OpenKalman::GaussianDistribution< StaticDescriptor, MeanNestedMatrix, CovarianceNestedMatrix, random_number_engine > Struct Template Reference

A Gaussian distribution, defined in terms of a Mean and a Covariance. More...

#include <forward-class-declarations.hpp>

Collaboration diagram for OpenKalman::GaussianDistribution< StaticDescriptor, MeanNestedMatrix, CovarianceNestedMatrix, random_number_engine >:

Public Member Functions
template<typename Arg , std::enable_if_t< gaussian_distribution< Arg > and not std::is_base_of_v< GaussianDistribution, std::decay_t< Arg >> and compares_with< typename DistributionTraits< Arg >::StaticDescriptor, StaticDescriptor >, int > = 0>
	GaussianDistribution (Arg &&arg)
	Construct from related distribution.
	GaussianDistribution (Mean &&mean, Covariance &&cov)
	Construct from an rvalue of a mean and a covariance.
template<typename M , std::enable_if_t< typed_matrix< M > and vector< M > and has_untyped_index< M, 1 > and compares_with< vector_space_descriptor_of_t< M, 0 >, StaticDescriptor >, int > = 0>
	GaussianDistribution (M &&mean, Covariance &&cov)
	Construct from a typed_matrix and an rvalue of a covariance.
template<typename M , std::enable_if_t< typed_matrix_nestable< M > and vector< M > and(index_dimension_of< M, 0 >::value==dim), int > = 0>
	GaussianDistribution (M &&mean, Covariance &&cov)
	Construct from a typed_matrix_nestable and an rvalue of a covariance.
template<typename Cov , std::enable_if_t<(covariance< Cov > or(typed_matrix< Cov > and square_shaped< Cov >)) and compares_with< vector_space_descriptor_of_t< Cov, 0 >, StaticDescriptor >, int > = 0>
	GaussianDistribution (Mean &&mean, Cov &&cov)
	Construct from an rvalue of a mean and a covariance, typed_matrix, or covariance_nestable.
template<typename Cov , std::enable_if_t< covariance_nestable< Cov > and(index_dimension_of< Cov, 0 >::value==dim), int > = 0>
	GaussianDistribution (Mean &&mean, Cov &&cov)
template<typename M , typename Cov , std::enable_if_t< typed_matrix< M > and vector< M > and has_untyped_index< M, 1 > and compares_with< vector_space_descriptor_of_t< M, 0 >, StaticDescriptor > and(covariance< Cov > or typed_matrix< Cov >) and compares_with< vector_space_descriptor_of_t< Cov, 0 >, StaticDescriptor >, int > = 0>
	GaussianDistribution (M &&mean, Cov &&cov)
	Construct from matrices representing a mean and a covariance. More...
template<typename M , typename Cov , std::enable_if_t< typed_matrix< M > and vector< M > and has_untyped_index< M, 1 > and compares_with< vector_space_descriptor_of_t< M, 0 >, StaticDescriptor > and covariance_nestable< Cov > and(index_dimension_of< Cov, 0 >::value==dim), int > = 0>
	GaussianDistribution (M &&mean, Cov &&cov)
	Construct from matrices representing a mean and a covariance. More...
template<typename M , typename Cov , std::enable_if_t< typed_matrix_nestable< M > and vector< M > and(index_dimension_of< M, 0 >::value==dim) and(covariance< Cov > or typed_matrix< Cov >) and compares_with< vector_space_descriptor_of_t< Cov, 0 >, StaticDescriptor >, int > = 0>
	GaussianDistribution (M &&mean, Cov &&cov)
	Construct from matrices representing a mean and a covariance. More...
template<typename M , typename Cov , std::enable_if_t< typed_matrix_nestable< M > and vector< M > and(index_dimension_of< M, 0 >::value==dim) and covariance_nestable< Cov > and(index_dimension_of< Cov, 0 >::value==dim), int > = 0>
	GaussianDistribution (M &&mean, Cov &&cov)
	Construct from matrices representing a mean and a covariance. More...
template<typename Cov , std::enable_if_t<(covariance< Cov > or(typed_matrix< Cov > and square_shaped< Cov >)) and compares_with< vector_space_descriptor_of_t< Cov, 0 >, StaticDescriptor >, int > = 0>
	GaussianDistribution (Cov &&cov)
	Construct with only a covariance or square typed_matrix (mean is set to zero).
template<typename Cov , std::enable_if_t< covariance_nestable< Cov > and(index_dimension_of< Cov, 0 >::value==dim), int > = 0>
	GaussianDistribution (Cov &&cov)
	Construct using only a covariance_nestable (the mean is set to zero).
template<typename Arg , std::enable_if_t< gaussian_distribution< Arg > and compares_with< typename DistributionTraits< Arg >::StaticDescriptor, StaticDescriptor >, int > = 0>
GaussianDistribution &	operator= (Arg &&arg)
	Assign from another compatible distribution.
auto &	operator+= (const GaussianDistribution &arg)
auto &	operator-= (const GaussianDistribution &arg)
template<typename S , std::enable_if_t< stdex::convertible_to< S, const Scalar >, int > = 0>
auto &	operator*= (const S scale)
template<typename S , std::enable_if_t< stdex::convertible_to< S, const Scalar >, int > = 0>
auto &	operator/= (const S scale)
auto	operator() () const
	Generate a random value from the distribution. More...
template<typename... Z, std::enable_if_t<(sizeof...(Z) > 0>
Scalar	log_likelihood (const Z &...z) const
	Log-likelihood function for a set of i.i.d. More...
Scalar	entropy () const
	Entropy of the distribution, in bits.

Public Attributes
Mean	mu
	The mean of the distribution.
Covariance	sigma
	The Covariance matrix of the distribution.

