Framework for fitting functions to data with SciPy
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
Ludwig Schwardt <ludwig at ska.ac.za>
- Fix pip installation, clean up setup procedure, flake8 and add README
- PiecewisePolynomial1DFit updated to work with scipy 0.18.0
- Delaunay2DScatterFit now based on scipy.interpolate.griddata, which is orders of magnitude faster, more robust and smoother. Its default interpolation changed from ‘nn’ (natural neighbours - no longer available) to ‘cubic’.
- Delaunay2DGridFit removed as there is no equivalent anymore
- Use proper name for np.linalg.LinAlgError
- Initial release of scikits.fitting
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