ttim.invlapnumba#

Functions#

invlap(t, tmax, fp, M[, alpha, tol])

Inverse Laplace tansform with algorithm of De Hoog, Knight and Stokes.

compute_laplace_parameters_numba(tmax[, M, alpha, tol])

invlaptest()

invlapcomp(time, pot, npint, M, tintervals, enumber, ...)

Compute time domain solution for given laplace domain solution.

invlapgen(time, pot, M, tintervals, tstart, ebc)

Compute time domain solution for given Laplace domain solution.

Module Contents#

ttim.invlapnumba.invlap(t, tmax, fp, M, alpha=1e-10, tol=1e-09)[source]#

Inverse Laplace tansform with algorithm of De Hoog, Knight and Stokes.

Parameters:

  • t (array) – times for which inverse is computed

  • tmax (float) – maximum time

  • fp (complex array) – Laplace transformed solution

  • M (integer) – number of terms (number of values of fp)

  • alpha (is the real part of the rightmost pole or singularity, which) – is chosen based on the desired accuracy (assuming the rightmost singularity is 0), and tol=10α is the desired tolerance

Returns:

  • result (array) – time domain solution for specified times

  • Reference

  • ———

  • de Hoog, F., J. Knight, A. Stokes (1982). An improved method for

  • numerical inversion of Laplace transforms. SIAM Journal of Scientific

  • and Statistical Computing 3 (357-366, http://dx.doi.org/10.1137/0903022)

  • https (//bitbucket.org/klkuhlm/invlap/src/default/invlap.py)

ttim.invlapnumba.compute_laplace_parameters_numba(tmax, M=20, alpha=1e-10, tol=1e-09)[source]#
ttim.invlapnumba.invlaptest()[source]#
ttim.invlapnumba.invlapcomp(time, pot, npint, M, tintervals, enumber, etstart, ebc, nlayers)[source]#

Compute time domain solution for given laplace domain solution.

Parameters:

  • time (array, must be ordered) – times for which time domain solution is computed, must start at 0

  • pot (array of laplace domain solution conform the ttim shape)

  • npint (int) – number of p values per interval (=2M + 1)

  • M (int) – order of the approximation

  • tintervals (time intervals)

  • enumber (array with number of element)

  • etstart (array with starting time of bc in element)

  • ebc (array with boundary condition value of element)

  • nlayers (integer or None (default)) – number of layers

Notes

enumber, etstart, and ebc are used because numba cannot deal with a list of arrays of different lengths (makes sense, actually)

Returns:

  • pot[naq, ntimes] if layers=None,

  • otherwise pot[len(layers) ,ntimes]

  • t must be ordered

ttim.invlapnumba.invlapgen(time, pot, M, tintervals, tstart, ebc)[source]#

Compute time domain solution for given Laplace domain solution.

Parameters:

  • time (array, must be ordered) – times for which time domain solution is computed, must start at 0

  • pot (1D array of laplace domain solution of length nint * (2M + 1))

  • M (int order of the approximation (i.e., (2M + 1) p values per interval))

  • tintervals (1D array of time intervals, length nint + 1)

  • tstart (1D array with starting times of bc in element, length nstart)

  • ebc (1D array with change in boundary condition value, length nstart)

Notes

ebc is the difference with the previous value

Return type:

rv[ntimes]