#include <FminBrent.h>

Inheritance diagram for FDescent:

Public Member Functions
virtual C_FLOAT64	operator() (const C_FLOAT64 &C_UNUSED(value))

virtual	~FDescent ()

Detailed Description

Adapted by Pedro Mendes to suit Gepasi's optimisation framework 9 Aug 1997

ORIGINAL**in**netlib********************************************** C math library function FMINBR - one-dimensional search for a function minimum over the given range

Input double FminBrent(a, b, f, min, fmin, tol, maxiter)

Parameters

double	a; Minimum will be seeked for over
double	b; a range [a,b], a being < b.
double	(*f)(double x); Name of the function whose minimum will be seeked for
double	*min, Location of minimum (output)
double	*fmin, Value of minimum (ouput)
double	tol; Acceptable tolerance for the minimum location. It have to be positive (e.g. may be specified as EPSILON)
int	maxiter Maximum number of iterations

Output Fminbr returns an estimate for the minimum location with accuracy 3*SQRT_EPSILON*abs(x) + tol. The function always obtains a local minimum which coincides with the global one only if a function under investigation being unimodular. If a function being examined possesses no local minimum within the given range, Fminbr returns 'a' (if f(a) < f(b)), otherwise it returns the right range boundary value b.

@ return int (0: success, 1: negative tolerance, 2: b < a 3: iteration limit exceeded)

Algorithm G.Forsythe, M.Malcolm, C.Moler, Computer methods for mathematical computations. M., Mir, 1980, p.202 of the Russian edition

The function makes use of the "gold section" procedure combined with the parabolic interpolation. At every step program operates three abscissae - x,v, and w. x - the last and the best approximation to the minimum location, i.e. f(x) <= f(a) or/and f(x) <= f(b) (if the function f has a local minimum in (a,b), then the both conditions are fulfiled after one or two steps). v,w are previous approximations to the minimum location. They may coincide with a, b, or x (although the algorithm tries to make all u, v, and w distinct). Points x, v, and w are used to construct interpolating parabola whose minimum will be treated as a new approximation to the minimum location if the former falls within [a,b] and reduces the range enveloping minimum more efficient than the gold section procedure. When f(x) has a second derivative positive at the minimum location (not coinciding with a or b) the procedure converges superlinearly at a rate order about 1.324

Constructor & Destructor Documentation

◆ ~FDescent()

virtual FDescent::~FDescent ( )

inlinevirtual

Member Function Documentation

◆ operator()()

virtual C_FLOAT64 FDescent::operator() ( const C_FLOAT64 & C_UNUSEDvalue )