density Namespace Reference

Collection of multivariate Gaussian distributions (members listed in density.hpp) More...

Classes
class	AR1_t
	Stationary AR1 process. More...
class	ARk_t
	Stationary AR(k) process. More...
class	contAR2_t
	Continuous AR(2) process. More...
class	GMRF_t
	Gaussian Markov Random Field. More...
class	MVNORM_t
	Multivariate normal distribution with user supplied covariance matrix. More...
class	N01
	Standardized normal distribution. More...
class	PROJ_t
	Projection of multivariate gaussian variable. More...
class	SCALE_t
	Apply scale transformation on a density. More...
class	SEPARABLE_t
	Separable extension of two densitites. More...
class	UNSTRUCTURED_CORR_t
	Multivariate normal distribution with unstructered correlation matrix. More...
class	VECSCALE_t
	Apply a vector scale transformation on a density. More...

Functions
template<class scalartype >
GMRF_t< scalartype >	GMRF (Eigen::SparseMatrix< scalartype > Q, int order, bool normalize=true)
	Construct object to evaluate density of Gaussian Markov Random Field (GMRF) for sparse Q. More...
template<class scalartype >
MVNORM_t< scalartype >	MVNORM (matrix< scalartype > Sigma, bool use_atomic=true)
	Construct object to evaluate multivariate zero-mean normal density with user supplied covariance matrix. More...
template<class distribution1 , class distribution2 >
SEPARABLE_t< distribution1, distribution2 >	SEPARABLE (distribution1 f_, distribution2 g_)
	Construct object to evaluate the separable extension of two multivariate zero-mean normal densities. See SEPARABLE_t for details. More...
template<class scalartype >
UNSTRUCTURED_CORR_t< scalartype >	UNSTRUCTURED_CORR (vector< scalartype > x)
	Construct object to evaluate the density with unstructured correlation matrix. See UNSTRUCTURED_CORR_t for details.
template<class vectortype , class distribution >
VECSCALE_t< distribution >	VECSCALE (distribution f_, vectortype scale_)
	Construct object to evaluate a scaled density. See VECSCALE_t for details.

Detailed Description

Collection of multivariate Gaussian distributions (members listed in density.hpp)

For use of the namespace see Multivariate distributions

Function Documentation

GMRF()

template<class scalartype >

GMRF_t<scalartype> density::GMRF	(	Eigen::SparseMatrix< scalartype >	Q,
		int	order,
		bool	normalize = true
	)

Construct object to evaluate density of Gaussian Markov Random Field (GMRF) for sparse Q.

For detailed explanation of GMRFs see the class definition GMRF_t

Parameters

Q	precision matrix
order	Convolution order, i.e. the precision matrix is Q^order (matrix product)
normalize	Add normalizing constant ?

Examples:

spde.cpp, spde_aniso.cpp, spde_aniso_speedup.cpp, and TMBad/spde_epsilon.cpp.

Definition at line 934 of file density.hpp.

MVNORM()

template<class scalartype >

MVNORM_t<scalartype> density::MVNORM	(	matrix< scalartype >	Sigma,
		bool	use_atomic = true
	)

Construct object to evaluate multivariate zero-mean normal density with user supplied covariance matrix.

Parameters

Sigma	Positive definite covariance matrix.
use_atomic	Determines if "atomic functions" are used for the linear algebra (default).

Shortform version for working with the density of the MVNORM_t distribution (C++ class). Typical use:

MVNORM(Sigma)(x);

where Sigma is a covariance matrix. The part MVNORM(Sigma) creates an object of MVNORM_t, which is then evaluated by the part (x).

Examples:

multivariate_distributions.cpp, and sdv_multi.cpp.

Definition at line 208 of file density.hpp.

SEPARABLE()

template<class distribution1 , class distribution2 >

SEPARABLE_t<distribution1,distribution2> density::SEPARABLE	(	distribution1	f_,
		distribution2	g_
	)

Construct object to evaluate the separable extension of two multivariate zero-mean normal densities. See SEPARABLE_t for details.

Parameters

f_	First density object.
g_	Second density object.

Shortform version to combine two densities using the class SEPARABLE_t . Typical use:

PARAMETER_ARRAY(x); // 2D array
SEPARABLE(AR1(phi), MVNORM(Sigma))(x);

where MVNORM(Sigma) acts in the first dimension of x and AR1(phi) acts in the second dimension of x.

Note

The order of array dimensions is reversed in the sense that f_ acts in the second dimension and g_ acts in the first dimension (This order is consistent with how Kronecker products work in R).

Definition at line 1247 of file density.hpp.