#include <Mixture.h>

Inheritance diagram for lsst::meas::modelfit::Mixture:

Public Types
typedef MixtureComponent	Component

typedef MixtureUpdateRestriction	UpdateRestriction

typedef std::vector< Component >	ComponentList

typedef ComponentList::iterator	iterator

typedef ComponentList::const_iterator	const_iterator

Public Member Functions
std::size_t	size () const
	Return the number of components. More...

virtual int	getComponentCount () const
	Return the number of components. More...

boost::shared_ptr< Mixture >	project (int dim) const
	Project the distribution onto the given dimensions (marginalize over all others) More...

boost::shared_ptr< Mixture >	project (int dim1, int dim2) const
	Project the distribution onto the given dimensions (marginalize over all others) More...

int	getDimension () const
	Return the number of dimensions. More...

void	normalize ()
	Iterate over all components, rescaling their weights so they sum to one. More...

void	shift (int dim, Scalar offset)
	Shift the mixture in the given dimension, adding the given offset to all mu vectors. More...

std::size_t	clip (Scalar threshold=0.0)
	Iterate over all components, removing those with weight less than or equal to threshold. More...

Scalar	getDegreesOfFreedom () const
	Get the number of degrees of freedom in the component Student's T distributions (inf=Gaussian) More...

void	setDegreesOfFreedom (Scalar df=std::numeric_limits< Scalar >::infinity())
	Set the number of degrees of freedom in the component Student's T distributions (inf=Gaussian) More...

template<typename Derived >
Scalar	evaluate (Component const &component, Eigen::MatrixBase< Derived > const &x) const
	Evaluate the probability density at the given point for the given component distribution. More...

template<typename Derived >
Scalar	evaluate (Eigen::MatrixBase< Derived > const &x) const
	Evaluate the mixture distribution probability density function (PDF) at the given points. More...

void	evaluate (ndarray::Array< Scalar const, 2, 1 > const &x, ndarray::Array< Scalar, 1, 0 > const &p) const
	Evaluate the distribution probability density function (PDF) at the given points. More...

void	evaluateComponents (ndarray::Array< Scalar const, 2, 1 > const &x, ndarray::Array< Scalar, 2, 1 > const &p) const
	Evaluate the contributions of each component to the full probability at the given points. More...

void	evaluateDerivatives (ndarray::Array< Scalar const, 1, 1 > const &x, ndarray::Array< Scalar, 1, 1 > const &gradient, ndarray::Array< Scalar, 2, 1 > const &hessian) const
	Evaluate the derivative of the distribution at the given point. More...

void	evaluateDerivatives (Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > &x, Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > &gradient, Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > &hessian) const
	Evaluate the derivative of the distribution at the given point. More...

void	evaluateDerivatives (Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > &x, Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > &gradient) const
	Evaluate the derivative of the distribution at the given point. More...

void	draw (afw::math::Random &rng, ndarray::Array< Scalar, 2, 1 > const &x) const
	Draw random variates from the distribution. More...

void	updateEM (ndarray::Array< Scalar const, 2, 1 > const &x, ndarray::Array< Scalar const, 1, 0 > const &w, Scalar tau1=0.0, Scalar tau2=0.5)
	Perform an Expectation-Maximization step, updating the component parameters to match the given weighted samples. More...

void	updateEM (ndarray::Array< Scalar const, 2, 1 > const &x, ndarray::Array< Scalar const, 1, 0 > const &w, UpdateRestriction const &restriction, Scalar tau1=0.0, Scalar tau2=0.5)
	Perform an Expectation-Maximization step, updating the component parameters to match the given weighted samples. More...

void	updateEM (ndarray::Array< Scalar const, 2, 1 > const &x, UpdateRestriction const &restriction, Scalar tau1=0.0, Scalar tau2=0.5)
	Perform an Expectation-Maximization step, updating the component parameters to match the given unweighted samples. More...

virtual boost::shared_ptr< Mixture >	clone () const
	Polymorphic deep copy. More...

