Special mathematical functions

Special mathematical functions for which derivatives are implemented. More...

Functions
template<class Type >
Type	besselI (Type x, Type nu)
	besselI function (same as besselI from R). More...
template<class Type >
Type	besselJ (Type x, Type nu)
	besselJ function (same as besselJ from R). More...
template<class Type >
Type	besselK (Type x, Type nu)
	besselK function (same as besselK from R). More...
template<class Type >
Type	besselY (Type x, Type nu)
	besselY function (same as besselY from R). More...
template<class Type >
Type	lfactorial (Type x)
	Logarithm of factorial function (following R argument convention).
template<class Type >
Type	lgamma (Type x)
	Logarithm of gamma function (following R argument convention).
template<class Type >
Type	logspace_add (Type logx, Type logy)
	Addition in log-space. More...
template<class Type >
Type	logspace_sub (Type logx, Type logy)
	Subtraction in log-space. More...
template<class Type >
Type	matern (Type u, Type phi, Type kappa)

Detailed Description

Special mathematical functions for which derivatives are implemented.

Function Documentation

besselI()

template<class Type >

Type besselI	(	Type	x,
		Type	nu
	)

besselI function (same as besselI from R).

Note

Derivatives wrt. both arguments are implemented

Definition at line 488 of file distributions_R.hpp.

besselJ()

template<class Type >

Type besselJ	(	Type	x,
		Type	nu
	)

besselJ function (same as besselJ from R).

Note

Derivatives wrt. both arguments are implemented

Definition at line 511 of file distributions_R.hpp.

besselK()

template<class Type >

Type besselK	(	Type	x,
		Type	nu
	)

besselK function (same as besselK from R).

Note

Derivatives wrt. both arguments are implemented

Definition at line 465 of file distributions_R.hpp.

besselY()

template<class Type >

Type besselY	(	Type	x,
		Type	nu
	)

besselY function (same as besselY from R).

Note

Derivatives wrt. both arguments are implemented

Definition at line 526 of file distributions_R.hpp.

logspace_add()

template<class Type >

Type logspace_add	(	Type	logx,
		Type	logy
	)

Addition in log-space.

Calculates \(log( exp(logx) + exp(logy) )\) without causing unnecessary overflows or throwing away too much accuracy (see 'writing R-extensions'). The following reductions are applied while taping:

• log(exp(logx) + exp(-INFINITY)) = logx
• log(exp(-INFINITY) + exp(logy)) = logy

Parameters

logx	The logarithm of x.
logy	The logarithm of y.

Definition at line 181 of file convenience.hpp.

logspace_sub()

template<class Type >

Type logspace_sub	(	Type	logx,
		Type	logy
	)

Subtraction in log-space.

Calculates \(log( exp(logx) - exp(logy) )\) without causing unnecessary overflows or throwing away too much accuracy (see 'writing R-extensions').

Parameters

logx	The logarithm of x.
logy	The logarithm of y.

Definition at line 205 of file convenience.hpp.

matern()

template<class Type >

Type matern	(	Type	u,
		Type	phi,
		Type	kappa
	)

Matern correlation function

Compute values of the Matern correlation function for given distances and parameters. Same as 'matern' from the geoR package.

Parameters

u	Distance.
phi	Range parameter.
kappa	Smoothness parameter.

Examples:

matern.cpp.

Definition at line 129 of file convenience.hpp.