https://github.com/bjodah/finitediff
Finite difference weights for any derivative order on arbitrarily spaced grids. C89, C++ and Fortran 90 implementations with Python bindings.
https://github.com/bjodah/finitediff
finite-differences grid method-of-lines stencil
Last synced: 6 months ago
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Finite difference weights for any derivative order on arbitrarily spaced grids. C89, C++ and Fortran 90 implementations with Python bindings.
- Host: GitHub
- URL: https://github.com/bjodah/finitediff
- Owner: bjodah
- License: bsd-2-clause
- Created: 2013-12-06T17:10:24.000Z (almost 12 years ago)
- Default Branch: master
- Last Pushed: 2024-05-23T14:35:03.000Z (over 1 year ago)
- Last Synced: 2025-04-28T11:16:46.878Z (6 months ago)
- Topics: finite-differences, grid, method-of-lines, stencil
- Language: Python
- Homepage:
- Size: 2.84 MB
- Stars: 40
- Watchers: 5
- Forks: 5
- Open Issues: 1
-
Metadata Files:
- Readme: README.rst
- Changelog: CHANGES.rst
- License: LICENSE
- Authors: AUTHORS
Awesome Lists containing this project
README
finitediff
==========
.. image:: http://hackspett.bjodah.se/api/badges/12/status.svg
:target: http://hackspett.bjodah.se/repos/12
:alt: Build status
.. image:: https://img.shields.io/pypi/v/finitediff.svg
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:alt: PyPI version
.. image:: https://zenodo.org/badge/14988640.svg
:target: https://zenodo.org/badge/latestdoi/14988640
:alt: Zenodo DOI
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: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 `_
- `Fortran 90 `_
- `C++ `_
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:
``_
(and the development version for the current master branch is found here:
``_).
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::vector 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 `_:
::
$ 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 `_ 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" `_.
See `LICENSE `_ for further details.
Author
------
Björn Ingvar Dahlgren (gmail address: bjodah). See file `AUTHORS `_ in root for a list of all authors.