Metadata-Version: 1.1
Name: finitediff
Version: 0.4.0
Summary: Finite difference weights for any derivative order on arbitrarily spaced grids.
Home-page: https://github.com/bjodah/finitediff
Author: Björn Dahlgren
Author-email: bjodah@gmail.com
License: BSD
Description-Content-Type: UNKNOWN
Description: finitediff
        ==========
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        ``finitediff`` containts two implementations (`Fortran 90
        <src/finitediff_fort.f90>`_ and `C++ <finitediff/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
        ``calculate_weights``)
        
        
        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 <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:
        
        .. 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
        
        
        see the ``examples/`` directory for more examples.
        
        Installation
        ------------
        The simplest way to install finitediff is to use
        `conda package manager <http://conda.pydata.org/docs/>`_:
        
        ::
        
           $ conda install -c bjodah finitediff pytest
        
        alternatively, you may also use `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++ or a Fortran 90 compiler. On debian based linux systems you may install one by issuing::
        
            $ sudo apt-get install gfortran g++
        
        See `setup.py <setup.py>`_ for optional (Python) dependencies.
        
        Notes
        =====
        There is a git subtree under finitediff, update through::
        
            git subtree pull --prefix finitediff/external/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 subtree add --prefix finitediff/external/newton_interval git://github.com/bjodah/newton_interval master
        
        
        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
        =======
        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.
        
        
        Authors
        =======
        See file `AUTHORS <AUTHORS>`_ in root.
        
Keywords: finite-difference,taylor series,extrapolation
Platform: UNKNOWN
Classifier: Development Status :: 4 - Beta
Classifier: License :: OSI Approved :: BSD License
Classifier: Operating System :: OS Independent
Classifier: Topic :: Scientific/Engineering
Classifier: Topic :: Scientific/Engineering :: Mathematics
