson (double a, double b, double (*f) (double x), double tol){
double sab, sacb, c;
if(tol == 0){
puts("[Warning] Machine Precision has been reached");
return DoubleSimpson(a,b,f);
}
sab = Simpson(a,b,f);
sacb = DoubleSimpson(a,b,f);
if(fabs(sab -sacb) < tol*15 ){
//printf("\t dif: %0.7f 15*tol: %0.7f\n",sab-sacb,15*tol);
return sacb;
}
c = (a+b)/2;
sacb = AdaptiveSimpson(a,c,f,tol/2);
sacb += AdaptiveSimpson(c,b,f,tol/2);
return sacb;
}
