vpdl_distribution< T, n > Class Template Reference

#include <vpdl_distribution.h>

Inheritance diagram for vpdl_distribution< T, n >:

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List of all members.


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.


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.

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_default<T,n>::type vpdl_distribution< T, n >::vector

template<class T, unsigned int n = 0>
typedef vpdt_field_traits<field_type>::matrix_type vpdl_distribution< T, n >::matrix


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 = 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_gaussian< T, n >, vpdl_gaussian_indep< T, n >, vpdl_gaussian_sphere< T, n >, vpdl_kernel_base< T, n >, vpdl_mixture< T, n >, and vpdl_mixture_of< dist_t >.

template<class T, unsigned int n = 0>
virtual vpdl_distribution<T,n>* vpdl_distribution< T, n >::clone (  )  const [pure virtual]

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_gaussian< T, n >, vpdl_gaussian_indep< T, n >, vpdl_gaussian_sphere< T, n >, vpdl_kernel_gaussian_sfbw< T, n >, vpdl_mixture< T, n >, and vpdl_mixture_of< dist_t >.

template<class T, unsigned int n = 0>
virtual T vpdl_distribution< T, n >::prob_density ( const vector pt  )  const [inline, virtual]

template<class T, unsigned int n = 0>
virtual T vpdl_distribution< T, n >::log_prob_density ( const vector pt  )  const [inline, virtual]

Evaluate the log probability density at a point.

Reimplemented in vpdl_gaussian< T, n >, vpdl_gaussian_indep< T, n >, and vpdl_gaussian_sphere< T, n >.

Definition at line 62 of file vpdl_distribution.h.

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_gaussian< T, n >, vpdl_gaussian_indep< T, n >, vpdl_gaussian_sphere< T, n >, vpdl_kernel_gaussian_sfbw< T, n >, vpdl_mixture< T, n >, and vpdl_mixture_of< dist_t >.

template<class T, unsigned int n = 0>
virtual T vpdl_distribution< T, n >::norm_const (  )  const [pure virtual]

The normalization constant for the density.

When density() is multiplied by this value it becomes prob_density norm_const() is reciprocal of the integral of density over the entire field

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

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_gaussian< T, n >, vpdl_gaussian_indep< T, n >, vpdl_gaussian_sphere< T, n >, vpdl_kernel_gaussian_sfbw< T, n >, vpdl_mixture< T, n >, and vpdl_mixture_of< dist_t >.

template<class T, unsigned int n>
vpdl_distribution< T, n >::vector vpdl_distribution< T, n >::inverse_cdf ( const T &  p  )  const [inline, 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>
T vpdl_distribution< T, n >::box_prob ( const vector min_pt,
const vector max_pt 
) const [inline, 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_gaussian_sphere< T, n >, vpdl_kernel_gaussian_sfbw< T, n >, vpdl_mixture< 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 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_gaussian< T, n >, vpdl_gaussian_indep< T, n >, vpdl_gaussian_sphere< T, n >, vpdl_kernel_base< T, n >, vpdl_mixture< T, n >, and vpdl_mixture_of< dist_t >.

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_of< dist_t >.


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

Generated on Sun Nov 22 06:22:38 2009 for core/vpdl by  doxygen 1.5.5