Gaver-Wynn-Rho Algorithm
------------------------
This is a Python reproduction of the Mathematica package that provides the GWR
function, ``NumericalLaplaceInversion.m``.
https://library.wolfram.com/infocenter/MathSource/4738/
This package provides only one function: ``gwr``. The function calculates the
value of the inverse of a Laplace transform at a specified time value,
``Sequence`` of time values, or numpy array of time values.
The Laplace transform should be provided as a function that uses the ``mpmath``
library for a scalar value of the Laplace parameter. The ``math`` library and
``numpy`` functions do not support multiprecision math and will return invalid
results if they are used.
Simple Example
--------------
.. code-block:: python
>>> import math
>>> from gwr_inversion import gwr
>>> from mpmath import mp
>>> def lap_ln_fn(s: float):
... # log function
... return -mp.log(s) / s - 0.577216 / s
>>> gwr(lap_log_fn, time=5.0, M=32)
mpf('1.6094375773356333')
>>> math.log(5.0)
1.6094379124341003
See the notebooks in ``test\`` for other use examples.
The method is described in: Valkó, P.P., and Abate J. 2002. Comparison of
Sequence Accelerators for the Gaver Method of Numerical Laplace Transform
Inversion. *Computers and Mathematics with Application* **48** (3): 629–636.
https://doi.org/10.1016/j.camwa.2002.10.017.
More information on multi-precision inversion can be found in: Valkó, P.P.and
Vajda, S. 2002. Inversion of Noise-Free Laplace Transforms: Towards a
Standardized Set of Test Problems. *Inverse Problems in Engineering* **10** (5):
467-483. https://doi.org/10.1080/10682760290004294.
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"description": "Gaver-Wynn-Rho Algorithm\n------------------------\n\nThis is a Python reproduction of the Mathematica package that provides the GWR\nfunction, ``NumericalLaplaceInversion.m``.\n\nhttps://library.wolfram.com/infocenter/MathSource/4738/\n\nThis package provides only one function: ``gwr``. The function calculates the\nvalue of the inverse of a Laplace transform at a specified time value,\n``Sequence`` of time values, or numpy array of time values.\n\nThe Laplace transform should be provided as a function that uses the ``mpmath``\nlibrary for a scalar value of the Laplace parameter. The ``math`` library and\n``numpy`` functions do not support multiprecision math and will return invalid\nresults if they are used.\n\nSimple Example\n--------------\n\n.. code-block:: python\n\n >>> import math\n >>> from gwr_inversion import gwr\n >>> from mpmath import mp\n\n >>> def lap_ln_fn(s: float):\n ... # log function\n ... return -mp.log(s) / s - 0.577216 / s\n\n >>> gwr(lap_log_fn, time=5.0, M=32)\n mpf('1.6094375773356333')\n\n >>> math.log(5.0)\n 1.6094379124341003\n\n\nSee the notebooks in ``test\\`` for other use examples.\n\nThe method is described in: Valk\u00c3\u00b3, P.P., and Abate J. 2002. Comparison of\nSequence Accelerators for the Gaver Method of Numerical Laplace Transform\nInversion. *Computers and Mathematics with Application* **48** (3): 629\u00e2\u20ac\u201c636.\nhttps://doi.org/10.1016/j.camwa.2002.10.017.\n\nMore information on multi-precision inversion can be found in: Valk\u00c3\u00b3, P.P.and\nVajda, S. 2002. Inversion of Noise-Free Laplace Transforms: Towards a\nStandardized Set of Test Problems. *Inverse Problems in Engineering* **10** (5):\n467-483. https://doi.org/10.1080/10682760290004294.\n\n\n",
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