A framework for fitting functions to data with SciPy which unifies the various available interpolation methods and provides a common interface to them based on the following simple methods:

• Fitter.__init__(p): set parameters of interpolation function, e.g. polynomial degree
• Fitter.fit(x, y): fit given input-output data
• Fitter.__call__(x) or Fitter.eval(x): evaluate function on new input data

Each interpolation routine falls in one of two categories: scatter fitting or grid fitting. They share the same interface, only differing in the definition of input data x.

Scatter-fitters operate on unstructured scattered input data (i.e. not on a grid). The input data consists of a sequence of x coordinates and a sequence of corresponding y data, where the order of the x coordinates does not matter and their location can be arbitrary. The x coordinates can have an arbritrary dimension (although most classes are specialised for 1-D or 2-D data). If the dimension is bigger than 1, the coordinates are provided as an array of column vectors. These fitters have ScatterFit as base class.

Grid-fitters operate on input data that lie on a grid. The input data consists of a sequence of x-axis tick sequences and the corresponding array of y data. These fitters have GridFit as base class.

The module is organised as follows:

• ScatterFit: Abstract base class for scatter fitters
• LinearLeastSquaresFit: Fit linear regression model to data using SVD
• Polynomial1DFit: Fit polynomial to 1-D data
• Polynomial2DFit: Fit polynomial to 2-D data
• PiecewisePolynomial1DFit: Fit piecewise polynomial to 1-D data
• Independent1DFit: Interpolate N-dimensional matrix along given axis
• Delaunay2DScatterFit: Interpolate scalar function of 2-D data, based on Delaunay triangulation and cubic / linear interpolation
• NonLinearLeastSquaresFit: Fit a generic function to data, based on non-linear least squares optimisation
• GaussianFit: Fit Gaussian curve to multi-dimensional data
• Spline1DFit: Fit a B-spline to 1-D data
• Spline2DScatterFit: Fit a B-spline to scattered 2-D data
• RbfScatterFit: Do radial basis function (RBF) interpolation

• GridFit: Abstract base class for grid fitters
• Spline2DGridFit: Fit a B-spline to 2-D data on a rectangular grid

• squash: Flatten array, but not necessarily all the way to a 1-D array
• unsquash: Restore an array that was reshaped by squash
• sort_grid: Ensure that the coordinates of a rectangular grid are in ascending order
• desort_grid: Undo the effect of sort_grid
• vectorize_fit_func: Factory that creates vectorised version of function to be fitted to data
• randomise: Randomise fitted function parameters by resampling residuals

https://github.com/ska-sa/scikits.fitting

Ludwig Schwardt <ludwig at ska.ac.za>