Function intdei

I = integral of f(x) over (a,infinity), f(x) has not oscillatory factor.

void intdei(Real, Func) (
  Func f,
  Real a,
  Real* aw,
  Real* i,
  Real* err
);

Examples

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

Parameters

NameDescription
lenaw length of aw
tiny minimum value that 1/tiny does not overflow
eps relative error requested
aw points and weights of the quadrature formula, aw[0...lenaw-1]
f integrand f(x)
a lower limit of integration
i approximation to the integral
err estimate of the absolute error

Remarks

        initial parameters
            lenaw > 1000,
            IEEE double :
                lenaw = 8000;
                tiny = 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^infinity |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.
                           3. f(x) has oscillatory factor
                              and decay of f(x) is very slow
                              as x -> infinity.