A multi-dimensional Gaussian probability density function using a Cholesky decomposition. More...

#include <prob_dens_func.h>

Inheritance diagram for o2scl::prob_dens_mdim_gaussian< vec_t, mat_t >:

Detailed Description

template<class vec_t = boost::numeric::ublas::vector<double>, class mat_t = boost::numeric::ublas::matrix<double>>
class o2scl::prob_dens_mdim_gaussian< vec_t, mat_t >

Given a (square) covariance matrix, $\Sigma$ , and a mean vector $\mu$ the PDF is

$P(x) = \det \left( 2 \pi \Sigma \right)^{-1/2} \exp \left[ -\frac{1}{2} (x-\mu)^T \Sigma^{-1} (x-\mu) \right]$

Given the Cholesky decomposition $A A^{T} = \Sigma$ , and a vector, $ z $ of samples from the standard Gaussian with 0 mean and unit variance, one can create a sample $ x $ from $x = \mu + A z$ .

Note: This class inverts the matrix, necessary for computing the pdf, but not for sampling the distribution, so for large matrices the inversion can be a waste of computation if the pdf is not needed.

A separate class for the two-dimensional case is prob_dens_mdim_biv_gaussian .

Note: Const functions are not thread-safe because mutable storage is used.

Idea for Future:: Create alternate versions based on other matrix decompositions?

Definition at line 987 of file prob_dens_func.h.

Public Member Functions
const mat_t &	get_chol ()
	Get the Cholesky decomposition.

const mat_t &	get_covar_inv ()
	Get the inverse of the covariance matrix.

const vec_t &	get_peak ()
	Get the peak location.

const double &	get_norm ()
	Get the normalization.

virtual size_t	dim () const
	The dimensionality.

	prob_dens_mdim_gaussian ()
	Create an empty distribution.

	prob_dens_mdim_gaussian (const prob_dens_mdim_gaussian &pdmg_loc)
	Copy constructor.

prob_dens_mdim_gaussian &	operator= (const prob_dens_mdim_gaussian &pdmg_loc)
	Copy constructor with operator=.

template<class mat2_t , class vec2_t , class mat2_col_t = const_matrix_column_gen<mat2_t>>
int	set (size_t p_mdim, size_t n_pts, const mat2_t &pts, const vec2_t &vals, vec_t &peak_arg, mat_t &covar_arg)
	Create a distribution from a set of samples from a multidimensional Gaussian, returning the peak values and covariance matrix. More...

template<class mat2_t , class vec2_t , class mat2_col_t = const_matrix_column_gen<mat2_t>>
int	set (size_t p_mdim, size_t n_pts, const mat2_t &pts, const vec2_t &vals)
	Create a distribution from a set of samples from a multidimensional Gaussian. More...

	prob_dens_mdim_gaussian (size_t p_ndim, vec_t &p_peak, mat_t &covar)
	Create a distribution from the covariance matrix.

void	set (size_t p_ndim, vec_t &p_peak, mat_t &covar)
	Set the peak and covariance matrix for the distribution. More...

void	set_alt (size_t p_ndim, vec_t &p_peak, mat_t &p_chol, mat_t &p_covar_inv, double p_norm)
	Alternate set function for use when covariance matrix has already been decomposed and inverted.

template<class vec_vec_t , class mat_col_t , class func_t >
void	set_gproc (size_t n_dim, size_t n_init, vec_vec_t &x, vec_t &y, func_t &fcovar)
	Given a data set and a covariance function, construct probability distribution based on a Gaussian process which includes noise. More...

virtual double	pdf (const vec_t &x) const
	The normalized density.

virtual double	log_pdf (const vec_t &x) const
	The log of the normalized density.

virtual void	operator() (vec_t &x) const
	Sample the distribution.

Public Member Functions inherited from o2scl::prob_dens_mdim< boost::numeric::ublas::vector< double > >
virtual size_t	dim () const
	Return the dimensionality.

virtual double	pdf (const boost::numeric::ublas::vector< double > &x) const
	The normalized density.

virtual double	log_pdf (const boost::numeric::ublas::vector< double > &x) const
	The log of the normalized density.

virtual void	operator() (boost::numeric::ublas::vector< double > &x) const
	Sample the distribution.

