vpdl_gaussian_sphere< T, n > Class Template Reference

#include <vpdl_gaussian_sphere.h>

Inheritance diagram for vpdl_gaussian_sphere< T, n >:

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List of all members.


Detailed Description

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

A Gaussian with (hyper-)spherical covariance.

Definition at line 26 of file vpdl_gaussian_sphere.h.


Public Types

typedef vpdt_field_default< T,
n >::type 
vector
 the data type used for vectors.
typedef vpdt_field_traits
< vector >::matrix_type 
matrix
 the data type used for matrices.
typedef T covar_type
 the type used internally for covariance.
typedef vpdt_field_default< T,
n >::type 
field_type
 the data type used for vectors.

Public Member Functions

 vpdl_gaussian_sphere (unsigned int var_dim=n)
 Constructor.
 vpdl_gaussian_sphere (const vector &mean, const covar_type &var)
 Constructor - from mean and variance.
virtual ~vpdl_gaussian_sphere ()
 Destructor.
virtual vpdl_distribution< T, n > * clone () const
 Create a copy on the heap and return base class pointer.
virtual unsigned int dimension () const
 Return the run time dimension, which does not equal n when n==0.
virtual T density (const vector &pt) const
 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
 Compute the gradient of the unnormalized density at a point.
norm_const () const
 The normalization constant for the density.
sqr_mahal_dist (const vector &pt) const
 The squared Mahalanobis distance to this point.
virtual T cumulative_prob (const vector &pt) const
 Evaluate the cumulative distribution function at a point.
box_prob (const vector &min_pt, const vector &max_pt) const
 The probability of being in an axis-aligned box.
virtual const vectormean () const
 Access the mean directly.
virtual void set_mean (const vector &mean)
 Set the mean.
virtual void compute_mean (vector &mean) const
 Compute the mean of the distribution.
const covar_typecovariance () const
 Access the scalar variance.
void set_covariance (const covar_type &var)
 Set the scalar variance.
virtual void compute_covar (matrix &covar) const
 Compute the covariance of the distribution.
virtual vector inverse_cdf (const T &p) const
 Compute the inverse of the cumulative_prob() function.
virtual void compute_covar (matrix &covar) const =0
 Compute the covariance of the distribution.

Protected Attributes

vpdt_gaussian< vector, covar_typeimpl_
 the Gaussian implementation from vpdt.

Member Typedef Documentation

template<class T, unsigned int n = 0>
typedef vpdt_field_default<T,n>::type vpdl_gaussian_sphere< T, n >::vector

the data type used for vectors.

Reimplemented from vpdl_gaussian_base< T, n >.

Definition at line 30 of file vpdl_gaussian_sphere.h.

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

the data type used for matrices.

Reimplemented from vpdl_distribution< T, n >.

Definition at line 32 of file vpdl_gaussian_sphere.h.

template<class T, unsigned int n = 0>
typedef T vpdl_gaussian_sphere< T, n >::covar_type

the type used internally for covariance.

Definition at line 34 of file vpdl_gaussian_sphere.h.

template<class T, unsigned int n = 0>
typedef vpdt_field_default<T,n>::type vpdl_distribution< T, n >::field_type [inherited]

the data type used for vectors.

Reimplemented in vpdl_mixture_of< dist_t >.

Definition at line 36 of file vpdl_distribution.h.


Constructor & Destructor Documentation

template<class T, unsigned int n = 0>
vpdl_gaussian_sphere< T, n >::vpdl_gaussian_sphere ( unsigned int  var_dim = n  )  [inline]

Constructor.

Optionally initialize the dimension for when n==0. Otherwise var_dim is ignored

Definition at line 39 of file vpdl_gaussian_sphere.h.

template<class T, unsigned int n = 0>
vpdl_gaussian_sphere< T, n >::vpdl_gaussian_sphere ( const vector mean,
const covar_type var 
) [inline]

Constructor - from mean and variance.

Definition at line 43 of file vpdl_gaussian_sphere.h.

template<class T, unsigned int n = 0>
virtual vpdl_gaussian_sphere< T, n >::~vpdl_gaussian_sphere (  )  [inline, virtual]

Destructor.

