The Model on two states. More...

#include <Bpp/Phyl/Model/BinarySubstitutionModel.h>

Inheritance diagram for bpp::BinarySubstitutionModel:

Collaboration diagram for bpp::BinarySubstitutionModel:

Public Member Functions
	BinarySubstitutionModel (const BinaryAlphabet *alpha, double kappa=1.)
virtual	~BinarySubstitutionModel ()
BinarySubstitutionModel *	clone () const
double	Pij_t (size_t i, size_t j, double d) const
double	dPij_dt (size_t i, size_t j, double d) const
double	d2Pij_dt2 (size_t i, size_t j, double d) const
const Matrix< double > &	getPij_t (double d) const
const Matrix< double > &	getdPij_dt (double d) const
const Matrix< double > &	getd2Pij_dt2 (double d) const
std::string	getName () const
	Get the name of the model.
void	setFreq (std::map< int, double > &freqs)
	Set equilibrium frequencies.
size_t	getNumberOfStates () const
	Get the number of states.
const Alphabet *	getAlphabet () const
const std::vector< int > &	getAlphabetChars () const
int	getAlphabetChar (size_t i) const
	Get the char in the alphabet corresponding to a given state in the model.
std::vector< size_t >	getModelStates (int i) const
	Get the state in the model corresponding to a particular char in the alphabet.
virtual const Vdouble &	getFrequencies () const
const Matrix< double > &	getGenerator () const
const Matrix< double > &	getExchangeabilityMatrix () const
double	Sij (size_t i, size_t j) const
const Vdouble &	getEigenValues () const
const Vdouble &	getIEigenValues () const
bool	isDiagonalizable () const
bool	isNonSingular () const
const Matrix< double > &	getRowLeftEigenVectors () const
const Matrix< double > &	getColumnRightEigenVectors () const
virtual double	freq (size_t i) const
virtual double	Qij (size_t i, size_t j) const
double	getInitValue (size_t i, int state) const throw (IndexOutOfBoundsException, BadIntException)
void	setFreqFromData (const SequenceContainer &data, double pseudoCount=0)
	Set equilibrium frequencies equal to the frequencies estimated from the data.
void	enableEigenDecomposition (bool yn)
	Set if eigenValues and Vectors must be computed.
bool	enableEigenDecomposition ()
	Tell if eigenValues and Vectors must be computed.
virtual void	fireParameterChanged (const ParameterList &parameters)
	Tells the model that a parameter value has changed.
void	addRateParameter ()
double	getScale () const
	Get the scalar product of diagonal elements of the generator and the frequencies vector. If the generator is normalized, then scale=1. Otherwise each element must be multiplied by 1/scale.
void	setScale (double scale)
	Set the rate of the generator, defined as the scalar product of diagonal elements of the generator and the frequencies vector.
virtual double	getRate () const
	Get the rate.
virtual void	setRate (double rate)
	Set the rate of the model (must be positive).
virtual const FrequenciesSet *	getFrequenciesSet () const
	If the model owns a FrequenciesSet, returns a pointer to it, otherwise return 0.
virtual size_t	getNumberOfIndependentParameters () const =0
size_t	getNumberOfIndependentParameters () const
virtual void	aliasParameters (const std::string &p1, const std::string &p2)=0
void	aliasParameters (const std::string &p1, const std::string &p2)
virtual void	unaliasParameters (const std::string &p1, const std::string &p2)=0
void	unaliasParameters (const std::string &p1, const std::string &p2)
virtual const ParameterList &	getIndependentParameters () const =0
const ParameterList &	getIndependentParameters () const
virtual std::vector< std::string >	getAlias (const std::string &name) const =0
std::vector< std::string >	getAlias (const std::string &name) const
virtual bool	hasParameter (const std::string &name) const =0
bool	hasParameter (const std::string &name) const