	Mixture (int dim, ComponentList &components, Scalar df=std::numeric_limits< Scalar >::infinity())
	Construct a mixture model. More...

virtual bool	isPersistable () const noexcept override

void	writeFits (std::string const &fileName, std::string const &mode="w") const

void	writeFits (fits::MemFileManager &manager, std::string const &mode="w") const

void	writeFits (fits::Fits &fitsfile) const


iterator	begin ()
	Iterator and indexed access to components. More...

iterator	end ()
	Iterator and indexed access to components. More...

const_iterator	begin () const
	Iterator and indexed access to components. More...

const_iterator	end () const
	Iterator and indexed access to components. More...

Component &	operator[] (std::size_t i)
	Iterator and indexed access to components. More...

Component const &	operator[] (std::size_t i) const
	Iterator and indexed access to components. More...

Static Public Member Functions
static std::shared_ptr< Mixture >	readFits (fits::Fits &fitsfile)

static std::shared_ptr< Mixture >	readFits (std::string const &fileName, int hdu=fits::DEFAULT_HDU)

static std::shared_ptr< Mixture >	readFits (fits::MemFileManager &manager, int hdu=fits::DEFAULT_HDU)

static std::shared_ptr< Mixture >	dynamicCast (std::shared_ptr< Persistable > const &ptr)

Protected Types
typedef io::OutputArchiveHandle	OutputArchiveHandle

Protected Member Functions
std::string	getPythonModule () const override

std::string	getPersistenceName () const override

void	write (OutputArchiveHandle &handle) const override

Friends
std::ostream &	operator<< (std::ostream &os, Mixture const &self)

Detailed Description

Definition at line 128 of file Mixture.h.

Member Typedef Documentation

◆ Component

typedef MixtureComponent lsst::meas::modelfit::Mixture::Component

Definition at line 131 of file Mixture.h.

◆ ComponentList

typedef std::vector<Component> lsst::meas::modelfit::Mixture::ComponentList

Definition at line 133 of file Mixture.h.

◆ const_iterator

typedef ComponentList::const_iterator lsst::meas::modelfit::Mixture::const_iterator

Definition at line 135 of file Mixture.h.

◆ iterator

typedef ComponentList::iterator lsst::meas::modelfit::Mixture::iterator

Definition at line 134 of file Mixture.h.

◆ UpdateRestriction

typedef MixtureUpdateRestriction lsst::meas::modelfit::Mixture::UpdateRestriction

Definition at line 132 of file Mixture.h.

Constructor & Destructor Documentation

◆ Mixture()

lsst::meas::modelfit::Mixture::Mixture	(	int	dim,
		ComponentList &	components,
		Scalar	df = `std::numeric_limits< Scalar >::infinity()`
	)

explicit

Construct a mixture model.

Parameters

[in]	dim	Dimensionality of the distribution
[in]	df	Number of degrees of freedom for component Student's T distributions (inf=Gaussian)
[in]	components	List of components; will be emptied on return.

The components will be automatically normalized after construction.

Member Function Documentation

◆ begin() [1/2]

iterator lsst::meas::modelfit::Mixture::begin ( )

inline

Iterator and indexed access to components.

While mutable iterators and accessors are provided, any modifications to the component weights should be followed by a call to normalize(), as other member functions will not work properly if the mixture is not normalized.

Definition at line 146 of file Mixture.h.

◆ begin() [2/2]

const_iterator lsst::meas::modelfit::Mixture::begin ( ) const

inline

Iterator and indexed access to components.

While mutable iterators and accessors are provided, any modifications to the component weights should be followed by a call to normalize(), as other member functions will not work properly if the mixture is not normalized.

Definition at line 149 of file Mixture.h.

◆ clip()

std::size_t lsst::meas::modelfit::Mixture::clip ( Scalar threshold = 0.0 )

Iterate over all components, removing those with weight less than or equal to threshold.

The weights will be normalized if any are removed.

Returns: the number of components removed.

