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gnn_line_search.h File Reference

#include "gnn_evaluation.h"

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Defines
#define	GNN_GOLDEN_LIMIT   100.0
	Golden Section maximum magnification for parabolic fit.
#define	GNN_GOLDEN_TINY   1.0e-20
	Golden Section tiny value.
#define	GNN_GOLDEN_OLD   1.61803399
	Ratio for Golden Section interval magnification.
#define	GNN_GOLDEN_R   0.61803399
	Golden Ratios.
#define	GNN_GOLDEN_C   (1.0 - GNN_GOLDEN_R)
	Golden Ratios.
#define	GNN_BRENT_ITMAX   100
	Maximum number of iterations for Brent's line search.
#define	GNN_BRENT_CGOLD   0.3819660
	Golden Ratio.
#define	GNN_BRENT_ZEPS   1.0e-10
	Small number that protects against too much fractional accuracy.
Typedefs
typedef double(*	gnn_line_search_type )(gnn_line *line, size_t s, size_t n, double ax, double bx, double cx, double *xmin, double tol)
	The type of line search routines.
Functions
int	gnn_line_search_bracket (gnn_line *line, size_t s, size_t n, double *ax, double *bx, double *cx, double *fa, double *fb, double *fc)
	Bracketing procedure.
double	gnn_line_search_golden (gnn_line *line, size_t s, size_t n, double ax, double bx, double cx, double *xmin, double tol)
	Bracketing procedure.
double	gnn_line_search_brent (gnn_line *line, size_t s, size_t n, double ax, double bx, double cx, double *xmin, double tol)
	Bracketing procedure.
double	gnn_line_search_charalambous (gnn_line *line, size_t s, size_t n, double ax, double bx, double cx, double *xmin, double tol)
	Simple line search procedure.
double	gnn_line_search_simple (gnn_line *line, size_t s, size_t n, double ax, double bx, double cx, double *xmin, double tol)
	Simple line search procedure.

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Function Documentation

int gnn_line_search_bracket (  gnn_line *    line, size_t    s, size_t    n, double *    ax, double *    bx, double *    cx, double *    fa, double *    fb, double *    fc )

Given a Evaluations. buffer, and given distinct initial points ax and bx, this routine searches in the downhill direction (defined by the function associated to line as evaluated at the initial points) and returns new points ax, bx, cx that bracket a minimum of the function. Also returned are the function values at the three points, fa, fb, and fc. [Adapted from Numerical Recipes in C.] Parameters: line  A pointer to a Evaluations. buffer. s  The index of the first pattern in the minibatch to be evaluated. n  The size of the minibatch to be evaluated. ax  A pointer to an initial point. bx  A pointer to the second initial point. cx  A pointer where the middle point should be placed in. fa  A pointer where the value should be placed in. fb  A pointer where the value should be placed in. fc  A pointer where the value should be placed in. Returns: Returns 0 if succeeded. Definition at line 90 of file gnn_line_search.c.

double gnn_line_search_brent (  gnn_line *    line, size_t    s, size_t    n, double    ax, double    bx, double    cx, double *    xmin, double    tol )

Given a Evaluations. buffer line, and given a bracketing triplet of abscissas ax, bx, cx (such that bx is between ax and cx, and f(bx) is less than both f(ax) and f(cx)), this routine isolates the minimum to a fractional precision of about tol using Brent’s method. The abscissa of the minimum is returned as xmin, and the minimum function value is returned as brent, the returned function value. Parameters: line  A pointer to a Evaluations. buffer. s  The index of the first pattern in the minibatch to be evaluated. n  The size of the minibatch to be evaluated. ax  Initial point of the bracketing triplet. bx  Middle point of the bracketing triplet. cx  Last point of the bracketing triplet. xmin  The location of the minimum. tol  Fractional precision tolerance. Returns: Returns the minimum function value. Definition at line 323 of file gnn_line_search.c.

double gnn_line_search_charalambous (  gnn_line *    line, size_t    s, size_t    n, double    ax, double    bx, double    cx, double *    xmin, double    tol )

Todo: Not implemented yet. Parameters: line  A pointer to a Evaluations. buffer. s  The index of the first pattern in the minibatch to be evaluated. n  The size of the minibatch to be evaluated. ax  Initial point of the bracketing triplet. bx  Middle point of the bracketing triplet. cx  Last point of the bracketing triplet. xmin  The location of the minimum. tol  Fractional precision tolerance. Returns: Returns the minimum function value. Definition at line 463 of file gnn_line_search.c.

double gnn_line_search_golden (  gnn_line *    line, size_t    s, size_t    n, double    ax, double    bx, double    cx, double *    xmin, double    tol )

Given a Evaluations. buffer line, and given a bracketing triplet of abscissas ax, bx, cx (such that bx is between ax and cx, and f(bx) is less than both f(ax) and f(cx)), this routine performs a golden section search for the minimum error, isolating it to a fractional precision of about tol. The abscissa of the minimum is returned as xmin, and the minimum function value is returned as golden, the returned function value. [Adapted from Numerical Recipes in C.] Parameters: line  A pointer to a Evaluations. buffer. s  The index of the first pattern in the minibatch to be evaluated. n  The size of the minibatch to be evaluated. ax  Initial point of the bracketing triplet. bx  Middle point of the bracketing triplet. cx  Last point of the bracketing triplet. xmin  The location of the minimum. tol  Fractional precision tolerance. Returns: Returns the minimum function value. Definition at line 226 of file gnn_line_search.c.

double gnn_line_search_simple (  gnn_line *    line, size_t    s, size_t    n, double    ax, double    bx, double    cx, double *    xmin, double    tol )

This function implements a simple but robust line search routine. It returns the , where is minimized. The strategy is the following: Start with a fixed Compute , , If , then proceed to interpolate. If , then and retry. If , then and retry. The interpolation is performed by a quadratic polynom: where the coefficients are which gives the solution for : Parameters: line  A pointer to a Evaluations. buffer. s  The index of the first pattern in the minibatch to be evaluated. n  The size of the minibatch to be evaluated. ax  Initial point of the bracketing triplet. bx  Middle point of the bracketing triplet. cx  Last point of the bracketing triplet. xmin  The location of the minimum. tol  Fractional precision tolerance. Returns: Returns the minimum function value. Definition at line 510 of file gnn_line_search.c.

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