virtual const ParameterList &	getParameters () const =0
const ParameterList &	getParameters () const
virtual const Parameter &	getParameter (const std::string &name) const =0
const Parameter &	getParameter (const std::string &name) const
virtual double	getParameterValue (const std::string &name) const =0
double	getParameterValue (const std::string &name) const
virtual void	setAllParametersValues (const ParameterList &parameters)=0
void	setAllParametersValues (const ParameterList &parameters)
virtual void	setParameterValue (const std::string &name, double value)=0
void	setParameterValue (const std::string &name, double value)
virtual void	setParametersValues (const ParameterList &parameters)=0
void	setParametersValues (const ParameterList &parameters)
virtual bool	matchParametersValues (const ParameterList &parameters)=0
bool	matchParametersValues (const ParameterList &parameters)
virtual size_t	getNumberOfParameters () const =0
size_t	getNumberOfParameters () const
virtual void	setNamespace (const std::string &prefix)=0
void	setNamespace (const std::string &prefix)
virtual std::string	getNamespace () const =0
std::string	getNamespace () const
virtual std::string	getParameterNameWithoutNamespace (const std::string &name) const =0
std::string	getParameterNameWithoutNamespace (const std::string &name) const
std::string	getFrom (const std::string &name) const
Protected Member Functions
void	updateMatrices ()
	Compute and diagonalize the matrix, and fill the eigenValues_, leftEigenVectors_ and rightEigenVectors_ matrices.
void	addParameter_ (Parameter *parameter)
void	addParameters_ (const ParameterList &parameters)
void	deleteParameter_ (size_t index)
void	resetParameters_ ()
Parameter &	getParameter_ (const std::string &name)
Parameter &	getParameter_ (size_t index)
const Parameter &	getParameter_ (size_t index) const
Parameter &	getParameterWithNamespace_ (const std::string &name)
const Parameter &	getParameterWithNamespace_ (const std::string &name) const
ParameterList &	getParameters_ ()
Protected Attributes
double	lambda_
double	exp_
RowMatrix< double >	p_
const Alphabet *	alphabet_
	The alphabet relevant to this model.
size_t	size_
	The size of the generator, i.e. the number of states.
double	rate_
	The rate of the model (default: 1). The generator (and all its vectorial components) is independent of the rate, since it should be normalized.
std::vector< int >	chars_
	The list of supported chars.
RowMatrix< double >	generator_
	The generator matrix of the model.
Vdouble	freq_
	The vector $\pi_e$ of equilibrium frequencies.
RowMatrix< double >	exchangeability_
	The exchangeability matrix of the model, defined as $S_{ij}=\frac{Q_{ij}}{\pi_j}$ . When the model is reversible, this matrix is symetric.
RowMatrix< double >	pijt_
	These ones are for bookkeeping:
RowMatrix< double >	dpijt_
RowMatrix< double >	d2pijt_
bool	eigenDecompose_
	Tell if the eigen decomposition should be performed.
Vdouble	eigenValues_
	The vector of eigen values.
Vdouble	iEigenValues_
	The vector of the imaginary part of the eigen values.
bool	isDiagonalizable_
	boolean value for diagonalizability in R of the generator_
RowMatrix< double >	rightEigenVectors_
	The matrix made of right eigen vectors (by column).
bool	isNonSingular_
	boolean value for non-singularity of rightEigenVectors_
RowMatrix< double >	leftEigenVectors_
	The matrix made of left eigen vectors (by row) if rightEigenVectors_ is non-singular.
std::vector< RowMatrix< double > >	vPowGen_
	vector of the powers of generator_ for Taylor development (if rightEigenVectors_ is singular).
RowMatrix< double >	tmpMat_
	For computational issues.
Private Attributes
double	kappa_
Friends
class	AbstractBiblioSubstitutionModel

