Numerical inverse Laplace transform ----------------------------------- One-step algorithm (``invertlaplace``) ...................................... .. autofunction:: mpmath.invertlaplace Specific algorithms ................... Fixed Talbot algorithm ~~~~~~~~~~~~~~~~~~~~~~ .. autoclass:: mpmath.calculus.inverselaplace.FixedTalbot :members: Gaver-Stehfest algorithm ~~~~~~~~~~~~~~~~~~~~~~~~ .. autoclass:: mpmath.calculus.inverselaplace.Stehfest :members: de Hoog, Knight & Stokes algorithm ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. autoclass:: mpmath.calculus.inverselaplace.deHoog :members: Manual approach ............... It is possible and sometimes beneficial to re-create some of the functionality in ``invertlaplace``. This could be used to compute the Laplace-space function evaluations in a different way. For example, the Laplace-space function evaluations could be the result of a quadrature or sum, solution to a system of ordinary differential equations, or possibly computed in parallel from some external library or function call. A trivial example showing the process (which could be implemented using the existing interface): >>> from mpmath import * >>> myTalbot = calculus.inverselaplace.FixedTalbot(mp) >>> t = convert(0.25) >>> myTalbot.calc_laplace_parameter(t) >>> fp = lambda p: 1/(p + 1) - 1/(p + 1000) >>> ft = lambda t: exp(-t) - exp(-1000*t) >>> fpvec = [fp(p) for p in myTalbot.p] >>> ft(t)-myTalbot.calc_time_domain_solution(fpvec,t,manual_prec=True) mpf('1.928300179528890061756872185e-21') This manual approach is also useful to look at the Laplace parameter, order, or working precision which were computed. >>> myTalbot.degree 34 Credit ...... The numerical inverse Laplace transform functionality was contributed to mpmath by Kristopher L. Kuhlman in 2017.