ExtendedMath.h

Go to the documentation of this file.

// This file is part of the MercuryDPM project (https://www.mercurydpm.org).
// Copyright (c), The MercuryDPM Developers Team. All rights reserved.
// License: BSD 3-Clause License; see the LICENSE file in the root directory.
 
#ifndef MECURYDPM_EXTENDEDMATH_H
#define MECURYDPM_EXTENDEDMATH_H
 
#include <iostream> //std::istream and std::stringstream
#include <fstream> //std::fstream
#include <cmath>
#include <complex>
#include <limits>
 
#include "NumericalVector.h"
#include "Vector.h"
#include "Quaternion.h"
 
/*
 * \brief
 */
namespace constants
{
const Mdouble pi = 3.1415926535897932384626433832795;
const Mdouble sqrt_pi = 1.7724538509055160272981674833411;
const Mdouble sqr_pi = 9.8696044010893586188344909998762;
const Mdouble sqrt_2 = 1.4142135623730950488016887242097;
const Mdouble sqrt_3 = 1.7320508075688772935274463415059;
const Mdouble cbrt_2 = 1.2599210498948731906665443602833;
const Mdouble R = 8.31446261815324;
const Mdouble stefanBoltzmanConstant = 5.67e-8;
const std::complex<Mdouble> i = {0.0, 1.0};
const Mdouble degree = pi / 180.;  // degree-to-radian conversion
}
 
namespace mathsFunc
{
Mdouble gamma(Mdouble gamma_in);
 
Mdouble beta(Mdouble z, Mdouble w);
 
 
Mdouble chi_squared(Mdouble x, unsigned int k);
 
Mdouble chi_squared_prob(Mdouble x, unsigned int k);
 
Mdouble goldenSectionSearch(Mdouble (* function)(const Mdouble), Mdouble min, Mdouble cur, Mdouble max,
                            Mdouble endCondition, Mdouble curVal = std::numeric_limits<Mdouble>::quiet_NaN());
 
template<typename T>
int sign(T val)
{
    return (T(0) < val) - (val < T(0));
}
 
template<typename T>
T square(const T val)
{
    return val * val;
}
 
template<typename T>
T cubic(const T val)
{
    return val * val * val;
}
 
bool isEqual(Mdouble v1, Mdouble v2, Mdouble absError);
 
bool isEqual(Vec3D v1, Vec3D v2, Mdouble absError);
 
bool isEqual(Matrix3D m1, Matrix3D m2, Mdouble absError);
 
bool isEqual(MatrixSymmetric3D m1, MatrixSymmetric3D m2, Mdouble absError);
 
bool isEqual(Quaternion v1, Quaternion v2, double absError);
 
template<typename T>
constexpr T factorial(const T t)
{
    return (t == 0) ? 1 : t * factorial(t - 1);
}
 
//platform independent implementation of sine and cosine, taken from
// http://stackoverflow.com/questions/18662261/fastest-implementation-of-sine-cosine-and-square-root-in-c-doesnt-need-to-b
// (cosine was implemented wrongly on the website, here is a corrected version)
 
// sin(x) = x - x^3/3! + x^5/5! - x^7/7! + ...
Mdouble sin(Mdouble x);
 
// cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...
Mdouble cos(Mdouble x);
 
Mdouble exp(Mdouble Exponent);
 
Mdouble log(Mdouble Power);
 
 
// tan=sin/cos
template<typename T>
T tan(T x)
{
    return sin(x) / cos(x);
}
 
 
Mdouble chebyshev(Mdouble x, const Mdouble coef[], int N);
 
Mdouble I0_exp(Mdouble x);
 
Mdouble I0(Mdouble x);
    
}
 
/*
 * \brief Namespace for functions required to calculate spherical harmonics
 */
 
namespace sphericalHarmonics
{
 
//Compute all the associated LegenderePolynomials up to order n, and only positive order m at location x
NumericalVector<> associatedLegendrePolynomials(int n, Mdouble x);
 
//Compute all spherical harmonics up to order p, at angles theta and phi
NumericalVector<std::complex<Mdouble>> sphericalHarmonics(int p, Mdouble theta, Mdouble phi);
 
//Compute all squaredFactorials (see eqn 5.23 in a short course on fast multipole methods) up to order p
NumericalVector<> computeSquaredFactorialValues(int p);
}
 
#endif