intdeoini

I = integral of f(x) over (a,infinity), f(x) has oscillatory factor :

f(x) = g(x) * sin(omega * x + theta) as x -> infinity

void

intdeoini

(

Real

)

(

size_t lenaw

Real tiny

Real eps

Real* aw

)

Parameters

lenaw size_t: length of aw
tiny Real: minimum value that 1/tiny does not overflow
eps Real: relative error requested
aw Real*: points and weights of the quadrature formula, aw[0...lenaw-1]
lenaw size_t: 8000;
tiny Real: 1.0e-307; function f(x) needs to be analytic over (a,infinity). relative error eps is relative error requested excluding cancellation of significant digits. i.e. eps means : (absolute error) / (integral_a^R |f(x)| dx). eps does not mean : (absolute error) / I. error message err >= 0 : normal termination. err < 0 : abnormal termination. i.e. convergent error is detected : 1. f(x) or (d/dx)^n f(x) has discontinuous points or sharp peaks over (a,infinity). you must divide the interval (a,infinity) at this points. 2. relative error of f(x) is greater than eps. </pre>

auto aw = new real[8000];
intdeoini(aw.length, tiny, eps, aw.ptr);  // initialization of aw
...
intdeo(f, a, omega, aw.ptr, &i, &err);