math_functions.hpp File Reference

general mathematical functions More...

#include <boost/math/constants/constants.hpp>
#include <cmath>
#include <complex>
#include <iostream>
#include <stdexcept>

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Classes
struct	NiHu::bessel::make_complex< T >
	metafunction converting a floating point type to a complex type More...
struct	NiHu::bessel::make_complex< std::complex< T > >
struct	NiHu::IpowC< Base, Exp >
	metafunction computing integer power More...
struct	NiHu::IpowC< Base, 0 >
	terminating case of the recursion IpowC More...
struct	NiHu::IpowC< 0, Exp >
	terminating case of the recursion IpowC More...
struct	NiHu::IpowC< 0, 0 >
	terminating case of the recursion IpowC More...

Namespaces
	NiHu::bessel
	namespace encapsulating Bessel functions

Functions
template<typename T >
int	NiHu::sgn (T val)
	signum function More...
const double	NiHu::bessel::large_lim (7.)
	limit between small and large argument series
template<class T >
void	NiHu::bessel::mag_arg_large (int nu, T const &z, T &u, T &phi)
	large argument Bessel function Taylor series coefficients More...
template<int nu, class T >
T	NiHu::bessel::J_small (T const &z)
	small argument expansion of J_nu(z) for nu = 0, 1, 2 More...
template<int nu, class T >
T	NiHu::bessel::J_large (T const &z)
	large argument expansion of J_nu(z) for nu = 0, 1, 2 More...
template<int nu, class T >
T	NiHu::bessel::J (T const &z)
	Bessel function J_nu(z) More...
template<int nu>
std::complex< double >	NiHu::bessel::Y_small (std::complex< double > const &z)
	small argument expansion of Y_nu(z) More...
template<int nu>
std::complex< double >	NiHu::bessel::Y_large (std::complex< double > const &z)
	large argument expansion of Y_nu(z) for nu = 0, 1, 2 More...
template<int nu>
std::complex< double >	NiHu::bessel::Y (std::complex< double > const &z)
	Bessel function Y_nu(z) More...
template<int nu, int kind, class T >
make_complex< T >::type	NiHu::bessel::H_large (T const &z)
	large argument expansion of H^(K)_nu(z) More...
template<int nu, int kind, class T >
make_complex< T >::type	NiHu::bessel::H (T const &z)
	H^(K)_nu(z) Bessel function. More...
template<int nu, class T >
make_complex< T >::type	NiHu::bessel::K (T const &z)
	K_nu(z) modified Bessel function. More...
template<class T = double>
T	NiHu::chebroot (size_t n, size_t i)
	roots of Chebyshev polynomials More...
template<class I >
I	NiHu::Ipow (I base, I exp)
	compute integer power More...

Detailed Description

general mathematical functions

Definition in file math_functions.hpp.

Function Documentation

chebroot()

template<class T = double>

T NiHu::chebroot	(	size_t	n,
		size_t	i
	)

roots of Chebyshev polynomials

Template Parameters

T	the scalar type

Parameters

[in]	n	the polynomial order
[in]	i	the root index

Returns

the i-th root of T_n(x)

Definition at line 395 of file math_functions.hpp.

Ipow()

template<class I >

I NiHu::Ipow	(	I	base,
		I	exp
	)

compute integer power

Template Parameters

I	the integer type

Parameters

[in]	base	the base
[in]	exp	the exponent

Returns

base^exp

Definition at line 409 of file math_functions.hpp.

sgn()

template<typename T >

int NiHu::sgn

(

T

val

)

signum function

Template Parameters

T	the input type

Parameters

[in]

val

the function input

Returns

the signum(val)

Definition at line 43 of file math_functions.hpp.