This shows you the differences between two versions of the page.
Both sides previous revision Previous revision Next revision | Previous revision | ||
fit_formulas [Fri Jul 12 11:31:28 2013] Alexander |
fit_formulas [Tue May 30 16:28:13 2017] (current) Alexander |
||
---|---|---|---|
Line 1: | Line 1: | ||
====== Fitting Algorithm and Computational Formulas ====== | ====== Fitting Algorithm and Computational Formulas ====== | ||
- | MagicPlot uses iterative [[wp> | + | MagicPlot uses iterative [[wp> |
MagicPlot implementation of Levenberg–Marquardt algorithm is optimised for using with multi-core processors. MagicPlot successfully passed testing with NIST Nonlinear Regression datasets (see our [[http:// | MagicPlot implementation of Levenberg–Marquardt algorithm is optimised for using with multi-core processors. MagicPlot successfully passed testing with NIST Nonlinear Regression datasets (see our [[http:// | ||
Line 15: | Line 15: | ||
* //f//(//x, β< | * //f//(//x, β< | ||
* //p// is the number of fit parameters // | * //p// is the number of fit parameters // | ||
- | * // | + | * // |
An initial guess for the parameters has to be provided to start minimization. Calculation of the new guess of parameters on each fit iteration is based on the fit function partial derivatives for current values of fit parameters for each //x// value: | An initial guess for the parameters has to be provided to start minimization. Calculation of the new guess of parameters on each fit iteration is based on the fit function partial derivatives for current values of fit parameters for each //x// value: | ||
Line 25: | Line 25: | ||
===== Weighting of Data Points Using Y Errors ===== | ===== Weighting of Data Points Using Y Errors ===== | ||
MagicPlot can use weighting of //y// values based on y errors // | MagicPlot can use weighting of //y// values based on y errors // | ||
- | * If standard //y// errors are **not** specified: all // | ||
- | * If standard //y// errors // | ||
- | <m>w_i=C 1/{{s_i}^2}</m> | + | * If standard //y// errors //s<sub>i</ |
- | + | * Otherwise: all //w<sub>i</sub>// = 1. | |
- | here //C// is normalizing coefficient | + | |
- | + | ||
- | <m>C=N sum{i=1}{N}{{s_i}^2}</m> | + | |
In '' | In '' | ||
Line 57: | Line 52: | ||
Because of some confusion in the names of the parameters in different sources (books and software), we also give many different names of same parameter in //note// column. | Because of some confusion in the names of the parameters in different sources (books and software), we also give many different names of same parameter in //note// column. | ||
+ | |< 100% 15% 10% 45% 30% >| | ||
^ Parameter Name ^ Symbol | ^ Parameter Name ^ Symbol | ||
^ Original Data and Fit Model Properties | ^ Original Data and Fit Model Properties |