finitediff

.. image:: http://hera.physchem.kth.se:8080/api/badges/bjodah/finitediff/status.svg :target: http://hera.physchem.kth.se:8080/bjodah/finitediff :alt: Build status .. image:: https://img.shields.io/pypi/v/finitediff.svg :target: https://pypi.python.org/pypi/finitediff :alt: PyPI version .. image:: https://zenodo.org/badge/14988640.svg :target: https://zenodo.org/badge/latestdoi/14988640 :alt: Zenodo DOI .. image:: https://img.shields.io/badge/python-2.7,3.6,3.7-blue.svg :target: https://www.python.org/ :alt: Python version .. image:: https://img.shields.io/pypi/l/finitediff.svg :target: https://github.com/bjodah/finitediff/blob/master/LICENSE :alt: License .. image:: http://hera.physchem.kth.se/~finitediff/branches/master/htmlcov/coverage.svg :target: http://hera.physchem.kth.se/~finitediff/branches/master/htmlcov :alt: coverage

finitediff containts three implementations of Begnt Fornberg's formulae for generation of finite difference weights on aribtrarily spaced one dimensional grids:

• C89 <src/finitediff_c.c>_
• Fortran 90 <src/finitediff_fort.f90>_
• C++ <finitediff/include/finitediff_templated.hpp>_

The finite difference weights can be used for optimized inter-/extrapolation data series for up to arbitrary derivative order. Python_ bindings (to the C versions) are also 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 calculate_weights)

Finitediff can be conditionally compiled to make finitediff_interpolate_by_finite_diff multithreaded (when FINITEDIFF_OPENMP is defined). Then the number of threads used is set through the environment variable FINITEDIFF_NUM_THREADS (or OMP_NUM_THREADS).

Documentation

Autogenerated API documentation for latest stable release is found here: <https://bjodah.github.io/finitediff/latest>_ (and the development version for the current master branch is found here: <http://hera.physchem.kth.se/~finitediff/branches/master/html>_).

Examples

Generating finite difference weights is simple using C++11:

.. code:: C++

#include "finitediff_templated.hpp" #include #include #include

int main(){ const unsigned max_deriv = 2; std::vectorstd::string labels {"0th derivative", "1st derivative", "2nd derivative"}; std::vector x {0, 1, -1, 2, -2}; // Fourth order of accuracy auto coeffs = finitediff::generate_weights(x, max_deriv); for (unsigned deriv_i = 0; deriv_i <= max_deriv; deriv_i++){ std::cout << labels[deriv_i] << ": "; for (unsigned idx = 0; idx < x.size(); idx++){ std::cout << coeffs[deriv_i*x.size() + idx] << " "; } std::cout << std::endl; } }

::

$ cd examples/ $ g++ -std=c++11 demo.cpp -I../include $ ./a.out Zeroth derivative (interpolation): 1 -0 0 0 -0 First derivative: -0 0.666667 -0.666667 -0.0833333 0.0833333 Second derivative: -2.5 1.33333 1.33333 -0.0833333 -0.0833333

and of course using the python bindings:

.. code:: python

from finitediff import get_weights import numpy as np c = get_weights(np.array([0, -1., 1]), 0, maxorder=1) np.allclose(c[:, 1], [0, -.5, .5]) True

from Python you can also use the finite differences to interpolate values (or derivatives thereof):

.. code:: python

>>> from finitediff import interpolate_by_finite_diff as ifd
>>> x = np.array([0, 1, 2])
>>> y = np.array([[2, 3, 5], [3, 4, 7], [7, 8, 9], [3, 4, 6]])
>>> xout = np.linspace(0.5, 1.5, 5)
>>> r = ifd(x, y, xout, maxorder=2)
>>> r.shape
(5, 4, 3)

see the examples/ directory for more examples.

Installation

Simplest way to install is to use the conda package manager <http://conda.pydata.org/docs/>_:

::

$ conda install -c conda-forge finitediff pytest $ python -m pytest --pyargs finitediff

tests should pass.

Manual installation

You can install ``finitediff`` by using ``pip``::

   $ python -m pip install --user finitediff

(you can skip the ``--user`` flag if you have got root permissions),
to run the tests you need ``pytest`` too::

   $ python -m pip install --user --upgrade pytest
   $ python -m pytest --pyargs finitediff


Dependencies
------------
You need either a C, C++ or a Fortran 90 compiler. On debian based linux systems you may install (all) by issuing::

    $ sudo apt-get install gfortran g++ gcc

See `setup.py <setup.py>`_ for optional (Python) dependencies.


Citing
------
The algortihm is from the following paper:

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}
    }

You may want to, in addition to the paper, cite finitediff (for e.g. reproducibility),
and you can get per-version DOIs from the zenodo archive:

.. image:: https://zenodo.org/badge/14988640.svg
   :target: https://zenodo.org/badge/latestdoi/14988640
   :alt: Zenodo DOI


Licensing
---------
The source code is Open Source and is released under the very permissive
`"simplified (2-clause) BSD license" <https://opensource.org/licenses/BSD-2-Clause>`_.
See `LICENSE <LICENSE>`_ for further details.


Author
------
Björn Ingvar Dahlgren (gmail address: bjodah). See file `AUTHORS <AUTHORS>`_ in root for a list of all authors.