Some utilitary function for numerical calculus. More...

#include <Bpp/Numeric/NumTools.h>

Static Public Member Functions
template<class T >
static T	abs (T a)
	Get the magnitude of a value. More...

template<class T >
static T	sign (T a)
	Get the sign of a value. More...

template<class T >
static T	max (T a, T b)
	Get the max between 2 values. More...

template<class T >
static T	min (T a, T b)
	Get the min between 2 values. More...

template<class T >
static T	sign (T a, T b)
	Get the magnitude of a times the sign of b. More...

template<class T >
static T	sqr (T a)
	Get the square of a number. More...

template<class T >
static T	logsum (T lnx, T lny)
	Compute the logarithm of a sum from the sum of logarithms. More...

template<class T >
static void	swap (T &a, T &b)

template<class T >
static void	shift (T &a, T &b, T c)

template<class T >
static void	shift (T &a, T &b, T &c, T d)

template<class T >
static T	fact (T n)

template<class T >
static T	logFact (T n)

static double	uniRoot (FunctionInterface &f, const std::string &param, double a, double b, double tolerance)
	Find one root of the given function. More...

static std::unique_ptr< RowMatrix< double > >	computeHessianMatrix (SecondOrderDerivable &function, const ParameterList &parameters)
	Compute the Hessian matrix for a function at a given point. More...

Detailed Description

Some utilitary function for numerical calculus.

Definition at line 19 of file NumTools.h.

Member Function Documentation

◆ abs()

template<class T >

static T bpp::NumTools::abs ( T a )

inlinestatic

Get the magnitude of a value.

This template function may work with any type for which the operators < and - are defined.

Parameters

a	The value for which the magnitude must be returned.

Returns: The magnitude of the value a.

Definition at line 31 of file NumTools.h.

Referenced by bpp::OneDimensionOptimizationTools::bracketMinimum(), bpp::GoldenSectionSearch::doInit(), bpp::BrentOneDimension::doStep(), bpp::GoldenSectionSearch::GSSStopCondition::getCurrentTolerance(), bpp::PowellMultiDimensions::PMDStopCondition::getCurrentTolerance(), bpp::BrentOneDimension::BODStopCondition::getCurrentTolerance(), and bpp::DownhillSimplexMethod::DSMStopCondition::getCurrentTolerance().

◆ computeHessianMatrix()

unique_ptr< RowMatrix< double > > NumTools::computeHessianMatrix	(	SecondOrderDerivable &	function,
		const ParameterList &	parameters
	)

static

Compute the Hessian matrix for a function at a given point.

$H(f(\theta)) = \begin{pmatrix} \frac{\partial^2 f(\theta)}{\partial \theta_1^2} & \frac{\partial^2 f(\theta)}{\partial \theta_1 \partial \theta_2} & \cdots & \frac{\partial^2 f(\theta)}{\partial \theta_1 \partial \theta_n}\\ \frac{\partial^2 f(\theta)}{\partial \theta_2 \partial \theta_1} & \frac{\partial^2 f(\theta)}{\partial \theta_2^2} & \cdots & \frac{\partial^2 f(\theta)}{\partial \theta_2 \partial \theta_n}\\ \vdots & \vdots & \ddots & \vdots \\ \frac{\partial^2 f(\theta)}{\partial \theta_n \partial \theta_1} & \frac{\partial^2 f(\theta)}{\partial \theta_n \partial \theta_2} & \cdots & \frac{\partial^2 f(\theta)}{\partial \theta_n^2} \end{pmatrix}$

Parameters

function	A function with second order derivatives.
parameters	The set of parameters for which to compute the hessian matrix.

Returns: A matrix with size equal to the number of parameters.

Definition at line 46 of file NumTools.cpp.

References bpp::ParameterList::getParameterNames(), and bpp::ParameterList::size().

Referenced by logFact().

◆ fact()

template<class T >

static T bpp::NumTools::fact ( T n )

inlinestatic

Definition at line 124 of file NumTools.h.

References fact().

Referenced by fact().

◆ logFact()

template<class T >

static T bpp::NumTools::logFact ( T n )

inlinestatic

Definition at line 128 of file NumTools.h.

References computeHessianMatrix(), logFact(), and uniRoot().

Referenced by logFact().