Definition at line 47 of file vpdl_gaussian_sphere.h.


Member Function Documentation

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

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

Implements vpdl_distribution< T, n >.

Definition at line 50 of file vpdl_gaussian_sphere.h.

template<class T, unsigned int n = 0>
virtual unsigned int vpdl_gaussian_sphere< T, n >::dimension (  )  const [inline, virtual]

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

Implements vpdl_distribution< T, n >.

Definition at line 56 of file vpdl_gaussian_sphere.h.

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

Evaluate the unnormalized density at a point.

Implements vpdl_distribution< T, n >.

Definition at line 59 of file vpdl_gaussian_sphere.h.

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

Evaluate the probability density at a point.

Reimplemented from vpdl_distribution< T, n >.

Definition at line 65 of file vpdl_gaussian_sphere.h.

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

Evaluate the log probability density at a point.

Reimplemented from vpdl_distribution< T, n >.

Definition at line 71 of file vpdl_gaussian_sphere.h.

template<class T, unsigned int n = 0>
virtual T vpdl_gaussian_sphere< T, n >::gradient_density ( const vector pt,
vector g 
) const [inline, 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

Implements vpdl_distribution< T, n >.

Definition at line 80 of file vpdl_gaussian_sphere.h.

template<class T, unsigned int n = 0>
T vpdl_gaussian_sphere< T, n >::norm_const (  )  const [inline, 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

Implements vpdl_distribution< T, n >.

Definition at line 88 of file vpdl_gaussian_sphere.h.

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

The squared Mahalanobis distance to this point.

Non-virtual for efficiency

Definition at line 95 of file vpdl_gaussian_sphere.h.

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

Implements vpdl_distribution< T, n >.

Definition at line 103 of file vpdl_gaussian_sphere.h.

template<class T, unsigned int n = 0>
T vpdl_gaussian_sphere< 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. Reimplemented for effeciency since the axis are independent

Reimplemented from vpdl_distribution< T, n >.

Definition at line 111 of file vpdl_gaussian_sphere.h.

template<class T, unsigned int n = 0>
virtual const vector& vpdl_gaussian_sphere< T, n >::mean (  )  const [inline, virtual]

Access the mean directly.

Implements vpdl_gaussian_base< T, n >.

Definition at line 128 of file vpdl_gaussian_sphere.h.

template<class T, unsigned int n = 0>
virtual void vpdl_gaussian_sphere< T, n >::set_mean ( const vector mean  )  [inline, virtual]

Set the mean.

Implements vpdl_gaussian_base< T, n >.

Definition at line 131 of file vpdl_gaussian_sphere.h.

template<class T, unsigned int n = 0>
virtual void vpdl_gaussian_sphere< T, n >::compute_mean ( vector mean  )  const [inline, virtual]

Compute the mean of the distribution.

Implements vpdl_distribution< T, n >.

Definition at line 134 of file vpdl_gaussian_sphere.h.

template<class T, unsigned int n = 0>
const covar_type& vpdl_gaussian_sphere< T, n >::covariance (  )  const [inline]

Access the scalar variance.

Definition at line 137 of file vpdl_gaussian_sphere.h.

template<class T, unsigned int n = 0>
void vpdl_gaussian_sphere< T, n >::set_covariance ( const covar_type var  )  [inline]

Set the scalar variance.

Definition at line 140 of file vpdl_gaussian_sphere.h.

template<class T, unsigned int n = 0>
virtual void vpdl_gaussian_sphere< T, n >::compute_covar ( matrix covar  )  const [inline, virtual]

Compute the covariance of the distribution.

Should be the identity matrix times var_

Definition at line 145 of file vpdl_gaussian_sphere.h.

template<class T, unsigned int n>
vpdl_distribution< T, n >::vector vpdl_distribution< T, n >::inverse_cdf ( const T &  p  )  const [inline, virtual, inherited]

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

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 >.


Member Data Documentation

template<class T, unsigned int n = 0>
vpdt_gaussian<vector,covar_type> vpdl_gaussian_sphere< T, n >::impl_ [protected]

the Gaussian implementation from vpdt.

Definition at line 152 of file vpdl_gaussian_sphere.h.


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

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