26 #ifndef EXTENDEDMATH_H
27 #define EXTENDEDMATH_H
45 const Mdouble pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068;
46 const Mdouble sqrt_pi = 1.772453850905516027298167483341145182797549456122387128213807789852911284591032181374950656738544665;
47 const Mdouble sqr_pi = 9.869604401089358618834490999876151135313699407240790626413349376220044822419205243001773403718552232;
48 const Mdouble sqrt_2 = 1.414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641573;
49 const Mdouble sqrt_3 = 1.732050807568877293527446341505872366942805253810380628055806979451933016908800037081146186757248576;
51 const std::complex<Mdouble>
i = {0.0, 1.0};
91 Mdouble endCondition,
Mdouble curVal = std::numeric_limits<Mdouble>::quiet_NaN());
99 return (T(0) < val) - (val < T(0));
117 return val * val * val;
157 return (t == 0) ? 1 : t *
factorial(t - 1);
Implementation of a 3D quaternion (by Vitaliy).
Mdouble goldenSectionSearch(Mdouble(*function)(const Mdouble), Mdouble min, Mdouble cur, Mdouble max, Mdouble endCondition, Mdouble curVal=std::numeric_limits< Mdouble >::quiet_NaN())
This function performs a golden section search to find the location of the minimum of a function...
Mdouble exp(Mdouble Exponent)
Mdouble beta(Mdouble z, Mdouble w)
This is the beta function, returns the approximation based on cmath's implementation of ln(gamma) ...
const std::complex< Mdouble > i
int sign(T val)
This is a sign function, it returns -1 for negative numbers, 1 for positive numbers and 0 for 0...
T cubic(const T val)
calculates the cube of a number
Mdouble log(Mdouble Power)
bool isEqual(Mdouble v1, Mdouble v2, Mdouble absError)
Compares the difference of two Mdouble with an absolute error, useful in UnitTests.
Mdouble chi_squared_prob(Mdouble x, unsigned int k)
This is the function which actually gives the probability back using a chi squared test...
constexpr T factorial(const T t)
factorial function
Mdouble chi_squared(Mdouble x, unsigned int k)
This is a chi_squared function return the value x and degrees of freedom k.
Mdouble I0_exp(Mdouble x)
Mdouble chebyshev(Mdouble x, const Mdouble coef[], int N)
Namespace for evaluating the zeroth modified Bessel function of the first kind, I0(x), required in StatisticsPoint.hcc.
NumericalVector< std::complex< Mdouble > > sphericalHarmonics(int p, Mdouble theta, Mdouble phi)
Mdouble gamma(Mdouble gamma_in)
This is the gamma function returns the true value for the half integer value.
NumericalVector associatedLegendrePolynomials(int n, Mdouble x)
Implementation of a 3D matrix.
T square(const T val)
squares a number
Implementation of a 3D symmetric matrix.
NumericalVector computeSquaredFactorialValues(int p)