A Gaussian with (hyper-)spherical covariance. More...

#include <vpdl_gaussian_sphere.h>

Inheritance diagram for vpdl_gaussian_sphere< T, n >:

Public Types
typedef vpdt_field_default< T, n >::type	vector
	the data type used for vectors. More...

typedef vpdt_field_traits< vector >::matrix_type	matrix
	the data type used for matrices. More...

typedef T	covar_type
	the type used internally for covariance. More...

typedef vpdt_field_default< T, n >::type	field_type
	the data type used for vectors. More...

Public Member Functions
	vpdl_gaussian_sphere (unsigned int var_dim=n)
	Constructor. More...

	vpdl_gaussian_sphere (const vector &mean_val, const covar_type &var)
	Constructor - from mean and variance. More...

virtual	~vpdl_gaussian_sphere ()
	Destructor. More...

virtual vpdl_distribution< T, n > *	clone () const
	Create a copy on the heap and return base class pointer. More...

virtual unsigned int	dimension () const
	Return the run time dimension, which does not equal `n` when `n==0`. More...

virtual T	density (const vector &pt) const
	Evaluate the unnormalized density at a point. More...

virtual T	prob_density (const vector &pt) const
	Evaluate the probability density at a point. More...

virtual T	log_prob_density (const vector &pt) const
	Evaluate the log probability density at a point. More...

virtual T	gradient_density (const vector &pt, vector &g) const
	Compute the gradient of the unnormalized density at a point. More...

T	norm_const () const
	The normalization constant for the density. More...

T	sqr_mahal_dist (const vector &pt) const
	The squared Mahalanobis distance to this point. More...

virtual T	cumulative_prob (const vector &pt) const
	Evaluate the cumulative distribution function at a point. More...

T	box_prob (const vector &min_pt, const vector &max_pt) const
	The probability of being in an axis-aligned box. More...

virtual const vector &	mean () const
	Access the mean directly. More...

virtual void	set_mean (const vector &mean_val)
	Set the mean. More...

virtual void	compute_mean (vector &mean_val) const
	Compute the mean of the distribution. More...

const covar_type &	covariance () const
	Access the scalar variance. More...

void	set_covariance (const covar_type &var)
	Set the scalar variance. More...

virtual void	compute_covar (matrix &covar) const
	Compute the covariance of the distribution. More...

virtual vector	inverse_cdf (const T &p) const
	Compute the inverse of the cumulative_prob() function. More...

Protected Attributes
vpdt_gaussian< vector, covar_type >	impl_
	the Gaussian implementation from vpdt. More...

Detailed Description

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

A Gaussian with (hyper-)spherical covariance.

Definition at line 29 of file vpdl_gaussian_sphere.h.

Member Typedef Documentation

◆ covar_type

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 37 of file vpdl_gaussian_sphere.h.

◆ field_type

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.

Definition at line 39 of file vpdl_distribution.h.

◆ matrix

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.

Definition at line 35 of file vpdl_gaussian_sphere.h.

◆ vector

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.

Definition at line 33 of file vpdl_gaussian_sphere.h.

Constructor & Destructor Documentation

◆ vpdl_gaussian_sphere() [1/2]

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 42 of file vpdl_gaussian_sphere.h.

◆ vpdl_gaussian_sphere() [2/2]

template<class T , unsigned int n = 0>

vpdl_gaussian_sphere< T, n >::vpdl_gaussian_sphere	(	const vector &	mean_val,
		const covar_type &	var
	)

inline

Constructor - from mean and variance.

Definition at line 46 of file vpdl_gaussian_sphere.h.

◆ ~vpdl_gaussian_sphere()

template<class T , unsigned int n = 0>

virtual vpdl_gaussian_sphere< T, n >::~vpdl_gaussian_sphere ( )

inlinevirtual

Destructor.

Definition at line 50 of file vpdl_gaussian_sphere.h.

Member Function Documentation

◆ box_prob()

template<class T , unsigned int n = 0>

T vpdl_gaussian_sphere< T, n >::box_prob	(	const vector &	min_pt,
		const vector &	max_pt
	)		const

inlinevirtual

The probability of being in an axis-aligned box.

The box is defined by two points, the minimum and maximum. Reimplemented for efficiency since the axis are independent

Reimplemented from vpdl_distribution< T, n >.

Definition at line 114 of file vpdl_gaussian_sphere.h.

◆ clone()

template<class T , unsigned int n = 0>

virtual vpdl_distribution<T,n>* vpdl_gaussian_sphere< T, n >::clone ( ) const

inlinevirtual

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

Implements vpdl_distribution< T, n >.

Definition at line 53 of file vpdl_gaussian_sphere.h.

