finitediff containts three implementations 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 (to the C versions) are also provided.
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).
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).
Generating finite difference weights is simple using C++11:
#include "finitediff_templated.hpp"
#include <vector>
#include <string>
#include <iostream>
int main(){
const unsigned max_deriv = 2;
std::vector<std::string> labels {"0th derivative", "1st derivative", "2nd derivative"};
std::vector<double> 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:
>>> 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])
Truefrom Python you can also use the finite differences to interpolate values (or derivatives thereof):
>>> 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.
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.
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
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.
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:
The source code is Open Source and is released under the very permissive "simplified (2-clause) BSD license". See LICENSE for further details.
Björn Ingvar Dahlgren (gmail address: bjodah). See file AUTHORS in root for a list of all authors.