The base class for all probability distributions. More...

#include <vpdl_distribution.h>

Inheritance diagram for vpdl_distribution< T, n >:

Public Types
typedef vpdt_field_default< T, n >::type	field_type
	the data type used for vectors.
typedef vpdt_field_default< T, n >::type	vector
	the data type used for vectors.
typedef vpdt_field_traits < field_type >::matrix_type	matrix
	the data type used for matrices.
Public Member Functions
virtual	~vpdl_distribution ()
virtual unsigned int	dimension () const =0
	Return the run time dimension, which does not equal `n` when `n==0`.
virtual vpdl_distribution< T, n > *	clone () const =0
	Create a copy on the heap and return base class pointer.
virtual T	density (const vector &pt) const =0
	Evaluate the unnormalized density at a point.
virtual T	prob_density (const vector &pt) const
	Evaluate the probability density at a point.
virtual T	log_prob_density (const vector &pt) const
	Evaluate the log probability density at a point.
virtual T	gradient_density (const vector &pt, vector &g) const =0
	Compute the gradient of the unnormalized density at a point.
virtual T	norm_const () const =0
	The normalization constant for the density.
virtual T	cumulative_prob (const vector &pt) const =0
	Evaluate the cumulative distribution function at a point.
virtual vector	inverse_cdf (const T &p) const
	Compute the inverse of the cumulative_prob() function.
virtual T	box_prob (const vector &min_pt, const vector &max_pt) const
	The probability of being in an axis-aligned box.
virtual void	compute_mean (vector &mean) const =0
	Compute the mean of the distribution.
virtual void	compute_covar (matrix &covar) const =0
	Compute the covariance of the distribution.

Detailed Description

template<class T, unsigned int n = 0>
class vpdl_distribution< T, n >

The base class for all probability distributions.

There is a distinct polymorphic class hierarchy for each choice of template parameters. The vector and matrix data types vary with both T and n.

Template Parameters:

T	is the scalar type use for numerical calculations (generally double or float)
n	is the fixed dimension of the space with special case 0 (the default) indicating dynamic dimension set at run time. For n > 1 the data types are vnl_vector_fixed<T,n> and vnl_matrix_fixed<T,n,n> For n == 1 the data types are T and T For n == 0 the data types are vnl_vector<T> and vnl_matrix<T>

Definition at line 30 of file vpdl_distribution.h.

Member Typedef Documentation

template<class T, unsigned int n = 0>

typedef vpdt_field_default<T,n>::type vpdl_distribution< T, n >::field_type

the data type used for vectors.

Reimplemented in vpdl_mixture_of< dist_t >.

Definition at line 36 of file vpdl_distribution.h.

template<class T, unsigned int n = 0>

typedef vpdt_field_traits<field_type>::matrix_type vpdl_distribution< T, n >::matrix

the data type used for matrices.

Reimplemented in vpdl_kernel_vbw_base< T, n >, vpdl_kernel_fbw_base< T, n >, vpdl_mixture_of< dist_t >, vpdl_mixture< T, n >, vpdl_gaussian_sphere< T, n >, vpdl_kernel_base< T, n >, vpdl_gaussian_indep< T, n >, vpdl_kernel_gaussian_sfbw< T, n >, vpdl_gaussian< T, n >, vpdl_multi_cmp_dist< T, n >, and vpdl_multi_cmp_dist< vpdt_dist_traits< dist_t >::scalar_type, vpdt_dist_traits< dist_t >::dimension >.

Definition at line 41 of file vpdl_distribution.h.

template<class T, unsigned int n = 0>

typedef vpdt_field_default<T,n>::type vpdl_distribution< T, n >::vector

the data type used for vectors.

Reimplemented in vpdl_kernel_vbw_base< T, n >, vpdl_kernel_fbw_base< T, n >, vpdl_mixture_of< dist_t >, vpdl_mixture< T, n >, vpdl_gaussian_sphere< T, n >, vpdl_kernel_base< T, n >, vpdl_gaussian_indep< T, n >, vpdl_kernel_gaussian_sfbw< T, n >, vpdl_gaussian< T, n >, vpdl_gaussian_base< T, n >, vpdl_multi_cmp_dist< T, n >, and vpdl_multi_cmp_dist< vpdt_dist_traits< dist_t >::scalar_type, vpdt_dist_traits< dist_t >::dimension >.

Definition at line 39 of file vpdl_distribution.h.

Constructor & Destructor Documentation

template<class T, unsigned int n = 0>

virtual vpdl_distribution< T, n >::~vpdl_distribution ( ) [inline, virtual]

Definition at line 33 of file vpdl_distribution.h.

Member Function Documentation

template<class T , unsigned int n>

T vpdl_distribution< T, n >::box_prob	(	const vector &	min_pt,
		const vector &	max_pt
	)		const `[virtual]`

The probability of being in an axis-aligned box.

The box is defined by two points, the minimum and maximum. Implemented in terms of cumulative_prob() by default.

