numcertain
==========
|code_ci| |docs_ci| |coverage| |pypi_version| |license|
This package provides a python and numpy data type (`uncertain`) which implements a
floating point value with quantified uncertainity, allowing for forward uncertainity
propagation of uncorrelated values.
============== ==============================================
PyPI ``pip install numcertain``
Source code https://github.com/garryod/numcertain
Documentation https://garryod.github.io/numcertain
Releases https://github.com/garryod/numcertain/releases
============== ==============================================
Aritmatic Examples
------------------
A brief example of arithmatic with the provided uncertain data type is presented below:
.. code:: python
a = uncertain(42.0, 5.0)
b = uncertain(36, 12)
print(a + b)
print(a - b)
print(a * b)
print(a / b)
.. code::
>> 78.0±13.0
>> 6.0±13.0
>> 1512.0±535.1784749034662
>> 1.1666666666666667±0.41294635409218067
A brief example of arithmatic with numpy arrays with the uncertain dtype is presented
below:
.. code:: python
a = array([uncertain(5.0, 3.0), uncertain(7.0, 6.0)])
b = array([uncertain(12.0, 4.0), uncertain(24.0, 8.0)])
print(a + b)
print(a - b)
print(a * b)
print(a / b)
.. code::
>> [uncertain(17.0, 5.0) uncertain(31.0, 10.0)]
>> [uncertain(-7.0, 5.0) uncertain(-17.0, 10.0)]
>> [uncertain(60.0, 41.182520563948) uncertain(168.0, 154.50566332662373)]
>> [uncertain(0.4166666666666667, 0.2859897261385278) uncertain(0.2916666666666667, 0.268238998830944)]
Alternative Methods
-------------------
In order to accurately propagate uncertainties of related values the derivative of the
computed expectation must be known with respect to expectations it is comprised of.
Automatic differentiation (autodiff) provides a mechanism for computing the derivative
of arbitrary functions with respect to their components by exploiting the fact that all
codes, regardless of complexity, are reduced to a sequence of primative arithmetic
operations during execution for which the derivatives are known, by applying the chain
rule the overall derivative can be determined automatically.
The python package `Uncertainties`_ provides a python data type which performs autodiff
to propagate the corresponding uncertainity, unforunately due to Implementation as a
python object the library is non-performant when used for array math.
Whilst `Propagation of Uncertainty with autodiff`_, describes the use of autodiff
provided by the python package `JAX`_ in propagating uncertainities for array math.
.. _Uncertainties: https://uncertainties-python-package.readthedocs.io/en/latest/
.. _Propagation of Uncertainty with autodiff: http://theoryandpractice.org/intro-exp-phys-book/error-propagation/error_propagation_with_jax.html
.. _JAX: https://jax.readthedocs.io/en/latest/
.. |code_ci| image:: https://github.com/garryod/numcertain/workflows/Code%20CI/badge.svg?branch=master
:target: https://github.com/garryod/numcertain/actions?query=workflow%3A%22Code+CI%22
:alt: Code CI
.. |docs_ci| image:: https://github.com/garryod/numcertain/workflows/Docs%20CI/badge.svg?branch=master
:target: https://github.com/garryod/numcertain/actions?query=workflow%3A%22Docs+CI%22
:alt: Docs CI
.. |coverage| image:: https://codecov.io/gh/garryod/numcertain/branch/master/graph/badge.svg
:target: https://codecov.io/gh/garryod/numcertain
:alt: Test Coverage
.. |pypi_version| image:: https://img.shields.io/pypi/v/numcertain.svg
:target: https://pypi.org/project/numcertain
:alt: Latest PyPI version
.. |license| image:: https://img.shields.io/badge/License-Apache%202.0-blue.svg
:target: https://opensource.org/licenses/Apache-2.0
:alt: Apache License
..
Anything below this line is used when viewing README.rst and will be replaced
when included in index.rst
See https://garryod.github.io/numcertain for more detailed documentation.
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"description": "numcertain\n==========\n\n|code_ci| |docs_ci| |coverage| |pypi_version| |license|\n\nThis package provides a python and numpy data type (`uncertain`) which implements a\nfloating point value with quantified uncertainity, allowing for forward uncertainity\npropagation of uncorrelated values.\n\n============== ==============================================\nPyPI ``pip install numcertain``\nSource code https://github.com/garryod/numcertain\nDocumentation https://garryod.github.io/numcertain\nReleases https://github.com/garryod/numcertain/releases\n============== ==============================================\n\nAritmatic Examples\n------------------\n\nA brief example of arithmatic with the provided uncertain data type is presented below:\n\n.. code:: python\n\n a = uncertain(42.0, 5.0)\n b = uncertain(36, 12)\n\n print(a + b)\n print(a - b)\n print(a * b)\n print(a / b)\n\n.. code::\n\n >> 78.0\u00b113.0\n >> 6.0\u00b113.0\n >> 1512.0\u00b1535.1784749034662\n >> 1.1666666666666667\u00b10.41294635409218067\n\nA brief example of arithmatic with numpy arrays with the uncertain dtype is presented\nbelow:\n\n.. code:: python\n\n a = array([uncertain(5.0, 3.0), uncertain(7.0, 6.0)])\n b = array([uncertain(12.0, 4.0), uncertain(24.0, 8.0)])\n\n print(a + b)\n print(a - b)\n print(a * b)\n print(a / b)\n\n.. code::\n\n >> [uncertain(17.0, 5.0) uncertain(31.0, 10.0)]\n >> [uncertain(-7.0, 5.0) uncertain(-17.0, 10.0)]\n >> [uncertain(60.0, 41.182520563948) uncertain(168.0, 154.50566332662373)]\n >> [uncertain(0.4166666666666667, 0.2859897261385278) uncertain(0.2916666666666667, 0.268238998830944)]\n\nAlternative Methods\n-------------------\n\nIn order to accurately propagate uncertainties of related values the derivative of the\ncomputed expectation must be known with respect to expectations it is comprised of.\nAutomatic differentiation (autodiff) provides a mechanism for computing the derivative\nof arbitrary functions with respect to their components by exploiting the fact that all\ncodes, regardless of complexity, are reduced to a sequence of primative arithmetic\noperations during execution for which the derivatives are known, by applying the chain\nrule the overall derivative can be determined automatically.\n\nThe python package `Uncertainties`_ provides a python data type which performs autodiff\nto propagate the corresponding uncertainity, unforunately due to Implementation as a\npython object the library is non-performant when used for array math.\n\nWhilst `Propagation of Uncertainty with autodiff`_, describes the use of autodiff\nprovided by the python package `JAX`_ in propagating uncertainities for array math.\n\n.. _Uncertainties: https://uncertainties-python-package.readthedocs.io/en/latest/\n\n.. _Propagation of Uncertainty with autodiff: http://theoryandpractice.org/intro-exp-phys-book/error-propagation/error_propagation_with_jax.html\n\n.. _JAX: https://jax.readthedocs.io/en/latest/\n\n.. |code_ci| image:: https://github.com/garryod/numcertain/workflows/Code%20CI/badge.svg?branch=master\n :target: https://github.com/garryod/numcertain/actions?query=workflow%3A%22Code+CI%22\n :alt: Code CI\n\n.. |docs_ci| image:: https://github.com/garryod/numcertain/workflows/Docs%20CI/badge.svg?branch=master\n :target: https://github.com/garryod/numcertain/actions?query=workflow%3A%22Docs+CI%22\n :alt: Docs CI\n\n.. |coverage| image:: https://codecov.io/gh/garryod/numcertain/branch/master/graph/badge.svg\n :target: https://codecov.io/gh/garryod/numcertain\n :alt: Test Coverage\n\n.. |pypi_version| image:: https://img.shields.io/pypi/v/numcertain.svg\n :target: https://pypi.org/project/numcertain\n :alt: Latest PyPI version\n\n.. |license| image:: https://img.shields.io/badge/License-Apache%202.0-blue.svg\n :target: https://opensource.org/licenses/Apache-2.0\n :alt: Apache License\n\n..\n Anything below this line is used when viewing README.rst and will be replaced\n when included in index.rst\n\nSee https://garryod.github.io/numcertain for more detailed documentation.\n",
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