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72 lines
2.0 KiB
ReStructuredText
72 lines
2.0 KiB
ReStructuredText
Numerical inverse Laplace transform
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-----------------------------------
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One-step algorithm (``invertlaplace``)
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......................................
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.. autofunction:: mpmath.invertlaplace
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Specific algorithms
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...................
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Fixed Talbot algorithm
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~~~~~~~~~~~~~~~~~~~~~~
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.. autoclass:: mpmath.calculus.inverselaplace.FixedTalbot
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:members:
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Gaver-Stehfest algorithm
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~~~~~~~~~~~~~~~~~~~~~~~~
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.. autoclass:: mpmath.calculus.inverselaplace.Stehfest
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:members:
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de Hoog, Knight & Stokes algorithm
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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.. autoclass:: mpmath.calculus.inverselaplace.deHoog
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:members:
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Cohen acceleration algorithm
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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.. autoclass:: mpmath.calculus.inverselaplace.Cohen
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:members:
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Manual approach
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...............
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It is possible and sometimes beneficial to re-create some of the
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functionality in ``invertlaplace``. This could be used to compute the
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Laplace-space function evaluations in a different way. For example,
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the Laplace-space function evaluations could be the result of a
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quadrature or sum, solution to a system of ordinary differential
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equations, or possibly computed in parallel from some external library
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or function call.
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A trivial example showing the process (which could be implemented
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using the existing interface):
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>>> from mpmath import calculus, convert, exp, mp
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>>> myTalbot = calculus.inverselaplace.FixedTalbot(mp)
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>>> t = convert(0.25)
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>>> myTalbot.calc_laplace_parameter(t)
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>>> fp = lambda p: 1/(p + 1) - 1/(p + 1000)
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>>> ft = lambda t: exp(-t) - exp(-1000*t)
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>>> fpvec = [fp(p) for p in myTalbot.p]
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>>> ft(t)-myTalbot.calc_time_domain_solution(fpvec,t,manual_prec=True)
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mpf('1.92830017952889006175687218e-21')
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This manual approach is also useful to look at the Laplace parameter,
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order, or working precision which were computed.
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>>> myTalbot.degree
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34
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Credit
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......
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The numerical inverse Laplace transform functionality was contributed
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to mpmath by Kristopher L. Kuhlman in 2017. The Cohen method was contributed
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to mpmath by Guillermo Navas-Palencia in 2022.
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