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 .

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

Definition at line 924 of file prob_dens_func.h.

Public Member Functions
virtual size_t	dim () const
	The dimensionality.

	prob_dens_mdim_gaussian ()
	Create an empty distribution.

	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.

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.

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.

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.

o2scl::prob_dens_gaussian	pdg
	Standard normal.

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

Protected Attributes

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 >