Vladimir-Kryzhniy/inversion-of-real-valued-Laplace-transforms

inversion-of-real-valued-Laplace-transforms

Implementation of inversion of real valued Laplace transforms [1,2].

See InverLT.ipynb for more details

References:

1. Kryzhniy V. V. On regularization method for numerical inversion of the Laplace transforms computable at any point on the real axis. Journal of Inverse and Ill-Posed Problems,18(4), 2010
2. Kryzhniy V. V. Numerical inversion of the Laplace transform: Analysis via regularized analytic continuation. Inverse Problems 22, 2006
3. H. Bateman, A. Erdelyi, Higher Transcendental Functions, Volume 2
4. H. Bateman, A. Erdelyi, Tables of Integral Transforms, Volume 1
5. W.H.Press at al, Numerical Recipes, any edition

''' Invert a Laplace transforms computable at any point on the real axis.
Input parameters:
image - a function that comtutes a Laplace transform at any p > 0;
t - a numpy array of points to compute inverse Laplace transform, t > 0;
Optional parameters (recommended):
digits - input precision; the number of correct digits in Laplace transform
pw - a power of asymptotic of F(p) ~ 1 / p^pw as p -> 0
pw = np.inf when p^pw / F(p) -> 0 for any pw;
Method's free parameters (a, alpha, r)
1. Invert a Laplace transform F1 using information input precision and asymptotic of F(p) as p -> 0
ret= iltinvert(F1,t_array,digits1, pw1)
inverse = ret[0]
2. Invert a Laplace transform F1 using known parameters a, alpha, r:
ilt = InvertLT()
ret= ilt.invert(F1,t_array,params = (a,alpha,r))
inverse = ret[0]
3. No additional information is known. Program attepmts to compute appropriate papameters
by solving a minimization problem and using a default value as a starting point.
ret= ilt.invert(F1,t_array)
inverse = ret[0]
'''