| .\" Automatically generated by Pod::Man 2.28 (Pod::Simple 3.28) |
| .\" |
| .\" Standard preamble: |
| .\" ======================================================================== |
| .de Sp \" Vertical space (when we can't use .PP) |
| .if t .sp .5v |
| .if n .sp |
| .. |
| .de Vb \" Begin verbatim text |
| .ft CW |
| .nf |
| .ne \\$1 |
| .. |
| .de Ve \" End verbatim text |
| .ft R |
| .fi |
| .. |
| .\" Set up some character translations and predefined strings. \*(-- will |
| .\" give an unbreakable dash, \*(PI will give pi, \*(L" will give a left |
| .\" double quote, and \*(R" will give a right double quote. \*(C+ will |
| .\" give a nicer C++. Capital omega is used to do unbreakable dashes and |
| .\" therefore won't be available. \*(C` and \*(C' expand to `' in nroff, |
| .\" nothing in troff, for use with C<>. |
| .tr \(*W- |
| .ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p' |
| .ie n \{\ |
| . ds -- \(*W- |
| . ds PI pi |
| . if (\n(.H=4u)&(1m=24u) .ds -- \(*W\h'-12u'\(*W\h'-12u'-\" diablo 10 pitch |
| . if (\n(.H=4u)&(1m=20u) .ds -- \(*W\h'-12u'\(*W\h'-8u'-\" diablo 12 pitch |
| . ds L" "" |
| . ds R" "" |
| . ds C` "" |
| . ds C' "" |
| 'br\} |
| .el\{\ |
| . ds -- \|\(em\| |
| . ds PI \(*p |
| . ds L" `` |
| . ds R" '' |
| . ds C` |
| . ds C' |
| 'br\} |
| .\" |
| .\" Escape single quotes in literal strings from groff's Unicode transform. |
| .ie \n(.g .ds Aq \(aq |
| .el .ds Aq ' |
| .\" |
| .\" If the F register is turned on, we'll generate index entries on stderr for |
| .\" titles (.TH), headers (.SH), subsections (.SS), items (.Ip), and index |
| .\" entries marked with X<> in POD. Of course, you'll have to process the |
| .\" output yourself in some meaningful fashion. |
| .\" |
| .\" Avoid warning from groff about undefined register 'F'. |
| .de IX |
| .. |
| .nr rF 0 |
| .if \n(.g .if rF .nr rF 1 |
| .if (\n(rF:(\n(.g==0)) \{ |
| . if \nF \{ |
| . de IX |
| . tm Index:\\$1\t\\n%\t"\\$2" |
| .. |
| . if !\nF==2 \{ |
| . nr % 0 |
| . nr F 2 |
| . \} |
| . \} |
| .\} |
| .rr rF |
| .\" |
| .\" Accent mark definitions (@(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2). |
| .\" Fear. Run. Save yourself. No user-serviceable parts. |
| . \" fudge factors for nroff and troff |
| .if n \{\ |
| . ds #H 0 |
| . ds #V .8m |
| . ds #F .3m |
| . ds #[ \f1 |
| . ds #] \fP |
| .\} |
| .if t \{\ |
| . ds #H ((1u-(\\\\n(.fu%2u))*.13m) |
| . ds #V .6m |
| . ds #F 0 |
| . ds #[ \& |
| . ds #] \& |
| .\} |
| . \" simple accents for nroff and troff |
| .if n \{\ |
| . ds ' \& |
| . ds ` \& |
| . ds ^ \& |
| . ds , \& |
| . ds ~ ~ |
| . ds / |
| .\} |
| .if t \{\ |
| . ds ' \\k:\h'-(\\n(.wu*8/10-\*(#H)'\'\h"|\\n:u" |
| . ds ` \\k:\h'-(\\n(.wu*8/10-\*(#H)'\`\h'|\\n:u' |
| . ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'^\h'|\\n:u' |
| . ds , \\k:\h'-(\\n(.wu*8/10)',\h'|\\n:u' |
| . ds ~ \\k:\h'-(\\n(.wu-\*(#H-.1m)'~\h'|\\n:u' |
| . ds / \\k:\h'-(\\n(.wu*8/10-\*(#H)'\z\(sl\h'|\\n:u' |
| .\} |
| . \" troff and (daisy-wheel) nroff accents |
| .ds : \\k:\h'-(\\n(.wu*8/10-\*(#H+.1m+\*(#F)'\v'-\*(#V'\z.\h'.2m+\*(#F'.\h'|\\n:u'\v'\*(#V' |
| .ds 8 \h'\*(#H'\(*b\h'-\*(#H' |
| .ds o \\k:\h'-(\\n(.wu+\w'\(de'u-\*(#H)/2u'\v'-.3n'\*(#[\z\(de\v'.3n'\h'|\\n:u'\*(#] |
| .ds d- \h'\*(#H'\(pd\h'-\w'~'u'\v'-.25m'\f2\(hy\fP\v'.25m'\h'-\*(#H' |
| .ds D- D\\k:\h'-\w'D'u'\v'-.11m'\z\(hy\v'.11m'\h'|\\n:u' |
| .ds th \*(#[\v'.3m'\s+1I\s-1\v'-.3m'\h'-(\w'I'u*2/3)'\s-1o\s+1\*(#] |
| .ds Th \*(#[\s+2I\s-2\h'-\w'I'u*3/5'\v'-.3m'o\v'.3m'\*(#] |
| .ds ae a\h'-(\w'a'u*4/10)'e |
| .ds Ae A\h'-(\w'A'u*4/10)'E |
| . \" corrections for vroff |
| .if v .ds ~ \\k:\h'-(\\n(.wu*9/10-\*(#H)'\s-2\u~\d\s+2\h'|\\n:u' |
| .if v .ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'\v'-.4m'^\v'.4m'\h'|\\n:u' |
| . \" for low resolution devices (crt and lpr) |
| .if \n(.H>23 .if \n(.V>19 \ |
| \{\ |
| . ds : e |
| . ds 8 ss |
| . ds o a |
| . ds d- d\h'-1'\(ga |
| . ds D- D\h'-1'\(hy |
| . ds th \o'bp' |
| . ds Th \o'LP' |
| . ds ae ae |
| . ds Ae AE |
| .\} |
| .rm #[ #] #H #V #F C |
| .\" ======================================================================== |
| .\" |
| .IX Title "lmmin 3" |
| .TH lmmin 3 "2015-11-27" "perl v5.20.2" "lmfit manual" |
| .\" For nroff, turn off justification. 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>. |