Protected Types
using	Mean = Mean< StaticDescriptor, MeanNestedMatrix >
using	Covariance = Covariance< StaticDescriptor, CovarianceNestedMatrix >
using	Scalar = scalar_type_of_t< Mean >

Static Protected Attributes
static constexpr auto	dim = coordinates::dimension_of_v<StaticDescriptor>

Detailed Description

template<typename StaticDescriptor, typename MeanNestedMatrix, typename CovarianceNestedMatrix, typename random_number_engine>
struct OpenKalman::GaussianDistribution< StaticDescriptor, MeanNestedMatrix, CovarianceNestedMatrix, random_number_engine >

A Gaussian distribution, defined in terms of a Mean and a Covariance.

Template Parameters

Descriptor	Coefficient types.
MeanNestedMatrix	The underlying native matrix for the Mean.
CovarianceNestedMatrix	The underlying native matrix (triangular or self-adjoint) for the Covariance.
random_number_engine	A random number engine compatible with the c++ standard library (e.g., std::mt19937).

Todo:

Change to std::mt19937_64 ?

Constructor & Destructor Documentation

GaussianDistribution() [1/4]

template<typename StaticDescriptor, typename MeanNestedMatrix, typename CovarianceNestedMatrix, typename random_number_engine>

template<typename M , typename Cov , std::enable_if_t< typed_matrix< M > and vector< M > and has_untyped_index< M, 1 > and compares_with< vector_space_descriptor_of_t< M, 0 >, StaticDescriptor > and(covariance< Cov > or typed_matrix< Cov >) and compares_with< vector_space_descriptor_of_t< Cov, 0 >, StaticDescriptor >, int > = 0>

OpenKalman::GaussianDistribution< StaticDescriptor, MeanNestedMatrix, CovarianceNestedMatrix, random_number_engine >::GaussianDistribution ( M &&  mean, Cov &&  cov  )

inline

Construct from matrices representing a mean and a covariance.

Template Parameters

M	A typed_matrix.
Cov	A covariance or square typed_matrix.

GaussianDistribution() [2/4]

template<typename StaticDescriptor, typename MeanNestedMatrix, typename CovarianceNestedMatrix, typename random_number_engine>

template<typename M , typename Cov , std::enable_if_t< typed_matrix< M > and vector< M > and has_untyped_index< M, 1 > and compares_with< vector_space_descriptor_of_t< M, 0 >, StaticDescriptor > and covariance_nestable< Cov > and(index_dimension_of< Cov, 0 >::value==dim), int > = 0>

OpenKalman::GaussianDistribution< StaticDescriptor, MeanNestedMatrix, CovarianceNestedMatrix, random_number_engine >::GaussianDistribution ( M &&  mean, Cov &&  cov  )

inline

Construct from matrices representing a mean and a covariance.

Template Parameters

M	A typed_matrix.
Cov	A covariance_nestable.

GaussianDistribution() [3/4]

template<typename StaticDescriptor, typename MeanNestedMatrix, typename CovarianceNestedMatrix, typename random_number_engine>

template<typename M , typename Cov , std::enable_if_t< typed_matrix_nestable< M > and vector< M > and(index_dimension_of< M, 0 >::value==dim) and(covariance< Cov > or typed_matrix< Cov >) and compares_with< vector_space_descriptor_of_t< Cov, 0 >, StaticDescriptor >, int > = 0>

OpenKalman::GaussianDistribution< StaticDescriptor, MeanNestedMatrix, CovarianceNestedMatrix, random_number_engine >::GaussianDistribution ( M &&  mean, Cov &&  cov  )

inline

Construct from matrices representing a mean and a covariance.

Template Parameters

M	A typed_matrix_nestable.
Cov	A covariance or square typed_matrix.

GaussianDistribution() [4/4]

template<typename StaticDescriptor, typename MeanNestedMatrix, typename CovarianceNestedMatrix, typename random_number_engine>

template<typename M , typename Cov , std::enable_if_t< typed_matrix_nestable< M > and vector< M > and(index_dimension_of< M, 0 >::value==dim) and covariance_nestable< Cov > and(index_dimension_of< Cov, 0 >::value==dim), int > = 0>

OpenKalman::GaussianDistribution< StaticDescriptor, MeanNestedMatrix, CovarianceNestedMatrix, random_number_engine >::GaussianDistribution ( M &&  mean, Cov &&  cov  )

inline

Construct from matrices representing a mean and a covariance.

Template Parameters

M	A typed_matrix_nestable.
Cov	A covariance_nestable.

Member Function Documentation

log_likelihood()

template<typename StaticDescriptor, typename MeanNestedMatrix, typename CovarianceNestedMatrix, typename random_number_engine>

template<typename... Z, std::enable_if_t<(sizeof...(Z) > 0>

Scalar OpenKalman::GaussianDistribution< StaticDescriptor, MeanNestedMatrix, CovarianceNestedMatrix, random_number_engine >::log_likelihood ( const Z &...  z ) const

inline

Log-likelihood function for a set of i.i.d.

observations z.

Parameters

z	One or more i.i.d. observations in the same multivariate space as the mean of the distribution.

operator()()

template<typename StaticDescriptor, typename MeanNestedMatrix, typename CovarianceNestedMatrix, typename random_number_engine>

auto OpenKalman::GaussianDistribution< StaticDescriptor, MeanNestedMatrix, CovarianceNestedMatrix, random_number_engine >::operator() ( ) const

inline

Generate a random value from the distribution.

Returns

A random, single-column typed matrix with probability based on the distribution

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The documentation for this struct was generated from the following file:

• OpenKalman/distributions/GaussianDistribution.hpp