◆ clone()

virtual boost::shared_ptr< Mixture > lsst::meas::modelfit::Mixture::clone ( ) const

virtual

Polymorphic deep copy.

◆ draw()

void lsst::meas::modelfit::Mixture::draw	(	afw::math::Random &	rng,
		ndarray::Array< Scalar, 2, 1 > const &	x
	)		const

Draw random variates from the distribution.

Parameters

[in,out]	rng	random number generator
[out]	x	array of points, shape=(numSamples, dim)

◆ end() [1/2]

iterator lsst::meas::modelfit::Mixture::end ( )

inline

Iterator and indexed access to components.

While mutable iterators and accessors are provided, any modifications to the component weights should be followed by a call to normalize(), as other member functions will not work properly if the mixture is not normalized.

Definition at line 147 of file Mixture.h.

◆ end() [2/2]

const_iterator lsst::meas::modelfit::Mixture::end ( ) const

inline

Iterator and indexed access to components.

While mutable iterators and accessors are provided, any modifications to the component weights should be followed by a call to normalize(), as other member functions will not work properly if the mixture is not normalized.

Definition at line 150 of file Mixture.h.

◆ evaluate() [1/3]

template<typename Derived >

Scalar lsst::meas::modelfit::Mixture::evaluate	(	Component const &	component,
		Eigen::MatrixBase< Derived > const &	x
	)		const

inline

Evaluate the probability density at the given point for the given component distribution.

This evaluates the probability of a single component, including the current weight of that component.

Definition at line 198 of file Mixture.h.

◆ evaluate() [2/3]

template<typename Derived >

Scalar lsst::meas::modelfit::Mixture::evaluate ( Eigen::MatrixBase< Derived > const & x ) const

inline

Evaluate the mixture distribution probability density function (PDF) at the given points.

Parameters

[in] x point to evaluate, as an Eigen expression, shape=(dim,)

Definition at line 209 of file Mixture.h.

◆ evaluate() [3/3]

void lsst::meas::modelfit::Mixture::evaluate	(	ndarray::Array< Scalar const, 2, 1 > const &	x,
		ndarray::Array< Scalar, 1, 0 > const &	p
	)		const

Evaluate the distribution probability density function (PDF) at the given points.

Parameters

[in]	x	array of points, shape=(numSamples, dim)
[out]	p	array of probability values, shape=(numSamples,)

◆ evaluateComponents()

void lsst::meas::modelfit::Mixture::evaluateComponents	(	ndarray::Array< Scalar const, 2, 1 > const &	x,
		ndarray::Array< Scalar, 2, 1 > const &	p
	)		const

Evaluate the contributions of each component to the full probability at the given points.

Parameters

[in]	x	points to evaluate at, with number of columns equal to the number of dimensions
[in]	p	array to fill, with number of columns equal to the number of components

◆ evaluateDerivatives() [1/3]

void lsst::meas::modelfit::Mixture::evaluateDerivatives	(	ndarray::Array< Scalar const, 1, 1 > const &	x,
		ndarray::Array< Scalar, 1, 1 > const &	gradient,
		ndarray::Array< Scalar, 2, 1 > const &	hessian
	)		const

Evaluate the derivative of the distribution at the given point.

Parameters

[in]	x	point to evaluate the derivative, with size equal to the number of dimensions
[in]	gradient	1st derivative array to fill
[in]	hessian	2nd derivative array to fill

◆ evaluateDerivatives() [2/3]

void lsst::meas::modelfit::Mixture::evaluateDerivatives	(	Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > &	x,
		Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > &	gradient,
		Eigen::Matrix< Scalar, Eigen::Dynamic, Eigen::Dynamic > &	hessian
	)		const

Evaluate the derivative of the distribution at the given point.

Parameters

[in]	x	point to evaluate the derivative, with size equal to the number of dimensions
[in]	gradient	1st derivative array to fill
[in]	hessian	2nd derivative array to fill

◆ evaluateDerivatives() [3/3]

void lsst::meas::modelfit::Mixture::evaluateDerivatives	(	Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > &	x,
		Eigen::Matrix< Scalar, Eigen::Dynamic, 1 > &	gradient
	)		const

Evaluate the derivative of the distribution at the given point.

