Description:
hankel 1.2.2
Perform simple and accurate Hankel transformations using the method of
Ogata 2005.
Hankel transforms and integrals are commonplace in any area in which
Fourier Transforms are required over fields that
are radially symmetric (see
Wikipedia for a
thorough description).
They involve integrating an arbitrary function multiplied by a Bessel
function of arbitrary order (of the first kind).
Typical integration schemes often fail because of the highly
oscillatory nature of the transform. Ogata’s
quadrature method used in this package provides a fast and accurate
way of performing the integration based on
locating the zeros of the Bessel function.
Features
Accurate and fast solutions to many Hankel integrals
Easy to use and re-use
Arbitrary order transforms
Built-in support for radially symmetric Fourier Transforms
Thoroughly tested.
only Python 3 compatible.
Quick links
Documentation: https://hankel.readthedocs.io
Quickstart+Description: Getting Started
Installation
Either clone the repository and install locally (best for developer installs):
$ git clone https://github.com/steven-murray/hankel.git
$ cd hankel/
$ pip install -U .
Or install from PyPI:
$ pip install hankel
Or install with conda:
$ conda install -c conda-forge hankel
The only dependencies are numpy,
scipy and mpmath.
These will be installed automatically if they are not already installed.
Dependencies required purely for development (testing and linting etc.) can be installed
via the optional extra pip install hankel[dev]. If using conda, they can still be
installed via pip: pip install -r requirements_dev.txt.
For instructions on testing hankel or any other development- or contribution-related
issues, see the contributing guide.
Acknowledging
If you find hankel useful in your research, please cite
S. G. Murray and F. J. Poulin, “hankel: A Python library for performing simple and
accurate Hankel transformations”, Journal of Open Source Software,
4(37), 1397, https://doi.org/10.21105/joss.01397
Also consider starring this repository!
References
Based on the algorithm provided in
H. Ogata, A Numerical Integration Formula Based on the Bessel
Functions, Publications of the Research Institute for Mathematical
Sciences, vol. 41, no. 4, pp. 949-970, 2005. DOI: 10.2977/prims/1145474602
Also draws inspiration from
Fast Edge-corrected Measurement of the Two-Point Correlation
Function and the Power Spectrum Szapudi, Istvan; Pan, Jun; Prunet,
Simon; Budavari, Tamas (2005) The Astrophysical Journal vol. 631 (1)
DOI: 10.1086/496971
License
For personal and professional use. You cannot resell or redistribute these repositories in their original state.
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