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RBF                                                                             
+++                                                                             
Python package containing tools for radial basis function (RBF) applications.
Applications include interpolating scattered data and solving partial
differential equations (PDEs) over irregular domains. Much of this package was
inspired by the books "A Primer on Radial Basis Functions with Applications to
the Geosciences" by Bengt Fornberg and Natasha Flyer and "Meshfree
Approximation Methods with Matlab" by Gregory Fasshauer. RBF is developed by
Trever Hines (hinest@umich.edu), University of Michigan, and the source code
for this project can be found `here <http://www.github.com/treverhines/RBF>`_.
                                                                                
Features                                                                        
========                                                                        
* The `RBF` class, which is used to evaluate RBFs and their exact derivatives 
* The `RBFInterpolant` class, which is used to interpolate scattered and      
  potentially noisy N-dimensional data. One can also evaluate the exact         
  derivatives of the interpolant                                                
* The `weight_matrix` function, which generates radial basis function finite  
  difference (RBF-FD) weights. This is used for solving large scale PDEs over   
  irregular domains                                                             
* Node generation functions, such as `min_energy_nodes` and
  `poisson_disc_nodes`, which are used for solving PDEs with the spectral RBF
  method or the RBF-FD method
* Computational geometry functions (e.g. point in polygon testing) for two and  
  three spatial dimensions                                                      
* The `GaussianProcess` class, which is used for Gaussian process regression
  (GPR). GPR is similar to RBF interpolation, except it has a Bayesian
  statistical foundation

Table of contents
=================
.. toctree::
  :maxdepth: 2

  installation
  basis
  interpolate
  gproc
  pde
  linalg
  poly
  utils
  sputils

Quick demo
==========
Interpolating scattered data
----------------------------
.. literalinclude:: ../scripts/interpolate.a.py

.. figure:: ../figures/interpolate.a.png

  This plot was generated by the above code. Observations are shown as scatter
  points and the smoothed interpolant is the color field.

Solving PDEs
------------
There are two methods for solving PDEs with RBFs: the spectral method and the
RBF-FD method. The spectral method has been touted as having remarkable
accuracy; however it is only applicable for small scale problems and requires a
good choice for a shape parameter. The RBF-FD method is appealing because it
can be used for large scale problems, there is no need to tune a shape
parameter (assuming you use polyharmonic splines to generate the weights), and
higher order accuracy can be attained by simply increasing the stencil size or
increasing the order of the polynomial used to generate the weights. In short,
the RBF-FD method should always be preferred over the spectral RBF method. An
example of the two methods is provided below.

.. literalinclude:: ../scripts/basis.a.py

.. figure:: ../figures/basis.a.png

.. literalinclude:: ../scripts/fd.i.py

.. figure:: ../figures/fd.i.png

Indices and tables
==================
* :ref:`genindex`
* :ref:`modindex`
* :ref:`search`