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        "author": "Bj\u00f6rn Dahlgren",
        "author_email": "bjodah@gmail.com",
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        "classifiers": [
            "Development Status :: 4 - Beta",
            "License :: OSI Approved :: BSD License",
            "Operating System :: OS Independent",
            "Topic :: Scientific/Engineering",
            "Topic :: Scientific/Engineering :: Mathematics"
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        "description": "finitediff\n==========\n.. image:: http://hera.physchem.kth.se:9090/api/badges/bjodah/finitediff/status.svg\n   :target: http://hera.physchem.kth.se:9090/bjodah/finitediff\n   :alt: Build status\n.. image:: https://img.shields.io/pypi/v/finitediff.svg\n   :target: https://pypi.python.org/pypi/finitediff\n   :alt: PyPI version\n.. image:: https://zenodo.org/badge/14988640.svg\n   :target: https://zenodo.org/badge/latestdoi/14988640\n   :alt: Zenodo DOI\n.. image:: https://img.shields.io/badge/python-2.7,3.4,3.5-blue.svg\n   :target: https://www.python.org/\n   :alt: Python version\n.. image:: https://img.shields.io/pypi/l/finitediff.svg\n   :target: https://github.com/bjodah/finitediff/blob/master/LICENSE\n   :alt: License\n.. image:: http://hera.physchem.kth.se/~finitediff/branches/master/htmlcov/coverage.svg\n   :target: http://hera.physchem.kth.se/~finitediff/branches/master/htmlcov\n   :alt: coverage\n\n``finitediff`` containts three implementations of Begnt Fornberg's\nformulae for generation of finite difference weights on aribtrarily\nspaced one dimensional grids:\n\n- `C89 <src/finitediff_c.c>`_\n- `Fortran 90 <src/finitediff_fort.f90>`_\n- `C++ <finitediff/include/finitediff_templated.hpp>`_\n\nThe finite difference weights can be\nused for optimized inter-/extrapolation data series for up to\narbitrary derivative order. Python_ bindings (to the C versions) are also provided.\n\n.. _Python: https://www.python.org\n.. _finitediff: https://github.com/bjodah/finitediff\n\n\nCapabilities\n------------\n``finitediff`` currently provides callbacks for estimation of derivatives\nor interpolation either at a single point or over an array (available\nfrom the Python bindings).\n\nThe user may also manually generate the corresponding weights. (see\n``calculate_weights``)\n\nFinitediff can be conditionally compiled to make ``finitediff_interpolate_by_finite_diff``\nmultithreaded. Then the number of threads used is set through the environment variable\n``FINITEDIFF_NUM_THREADS`` (or ``OMP_NUM_THREADS``).\n\n\nDocumentation\n-------------\nAutogenerated API documentation for latest stable release is found here:\n`<https://bjodah.github.io/finitediff/latest>`_\n(and the development version for the current master branch is found here:\n`<http://hera.physchem.kth.se/~finitediff/branches/master/html>`_).\n\nExamples\n--------\nGenerating finite difference weights is simple using C++11:\n\n.. code:: C++\n\n   #include \"finitediff_templated.hpp\"\n   #include <vector>\n   #include <string>\n   #include <iostream>\n\n   int main(){\n       const unsigned max_deriv = 2;\n       std::vector<std::string> labels {\"0th derivative\", \"1st derivative\", \"2nd derivative\"};\n       std::vector<double> x {0, 1, -1, 2, -2};  // Fourth order of accuracy\n       auto coeffs = finitediff::generate_weights(x, max_deriv);\n       for (unsigned deriv_i = 0; deriv_i <= max_deriv; deriv_i++){\n           std::cout << labels[deriv_i] << \": \";\n           for (unsigned idx = 0; idx < x.size(); idx++){\n               std::cout << coeffs[deriv_i*x.size() + idx] << \" \";\n           }\n           std::cout << std::endl;\n       }\n   }\n\n\n::\n\n   $ cd examples/\n   $ g++ -std=c++11 demo.cpp -I../include\n   $ ./a.out\n   Zeroth derivative (interpolation): 1 -0 0 0 -0\n   First derivative: -0 0.666667 -0.666667 -0.0833333 0.0833333\n   Second derivative: -2.5 1.33333 1.33333 -0.0833333 -0.0833333\n\n\nand of course using the python bindings:\n\n.. code:: python\n\n   >>> from finitediff import get_weights\n   >>> import numpy as np\n   >>> c = get_weights(np.array([0, -1., 1]), 0, maxorder=1)\n   >>> np.allclose(c[:, 1], [0, -.5, .5])\n   True\n\n\nfrom Python you can also use the finite differences to interpolate\nvalues (or derivatives thereof):\n\n.. code:: python\n\n    >>> from finitediff import interpolate_by_finite_diff as ifd\n    >>> x = np.array([0, 1, 2])\n    >>> y = np.array([[2, 3, 5], [3, 4, 7], [7, 8, 9], [3, 4, 6]])\n    >>> xout = np.linspace(0.5, 1.5, 5)\n    >>> r = ifd(x, y, xout, maxorder=2)\n    >>> r.shape\n    (5, 4, 3)\n\n\nsee the ``examples/`` directory for more examples.\n\nInstallation\n------------\nSimplest way to install is to use the `conda package manager <http://conda.pydata.org/docs/>`_:\n\n::\n\n   $ conda install -c conda-forge finitediff pytest\n   $ python -m pytest --pyargs finitediff\n\ntests should pass.\n\nManual installation\n~~~~~~~~~~~~~~~~~~~\nYou can install ``finitediff`` by using ``pip``::\n\n   $ python -m pip install --user finitediff\n\n(you can skip the ``--user`` flag if you have got root permissions),\nto run the tests you need ``pytest`` too::\n\n   $ python -m pip install --user --upgrade pytest\n   $ python -m pytest --pyargs finitediff\n\n\nDependencies\n------------\nYou need either a C, C++ or a Fortran 90 compiler. On debian based linux systems you may install (all) by issuing::\n\n    $ sudo apt-get install gfortran g++ gcc\n\nSee `setup.py <setup.py>`_ for optional (Python) dependencies.\n\n\nCiting\n------\nThe algortihm is a rewrite of:\n\nhttp://dx.doi.org/10.1137/S0036144596322507\n\n::\n\n    @article{fornberg_classroom_1998,\n      title={Classroom note: Calculation of weights in finite difference formulas},\n      author={Fornberg, Bengt},\n      journal={SIAM review},\n      volume={40},\n      number={3},\n      pages={685--691},\n      year={1998},\n      publisher={SIAM}\n      doi={10.1137/S0036144596322507}\n    }\n\n\nWhich references an article by the same author:\n\nhttp://dx.doi.org/10.1090/S0025-5718-1988-0935077-0\n\n::\n\n    @article{fornberg_generation_1988,\n      title={Generation of finite difference formulas on arbitrarily spaced grids},\n      author={Fornberg, Bengt},\n      journal={Mathematics of computation},\n      volume={51},\n      number={184},\n      pages={699--706},\n      year={1988}\n      doi={10.1090/S0025-5718-1988-0935077-0}\n    }\n\nYou may want to, in addition to the paper, cite finitediff (for e.g. reproducibility),\nand you can get per-version DOIs from the zenodo archive:\n\n.. image:: https://zenodo.org/badge/14988640.svg\n   :target: https://zenodo.org/badge/latestdoi/14988640\n   :alt: Zenodo DOI\n\n\nLicensing\n---------\nThe source code is Open Source and is released under the very permissive\n`\"simplified (2-clause) BSD license\" <https://opensource.org/licenses/BSD-2-Clause>`_.\nSee `LICENSE <LICENSE>`_ for further details.\n\n\nAuthor\n------\nBj\u00f6rn Ingvar Dahlgren, contact:\n - gmail address: bjodah\n - kth.se address: bda\n\nSee file `AUTHORS <AUTHORS>`_ in root for a list of all authors.",
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