Public Attributes
o2scl::prob_dens_gaussian	pdg
	Standard normal.

Protected Attributes
mat_t	chol
	Cholesky decomposition.

mat_t	covar_inv
	Inverse of the covariance matrix.

vec_t	peak
	Location of the peak.

double	norm
	Normalization factor, $\det ( 2 \pi \Sigma)^{-1/2}$ .

size_t	ndim
	Number of dimensions.

vec_t	q
	Temporary storage 1.

vec_t	vtmp
	Temporary storage 2.

Member Function Documentation

◆ set() [1/3]

template<class vec_t = boost::numeric::ublas::vector<double>, class mat_t = boost::numeric::ublas::matrix<double>>

template<class mat2_t , class vec2_t , class mat2_col_t = const_matrix_column_gen<mat2_t>>

int o2scl::prob_dens_mdim_gaussian< vec_t, mat_t >::set	(	size_t	p_mdim,
		size_t	n_pts,
		const mat2_t &	pts,
		const vec2_t &	vals
	)

inline

The matrix pts should have a size of n_pts in the first index and p_mdim in the second index

Definition at line 1123 of file prob_dens_func.h.

◆ set() [2/3]

template<class vec_t = boost::numeric::ublas::vector<double>, class mat_t = boost::numeric::ublas::matrix<double>>

template<class mat2_t , class vec2_t , class mat2_col_t = const_matrix_column_gen<mat2_t>>

int o2scl::prob_dens_mdim_gaussian< vec_t, mat_t >::set	(	size_t	p_mdim,
		size_t	n_pts,
		const mat2_t &	pts,
		const vec2_t &	vals,
		vec_t &	peak_arg,
		mat_t &	covar_arg
	)

inline

The matrix pts should have a size of n_pts in the first index and p_mdim in the second index

Definition at line 1089 of file prob_dens_func.h.

◆ set() [3/3]

template<class vec_t = boost::numeric::ublas::vector<double>, class mat_t = boost::numeric::ublas::matrix<double>>

void o2scl::prob_dens_mdim_gaussian< vec_t, mat_t >::set	(	size_t	p_ndim,
		vec_t &	p_peak,
		mat_t &	covar
	)

inline

Note: This function is called in constructors and thus should not be virtual.

Definition at line 1144 of file prob_dens_func.h.

◆ set_gproc()

template<class vec_t = boost::numeric::ublas::vector<double>, class mat_t = boost::numeric::ublas::matrix<double>>

template<class vec_vec_t , class mat_col_t , class func_t >

void o2scl::prob_dens_mdim_gaussian< vec_t, mat_t >::set_gproc	(	size_t	n_dim,
		size_t	n_init,
		vec_vec_t &	x,
		vec_t &	y,
		func_t &	fcovar
	)

inline

Note: The type mat_col_t is a matrix column type for the internal object matrix type mat_t, and not associated with the data type vec_vec_t. Since the default matrix type is boost::numeric::ublas::matrix < double > a good matrix column type for this function is boost::numeric::ublas::matrix_column < boost::numeric::ublas::matrix < double > > . This matrix column type is needed for the LU decomposition and inversion.

Definition at line 1217 of file prob_dens_func.h.

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

/home/awsteiner/wcs/o2scl/src/other/prob_dens_func.h

Detailed Description

template<class vec_t = boost::numeric::ublas::vector<double>, class mat_t = boost::numeric::ublas::matrix<double>> class o2scl::prob_dens_mdim_gaussian< vec_t, mat_t >

Public Member Functions

Public Attributes

Protected Attributes

Member Function Documentation

◆ set() [1/3]

◆ set() [2/3]

◆ set() [3/3]

◆ set_gproc()

template<class vec_t = boost::numeric::ublas::vector<double>, class mat_t = boost::numeric::ublas::matrix<double>>
class o2scl::prob_dens_mdim_gaussian< vec_t, mat_t >