.\" 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 "lmcurve 3"
|
.TH lmcurve 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"
|
lmcurve \- Levenberg\-Marquardt least\-squares fit of a curve (t,y)
|
.SH "SYNOPSIS"
|
.IX Header "SYNOPSIS"
|
\&\fB#include <lmcurve.h\fR>
|
.PP
|
\&\fBvoid lmcurve( const int\fR \fIn_par\fR\fB, double *\fR\fIpar\fR\fB, const int\fR \fIm_dat\fR\fB,
|
const\ double *\fR\fIt\fR\fB, const\ double *\fR\fIy\fR\fB,
|
double (*\fR\fIf\fR\fB)( const double \fR\fIti\fR\fB, const double *\fR\fIpar\fR\fB ),
|
const\ lm_control_struct *\fR\fIcontrol\fR\fB,
|
lm_status_struct *\fR\fIstatus\fR\fB);\fR
|
.PP
|
\&\fBvoid lmcurve_tyd(
|
const int\fR \fIn_par\fR\fB, double *\fR\fIpar\fR\fB, const int\fR \fIm_dat\fR\fB,
|
const\ double *\fR\fIt\fR\fB, const\ double *\fR\fIy\fR\fB, const\ double *\fR\fIdy\fR\fB,
|
double (*\fR\fIf\fR\fB)( const double \fR\fIti\fR\fB, const double *\fR\fIpar\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(BIlmcurve()\fB\fR and \fB\f(BIlmcurve_tyd()\fB\fR wrap the more generic minimization function \fB\f(BIlmmin()\fB\fR, for use in curve fitting.
|
.PP
|
\&\fB\f(BIlmcurve()\fB\fR determines a vector \fIpar\fR that minimizes the sum of squared elements of a residue vector \fIr\fR[i] := \fIy\fR[i] \- \fIf\fR(\fIt\fR[i];\fIpar\fR). Typically, \fB\f(BIlmcurve()\fB\fR is used to approximate a data set \fIt\fR,\fIy\fR by a parametric function \fIf\fR(\fIti\fR;\fIpar\fR). On success, \fIpar\fR represents a local minimum, not necessarily a global one; it may depend on its starting value.
|
.PP
|
\&\fB\f(BIlmcurve_tyd()\fB\fR does the same for a data set \fIt\fR,\fIy\fR,\fIdy\fR, where \fIdy\fR represents the standard deviation of empirical data \fIy\fR. Residues are computed as \fIr\fR[i] := (\fIy\fR[i] \- \fIf\fR(\fIt\fR[i];\fIpar\fR))/\fIdy\fR[i]. Users must ensure that all \fIdy\fR[i] are positive.
|
.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 ||\fIr\fR||.
|
.IP "\fIm_dat\fR" 4
|
.IX Item "m_dat"
|
Number of data points.
|
Length of vectors \fIt\fR and \fIy\fR.
|
Must statisfy \fIn_par\fR <= \fIm_dat\fR.
|
.IP "\fIt\fR" 4
|
.IX Item "t"
|
Array of length \fIm_dat\fR.
|
Contains the abcissae (time, or \*(L"x\*(R") for which function \fIf\fR will be evaluated.
|
.IP "\fIy\fR" 4
|
.IX Item "y"
|
Array of length \fIm_dat\fR.
|
Contains the ordinate values that shall be fitted.
|
.IP "\fIdy\fR" 4
|
.IX Item "dy"
|
Only in \fB\f(BIlmcurve_tyd()\fB\fR.
|
Array of length \fIm_dat\fR.
|
Contains the standard deviations of the values \fIy\fR.
|
.IP "\fIf\fR" 4
|
.IX Item "f"
|
A user-supplied parametric function \fIf\fR(ti;\fIpar\fR).
|
.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.
|
Parameters are explained in \fB\f(BIlmmin\fB\|(3)\fR.
|
.IP "\fIstatus\fR" 4
|
.IX Item "status"
|
A record used to return information about the minimization process:
|
For details, see \fB\f(BIlmmin\fB\|(3)\fR.
|
.SH "EXAMPLE"
|
.IX Header "EXAMPLE"
|
Fit a data set y(x) by a curve f(x;p):
|
.PP
|
.Vb 2
|
\& #include "lmcurve.h"
|
\& #include <stdio.h>
|
\&
|
\& /* model function: a parabola */
|
\&
|
\& double f( double t, const double *p )
|
\& {
|
\& return p[0] + p[1]*t + p[2]*t*t;
|
\& }
|
\&
|
\& int main()
|
\& {
|
\& int n = 3; /* number of parameters in model function f */
|
\& double par[3] = { 100, 0, \-10 }; /* really bad starting value */
|
\&
|
\& /* data points: a slightly distorted standard parabola */
|
\& int m = 9;
|
\& int i;
|
\& double t[9] = { \-4., \-3., \-2., \-1., 0., 1., 2., 3., 4. };
|
\& double y[9] = { 16.6, 9.9, 4.4, 1.1, 0., 1.1, 4.2, 9.3, 16.4 };
|
\&
|
\& lm_control_struct control = lm_control_double;
|
\& lm_status_struct status;
|
\& control.verbosity = 7;
|
\&
|
\& printf( "Fitting ...\en" );
|
\& lmcurve( n, par, m, t, y, f, &control, &status );
|
\&
|
\& printf( "Results:\en" );
|
\& printf( "status after %d function evaluations:\en %s\en",
|
\& status.nfev, lm_infmsg[status.outcome] );
|
\&
|
\& printf("obtained parameters:\en");
|
\& for ( i = 0; i < n; ++i)
|
\& printf(" par[%i] = %12g\en", i, par[i]);
|
\& printf("obtained norm:\en %12g\en", status.fnorm );
|
\&
|
\& printf("fitting data as follows:\en");
|
\& for ( i = 0; i < m; ++i)
|
\& printf( " t[%2d]=%4g y=%6g fit=%10g residue=%12g\en",
|
\& i, t[i], y[i], f(t[i],par), y[i] \- f(t[i],par) );
|
\&
|
\& return 0;
|
\& }
|
.Ve
|
.SH "COPYING"
|
.IX Header "COPYING"
|
Copyright (C) 2009\-2015 Joachim Wuttke, Forschungszentrum Juelich GmbH
|
.PP
|
Software: FreeBSD License
|
.PP
|
Documentation: Creative Commons Attribution Share Alike
|
.SH "SEE ALSO"
|
.IX Header "SEE ALSO"
|
\fBlmmin\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>.
|
