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Fitting SciKit

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:

Scatter fitters

  • 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

Grid fitters

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

Helper functions

  • 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

Source

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

Contact

Ludwig Schwardt <ludwig at ska.ac.za>

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