The uniform distribution over a box in a space. More...

#include <EmrysFilter/Distributions/Uniform.h>

Public Types
using	Scalar = Scalar_
	the scalar type
using	Index = Eigen::Index
	Eigen's index type.
using	SpaceType = Space_
	the space the values live in
using	MomentsType = Moments<Space_, Scalar_>
	a mean and covariance together
using	VectorType = typename MomentsType::VectorType
	a value
using	MatrixType = typename MomentsType::MatrixType
	a matrix over differences

Public Member Functions
	Uniform (Space_ space={})
	Uniform over the whole of space.
Index	valueDimension () const
Index	differenceDimension () const
Space_ const &	space () const
VectorType const &	lower () const
VectorType	upper () const
VectorType const &	width () const
Scalar	logVolume () const
template<typename Derived>
bool	contains (Eigen::MatrixBase< Derived > const &x) const
template<typename Derived>
Scalar	logDensity (Eigen::MatrixBase< Derived > const &x) const
template<typename Derived>
Scalar	density (Eigen::MatrixBase< Derived > const &x) const
MomentsType	moments () const
template<typename Path>
auto	marginal () const
	marginal() of the subspace named by the tag path Path (see idx()), in that subspace.
template<typename Path>
auto	marginal (Index element) const
	marginal() of one repetition of a repeated block; see GaussianParams::marginal(element).
template<typename GivenPath, typename Derived>
auto	conditional (Eigen::MatrixBase< Derived > const &values) const

Static Public Member Functions
template<MatrixExpression Lower, typename UpperDerived>
static std::expected< Uniform, UniformError >	create (Space_ space, Lower &&lower, Eigen::MatrixBase< UpperDerived > const &upper)
template<MatrixExpression Lower, typename UpperDerived> requires internal::SizedByLength<Space_>
static std::expected< Uniform, UniformError >	create (Lower &&lower, Eigen::MatrixBase< UpperDerived > const &upper)
	create() in the default space.

Static Public Attributes
static constexpr int	ValueDimensionAtCompileTime = MomentsType::ValueDimensionAtCompileTime
	the length of a value, or Eigen::Dynamic
static constexpr int	MaxValueDimensionAtCompileTime = MomentsType::MaxValueDimensionAtCompileTime
	a bound on the length of a value, or Eigen::Dynamic
static constexpr int	DifferenceDimensionAtCompileTime = MomentsType::DifferenceDimensionAtCompileTime
	the length of a difference and the rows of a covariance, or Eigen::Dynamic
static constexpr int	MaxDifferenceDimensionAtCompileTime = MomentsType::MaxDifferenceDimensionAtCompileTime
	a bound on the length of a difference, or Eigen::Dynamic

Friends
template<Space, RealScalar>
class	Uniform
	Marginals build another instantiation from checked parts.

Detailed Description

template<Space Space_, RealScalar Scalar_ = double>
class Emrys::Uniform< Space_, Scalar_ >

The uniform distribution over a box in a space.

Each coordinate \( i \) is uniform on an interval of width \( w_i \) starting at \( \ell_i \), independently, so the density is \( 1 / \prod_i w_i \) inside the box and zero outside.

The space supplies the default box where it can: a Periodic coordinate is uniform over one whole period, and that constructor cannot fail. A Linear coordinate has no default and needs a box, which create() checks, since bounds are often computed at run time. A Periodic coordinate's interval may cross the seam: [3, 3.5] on an angle covers [3, π) and [-π, 3.5 - 2π].

auto const heading = Uniform<Heading>{}; // one whole period

auto const box = Uniform<Position>::create(Eigen::Vector2d{0, 0}, Eigen::Vector2d{10, 5}); // or a UniformError

Emrys::Uniform::create

static std::expected< Uniform, UniformError > create(Space_ space, Lower &&lower, Eigen::MatrixBase< UpperDerived > const &upper)

Definition Uniform.h:128

Emrys::Uniform::Uniform

friend class Uniform

Marginals build another instantiation from checked parts.

Definition Uniform.h:323

A Uniform is an immutable value that owns its box [checked-factories].

Template Parameters

Space_	space of the coordinates (see Spaces)
Scalar_	scalar type

See also: drawSamples(Uniform const &, Eigen::Index, G &)

Constructor & Destructor Documentation

◆ Uniform()

template<Space Space_, RealScalar Scalar_ = double>

Emrys::Uniform< Space_, Scalar_ >::Uniform ( Space_ space = {} )

inlineexplicit

Uniform over the whole of space.

Every coordinate must be Periodic.

