TMB Documentation  v1.9.9
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)

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.

## § 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.

template<class Type >
 Type logspace_add ( Type logx, Type logy )

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.