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Always turn off hyphenation; it makes +.\" way too many mistakes in technical documents. +.if n .ad l +.nh +.SH "NAME" +lmmin \- Levenberg\-Marquardt least\-squares minimization +.SH "SYNOPSIS" +.IX Header "SYNOPSIS" +\&\fB#include <lmmin.h\fR> +.PP +\&\fBvoid lmmin( const int\fR \fIn_par\fR\fB, double *\fR\fIpar\fR\fB, const int\fR \fIm_dat\fR\fB, + const\ void *\fR\fIdata\fR\fB, + void *\fR\fIevaluate\fR\fB( + const\ double *\fR\fIpar\fR\fB, const int \fR\fIm_dat\fR\fB, + const\ void *\fR\fIdata\fR\fB, double *\fR\fIfvec\fR\fB, int *\fR\fIuserbreak\fR\fB), + const\ lm_control_struct *\fR\fIcontrol\fR\fB, + lm_status_struct *\fR\fIstatus\fR\fB );\fR +.PP +\&\fBextern const lm_control_struct lm_control_double;\fR +.PP +\&\fBextern const lm_control_struct lm_control_float;\fR +.PP +\&\fBextern const char *lm_infmsg[];\fR +.PP +\&\fBextern const char *lm_shortmsg[];\fR +.SH "DESCRIPTION" +.IX Header "DESCRIPTION" +\&\fB\f(BIlmmin()\fB\fR determines a vector \fIpar\fR that minimizes the sum of squared elements of a vector \fIfvec\fR that is computed by a user-supplied function \fIevaluate\fR(). +On success, \fIpar\fR represents a local minimum, not necessarily a global one; it may depend on its starting value. +.PP +For applications in curve fitting, the wrapper function \fB\f(BIlmcurve\fB\|(3)\fR offers a simplified \s-1API.\s0 +.PP +The Levenberg-Marquardt minimization starts with a steepest-descent exploration of the parameter space, and achieves rapid convergence by crossing over into the Newton-Gauss method. +.PP +Function arguments: +.IP "\fIn_par\fR" 4 +.IX Item "n_par" +Number of free variables. +Length of parameter vector \fIpar\fR. +.IP "\fIpar\fR" 4 +.IX Item "par" +Parameter vector. +On input, it must contain a reasonable guess. +On output, it contains the solution found to minimize ||\fIfvec\fR||. +.IP "\fIm_dat\fR" 4 +.IX Item "m_dat" +Length of vector \fIfvec\fR. +Must statisfy \fIn_par\fR <= \fIm_dat\fR. +.IP "\fIdata\fR" 4 +.IX Item "data" +This pointer is ignored by the fit algorithm, +except for appearing as an argument in all calls to the user-supplied +routine \fIevaluate\fR. +.IP "\fIevaluate\fR" 4 +.IX Item "evaluate" +Pointer to a user-supplied function that computes \fIm_dat\fR elements of vector \fIfvec\fR for a given parameter vector \fIpar\fR. +If \fIevaluate\fR return with *\fIuserbreak\fR set to a negative value, \fB\f(BIlmmin()\fB\fR will interrupt the fitting and terminate. +.IP "\fIcontrol\fR" 4 +.IX Item "control" +Parameter collection for tuning the fit procedure. +In most cases, the default &\fIlm_control_double\fR is adequate. +If \fIf\fR is only computed with single-precision accuracy, +\&\fI&lm_control_float\fR should be used. +See also below, \s-1NOTES\s0 on initializing parameter records. +.Sp +\&\fIcontrol\fR has the following members (for more details, see the source file \fIlmstruct.h\fR): +.RS 4 +.IP "\fBdouble\fR \fIcontrol.ftol\fR" 4 +.IX Item "double control.ftol" +Relative error desired in the sum of squares. +Recommended setting: somewhat above machine precision; less if \fIfvec\fR is computed with reduced accuracy. +.IP "\fBdouble\fR \fIcontrol.xtol\fR" 4 +.IX Item "double control.xtol" +Relative error between last two approximations. +Recommended setting: as \fIftol\fR. +.IP "\fBdouble\fR \fIcontrol.gtol\fR" 4 +.IX Item "double control.gtol" +A measure for degeneracy. +Recommended setting: as \fIftol\fR. +.IP "\fBdouble\fR \fIcontrol.epsilon\fR" 4 +.IX Item "double control.epsilon" +Step used to calculate the Jacobian. +Recommended setting: as \fIftol\fR, but definitely less than the accuracy of \fIfvec\fR. +.IP "\fBdouble\fR \fIcontrol.stepbound\fR" 4 +.IX Item "double control.stepbound" +Initial bound to steps in the outer loop, generally between 0.01 and 100; recommended value is 100. +.IP "\fBint\fR \fIcontrol.patience\fR" 4 +.IX Item "int control.patience" +Used to set the maximum number of function evaluations to patience*n_par. +.IP "\fBint\fR \fIcontrol.scale_diag\fR" 4 +.IX Item "int control.scale_diag" +Logical switch (0 or 1). +If 1, then scale parameters to their initial value. +This is the recommended setting. +.IP "\fBFILE*\fR \fIcontrol.msgfile\fR" 4 +.IX Item "FILE* control.msgfile" +Progress messages will be written to this file. +Typically \fIstdout\fR or \fIstderr\fR. +The value \fI\s-1NULL\s0\fR will be interpreted as \fIstdout\fR. +.IP "\fBint\fR \fIcontrol.verbosity\fR" 4 +.IX Item "int control.verbosity" +If nonzero, some progress information from within the \s-1LM\s0 algorithm +is written to control.stream. +.IP "\fBint\fR \fIcontrol.n_maxpri\fR" 