◆ logsum()

template<class T >

static T bpp::NumTools::logsum	(	T	lnx,
		T	lny
	)

inlinestatic

Compute the logarithm of a sum from the sum of logarithms.

The following formula is used:

$\ln(x) + \ln\left(1+ \exp\left(\ln(y) - \ln(x)\right)\right) = \ln(x + y)$

see http://bozeman.genome.washington.edu/compbio/mbt599_2006/hmm_scaling_revised.pdf

Parameters

lnx	The value.
lny	The power

Returns: .

Definition at line 96 of file NumTools.h.

Referenced by bpp::LogsumHmmLikelihood::computeBackward_(), and bpp::LogsumHmmLikelihood::computeForward_().

◆ max()

template<class T >

static T bpp::NumTools::max	(	T	a,
		T	b
	)

inlinestatic

Get the max between 2 values.

This template function may work with any type for which the operator

is defined.

Parameters

a,b	The two values to compare.

Returns: a if a > b, b else.

Definition at line 53 of file NumTools.h.

Referenced by bpp::OneDimensionOptimizationTools::bracketMinimum().

◆ min()

template<class T >

static T bpp::NumTools::min	(	T	a,
		T	b
	)

inlinestatic

Get the min between 2 values.

This template function may work with any type for which the operator < is defined.

Parameters

a,b	The two values to compare.

Returns: a if a < b, b else.

Definition at line 64 of file NumTools.h.

◆ shift() [1/2]

template<class T >

static void bpp::NumTools::shift	(	T &	a,
		T &	b,
		T	c
	)

inlinestatic

Definition at line 112 of file NumTools.h.

Referenced by bpp::BrentOneDimension::doStep().

◆ shift() [2/2]

template<class T >

static void bpp::NumTools::shift	(	T &	a,
		T &	b,
		T &	c,
		T	d
	)

inlinestatic

Definition at line 117 of file NumTools.h.

◆ sign() [1/2]

template<class T >

static T bpp::NumTools::sign ( T a )

inlinestatic

Get the sign of a value.

This template function may work with any type for which the operators < and == are defined.

Parameters

a	The value for which the sign must be returned.

Returns: -1 if a < 0, 0 if a = 0, 1 else.

Definition at line 42 of file NumTools.h.

Referenced by bpp::OneDimensionOptimizationTools::bracketMinimum(), and bpp::BrentOneDimension::doStep().

◆ sign() [2/2]

template<class T >

static T bpp::NumTools::sign	(	T	a,
		T	b
	)

inlinestatic

Get the magnitude of a times the sign of b.

Parameters

a	The value whose magnitude must be used.
b	The value whose sign must be used.

Returns: abs<T>(a) * sign<T>(b).

Definition at line 73 of file NumTools.h.

◆ sqr()

template<class T >

static T bpp::NumTools::sqr ( T a )

inlinestatic

Get the square of a number.

Parameters

a	The value.

Returns: .

Definition at line 81 of file NumTools.h.

Referenced by bpp::PowellMultiDimensions::doStep().

◆ swap()

template<class T >

static void bpp::NumTools::swap	(	T &	a,
		T &	b
	)

inlinestatic

Definition at line 105 of file NumTools.h.

◆ uniRoot()

double NumTools::uniRoot	(	FunctionInterface &	f,
		const std::string &	param,
		double	a,
		double	b,
		double	tolerance
	)

static

Find one root of the given function.

Parameters

f	The function to analyse.
param	The name of the parameter to solve.
a	Lower bound of initial interval.
b	Upper bound of initial interval.
tolerance	The final precision requested.

Returns: The value of the parameter for which the function is zero.

Exceptions

Exception If something bad happened or if the initial interval do not contains a root.

Definition at line 13 of file NumTools.cpp.

References bpp::ParameterList::addParameter(), and bpp::FunctionInterface::f().

Referenced by logFact().

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

Bpp/Numeric/NumTools.h
Bpp/Numeric/NumTools.cpp

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ abs()

◆ computeHessianMatrix()

◆ fact()

◆ logFact()

◆ logsum()

◆ max()

◆ min()

◆ shift() [1/2]

◆ shift() [2/2]

◆ sign() [1/2]

◆ sign() [2/2]

◆ sqr()

◆ swap()

◆ uniRoot()