MR::Math Namespace Reference

Namespaces
namespace	Bessel
namespace	Chebyshev
namespace	Gaussian
namespace	ICLS
	functionality for solving constrained least-squares problems
namespace	Legendre
namespace	Rician
namespace	Sech
namespace	SH
namespace	Sphere
namespace	Stats
namespace	ZSH

Classes
class	CubicSpline
class	GradientDescent
	Computes the minimum of a function using a gradient descent approach. More...
class	GradientDescentBB
	Computes the minimum of a function using a Barzilai Borwein gradient descent approach. ENH: implement stabilised version https://arxiv.org/abs/1907.06409. More...
class	Hermite
class	HermiteSpline
class	LinearUpdateBB
class	QuadraticLineSearch
	Computes the minimum of a 1D function using a quadratic line search. More...
class	RNG
	random number generator More...
class	Sinc
class	Sn_scale_estimator
class	UniformBSpline
class	Zstatistic

Enumerations
enum	SplineProcessingType { Value = 1 , Derivative = 2 , ValueAndDerivative = Value | Derivative }

Functions
double	matrix_average (vector< Eigen::MatrixXd > const &mat_in, Eigen::MatrixXd &mat_avg, bool verbose=false)
default_type	betaincreg (const default_type a, const default_type b, const default_type x)
float	cauchy (float x, float s)
template<class Function >
Eigen::Matrix< typename Function::value_type, Eigen::Dynamic, Eigen::Dynamic >	check_function_gradient (Function &function, Eigen::Matrix< typename Function::value_type, Eigen::Dynamic, 1 > x, typename Function::value_type increment, bool show_hessian=false, Eigen::Matrix< typename Function::value_type, Eigen::Dynamic, 1 > conditioner=Eigen::Matrix< typename Function::value_type, Eigen::Dynamic, 1 >())
template<class M >
default_type	condition_number (const M &data)
default_type	erfinv (const default_type)
	Compute the inverse of the error function. More...
default_type	erfcinv (const default_type)
	Compute the inverse of the complementary error function. More...
template<typename T >
T	factorial (const T i)
template<class FunctionType , typename ValueType >
ValueType	golden_section_search (FunctionType &function, const std::string &message, ValueType min_bound, ValueType init_estimate, ValueType max_bound, ValueType tolerance=0.01)
	Computes the minimum of a 1D function using a golden section search. More...
template<class MatrixType >
Eigen::Matrix< typename MatrixType::Scalar, Eigen::Dynamic, Eigen::Dynamic >	pinv (const MatrixType &M)
	return Moore-Penrose pseudo-inverse of M More...
template<class MatrixType >
size_t	rank (const MatrixType &M)
template<typename T >
constexpr T	pow2 (const T &v)
template<typename T >
constexpr T	pow3 (const T &v)
template<typename T >
constexpr T	pow4 (const T &v)
template<typename T >
constexpr T	pow5 (const T &v)
template<typename T >
constexpr T	pow6 (const T &v)
template<typename T >
constexpr T	pow7 (const T &v)
template<typename T >
constexpr T	pow8 (const T &v)
template<typename T >
constexpr T	pow9 (const T &v)
template<typename T >
constexpr T	pow10 (const T &v)
template<typename I , typename T >
constexpr I	round (const T x) throw ()
template<typename I , typename T >
constexpr I	floor (const T x) throw ()
	template function with cast to different type More...
template<typename I , typename T >
constexpr I	ceil (const T x) throw ()
	template function with cast to different type More...
template<class Container >
Container::value_type	median (Container &list)
template<class MatrixType = Eigen::Matrix<default_type, 3, Eigen::Dynamic>, class VectorType = Eigen::Matrix<default_type, 3, 1>>
bool	median_weiszfeld (const MatrixType &X, VectorType &median, const size_t numIter=300, const default_type precision=0.00001)
template<class Cont >
default_type	polynomial (Cont &coeffs, const default_type x)
	Evaluate a polynomial expansion for a scalar term. More...
template<class VarArrayType , class CountArrayType >
default_type	welch_satterthwaite (const VarArrayType &variances, const CountArrayType &counts)
default_type	t2z (const default_type stat, const default_type dof)
default_type	F2z (const default_type stat, const size_t rank, const default_type dof)
template<typename T >
int	sgn (T val)

Variables
constexpr double	e = 2.71828182845904523536
constexpr double	pi = 3.14159265358979323846
constexpr double	pi_2 = pi / 2.0
constexpr double	pi_4 = pi / 4.0
constexpr double	sqrt2 = 1.41421356237309504880
constexpr double	sqrt1_2 = 1.0 / sqrt2

Enumeration Type Documentation

SplineProcessingType

enum MR::Math::SplineProcessingType

Enumerator
Value
Derivative
ValueAndDerivative

Definition at line 23 of file cubic_spline.h.

Function Documentation

betaincreg()

default_type MR::Math::betaincreg	(	const default_type	a,
		const default_type	b,
		const default_type	x
	)

cauchy()

float MR::Math::cauchy ( float  x, float  s  )

inline

Definition at line 25 of file cauchy.h.

check_function_gradient()

template<class Function >

Eigen::Matrix< typename Function::value_type, Eigen::Dynamic, Eigen::Dynamic > MR::Math::check_function_gradient	(	Function &	function,
		Eigen::Matrix< typename Function::value_type, Eigen::Dynamic, 1 >	x,
		typename Function::value_type	increment,
		bool	show_hessian = false,
		Eigen::Matrix< typename Function::value_type, Eigen::Dynamic, 1 >	conditioner = Eigen::Matrix<typename Function::value_type, Eigen::Dynamic, 1>()
	)

Definition at line 27 of file check_gradient.h.

condition_number()

template<class M >

default_type MR::Math::condition_number ( const M &  data )

inline

Definition at line 32 of file condition_number.h.

erfcinv()

default_type MR::Math::erfcinv

(

const

default_type

)

Compute the inverse of the complementary error function.

erfinv()

default_type MR::Math::erfinv

(

const

default_type

)

Compute the inverse of the error function.

Implementation based on Boost Math (https://github.com/boostorg/math) While the erfinv() function is exposed in the API, it will encounter floating-point precision issues if provided with input values greater than approx. +0.999999 or smaller than approx. -0.999999. If such extreme values are likely to arise during processing, it is highly recommended that programmers instead operate natively on the values q = 1.0 - p and/or qc = 1.0 + p, and pass the appropriate value (q or qc) directly to the erfcinv() function. This will ensure full use of available floating-point precision within these functions, which is otherwise lost if performing one of the above conversions (either implicitly within one of these functions, or explicitly by the programmer prior to invoking erfinv()).

F2z()

default_type MR::Math::F2z	(	const default_type	stat,
		const size_t	rank,
		const default_type	dof
	)

factorial()

template<typename T >

T MR::Math::factorial

(

const T

i

)

Definition at line 30 of file factorial.h.

matrix_average()

double MR::Math::matrix_average	(	vector< Eigen::MatrixXd > const &	mat_in,
		Eigen::MatrixXd &	mat_avg,
		bool	verbose = false
	)

median()

template<class Container >

Container::value_type MR::Math::median ( Container &  list )

inline

Definition at line 45 of file median.h.

median_weiszfeld()

template<class MatrixType = Eigen::Matrix<default_type, 3, Eigen::Dynamic>, class VectorType = Eigen::Matrix<default_type, 3, 1>>

bool MR::Math::median_weiszfeld	(	const MatrixType &	X,
		VectorType &	median,
		const size_t	numIter = 300,
		const default_type	precision = 0.00001
	)

Definition at line 74 of file median.h.

polynomial()

template<class Cont >

default_type MR::Math::polynomial	(	Cont &	coeffs,
		const default_type	x
	)

Evaluate a polynomial expansion for a scalar term.

Definition at line 28 of file polynomial.h.

sgn()

template<typename T >

int MR::Math::sgn ( T  val )

inline

Definition at line 24 of file robust_estimators.h.

t2z()

default_type MR::Math::t2z	(	const default_type	stat,
		const default_type	dof
	)

welch_satterthwaite()

template<class VarArrayType , class CountArrayType >

default_type MR::Math::welch_satterthwaite	(	const VarArrayType &	variances,
		const CountArrayType &	counts
	)

Definition at line 28 of file welch_satterthwaite.h.