double W2::operator()(double x, double k) const throw()
{
if(x < 0.0 || x - b > eps)
{
return 0.0;
}
const double z = std::min(2.0 * x, 2.0*(b - x));
double result = 0.;
// k != 0.0
/*
* The cube root of epsilon of my machine is approximately 6e-06
* The equation gets unstable approximately when k < 1e-06 probably due to
* the k^3 in the divisor. Can't say for sure. Just an educated guess.
*/
if(fabs(k) > cbrt(eps))
{
if(x-.5*z < C[0])
{
if(x+.5*z < C[0])
{
// Left slope
result = I(A_l, B_l, z, x, k);
}
else if(x < C[0])
{
// Both slopes, X on left slope
result = (I(A_l, B_l, 2.*(C[0] - x), x, k)
+ I_lr(z, x, k) - I_lr(2.*(C[0] - x), x, k));
}
else
{
// Both slopes, X on right slope
result = (I(A_r, B_r, 2.*(x - C[0]), x, k)
+ I_lr(z, x, k) - I_lr(2.*(x - C[0]), x, k));
}
}
else
{
// Right slope
result = I(A_r, B_r, z, x, k);
}
}
else
{
// k == 0
if((x - 0.5 * z) < C[0])
{
if((x + 0.5 * z) < C[0])
{
// Left slope
result = I_0(A_l, B_l, z, x);
}
else if(x < C[0])
{
// Both slopes, X on left slope
result = (I_0(A_l, B_l, 2.*(C[0] - x), x)
+ I_lr_0(z, x) - I_lr_0(2.*(C[0] - x), x));
}
else
{
// Both slopes, X on right slope
result = (I_0(A_r, B_r, 2.*(x - C[0]), x)
+ I_lr_0(z, x) - I_lr_0(2.*(x - C[0]), x));
}
}
else
{
// Right slope
result = I_0(A_r, B_r, z, x);
}
}
return result * N_sqr;
}
// -1.0 <= t <= 1.0
double kaiser(double t, double beta=8.0)
{
return I_0(beta*sqrt(1.0 - t*t)) / I_0(beta);
}
