Mathematical Library for 1D and 2D Inverse Laplace Transform
This Library is able to rapidly compute an estimate of the Inverse Laplace Transform of a data-set accquired on regular or irregular grid.
It uses the Nonnegativity-constrained least squares code from J. Kim and H. Park, found in nnls.py (see details and reference therein).
It read data from Bruker 1D (fid) and 2D (ser) files
Given a a set of N experimental points En, sampling at time Tn the evolution of a damping signal, following the Laplace law:
where the Dm are sampling the Laplace axis;
it solves the Laplace problem and computes an estimate of the Laplace spectrum S, assuming the positivity of the coefficients, by minimizing the least square estimate:
It is is a direct application of nnls.py
This code solves the 2D problem equivalent to the 1D problem above. The code uses the idea from Song et al of reducing the complexity of the 2D experimental matrix. The method of truncated SVD is implmented as well as a faster approach based on random projection.
This code is part of an ongoing project.
It contains many parts not fully tested, or even non-functional.
The sequence presented in the two main entries: ILT_1D.py and ILT_2D.py is functionnal though.
This program has been develped for internal usage in CASC4DE.
There is no warranty whatsoever for this program to actually execute correctly what it is meant for.
The program was tested with python 2.7 and python 3.6.
This programs depends on the following external libraries, which should be installed
- numpy: www.numpy.org
- scipy: www.scipy.org
- bokeh: bokeh.pydata.org
- jinja2: jinja.pocoo.org
- matplotlib: matplotlib.org
It also includes here parts of other open-source softwares, namely
- SPIKE: www.bitbucket.org/Delsuc/SPIKE
- nnlsm: J. Kim and H. Park, (2011)
This code is provided in a Free Open-Source form by CASC4DE: www.casc4de.eu
All inquiries about this code should be sent to contact@casc4de.eu
This code is released under the GPLv3 license.
This program was mostly developped by
- Lionel Chiron: lionel.chiron@gmail.com / lionel.chiron@casc4de.eu
- Marc-André Delsuc: mad@delsuc.net
- Laura Duciel: laura.duciel@casc4de.eu
with the help of
- Camille Marin-Beluffi: camille.Beluffi@casc4de.eu