math.hpp File Reference

Thin wrappers around C++17 <cmath> and <numeric> with readable names. More...

#include "core/types.hpp"
#include <cmath>
#include <numeric>
#include <random>
#include <vector>
#include <cassert>

Go to the source code of this file.

Classes
struct	num::Rng
	Seeded pseudo-random number generator (Mersenne Twister). Pass a pointer to rng_* functions to draw samples. More...

Namespaces
namespace	num

Functions
real	num::bessel_j (real nu, real x)
	J_nu(x) – Bessel function of the first kind.
real	num::bessel_y (real nu, real x)
	Y_nu(x) – Bessel function of the second kind (Neumann function)
real	num::bessel_i (real nu, real x)
	I_nu(x) – modified Bessel function of the first kind.
real	num::bessel_k (real nu, real x)
	K_nu(x) – modified Bessel function of the second kind.
real	num::sph_bessel_j (unsigned int n, real x)
	j_n(x) – spherical Bessel function of the first kind
real	num::sph_bessel_y (unsigned int n, real x)
	y_n(x) – spherical Neumann function (spherical Bessel of the second kind)
real	num::legendre (unsigned int n, real x)
	P_n(x) – Legendre polynomial of degree n.
real	num::assoc_legendre (unsigned int n, unsigned int m, real x)
	P_n^m(x) – associated Legendre polynomial.
real	num::sph_legendre (unsigned int l, unsigned int m, real theta)
	Y_l^m(theta) – spherical harmonic (real part, theta in radians)
real	num::hermite (unsigned int n, real x)
	H_n(x) – (physicists') Hermite polynomial.
real	num::laguerre (unsigned int n, real x)
	L_n(x) – Laguerre polynomial.
real	num::assoc_laguerre (unsigned int n, unsigned int m, real x)
	L_n^m(x) – associated Laguerre polynomial.
real	num::ellint_K (real k)
	K(k) – complete elliptic integral of the first kind.
real	num::ellint_E (real k)
	E(k) – complete elliptic integral of the second kind.
real	num::ellint_Pi (real n, real k)
	Pi(n, k) – complete elliptic integral of the third kind.
real	num::ellint_F (real k, real phi)
	F(k, phi) – incomplete elliptic integral of the first kind.
real	num::ellint_Ei (real k, real phi)
	E(k, phi) – incomplete elliptic integral of the second kind.
real	num::ellint_Pi_inc (real n, real k, real phi)
	Pi(n, k, phi) – incomplete elliptic integral of the third kind.
real	num::expint (real x)
	Ei(x) – exponential integral.
real	num::zeta (real x)
	zeta(x) – Riemann zeta function
real	num::beta (real a, real b)
	B(a, b) – beta function.
std::vector< real >	num::linspace (real start, real stop, idx n)
	Evenly spaced values from start to stop, inclusive. MATLAB/NumPy linspace.
std::vector< int >	num::int_range (int start, int n)
	Integer sequence [start, start+1, ..., start+n-1]. Wraps std::iota.
real	num::rng_uniform (Rng *r, real lo, real hi)
	Uniform real in [lo, hi).
real	num::rng_normal (Rng *r, real mean, real stddev)
	Normal (Gaussian) sample with given mean and standard deviation.
int	num::rng_int (Rng *r, int lo, int hi)
	Uniform integer in [lo, hi] (inclusive on both ends).

Variables
constexpr real	num::pi = 3.14159265358979323846
constexpr real	num::e = 2.71828182845904523536
constexpr real	num::phi = 1.61803398874989484820
	Golden ratio.
constexpr real	num::sqrt2 = 1.41421356237309504880
constexpr real	num::sqrt3 = 1.73205080756887729353
constexpr real	num::ln2 = 0.69314718055994530942
constexpr real	num::inv_pi = 0.31830988618379067154
	1/pi
constexpr real	num::two_pi = 6.28318530717958647692
	2pi
constexpr real	num::half_pi = 1.57079632679489661923
	pi/2

Detailed Description

Thin wrappers around C++17 <cmath> and <numeric> with readable names.

The standard library names for special functions (cyl_bessel_j, comp_ellint_1, cyl_neumann, etc.) are accurate but opaque. This header re-exports them under the names used in textbooks and mathematical literature.

Random number generation wraps the mt19937 boilerplate into a plain struct.

Include this header instead of pulling <cmath> special functions directly.

Definition in file math.hpp.