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.... 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 -- \(*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\} . 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.
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'.
.. .nr rF 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 . ds #H 0 . ds #V .8m . ds #F .3m . ds #[ \f1 . ds #] .\} . ds #H ((1u-(\\\\n(.fu%2u))*.13m) . ds #V .6m . ds #F 0 . ds #[ \& . ds #] \& .\} . \" simple accents for nroff and troff . ds ' \& . ds ` \& . ds ^ \& . ds , \& . ds ~ ~ . ds / .\} . 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 . \" corrections for vroff . \" for low resolution devices (crt and lpr) \{\ . 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 .\} ========================================================================
Title "lmcurve 3"
way too many mistakes in technical documents.
.nh
\fBvoid lmcurve( const int n_par, double *par, const int m_dat, const double *t, const double *y, double (*f)( const double ti, const double *par ), const lm_control_struct *control, lm_status_struct *status);
\fBvoid lmcurve_tyd( const int n_par, double *par, const int m_dat, const double *t, const double *y, const double *dy, double (*f)( const double ti, const double *par ), const lm_control_struct *control, lm_status_struct *status);
\fBextern const lm_control_struct lm_control_double;
\fBextern const lm_control_struct lm_control_float;
\fBextern const char *lm_infmsg[];
\fBextern const char *lm_shortmsg[];
\fB\f(BIlmcurve() determines a vector par that minimizes the sum of squared elements of a residue vector r[i] := y[i] - f(t[i];par). Typically, \f(BIlmcurve() is used to approximate a data set t,y by a parametric function f(ti;par). On success, par represents a local minimum, not necessarily a global one; it may depend on its starting value.
\fB\f(BIlmcurve_tyd() does the same for a data set t,y,dy, where dy represents the standard deviation of empirical data y. Residues are computed as r[i] := (y[i] - f(t[i];par))/dy[i]. Users must ensure that all dy[i] are positive.
Function arguments:
.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
Software: FreeBSD License
Documentation: Creative Commons Attribution Share Alike
Homepage: http://apps.jcns.fz-juelich.de/lmfit