Parameters

[in]	x	point to evaluate the derivative, with size equal to the number of dimensions
[in]	gradient	1st derivative array to fill

◆ getComponentCount()

virtual int lsst::meas::modelfit::Mixture::getComponentCount ( ) const

inlinevirtual

Return the number of components.

Definition at line 160 of file Mixture.h.

◆ getDegreesOfFreedom()

Scalar lsst::meas::modelfit::Mixture::getDegreesOfFreedom ( ) const

inline

Get the number of degrees of freedom in the component Student's T distributions (inf=Gaussian)

Definition at line 187 of file Mixture.h.

◆ getDimension()

int lsst::meas::modelfit::Mixture::getDimension ( ) const

inline

Return the number of dimensions.

Definition at line 169 of file Mixture.h.

◆ getPersistenceName()

std::string lsst::meas::modelfit::Mixture::getPersistenceName ( ) const

overrideprotectedvirtual

Reimplemented from lsst::afw::table::io::Persistable.

◆ getPythonModule()

std::string lsst::meas::modelfit::Mixture::getPythonModule ( ) const

inlineoverrideprotectedvirtual

Reimplemented from lsst::afw::table::io::Persistable.

Definition at line 368 of file Mixture.h.

◆ isPersistable()

virtual bool lsst::meas::modelfit::Mixture::isPersistable ( ) const

inlineoverridevirtualnoexcept

Reimplemented from lsst::afw::table::io::Persistable.

Definition at line 364 of file Mixture.h.

◆ normalize()

void lsst::meas::modelfit::Mixture::normalize ( )

Iterate over all components, rescaling their weights so they sum to one.

◆ operator[]() [1/2]

Component& lsst::meas::modelfit::Mixture::operator[] ( std::size_t i )

inline

Iterator and indexed access to components.

While mutable iterators and accessors are provided, any modifications to the component weights should be followed by a call to normalize(), as other member functions will not work properly if the mixture is not normalized.

Definition at line 152 of file Mixture.h.

◆ operator[]() [2/2]

Component const& lsst::meas::modelfit::Mixture::operator[] ( std::size_t i ) const

inline

Iterator and indexed access to components.

While mutable iterators and accessors are provided, any modifications to the component weights should be followed by a call to normalize(), as other member functions will not work properly if the mixture is not normalized.

Definition at line 153 of file Mixture.h.

◆ project() [1/2]

boost::shared_ptr< Mixture > lsst::meas::modelfit::Mixture::project ( int dim ) const

Project the distribution onto the given dimensions (marginalize over all others)

◆ project() [2/2]

boost::shared_ptr< Mixture > lsst::meas::modelfit::Mixture::project	(	int	dim1,
		int	dim2
	)		const

Project the distribution onto the given dimensions (marginalize over all others)

◆ setDegreesOfFreedom()

void lsst::meas::modelfit::Mixture::setDegreesOfFreedom ( Scalar df = std::numeric_limits< Scalar >::infinity() )

Set the number of degrees of freedom in the component Student's T distributions (inf=Gaussian)

◆ shift()

void lsst::meas::modelfit::Mixture::shift	(	int	dim,
		Scalar	offset
	)

Shift the mixture in the given dimension, adding the given offset to all mu vectors.

◆ size()

std::size_t lsst::meas::modelfit::Mixture::size ( ) const

inline

Return the number of components.

Definition at line 157 of file Mixture.h.

◆ updateEM() [1/3]

void lsst::meas::modelfit::Mixture::updateEM	(	ndarray::Array< Scalar const, 2, 1 > const &	x,
		ndarray::Array< Scalar const, 1, 0 > const &	w,
		Scalar	tau1 = `0.0`,
		Scalar	tau2 = `0.5`
	)

Perform an Expectation-Maximization step, updating the component parameters to match the given weighted samples.

