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Description:
gwrinversion 1.0.1
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
>>> 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.
License
For personal and professional use. You cannot resell or redistribute these repositories in their original state.
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