Levenberg Marquardt Least Squares Fitting. More...

#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <float.h>
#include "libraries/operaLMFit.h"

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Defines
#define	LM_MACHEP DBL_EPSILON
#define	LM_DWARF DBL_MIN
#define	LM_SQRT_DWARF sqrt(DBL_MIN)
#define	LM_SQRT_GIANT sqrt(DBL_MAX)
#define	LM_USERTOL 30*LM_MACHEP
#define	MIN(a, b) (((a)<=(b)) ? (a) : (b))
#define	MAX(a, b) (((a)>=(b)) ? (a) : (b))
#define	SQR(x) (x)*(x)
Functions
void	lmcurve_evaluate (int n_par, const double par, int m_dat, const void data, double fvec, int info)
void	lmcurve_fit (int n_par, double par, int m_dat, const double x, const double y, double(function)(double x, const double par, int n_par), lm_control_struct control, lm_status_struct *status)
void	lm_printout_std (int n_par, const double par, int m_dat, const void data, const double *fvec, int printflags, int iflag, int iter, int nfev)
void	lmmin (int n_par, double par, int m_dat, const void data, void(evaluate)(int n_par, const double par, int m_dat, const void data, double fvec, int info), const lm_control_struct control, lm_status_struct status, void(printout)(int n_par, const double par, int m_dat, const void data, const double *fvec, int printflags, int iflag, int iter, int nfev))
void	lm_lmpar (int n, double r, int ldr, int ipvt, double diag, double qtb, double delta, double par, double x, double sdiag, double aux, double *xdi)
void	lm_qrfac (int m, int n, double a, int pivot, int ipvt, double rdiag, double acnorm, double *wa)
void	lm_qrsolv (int n, double r, int ldr, int ipvt, double diag, double qtb, double x, double sdiag, double *wa)
void	lm_lmdif (int m, int n, double x, double fvec, double ftol, double xtol, double gtol, int maxfev, double epsfcn, double diag, int mode, double factor, int info, int nfev, double fjac, int ipvt, double qtf, double wa1, double wa2, double wa3, double wa4, void(evaluate)(int n_par, const double par, int m_dat, const void data, double fvec, int info), void(printout)(int n_par, const double par, int m_dat, const void data, const double fvec, int printflags, int iflag, int iter, int nfev), int printflags, const void data)
	Legacy low-level interface.
double	lm_enorm (int n, const double *x)
Variables
const lm_control_struct	lm_control_double
const lm_control_struct	lm_control_float
const char *	lm_infmsg []
const char *	lm_shortmsg []

Detailed Description

Levenberg Marquardt Least Squares Fitting.

Define Documentation

#define LM_DWARF DBL_MIN

#define LM_MACHEP DBL_EPSILON

#define LM_SQRT_DWARF sqrt(DBL_MIN)

#define LM_SQRT_GIANT sqrt(DBL_MAX)

#define LM_USERTOL 30*LM_MACHEP

#define MAX	(	a,
		b
	)	(((a)>=(b)) ? (a) : (b))

#define MIN	(	a,
		b
	)	(((a)<=(b)) ? (a) : (b))

#define SQR ( x ) (x)*(x)

Function Documentation

double lm_enorm	(	int	n,
		const double *	x
	)

sum squares.

calculation of norm.

void lm_lmdif	(	int	m,
		int	n,
		double *	x,
		double *	fvec,
		double	ftol,
		double	xtol,
		double	gtol,
		int	maxfev,
		double	epsfcn,
		double *	diag,
		int	mode,
		double	factor,
		int *	info,
		int *	nfev,
		double *	fjac,
		int *	ipvt,
		double *	qtf,
		double *	wa1,
		double *	wa2,
		double *	wa3,
		double *	wa4,
		void()(int n_par, const double par, int m_dat, const void data, double fvec, int *info)	evaluate,
		void()(int n_par, const double par, int m_dat, const void data, const double fvec, int printflags, int iflag, int iter, int nfev)	printout,
		int	printflags,
		const void *	data
	)

Legacy low-level interface.