Parameters

[in]	x	array of variables, shape=(numSamples, dim)
[in]	w	array of weights, shape=(numSamples,)
[in]	tau1	damping parameter (see below)
[in]	tau2	damping parameter (see below)

The updates to the \(\sigma\) matrices are damped according to:

\[ \sigma_d = \alpha\sigma_1 + (1-\alpha)\sigma_0 \]

Where \(\sigma_0\) is the previous matrix, \(\sigma_1\) is the undamped update, and \(\sigma_d\) is the damped update. The parameter \(\alpha\) is set by the ratio of the determinants:

\[ r \equiv \frac{|\sigma_1|}{|\sigma_0|} \]

When \(r \ge \tau_1\), \(\alpha=1\); when \(r \lt \tau_1\), it is rolled off quadratically to \(\tau_2\).

◆ updateEM() [2/3]

void lsst::meas::modelfit::Mixture::updateEM	(	ndarray::Array< Scalar const, 2, 1 > const &	x,
		ndarray::Array< Scalar const, 1, 0 > const &	w,
		UpdateRestriction const &	restriction,
		Scalar	tau1 = `0.0`,
		Scalar	tau2 = `0.5`
	)

Perform an Expectation-Maximization step, updating the component parameters to match the given weighted samples.

Parameters

[in]	x	array of variables, shape=(numSamples, dim)
[in]	w	array of weights, shape=(numSamples,)
[in]	restriction	Functor used to restrict the form of the updated mu and sigma
[in]	tau1	damping parameter (see Mixture::updateEM)
[in]	tau2	damping parameter (see Mixture::updateEM)

◆ updateEM() [3/3]

void lsst::meas::modelfit::Mixture::updateEM	(	ndarray::Array< Scalar const, 2, 1 > const &	x,
		UpdateRestriction const &	restriction,
		Scalar	tau1 = `0.0`,
		Scalar	tau2 = `0.5`
	)

Perform an Expectation-Maximization step, updating the component parameters to match the given unweighted samples.

Parameters

[in]	x	array of variables, shape=(numSamples, dim)
[in]	restriction	Functor used to restrict the form of the updated mu and sigma
[in]	tau1	damping parameter (see Mixture::updateEM)
[in]	tau2	damping parameter (see Mixture::updateEM)

◆ write()

void lsst::meas::modelfit::Mixture::write ( OutputArchiveHandle & handle ) const

overrideprotectedvirtual

Reimplemented from lsst::afw::table::io::Persistable.

Friends And Related Function Documentation

◆ operator<<

std::ostream& operator<<	(	std::ostream &	os,
		Mixture const &	self
	)

friend

Definition at line 359 of file Mixture.h.

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

include/lsst/meas/modelfit/Mixture.h

Public Types

Public Member Functions

Static Public Member Functions

Protected Types

Protected Member Functions

Friends

Detailed Description

Member Typedef Documentation

◆ Component

◆ ComponentList

◆ const_iterator

◆ iterator

◆ UpdateRestriction

Constructor & Destructor Documentation

◆ Mixture()

Member Function Documentation

◆ begin() [1/2]

◆ begin() [2/2]

◆ clip()

◆ clone()

◆ draw()

◆ end() [1/2]

◆ end() [2/2]

◆ evaluate() [1/3]

◆ evaluate() [2/3]

◆ evaluate() [3/3]

◆ evaluateComponents()

◆ evaluateDerivatives() [1/3]

◆ evaluateDerivatives() [2/3]

◆ evaluateDerivatives() [3/3]

◆ getComponentCount()

◆ getDegreesOfFreedom()

◆ getDimension()

◆ getPersistenceName()

◆ getPythonModule()

◆ isPersistable()

◆ normalize()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ project() [1/2]

◆ project() [2/2]

◆ setDegreesOfFreedom()

◆ shift()

◆ size()

◆ updateEM() [1/3]

◆ updateEM() [2/3]

◆ updateEM() [3/3]

◆ write()

Friends And Related Function Documentation

◆ operator<<