Reimplemented in vpdl_mixture< T, n >, vpdl_kernel_gaussian_sfbw< T, n >, vpdl_gaussian_sphere< T, n >, and vpdl_mixture_of< dist_t >.

Definition at line 86 of file vpdl_distribution.txx.

template<class T, unsigned int n = 0>

virtual vpdl_distribution<T,n>* vpdl_distribution< T, n >::clone ( ) const [pure virtual]

Create a copy on the heap and return base class pointer.

Implemented in vpdl_mixture< T, n >, vpdl_mixture_of< dist_t >, vpdl_gaussian_sphere< T, n >, vpdl_gaussian_indep< T, n >, vpdl_gaussian< T, n >, and vpdl_kernel_gaussian_sfbw< T, n >.

template<class T, unsigned int n = 0>

virtual void vpdl_distribution< T, n >::compute_covar ( matrix & covar ) const [pure virtual]

Compute the covariance of the distribution.

This may be trivial for distributions like Gaussians, but actually involves computation for others.

Implemented in vpdl_mixture< T, n >, vpdl_kernel_gaussian_sfbw< T, n >, vpdl_gaussian_sphere< T, n >, vpdl_gaussian< T, n >, vpdl_gaussian_indep< T, n >, and vpdl_mixture_of< dist_t >.

template<class T, unsigned int n = 0>

virtual void vpdl_distribution< T, n >::compute_mean ( vector & mean ) const [pure virtual]

Compute the mean of the distribution.

This may be trivial for distributions like Gaussians, but actually involves computation for others.

Implemented in vpdl_mixture< T, n >, vpdl_gaussian_sphere< T, n >, vpdl_mixture_of< dist_t >, vpdl_gaussian_indep< T, n >, vpdl_gaussian< T, n >, and vpdl_kernel_base< T, n >.

template<class T, unsigned int n = 0>

virtual T vpdl_distribution< T, n >::cumulative_prob ( const vector & pt ) const [pure virtual]

Evaluate the cumulative distribution function at a point.

This is the integral of the density function from negative infinity (in all dimensions) to the point in question

Note:: It is not possible to compute this value for all functions in closed form. In some cases, numerical integration may be used. If no good solutions exists the function should return a quiet NaN.

Implemented in vpdl_mixture< T, n >, vpdl_kernel_gaussian_sfbw< T, n >, vpdl_mixture_of< dist_t >, vpdl_gaussian_sphere< T, n >, vpdl_gaussian_indep< T, n >, and vpdl_gaussian< T, n >.

template<class T, unsigned int n = 0>

virtual T vpdl_distribution< T, n >::density ( const vector & pt ) const [pure virtual]

Evaluate the unnormalized density at a point.

Note:: This is not a probability density. To make this a probability multiply by norm_const()

See also:: prob_density

Implemented in vpdl_mixture< T, n >, vpdl_mixture_of< dist_t >, vpdl_gaussian_sphere< T, n >, vpdl_gaussian_indep< T, n >, vpdl_gaussian< T, n >, and vpdl_kernel_gaussian_sfbw< T, n >.

template<class T, unsigned int n = 0>

virtual unsigned int vpdl_distribution< T, n >::dimension ( ) const [pure virtual]

Return the run time dimension, which does not equal n when n==0.

Implemented in vpdl_mixture< T, n >, vpdl_mixture_of< dist_t >, vpdl_gaussian_sphere< T, n >, vpdl_gaussian_indep< T, n >, vpdl_gaussian< T, n >, and vpdl_kernel_base< T, n >.

template<class T, unsigned int n = 0>

virtual T vpdl_distribution< T, n >::gradient_density	(	const vector &	pt,
		vector &	g
	)		const `[pure virtual]`

Compute the gradient of the unnormalized density at a point.

Returns:: the density at pt since it is usually needed as well, and is often trivial to compute while computing gradient

Return values:

g	the gradient vector

Implemented in vpdl_mixture< T, n >, vpdl_mixture_of< dist_t >, vpdl_kernel_gaussian_sfbw< T, n >, vpdl_gaussian_sphere< T, n >, vpdl_gaussian_indep< T, n >, and vpdl_gaussian< T, n >.

template<class T, unsigned int n>

vpdl_distribution< T, n >::vector vpdl_distribution< T, n >::inverse_cdf ( const T & p ) const [virtual]

Compute the inverse of the cumulative_prob() function.

The value of x: P(x'<x) = P for x' drawn from the distribution.

Note:: This is only valid for univariate distributions multivariate distributions will return a quiet NaN

The value of x: P(x'<x) = P for x' drawn from the distribution. This is only valid for univariate distributions multivariate distributions will return -infinity

Definition at line 75 of file vpdl_distribution.txx.

template<class T, unsigned int n = 0>

virtual T vpdl_distribution< T, n >::log_prob_density ( const vector & pt ) const [inline, virtual]