Member Function Documentation

◆ conditional()

template<Space Space_, RealScalar Scalar_ = double>

template<typename GivenPath, typename Derived>

auto Emrys::Uniform< Space_, Scalar_ >::conditional ( Eigen::MatrixBase< Derived > const & values ) const

inlinenodiscard

Returns: the distribution of the other coordinates given that the subspace named by the path GivenPath equals values, in the space of the remaining blocks (see GaussianParams::conditional()): since the coordinates are independent, their marginal. Values outside the box have zero density, so strictly the conditional is undefined there; this returns the marginal anyway.

◆ contains()

template<Space Space_, RealScalar Scalar_ = double>

template<typename Derived>

bool Emrys::Uniform< Space_, Scalar_ >::contains ( Eigen::MatrixBase< Derived > const & x ) const

inlinenodiscard

Returns: whether x lies in the box, taking a Periodic coordinate's interval around the circle

◆ create()

template<Space Space_, RealScalar Scalar_ = double>

template<MatrixExpression Lower, typename UpperDerived>

std::expected< Uniform, UniformError > Emrys::Uniform< Space_, Scalar_ >::create	(	Space_	space,
		Lower &&	lower,
		Eigen::MatrixBase< UpperDerived > const &	upper )

inlinestaticnodiscard

Returns: the uniform distribution over the box from lower to upper in space, moving lower if it is an rvalue of the stored type, or a UniformError if a bound is not finite, an upper bound is not above its lower bound, or an interval on a Periodic coordinate is wider than one period. A space with one resizable block is resized to fit.

◆ density()

template<Space Space_, RealScalar Scalar_ = double>

template<typename Derived>

Scalar Emrys::Uniform< Space_, Scalar_ >::density ( Eigen::MatrixBase< Derived > const & x ) const

inlinenodiscard

Returns: the density at x

◆ differenceDimension()

template<Space Space_, RealScalar Scalar_ = double>

Index Emrys::Uniform< Space_, Scalar_ >::differenceDimension ( ) const

inlinenodiscard

Returns: the same: the box has plain differences

◆ logDensity()

template<Space Space_, RealScalar Scalar_ = double>

template<typename Derived>

Scalar Emrys::Uniform< Space_, Scalar_ >::logDensity ( Eigen::MatrixBase< Derived > const & x ) const

inlinenodiscard

Returns: the log of the density at x: \( -\log \prod_i w_i \) inside the box, and \( -\infty \) outside

◆ logVolume()

template<Space Space_, RealScalar Scalar_ = double>

Scalar Emrys::Uniform< Space_, Scalar_ >::logVolume ( ) const

inlinenodiscard

Returns: the log of the box's volume, \( \sum_i \log w_i \)

◆ lower()

template<Space Space_, RealScalar Scalar_ = double>

VectorType const & Emrys::Uniform< Space_, Scalar_ >::lower ( ) const

inlinenodiscard

Returns: the start \( \ell \) of each coordinate's interval, as given

◆ moments()

template<Space Space_, RealScalar Scalar_ = double>

MomentsType Emrys::Uniform< Space_, Scalar_ >::moments ( ) const

inlinenodiscard

Returns: the mean and covariance: the box's center, normalized, and \( \mathrm{diag}(w_i^2 / 12) \), the variance of a uniform interval of width \( w_i \).

For a Periodic coordinate these are tangent-space moments about the interval's center. Over a whole period every point is equally a center, so the reported mean is arbitrary and the variance \( p^2 / 12 \) only says the coordinate is unknown.

◆ space()

template<Space Space_, RealScalar Scalar_ = double>

Space_ const & Emrys::Uniform< Space_, Scalar_ >::space ( ) const

inlinenodiscard

Returns: the space the box is in, with its sizes

◆ upper()

template<Space Space_, RealScalar Scalar_ = double>

VectorType Emrys::Uniform< Space_, Scalar_ >::upper ( ) const

inlinenodiscard

Returns: the end \( \ell + w \) of each coordinate's interval, not normalized: on a Periodic coordinate it may lie past the space's range

◆ valueDimension()

template<Space Space_, RealScalar Scalar_ = double>

Index Emrys::Uniform< Space_, Scalar_ >::valueDimension ( ) const

inlinenodiscard

Returns: the number of coordinates of the box

◆ width()

template<Space Space_, RealScalar Scalar_ = double>

VectorType const & Emrys::Uniform< Space_, Scalar_ >::width ( ) const

inlinenodiscard

Returns: the width \( w \) of each coordinate's interval

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

EmrysFilter/Distributions/Uniform.h

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Uniform()

Member Function Documentation

◆ conditional()

◆ contains()

◆ create()

◆ density()

◆ differenceDimension()

◆ logDensity()

◆ logVolume()

◆ lower()

◆ moments()

◆ space()

◆ upper()

◆ valueDimension()

◆ width()