Curve Fitting
The purpose of constructing a line of approximation (fitting) - to discover the best model to describe your data and to show where the appearance of new points is most possible.
You have a table of points (X, Y). If you have model representation for these numeric Y( X ) data (Y=f( X,aj ) with parameters aj, j=1..m), you can find numeric values of aj that made table-defined curve Yi( Xi ) and model curve Y=f( X,aj ) most similar. This process is known as fitting. If you have not model representation you have to find this curve fit.
In this version of the program a series of points is esteemed as time-invariant flow of points (X, Y). Time (sequence number, parameter Z), X, Y sizes of a point are unused. Methods of approximation (fitting) are used in program:
- Regression line f( X ) or f( Y );
- Piece linear f( X ) or f( Y );
- Logistic functions f( X ) or f( Y );
- Fourier approximation;
- Rationals;
- Neural network;
- Non-linear least-square fitting;
- Formula;
- Parametric curve;
- B-spline curve;
- Sections ( X, Y );
- User defined function.
Built-in Wizard of Approximation will help you to apply a variety of curve fits to your plot.
You can add Plug-In module (DLL) to include your non-linear equations into FindGraph. Example C source code for a 'user model' Plug-In is provided in FindGraph install package. You can find it in the subfolder "UserModels". Alternatively, if you're unaccustomed to writing DLL's we'd be happy to produce a plugin for licensed users at no charge, provided that you can furnish the curve fitting model details.
Moreover you can use your own algorithm as Plug-In. Simple compile DLL with any name and place it in the subfolder "APPR". We shipped EXPPOW.DLL sample (pure C). You can find it in the subfolder "ApprSource".
Weighting scheme
Data points can be given greater or less influence over the fitting process by assigning a weight to each point. You can specify weights Wi for a set of data points (Xi,Yi, i=1..N) for curve fitting. Four different weighting methods are supported by FindGraph:
- No weight: Wi = 1.
- Instrumental weights: Wi = 1/Ci^2, where Ci are the error bar sizes stored in error bar column Z.
- Statistical: Wi = 1/Yi, or Wi = Yi, or Wi = 1/Xi, or Wi = Xi.
- Direct: Wi = Ci, where Ci are stored in column Z.
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