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@@ -4,6 +4,7 @@ This is the home page of **lmfit**, | |
| a self-contained C library for Levenberg-Marquardt | ||
| least-squares minimization and curve fitting. | ||
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| # Background information | ||
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| ## History | ||
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| Joachim Wuttke: lmfit – a C library for Levenberg-Marquardt least-squares minimization and curve fitting. Version […], retrieved on […] from https://jugit.fz-juelich.de/mlz/lmfit. | ||
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| # Usage | ||
| ## Contact | ||
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| * Concise documentation is available in form of manual pages: | ||
| * [lmfit(7)](http://apps.jcns.fz-juelich.de/man/lmfit.html): Summary. | ||
| * [lmmin2(3)](http://apps.jcns.fz-juelich.de/man/lmmin2.html): | ||
| Generic routine for minimizing whatever sum of squares. | ||
| * [lmmin(3)](http://apps.jcns.fz-juelich.de/man/lmmin.html): | ||
| Simpler legacy API without error estimates. | ||
| * [lmcurve(3)](http://apps.jcns.fz-juelich.de/man/lmcurve.html): | ||
| Simpler interface for fitting a parametric function f(x;p) to a data set y(x). | ||
| * Sample code: | ||
| * [curve fitting with lmcurve()]() | ||
| * [surface fitting as example for minimization with lmmin()]() | ||
| * [nonlinear equations solving with lmmin()]() | ||
| * Application questions: | ||
| * Constraining parameters | ||
| * Weighing data points | ||
| * Language bindings: | ||
| * https://github.com/jvail/lmfit.js by Jan Vaillant | ||
| For bug reports or suggestions, contact the maintainer: [email protected]. | ||
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| # Installation | ||
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| ## From source | ||
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| Get the latest source archive (tgz) from | ||
| [Repository > Tags](https://jugit.fz-juelich.de/mlz/lmfit/tags). | ||
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| Build&install are based on CMake. Out-of-source build is enforced. After unpacking the source, go to the source directory and do: | ||
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| ``` | ||
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| ctest | ||
| make | ||
| make install | ||
| ``` | ||
| ``` | ||
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| ## RPM Binaries | ||
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| * https://apps.fedoraproject.org/packages/lmfit maintained by Miro Hrončok | ||
| * http://fr2.rpmfind.net/linux/rpm2html/search.php?query=lmfit | ||
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| ## Language bindings: | ||
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| * https://github.com/jvail/lmfit.js by Jan Vaillant | ||
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| # Usage | ||
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| ## Manual pages: | ||
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| * [lmfit(7)](http://apps.jcns.fz-juelich.de/man/lmfit.html): Summary. | ||
| * [lmmin2(3)](http://apps.jcns.fz-juelich.de/man/lmmin2.html): | ||
| Generic routine for minimizing whatever sum of squares. | ||
| * [lmmin(3)](http://apps.jcns.fz-juelich.de/man/lmmin.html): | ||
| Simpler legacy API without error estimates. | ||
| * [lmcurve(3)](http://apps.jcns.fz-juelich.de/man/lmcurve.html): | ||
| Simpler interface for fitting a parametric function f(x;p) to a data set y(x). | ||
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| ## Sample code: | ||
| * [curve fitting with lmcurve()](http://apps.jcns.fz-juelich.de/doku/sc/lmfit:basic-curve-fitting-example) | ||
| * [surface fitting as example for minimization with lmmin()](http://apps.jcns.fz-juelich.de/doku/sc/lmfit:surface-fitting-example) | ||
| * [nonlinear equations solving with lmmin()](http://apps.jcns.fz-juelich.de/doku/sc/lmfit:nonlinear-equations-example) | ||
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| # FAQ | ||
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| ## How to constrain parameters? | ||
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| In many applications, it is desirable to impose constraints like p0>=0 or 10<p1<10. | ||
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| In lmfit, there is no explicit for mechanism for this, and it is unlikely that I will ever add one: In my experience, it is sufficient to mimick constraints by variable transform or by adding a penalty to the sum of squares. Variable transform seems to be the better solution. | ||
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| In the above examples: To enforce p0'>0, use e.g. p0'=exp(p0) or p0'=p0^2. To enforce -10<p1'<10, use p1'=10*tanh(p1). | ||
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| ## How to weigh data points? | ||
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| In least-squares curve fitting, data points _y_(_x_) are approximated by function values _f_(_x_;**p**). Sometimes, one wants to assign data points a weight _w_(_x_). One then has to minimize the sum of squares of _w_*(_y_-_f_). | ||
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| ### How to implement | ||
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| This can be implemented easily by copying _lmcurve.h_ and _lmcurve.c_, and modifying them in obvious ways, just introducing a new parameter _w_. | ||
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| ### How to choose weights | ||
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| Assuming that data points _y_(_x_) follow Gaussian distributions with standard deviations _dy_(_x_), the appropriate weight is _w_(_x_) = 1 / _dy_(_x_). | ||
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| ### How to deal with Poisson-distributed data | ||
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| Least-squares fitting is not justified for Poisson-distributed data -- except if the data are large enough (say, on average _y_ of the order of 10 or larger) so that the Poisson distribution is reasonably well approximated by a Gaussian with standard deviation _dy_=sqrt(_y_). When experimental data have on average too low values _y_ per channel, they should be binned into fewer channels with better statistics before any least-squares fitting. | ||
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