Classes and functions to perform function optimization. More...

Classes
struct	LineSearch< Size, Precision, Func >
	Turn a multidimensional function in to a 1D function by specifying a point and direction. More...
struct	ConjugateGradient< Size, Precision >
	This class provides a nonlinear conjugate-gradient optimizer. More...
class	DownhillSimplex< N, Precision >
	This is an implementation of the Downhill Simplex (Nelder & Mead, 1965) algorithm. More...
Functions
template<class Functor , class Precision >
Vector< 2, Precision >	brent_line_search (Precision a, Precision x, Precision b, Precision fx, const Functor &func, int maxiterations, Precision tolerance=sqrt(numeric_limits< Precision >::epsilon()), Precision epsilon=numeric_limits< Precision >::epsilon())
template<typename Precision , typename Func >
Matrix< 3, 2, Precision >	bracket_minimum_forward (Precision a_val, const Func &func, Precision initial_lambda, Precision zeps)
template<class Functor , class Precision >
Vector< 2, Precision >	golden_section_search (Precision a, Precision b, Precision c, Precision fb, const Functor &func, int maxiterations, Precision tol=sqrt(numeric_limits< Precision >::epsilon()))
template<class Functor , class Precision >
Vector< 2, Precision >	golden_section_search (Precision a, Precision b, Precision c, const Functor &func, int maxiterations, Precision tol=sqrt(numeric_limits< Precision >::epsilon()))

Detailed Description

Classes and functions to perform function optimization.

One dimensional function optimization

The following functions find the minimum of a 1-D function:

Multidimensional dimensional function optimization

The following classes perform multidimensional function minimization:

The mode of operation is to set up a mutable class, then repeatedly call an iterate function. This allows different sub algorithms (such as termination conditions) to be substituted in if need be.

Function Documentation

Vector<2, Precision> TooN::brent_line_search	(	Precision	a,
		Precision	x,
		Precision	b,
		Precision	fx,
		const Functor &	func,
		int	maxiterations,
		Precision	tolerance = `sqrt(numeric_limits<Precision>::epsilon())`,
		Precision	epsilon = `numeric_limits<Precision>::epsilon()`
	)

brent_line_search performs Brent's golden section/quadratic interpolation search on the functor provided.

The inputs a, x, b must bracket the minimum, and must be in order, so that $ a < x < b $ and $ f(a) > f(x) < f(b) $ .

Parameters:

a	The most negative point along the line.
x	The central point.
fx	The value of the function at the central point ( ).
b	The most positive point along the line.
func	The functor to minimize
maxiterations	Maximum number of iterations
tolerance	Tolerance at which the search should be stopped (defults to sqrt machine precision)
epsilon	Minimum bracket width (defaults to machine precision)

Returns:: The minima position is returned as the first element of the vector, and the minimal value as the second element.

References TooN::sqrt().

Referenced by ConjugateGradient< Size, Precision >::find_next_point().

Matrix<3,2,Precision> TooN::Internal::bracket_minimum_forward	(	Precision	a_val,
		const Func &	func,
		Precision	initial_lambda,
		Precision	zeps
	)

Bracket a 1D function by searching forward from zero.

The assumption is that a minima exists in $f(x),\ x>0$ , and this function searches for a bracket using exponentially growning or shrinking steps.

Parameters:

a_val	The value of the function at zero.
func	Function to bracket
initial_lambda	Initial stepsize
zeps	Minimum bracket size.

Returns:: m[i][0] contains the values of for the bracket, in increasing order, and m[i][1] contains the corresponding values of . If the bracket drops below the minimum bracket size, all zeros are returned.

References TooN::isnan(), and TooN::Zeros.

Referenced by ConjugateGradient< Size, Precision >::find_next_point().

Vector<2, Precision> TooN::golden_section_search	(	Precision	a,
		Precision	b,
		Precision	c,
		Precision	fb,
		const Functor &	func,
		int	maxiterations,
		Precision	tol = `sqrt(numeric_limits<Precision>::epsilon())`
	)

golden_section_search performs a golden section search line minimization on the functor provided.

The inputs a, b, c must bracket the minimum, and must be in order, so that $ a < b < c $ and $ f(a) > f(b) < f(c) $ .

Parameters:

a	The most negative point along the line.
b	The central point.
fb	The value of the function at the central point ( ).
c	The most positive point along the line.
func	The functor to minimize
maxiterations	Maximum number of iterations
tol	Tolerance at which the search should be stopped.

Returns:: The minima position is returned as the first element of the vector, and the minimal value as the second element.

References TooN::sqrt().

Referenced by TooN::golden_section_search().

Vector<2, Precision> TooN::golden_section_search	(	Precision	a,
		Precision	b,
		Precision	c,
		const Functor &	func,
		int	maxiterations,
		Precision	tol = `sqrt(numeric_limits<Precision>::epsilon())`
	)

golden_section_search performs a golden section search line minimization on the functor provided.

The inputs a, b, c must bracket the minimum, and must be in order, so that $ a < b < c $ and $ f(a) > f(b) < f(c) $ .

Parameters:

a	The most negative point along the line.
b	The central point.
c	The most positive point along the line.
func	The functor to minimize
maxiterations	Maximum number of iterations
tol	Tolerance at which the search should be stopped.

Returns:: The minima position is returned as the first element of the vector, and the minimal value as the second element.

References TooN::golden_section_search().

Classes

Functions

Detailed Description

One dimensional function optimization

Multidimensional dimensional function optimization

Function Documentation