282 lines
9.3 KiB
Groff
282 lines
9.3 KiB
Groff
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.\" ========================================================================
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.\"
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.IX Title "lmcurve 3"
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.TH lmcurve 3 "2015-11-27" "perl v5.20.2" "lmfit manual"
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.\" For nroff, turn off justification. Always turn off hyphenation; it makes
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.\" way too many mistakes in technical documents.
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.if n .ad l
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.nh
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.SH "NAME"
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lmcurve \- Levenberg\-Marquardt least\-squares fit of a curve (t,y)
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.SH "SYNOPSIS"
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.IX Header "SYNOPSIS"
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\&\fB#include <lmcurve.h\fR>
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.PP
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\&\fBvoid lmcurve( const int\fR \fIn_par\fR\fB, double *\fR\fIpar\fR\fB, const int\fR \fIm_dat\fR\fB,
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const\ double *\fR\fIt\fR\fB, const\ double *\fR\fIy\fR\fB,
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double (*\fR\fIf\fR\fB)( const double \fR\fIti\fR\fB, const double *\fR\fIpar\fR\fB ),
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const\ lm_control_struct *\fR\fIcontrol\fR\fB,
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lm_status_struct *\fR\fIstatus\fR\fB);\fR
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.PP
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\&\fBvoid lmcurve_tyd(
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const int\fR \fIn_par\fR\fB, double *\fR\fIpar\fR\fB, const int\fR \fIm_dat\fR\fB,
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const\ double *\fR\fIt\fR\fB, const\ double *\fR\fIy\fR\fB, const\ double *\fR\fIdy\fR\fB,
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double (*\fR\fIf\fR\fB)( const double \fR\fIti\fR\fB, const double *\fR\fIpar\fR\fB ),
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const\ lm_control_struct *\fR\fIcontrol\fR\fB,
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lm_status_struct *\fR\fIstatus\fR\fB);\fR
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.PP
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\&\fBextern const lm_control_struct lm_control_double;\fR
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.PP
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\&\fBextern const lm_control_struct lm_control_float;\fR
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.PP
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\&\fBextern const char *lm_infmsg[];\fR
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.PP
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\&\fBextern const char *lm_shortmsg[];\fR
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.SH "DESCRIPTION"
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.IX Header "DESCRIPTION"
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\&\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.
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.PP
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\&\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.
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.PP
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\&\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.
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.PP
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Function arguments:
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.IP "\fIn_par\fR" 4
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.IX Item "n_par"
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Number of free variables.
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Length of parameter vector \fIpar\fR.
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.IP "\fIpar\fR" 4
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.IX Item "par"
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Parameter vector.
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On input, it must contain a reasonable guess.
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On output, it contains the solution found to minimize ||\fIr\fR||.
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.IP "\fIm_dat\fR" 4
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.IX Item "m_dat"
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Number of data points.
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Length of vectors \fIt\fR and \fIy\fR.
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Must statisfy \fIn_par\fR <= \fIm_dat\fR.
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.IP "\fIt\fR" 4
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.IX Item "t"
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Array of length \fIm_dat\fR.
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Contains the abcissae (time, or \*(L"x\*(R") for which function \fIf\fR will be evaluated.
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.IP "\fIy\fR" 4
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.IX Item "y"
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Array of length \fIm_dat\fR.
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Contains the ordinate values that shall be fitted.
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.IP "\fIdy\fR" 4
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.IX Item "dy"
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Only in \fB\f(BIlmcurve_tyd()\fB\fR.
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Array of length \fIm_dat\fR.
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Contains the standard deviations of the values \fIy\fR.
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.IP "\fIf\fR" 4
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.IX Item "f"
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A user-supplied parametric function \fIf\fR(ti;\fIpar\fR).
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.IP "\fIcontrol\fR" 4
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.IX Item "control"
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Parameter collection for tuning the fit procedure.
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In most cases, the default &\fIlm_control_double\fR is adequate.
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If \fIf\fR is only computed with single-precision accuracy,
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\&\fI&lm_control_float\fR should be used.
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Parameters are explained in \fB\f(BIlmmin\fB\|(3)\fR.
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.IP "\fIstatus\fR" 4
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.IX Item "status"
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A record used to return information about the minimization process:
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For details, see \fB\f(BIlmmin\fB\|(3)\fR.
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.SH "EXAMPLE"
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.IX Header "EXAMPLE"
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Fit a data set y(x) by a curve f(x;p):
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.PP
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.Vb 2
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\& #include "lmcurve.h"
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\& #include <stdio.h>
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\&
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\& /* model function: a parabola */
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\&
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\& double f( double t, const double *p )
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\& {
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\& return p[0] + p[1]*t + p[2]*t*t;
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\& }
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\&
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\& int main()
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\& {
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\& int n = 3; /* number of parameters in model function f */
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\& double par[3] = { 100, 0, \-10 }; /* really bad starting value */
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\&
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\& /* data points: a slightly distorted standard parabola */
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\& int m = 9;
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\& int i;
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\& double t[9] = { \-4., \-3., \-2., \-1., 0., 1., 2., 3., 4. };
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\& double y[9] = { 16.6, 9.9, 4.4, 1.1, 0., 1.1, 4.2, 9.3, 16.4 };
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\&
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\& lm_control_struct control = lm_control_double;
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\& lm_status_struct status;
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\& control.verbosity = 7;
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\&
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\& printf( "Fitting ...\en" );
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\& lmcurve( n, par, m, t, y, f, &control, &status );
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\&
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\& printf( "Results:\en" );
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\& printf( "status after %d function evaluations:\en %s\en",
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\& status.nfev, lm_infmsg[status.outcome] );
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\&
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\& printf("obtained parameters:\en");
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\& for ( i = 0; i < n; ++i)
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\& printf(" par[%i] = %12g\en", i, par[i]);
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\& printf("obtained norm:\en %12g\en", status.fnorm );
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\&
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\& printf("fitting data as follows:\en");
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\& for ( i = 0; i < m; ++i)
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\& printf( " t[%2d]=%4g y=%6g fit=%10g residue=%12g\en",
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\& i, t[i], y[i], f(t[i],par), y[i] \- f(t[i],par) );
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\&
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\& return 0;
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\& }
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.Ve
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.SH "COPYING"
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.IX Header "COPYING"
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Copyright (C) 2009\-2015 Joachim Wuttke, Forschungszentrum Juelich GmbH
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.PP
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Software: FreeBSD License
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.PP
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Documentation: Creative Commons Attribution Share Alike
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.SH "SEE ALSO"
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.IX Header "SEE ALSO"
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\fBlmmin\fR(3)
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.PP
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Homepage: http://apps.jcns.fz\-juelich.de/lmfit
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.SH "BUGS"
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.IX Header "BUGS"
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Please send bug reports and suggestions to the author <j.wuttke@fz\-juelich.de>.
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