maths.hpp File Reference

Mathematical calculations. More...

#include <gsl/gsl_interp.h>
#include <gsl/gsl_sf_bessel.h>
#include <gsl/gsl_sf_coupling.h>
#include <gsl/gsl_sf_gamma.h>
#include <gsl/gsl_sf_legendre.h>
#include <gsl/gsl_sf_result.h>
#include <gsl/gsl_spline.h>
#include <cmath>
#include <complex>
#include <vector>
#include "monitor.hpp"

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Classes
class	trv::maths::SphericalHarmonicCalculator
	Reduced spherical harmonics. More...
class	trv::maths::SphericalBesselCalculator
	Interpolated spherical Bessel function \( j_\ell(x) \) of the first kind. More...

Namespaces
namespace	trv
namespace	trv::maths

Functions
std::complex< double >	trv::maths::eval_complex_in_polar (double r, double theta)
	Evaluate a complex number \( r e^{i \theta} \) in the polar form.
double	trv::maths::get_vec3d_magnitude (std::vector< double > vec)
	Return the magnitude of a 3-d vector.
double	trv::maths::get_vec3d_magnitude (double *vec)
	Return the magnitude of a 3-d vector.
std::complex< double >	trv::maths::eval_lanczos_approx_series (std::complex< double > z)
	Evaluate the Lanczos approximation series \( A_g(z) \) for the gamma function.
std::complex< double >	trv::maths::eval_gamma_lanczos (std::complex< double > z)
	Evaluate the gamma function \( \Gamma(z) \) on the complex plane using the Lanczos approximation.
void	trv::maths::get_lngamma_parts (double x, double y, double &lnr, double &theta)
	Get the real and imaginary parts of the log-gamma function \( \ln\Gamma(z = x + \mathrm{i}\,y) \).
std::complex< double >	trv::maths::eval_gamma_lnratio (double mu, std::complex< double > nu)
	Evaluate the logarithm of the ratio of two gamma functions.
double	trv::maths::wigner_3j (int j1, int j2, int j3, int m1, int m2, int m3)
	Calculate Wigner 3-j symbol.

Variables
const std::complex< double >	trv::maths::M_I
	imaginary unit
const double	trv::maths::eps_coupling = 1.e-9
	zero-tolerance for Wigner 3-j coupling coefficients

Detailed Description

Mathematical calculations.

Authors

Mike S Wang (https://github.com/MikeSWang), Naonori S Sugiyama (https://github.com/naonori)

Mathematical calculations provided include:

• spherical Bessel functions of the first kind with interpolation;
• (reduced) spherical harmonics include 3-d mesh grid storage;
• Wigner 3-j symbols;
• the gamma function and related quantities with Lanzcos approximation.

Definition in file maths.hpp.