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The Piece-wise Polynomial Package

Overview

This python package offers Piece-wise Polynomial (PP) and B-spline representations of multi-dimensional scalar real functions.

The main module pppack.py contains the definition of different classes and methods used to build function spaces, functions and tensors (intended here as multi-dimensional arrays). Multi- dimensionality is achieved by Cartesian products, which are implemented by overloading the multiplication methods.

Memory management is handled by python, whereas all the numerics is delegated to external FORTRAN libraries to achieve high computational performances. These libraries are C-wrapped by f2py [1]:

  1. pppack.f90 (main library)

    This F90 library is produced from the original Carl de Boor’s F77 library [2]. The current version used here was modified by D. Tomatis to comply with the latest F90 standards. Original files comes from J. Burkardt.

  2. newton_interp_1d.f90 (here appended at the end of pppack.f90)

    Interpolation of polynomials in Newton form by divided diffe- rences. The code has been upgraded with routines for multi- dimensional data.

  3. chebyshev_interp_1d.f90

    Interpolation by Chebyshev polynomials.

The implementation of multi-dimensional approximations follows De Boor’s array indexing as in [3].

Note

The use of the library DIVDIF to work with polynomials in Newton form is on stand-by status at present for the commented lines in data_to_dif which prevents osculatory fitting. However, please note that this library contains many more functionalities than newton_interp_1d.