◆ compute_covar()

template<class T , unsigned int n = 0>

virtual void vpdl_gaussian_sphere< T, n >::compute_covar ( matrix & covar ) const

inlinevirtual

Compute the covariance of the distribution.

Should be the identity matrix times var_

Implements vpdl_distribution< T, n >.

Definition at line 147 of file vpdl_gaussian_sphere.h.

◆ compute_mean()

template<class T , unsigned int n = 0>

virtual void vpdl_gaussian_sphere< T, n >::compute_mean ( vector & mean_val ) const

inlinevirtual

Compute the mean of the distribution.

Implements vpdl_distribution< T, n >.

Definition at line 137 of file vpdl_gaussian_sphere.h.

◆ covariance()

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 140 of file vpdl_gaussian_sphere.h.

◆ cumulative_prob()

template<class T , unsigned int n = 0>

virtual T vpdl_gaussian_sphere< T, n >::cumulative_prob ( const vector & pt ) const

inlinevirtual

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 106 of file vpdl_gaussian_sphere.h.

◆ density()

template<class T , unsigned int n = 0>

virtual T vpdl_gaussian_sphere< T, n >::density ( const vector & pt ) const

inlinevirtual

Evaluate the unnormalized density at a point.

Implements vpdl_distribution< T, n >.

Definition at line 62 of file vpdl_gaussian_sphere.h.

◆ dimension()

template<class T , unsigned int n = 0>

virtual unsigned int vpdl_gaussian_sphere< T, n >::dimension ( ) const

inlinevirtual

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

Implements vpdl_distribution< T, n >.

Definition at line 59 of file vpdl_gaussian_sphere.h.

◆ gradient_density()

template<class T , unsigned int n = 0>

virtual T vpdl_gaussian_sphere< T, n >::gradient_density	(	const vector &	pt,
		vector &	g
	)		const

inlinevirtual

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 83 of file vpdl_gaussian_sphere.h.

◆ inverse_cdf()

template<class T, unsigned int n>

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

virtualinherited

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 78 of file vpdl_distribution.hxx.

◆ log_prob_density()

template<class T , unsigned int n = 0>

virtual T vpdl_gaussian_sphere< T, n >::log_prob_density ( const vector & pt ) const

inlinevirtual

Evaluate the log probability density at a point.

Reimplemented from vpdl_distribution< T, n >.

Definition at line 74 of file vpdl_gaussian_sphere.h.

◆ mean()

template<class T , unsigned int n = 0>

virtual const vector& vpdl_gaussian_sphere< T, n >::mean ( ) const

inlinevirtual

Access the mean directly.

Implements vpdl_gaussian_base< T, n >.

Definition at line 131 of file vpdl_gaussian_sphere.h.

◆ norm_const()

template<class T , unsigned int n = 0>

T vpdl_gaussian_sphere< T, n >::norm_const ( ) const

inlinevirtual

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 91 of file vpdl_gaussian_sphere.h.

◆ prob_density()

template<class T , unsigned int n = 0>

virtual T vpdl_gaussian_sphere< T, n >::prob_density ( const vector & pt ) const

inlinevirtual

Evaluate the probability density at a point.

Reimplemented from vpdl_distribution< T, n >.

Definition at line 68 of file vpdl_gaussian_sphere.h.

◆ set_covariance()

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 143 of file vpdl_gaussian_sphere.h.

◆ set_mean()

template<class T , unsigned int n = 0>

virtual void vpdl_gaussian_sphere< T, n >::set_mean ( const vector & mean_val )

inlinevirtual

Set the mean.

Implements vpdl_gaussian_base< T, n >.

Definition at line 134 of file vpdl_gaussian_sphere.h.

◆ sqr_mahal_dist()

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 98 of file vpdl_gaussian_sphere.h.

Member Data Documentation

◆ impl_

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 154 of file vpdl_gaussian_sphere.h.

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

core/vpdl/vpdl_gaussian_sphere.h

Public Types

Public Member Functions

Protected Attributes

Detailed Description

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

Member Typedef Documentation

◆ covar_type

◆ field_type

◆ matrix

◆ vector

Constructor & Destructor Documentation

◆ vpdl_gaussian_sphere() [1/2]

◆ vpdl_gaussian_sphere() [2/2]

◆ ~vpdl_gaussian_sphere()

Member Function Documentation

◆ box_prob()

◆ clone()

◆ compute_covar()

◆ compute_mean()

◆ covariance()

◆ cumulative_prob()

◆ density()

◆ dimension()

◆ gradient_density()

◆ inverse_cdf()

◆ log_prob_density()

◆ mean()

◆ norm_const()

◆ prob_density()

◆ set_covariance()

◆ set_mean()

◆ sqr_mahal_dist()

Member Data Documentation

◆ impl_

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