4 +.IX Item "int control.n_maxpri" +\&\-1, or maximum number of parameters to print. +.IP "\fBint\fR \fIcontrol.m_maxpri\fR" 4 +.IX Item "int control.m_maxpri" +\&\-1, or maximum number of residuals to print. +.RE +.RS 4 +.RE +.IP "\fIstatus\fR" 4 +.IX Item "status" +A record used to return information about the minimization process: +.RS 4 +.IP "\fBdouble\fR \fIstatus.fnorm\fR" 4 +.IX Item "double status.fnorm" +Norm of the vector \fIfvec\fR; +.IP "\fBint\fR \fIstatus.nfev\fR" 4 +.IX Item "int status.nfev" +Actual number of iterations; +.IP "\fBint\fR \fIstatus.outcome\fR" 4 +.IX Item "int status.outcome" +Status of minimization; +for the corresponding text message, print \fIlm_infmsg\fR\fB[\fR\fIstatus.outcome\fR\fB]\fR; +for a short code, print \fIlm_shortmsg\fR\fB[\fR\fIstatus.outcome\fR\fB]\fR. +.IP "\fBint\fR \fIstatus.userbreak\fR" 4 +.IX Item "int status.userbreak" +Set when termination has been forced by the user-supplied routine \fIevaluate\fR. +.RE +.RS 4 +.RE +.SH "NOTES" +.IX Header "NOTES" +.SS "Initializing parameter records." +.IX Subsection "Initializing parameter records." +The parameter record \fIcontrol\fR should always be initialized +from supplied default records: +.PP +.Vb 1 +\& lm_control_struct control = lm_control_double; /* or _float */ +.Ve +.PP +After this, parameters may be overwritten: +.PP +.Vb 2 +\& control.patience = 500; /* allow more iterations */ +\& control.verbosity = 15; /* for verbose monitoring */ +.Ve +.PP +An application written this way is guaranteed to work even if new parameters +are added to \fIlm_control_struct\fR. +.PP +Conversely, addition of parameters is not considered an \s-1API\s0 change; it may happen without increment of the major version number. +.SH "EXAMPLES" +.IX Header "EXAMPLES" +.SS "Fitting a surface" +.IX Subsection "Fitting a surface" +Fit a data set y(t) by a function f(t;p) where t is a two-dimensional vector: +.PP +.Vb 2 +\& #include "lmmin.h" +\& #include <stdio.h> +\& +\& /* fit model: a plane p0 + p1*tx + p2*tz */ +\& double f( double tx, double tz, const double *p ) +\& { +\& return p[0] + p[1]*tx + p[2]*tz; +\& } +\& +\& /* data structure to transmit data arays and fit model */ +\& typedef struct { +\& double *tx, *tz; +\& double *y; +\& double (*f)( double tx, double tz, const double *p ); +\& } data_struct; +\& +\& /* function evaluation, determination of residues */ +\& void evaluate_surface( const double *par, int m_dat, +\& const void *data, double *fvec, int *userbreak ) +\& { +\& /* for readability, explicit type conversion */ +\& data_struct *D; +\& D = (data_struct*)data; +\& +\& int i; +\& for ( i = 0; i < m_dat; i++ ) +\& fvec[i] = D\->y[i] \- D\->f( D\->tx[i], D\->tz[i], par ); +\& } +\& +\& int main() +\& { +\& /* parameter vector */ +\& int n_par = 3; /* number of parameters in model function f */ +\& double par[3] = { \-1, 0, 1 }; /* arbitrary starting value */ +\& +\& /* data points */ +\& int m_dat = 4; +\& double tx[4] = { \-1, \-1, 1, 1 }; +\& double tz[4] = { \-1, 1, \-1, 1 }; +\& double y[4] = { 0, 1, 1, 2 }; +\& +\& data_struct data = { tx, tz, y, f }; +\& +\& /* auxiliary parameters */ +\& lm_status_struct status; +\& lm_control_struct control = lm_control_double; +\& control.verbosity = 3; +\& +\& /* perform the fit */ +\& printf( "Fitting:\en" ); +\& lmmin( n_par, par, m_dat, (const void*) &data, evaluate_surface, +\& &control, &status ); +\& +\& /* print results */ +\& printf( "\enResults:\en" ); +\& printf( "status after %d function evaluations:\en %s\en", +\& status.nfev, lm_infmsg[status.outcome] ); +\& +\& printf("obtained parameters:\en"); +\& int i; +\& for ( i=0; i<n_par; ++i ) +\& printf(" par[%i] = %12g\en", i, par[i]); +\& printf("obtained norm:\en %12g\en", status.fnorm ); +\& +\& printf("fitting data as follows:\en"); +\& double ff; +\& for ( i=0; i<m_dat; ++i ){ +\& ff = f(tx[i], tz[i], par); +\& printf( " t[%2d]=%12g,%12g y=%12g fit=%12g residue=%12g\en", +\& i, tx[i], tz[i], y[i], ff, y[i] \- ff ); +\& } +\& +\& return 0; +\& } +.Ve +.SS "More examples" +.IX Subsection "More examples" +For more examples, see the homepage and directories demo/ and test/ in the source distribution. +.SH "COPYING" +.IX Header "COPYING" +Copyright (C): + 1980\-1999 University of Chicago + 2004\-2015 Joachim Wuttke, Forschungszentrum Juelich GmbH +.PP +Software: FreeBSD License +.PP +Documentation: Creative Commons Attribution Share Alike +.SH "SEE ALSO" +.IX Header "SEE ALSO" +\fBlmcurve\fR(3) +.PP +Homepage: http://apps.jcns.fz\-juelich.de/lmfit +.SH "BUGS" +.IX Header "BUGS" +Please send bug reports and suggestions to the author <j.wuttke@fz\-juelich.de>. |