zeta.c File Reference

Calculates the (regularized) Epstein zeta function and the (regularized) anisotropic Epstein zeta function. More...

#include <complex.h>
#include <math.h>
#include <stdbool.h>
#include <stdlib.h>
#include "crandall.h"
#include "harmonics.h"
#include "tools.h"
#include "zeta.h"

Include dependency graph for zeta.c:

Macros
#define	G_BOUND   3.2
	Smallest value z such that G(nu, z) is negligible for nu < 10.
#define	EPS   ldexp(1, -30)
	epsilon for the cutoff around nu = dimension.
#define	EPS_ZERO_Y   1e-64
	epsilon for the cutoff around x = 0 and y = 0. It holds that M_PI * EPS_ZERO_Y = EPS_ZERO_PIY
#define	EPS_CANCELLATION   4e-16
	Epsilon to catch exact cancellation to zero in inner sum of the singular sum in real space for the set Zeta derivatives.

Functions
double complex	epsteinZetaInternal (double nu, unsigned int dim, const double *m, const double *x, const double *y, double lambda, bool reg, bool aniso, const unsigned int *alpha)
	calculates the (regularized) Epstein zeta function as well as the (regularized) anisotropic Epstein zeta function with a prefactor.

Detailed Description

Calculates the (regularized) Epstein zeta function and the (regularized) anisotropic Epstein zeta function.

Function Documentation

epsteinZetaInternal()

double complex epsteinZetaInternal	(	double	nu,
		unsigned int	dim,
		const double *	m,
		const double *	x,
		const double *	y,
		double	lambda,
		bool	reg,
		bool	aniso,
		const unsigned int *	alpha )

calculates the (regularized) Epstein zeta function as well as the (regularized) anisotropic Epstein zeta function with a prefactor.

Parameters

[in]	nu	exponent.
[in]	dim	dimension of the input vectors.
[in]	m	matrix that transforms the lattice.
[in]	x	shift vector.
[in]	y	wave vector.
[in]	lambda	relative weight of the sums in Crandall's formula.
[in]	reg	false for no regularization, true for the regularization.
[in]	aniso	false for no anisotropy, true for the anisotropic variant.
[in]	alpha	multiindex for the derivatives.

Returns

function value.