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void lm_lmpar	(	int	n,
		double *	r,
		int	ldr,
		int *	ipvt,
		double *	diag,
		double *	qtb,
		double	delta,
		double *	par,
		double *	x,
		double *	sdiag,
		double *	aux,
		double *	xdi
	)

evaluate the function at the current value of par.

if the function is small enough, accept the current value of par. Also test for the exceptional cases where parl is zero or the number of iterations has reached 10.

compute the Newton correction.

depending on the sign of the function, update parl or paru.

compute an improved estimate for par.

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void lm_printout_std	(	int	n_par,
		const double *	par,
		int	m_dat,
		const void *	data,
		const double *	fvec,
		int	printflags,
		int	iflag,
		int	iter,
		int	nfev
	)

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void lm_qrfac	(	int	m,
		int	n,
		double *	a,
		int	pivot,
		int *	ipvt,
		double *	rdiag,
		double *	acnorm,
		double *	wa
	)

bring the column of largest norm into the pivot position.

compute the Householder transformation to reduce the j-th column of a to a multiple of the j-th unit vector.

apply the transformation to the remaining columns and update the norms.

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void lm_qrsolv	(	int	n,
		double *	r,
		int	ldr,
		int *	ipvt,
		double *	diag,
		double *	qtb,
		double *	x,
		double *	sdiag,
		double *	wa
	)

determine a Givens rotation which eliminates the appropriate element in the current row of d.

compute the modified diagonal element of r and the modified element of ((q transpose)*b,0).

accumulate the tranformation in the row of s.

store the diagonal element of s and restore the corresponding diagonal element of r.

void lmcurve_evaluate	(	int	n_par,
		const double *	par,
		int	m_dat,
		const void *	data,
		double *	fvec,
		int *	info
	)

void lmcurve_fit	(	int	n_par,
		double *	par,
		int	m_dat,
		const double *	x,
		const double *	y,
		double()(double x, const double par, int n_par)	function,
		lm_control_struct *	control,
		lm_status_struct *	status
	)

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void lmmin	(	int	n_par,
		double *	par,
		int	m_dat,
		const void *	data,
		void()(int n_par, const double par, int m_dat, const void data, double fvec, int *info)	evaluate,
		const lm_control_struct *	control,
		lm_status_struct *	status,
		void()(int n_par, const double par, int m_dat, const void data, const double fvec, int printflags, int iflag, int iter, int nfev)	printout
	)

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Variable Documentation

const lm_control_struct lm_control_double

Initial value:

 {
    LM_USERTOL, LM_USERTOL, LM_USERTOL, LM_USERTOL, 100., 100, 1, 0 }

const lm_control_struct lm_control_float

Initial value:

 {
    1.e-7, 1.e-7, 1.e-7, 1.e-7, 100., 100, 0, 0 }

const char* lm_infmsg[]

Initial value:

 {
    "success (sum of squares below underflow limit)",
    "success (the relative error in the sum of squares is at most tol)",
    "success (the relative error between x and the solution is at most tol)",
    "success (both errors are at most tol)",
    "trapped by degeneracy (fvec is orthogonal to the columns of the jacobian)",
    "timeout (number of calls to fcn has reached maxcall*(n+1))",
    "failure (ftol<tol: cannot reduce sum of squares any further)",
    "failure (xtol<tol: cannot improve approximate solution any further)",
    "failure (gtol<tol: cannot improve approximate solution any further)",
    "exception (not enough memory)",
    "fatal coding error (improper input parameters)",
    "exception (break requested within function evaluation)"
}

const char* lm_shortmsg[]

Initial value:

 {
    "success (0)",
    "success (f)",
    "success (p)",
    "success (f,p)",
    "degenerate",
    "call limit",
    "failed (f)",
    "failed (p)",
    "failed (o)",
    "no memory",
    "invalid input",
    "user break"
}

Defines

Functions

Variables

Detailed Description

Define Documentation

Function Documentation

Variable Documentation