Detailed Description

The Model on two states.

$Q = r.\begin{pmatrix} -\kappa & \kappa \\ 1 & -1 \\ \end{pmatrix}$

$\pi = diag\left(\frac{1}{\kappa+1}, \frac{\kappa}{\kappa+1}\right)$

Normalization: $r$ is set so that $\sum_i Q_{i,i}\pi_i = -1$ :

$Q = \begin{pmatrix} -\frac{\kappa + 1}2 & \frac{\kappa + 1}2 \\ \frac{\kappa+1}{2\kappa} & -\frac{\kappa+1}{2\kappa}\\ \end{pmatrix}$

The eigen values are $\left(0, - \frac{(\kappa+1)^2}{2\kappa}\right)$ , and IF $\kappa \neq 1$ , the left eigen vectors are, by row:

$U = \begin{pmatrix} \frac{1}{1+\kappa} & \frac{\kappa}{1+\kappa} \\ \frac{\kappa-1}{\kappa+1} & -\frac{\kappa-1}{\kappa+1} \\ \end{pmatrix}$

and the right eigen vectors are by column:

$U^{-1} = \begin{pmatrix} 1 & \frac \kappa{\kappa-1} \\ 1 & - \frac 1{\kappa-1} \\ \end{pmatrix}$

The probabilities of changes are computed analytically using the formulas, with $\lambda= \frac{(\kappa+1)^2}{2\kappa}$ :

$P_{i,j}(t) = \begin{pmatrix} \frac{1}{\kappa+1} + \frac{\kappa}{\kappa+1}e^{-\lambda t} & \frac{\kappa}{\kappa+1} - \frac{\kappa}{\kappa+1}e^{-\lambda t} \\ \frac{1}{\kappa+1} - \frac{1}{\kappa+1}e^{-\lambda t} & \frac{\kappa}{\kappa+1} + \frac{1}{\kappa+1}e^{-\lambda t} \\ \end{pmatrix}$

$\frac{\partial P_{i,j}(t)}{\partial t} = \begin{pmatrix} -\frac {\kappa+1} 2 e^{-\lambda t} & \frac {\kappa+1} 2 e^{-\lambda t} \\ \frac {\kappa+1} {2\kappa} e^{-\lambda t} & - \frac {\kappa+1} {2\kappa} e^{-\lambda t} \\ \end{pmatrix}$

$\begin{multline*} \frac{\partial^2 P_{i,j}(t)}{\partial t^2} = \\ \begin{pmatrix} \frac {\lambda (\kappa+1)} 2 e^{-\lambda t} & -\ frac {\lambda (\kappa+1)} 2 e^{-\lambda t} \\ \frac {\lambda (\kappa+1)} {2\kappa} e^{-\lambda t} & - \frac {\lambda (\kappa+1)} {2\kappa} e^{-\lambda t} \\ \end{pmatrix} \end{multline*}$

The parameter is named "kappa" and its value may be retrieve with the command

 getParameterValue("kappa")

Definition at line 114 of file BinarySubstitutionModel.h.

Constructor & Destructor Documentation

BinarySubstitutionModel::BinarySubstitutionModel	(	const BinaryAlphabet *	alpha,
		double	kappa = `1.`
	)

Definition at line 53 of file BinarySubstitutionModel.cpp.

References bpp::AbstractParameterAliasable::addParameter_(), bpp::AbstractParameterAliasable::getNamespace(), kappa_, bpp::Parameter::R_PLUS_STAR, and updateMatrices().

Referenced by clone().

virtual bpp::BinarySubstitutionModel::~BinarySubstitutionModel ( ) [inline, virtual]

Definition at line 127 of file BinarySubstitutionModel.h.

Member Function Documentation

void AbstractSubstitutionModel::addRateParameter ( ) [virtual, inherited]

double BinarySubstitutionModel::d2Pij_dt2	(	size_t	i,
		size_t	j,
		double	t
	)		const `[virtual]`

double BinarySubstitutionModel::dPij_dt	(	size_t	i,
		size_t	j,
		double	t
	)		const `[virtual]`

double AbstractSubstitutionModel::getInitValue	(	size_t	i,
		int	state
	)		const throw (IndexOutOfBoundsException, BadIntException) `[virtual, inherited]`

i	the index of the state in the model.
state	An observed state in the sequence/site.

IndexOutOfBoundsException	if array position is out of range.
BadIntException	if states are not allowed in the associated alphabet.

double BinarySubstitutionModel::Pij_t	(	size_t	i,
		size_t	j,
		double	t
	)		const `[virtual]`

virtual double bpp::AbstractSubstitutionModel::Qij	(	size_t	i,
		size_t	j
	)		const `[inline, virtual, inherited]`

void AbstractSubstitutionModel::setFreqFromData	(	const SequenceContainer &	data,
		double	pseudoCount = `0`
	)		`[virtual, inherited]`

data	The sequences to use.
pseudoCount	A quantity $\psi$ to add to adjust the observed values in order to prevent issues due to missing states on small data set. The corrected frequencies shall be computed as $\pi_i = \frac{n_i+\psi}{\sum_j (f_j+\psi)}$

double bpp::AbstractSubstitutionModel::Sij	(	size_t	i,
		size_t	j
	)		const `[inline, virtual, inherited]`

Public Member Functions

Protected Member Functions

Protected Attributes

Private Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation