int
gsl_sf_complex_psi_e(
const double x,
const double y,
gsl_sf_result * result_re,
gsl_sf_result * result_im
)
{
if(x >= 0.0)
{
gsl_complex z = gsl_complex_rect(x, y);
return psi_complex_rhp(z, result_re, result_im);
}
else
{
/* reflection formula [Abramowitz+Stegun, 6.3.7] */
gsl_complex z = gsl_complex_rect(x, y);
gsl_complex omz = gsl_complex_rect(1.0 - x, -y);
gsl_complex zpi = gsl_complex_mul_real(z, M_PI);
gsl_complex cotzpi = gsl_complex_cot(zpi);
int ret_val = psi_complex_rhp(omz, result_re, result_im);
if(GSL_IS_REAL(GSL_REAL(cotzpi)) && GSL_IS_REAL(GSL_IMAG(cotzpi)))
{
result_re->val -= M_PI * GSL_REAL(cotzpi);
result_im->val -= M_PI * GSL_IMAG(cotzpi);
return ret_val;
}
else
{
GSL_ERROR("singularity", GSL_EDOM);
}
}
}
static double interpolate(double a, double fa, double fpa, double b, double fb, double fpb, double xmin, double xmax, int order)
{
/*
* Map [a,b] to [0,1]
*/
double z, alpha, zmin, zmax;
zmin = (xmin - a) / (b - a);
zmax = (xmax - a) / (b - a);
if (zmin > zmax) {
double tmp = zmin;
zmin = zmax;
zmax = tmp;
};
if (order > 2 && GSL_IS_REAL(fpb)) {
z = interp_cubic(fa, fpa * (b - a), fb, fpb * (b - a), zmin, zmax);
} else {
z = interp_quad(fa, fpa * (b - a), fb, zmin, zmax);
}
alpha = a + z * (b - a);
return alpha;
}