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.
template<class T >
static T	sign (T a)
	Get the sign of a value.
template<class T >
static T	max (T a, T b)
	Get the max between 2 values.
template<class T >
static T	min (T a, T b)
	Get the min between 2 values.
template<class T >
static T	sign (T a, T b)
	Get the magnitude of a times the sign of b.
template<class T >
static T	sqr (T a)
	Get the square of a number.
template<class T >
static T	logsum (T lnx, T lny)
	Compute the logarithm of a sum from the sum of logarithms.
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 (Function &f, const std::string &param, double a, double b, double tolerance) throw (Exception)
	Find one root of the given function.
static RowMatrix< double > *	computeHessianMatrix (DerivableSecondOrder &function, const ParameterList &parameters)
	Compute the Hessian matrix for a function at a given point.

Detailed Description

Some utilitary function for numerical calculus.

Definition at line 53 of file NumTools.h.

Member Function Documentation

template<class T >

static T bpp::NumTools::abs ( T a ) [inline, static]

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 66 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(), bpp::DownhillSimplexMethod::DSMStopCondition::getCurrentTolerance(), and bpp::Uniform01K::setSeed().

RowMatrix< double > * NumTools::computeHessianMatrix	(	DerivableSecondOrder &	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 80 of file NumTools.cpp.

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

template<class T >

static T bpp::NumTools::fact ( T n ) [inline, static]

Definition at line 157 of file NumTools.h.

References fact().

Referenced by fact().

template<class T >

static T bpp::NumTools::logFact ( T n ) [inline, static]

Definition at line 161 of file NumTools.h.

References logFact().

Referenced by logFact().

template<class T >

static T bpp::NumTools::logsum	(	T	lnx,
		T	lny
	)		`[inline, static]`

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 131 of file NumTools.h.

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

template<class T >

static T bpp::NumTools::max	(	T	a,
		T	b
	)		`[inline, static]`

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 88 of file NumTools.h.

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

template<class T >

static T bpp::NumTools::min	(	T	a,
		T	b
	)		`[inline, static]`

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 99 of file NumTools.h.

template<class T >

static void bpp::NumTools::shift	(	T &	a,
		T &	b,
		T	c
	)		`[inline, static]`

Definition at line 145 of file NumTools.h.

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

template<class T >

static void bpp::NumTools::shift	(	T &	a,
		T &	b,
		T &	c,
		T	d
	)		`[inline, static]`

Definition at line 150 of file NumTools.h.

template<class T >

static T bpp::NumTools::sign ( T a ) [inline, static]

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 77 of file NumTools.h.

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

template<class T >

static T bpp::NumTools::sign	(	T	a,
		T	b
	)		`[inline, static]`

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 108 of file NumTools.h.

template<class T >

static T bpp::NumTools::sqr ( T a ) [inline, static]

Get the square of a number.

Parameters:

a	The value.

Returns:: .

Definition at line 116 of file NumTools.h.

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

template<class T >

static void bpp::NumTools::swap	(	T &	a,
		T &	b
	)		`[inline, static]`

Definition at line 138 of file NumTools.h.

double NumTools::uniRoot	(	Function &	f,
		const std::string &	param,
		double	a,
		double	b,
		double	tolerance
	)		throw (Exception) `[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 48 of file NumTools.cpp.

References bpp::ParameterList::addParameter().

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