finitediff 0.2.0

Finite difference weights for any derivative order on arbitrarily spaced grids.

==========
finitediff
==========
.. image:: https://travis-ci.org/bjodah/finitediff.png?branch=master
:target: https://travis-ci.org/bjodah/finitediff

``finitediff`` containts two implementations (`Fortran 90
<src/finitediff_fort.f90>`_ and `C++ <include/finitediff_templated.hpp>`_) version of Begnt Fornberg's
formulae for generation of finite difference weights on aribtrarily
spaced one dimensional grids. The finite difference weights can be
used for optimized inter-/extrapolation data series for up to
arbitrary derivative order. Python_ bindings are provided.

.. _Python: https://www.python.org
.. _finitediff: https://github.com/bjodah/finitediff


Capabilities
============
finitediff currently provides callbacks for estimation of derivatives
or interpolation either at a single point or over an array (available
from the Python bindings).

The user may also manually generate the corresponding weights. (see
``populate_weights``)


Installation
============
See dependencies and make sure that manual dependencies are satisfied.

Example using pip (modify to your own needs):

::

$ pip install --user --upgrade -r https://raw.github.com/bjodah/finitediff/v0.1.10/requirements.txt
$ pip install --user --upgrade https://github.com/bjodah/finitediff/archive/v0.1.10.tar.gz

Manual installation:


1. Clone repository ``$ git clone https://github.com/bjodah/finitediff.git``
2. Install dependencies ``$ cd finitediff; pip install --user --upgrade -r requirements.txt``
3. To install run ``$ python setup.py install --user`` or ``$ sudo python setup.py install``.

See distutils documentation_ for more options.

.. _documentation: http://docs.python.org/2/library/distutils.html

Note that the behaviour of ``setup(...)`` is modified slightly through the use of "PCExtension" from pycompilation_.


Tests
=====
To run the full test suite, you need to build the python
bindings. (see Dependencies)
::

$ python setup.py build_ext --inplace
$ py.test


Dependencies
============
You need either a C++ or a Fortran 90 compiler. On a debian based
linux system you can install it easily by typing:
``$ sudo apt-get install gfortran g++``

Optional dependencies (for Python bindings):

- Python header files (``sudo apt-get install python-dev``)
- Python_ (tested with 2.7)
- NumPy_
- Cython_
- pycompilation_ (optional: enables use from python)
- pytest_ (``sudo apt-get install python-pytest``)
- matplotlib_ (``sudo apt-get install python-matplotlib``)

See `requirements.txt <requirements.txt>`_ for detailed information of versions tested for.

For all dependencies the following command may be issued on a debian
based system:

::

$ sudo apt-get install gfortran g++ python2.7 libpython2.7-dev
python-numpy cython python-pip python-pytest python-matplotlib; sudo
pip install --upgrade -r https://raw.github.com/bjodah/finitediff/v0.1.10/requirements.txt``


.. _NumPy: http://www.numpy.org/
.. _pycompilation: https://github.com/bjodah/pycompilation
.. _pytest: http://pytest.org/
.. _matplotlib: http://matplotlib.org/

Notes
=====
There is a git subtree under finitediff, update through:

``git subtree pull --prefix finitediff/newton_interval newton_interval master --squash``

where the repo "newton_interval" is https://github.com/bjodah/newton_interval.git

First time you need to add it:
``git remote add -f newton_interval https://github.com/bjodah/newton_interval.git``

(Users of Ubuntu 12.04 who want to use git subtree, see http://stackoverflow.com/questions/17797328)

References
==========
The algortihm is a Fortran 90 rewrite of:

http://dx.doi.org/10.1137/S0036144596322507

::

@article{fornberg_classroom_1998,
title={Classroom note: Calculation of weights in finite difference formulas},
author={Fornberg, Bengt},
journal={SIAM review},
volume={40},
number={3},
pages={685--691},
year={1998},
publisher={SIAM}
doi={10.1137/S0036144596322507}
}


Which is based on an article of the same author:

http://dx.doi.org/10.1090/S0025-5718-1988-0935077-0

::

@article{fornberg_generation_1988,
title={Generation of finite difference formulas on arbitrarily spaced grids},
author={Fornberg, Bengt},
journal={Mathematics of computation},
volume={51},
number={184},
pages={699--706},
year={1988}
doi={10.1090/S0025-5718-1988-0935077-0}
}


License
=======
Open Source. Released under the very permissive "simplified
(2-clause) BSD license". See LICENSE.txt for further details.


Authors
=======
See file `AUTHORS <AUTHORS>`_ in root.