Dimension-Adaptive Leja Interpolation (DALI)
(alternatively: DArmstadt's Leja Interpolation)

Adjusted to Python3 
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Development/maintenance: Dimitrios Loukrezis ([email protected])
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DALI is a Python software for multivariate approximation, using a 
dimension-adaptive stochastic collocation algorithm based on univariate Leja 
interpolation rules. The software has been developed during my PhD studies at 
the Institute for Theory of Electromagnetic Fields (TEMF) of TU Darmstadt, under 
the supervision of Prof. Dr.-Ing. Herbert De Gersem (TU Darmstadt) and 
Jun.-Prof. Dr.-Ing. Ulrich Römer (TU Braunschweig).

Extension (2019.11.19): An approach to compute Polynomial Chaos Expansions via
Leja interpolation has been added, either directly or using a basis transform. 
For the latter, check the test folder.
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The DALI software has been developed and used for the studies presented in the 
following papers:

@article{loukrezis2020approximation,
author = {{Loukrezis}, Dimitrios and {De Gersem}, Herbert},
title = "{Approximation and Uncertainty Quantification of Systems with Arbitrary 
          Parameter Distributions using Weighted Leja Interpolation}",
journal = {Algorithms},
year = "2020",
issue = "13",
number = "3",
doi = {10.3390/a13030051},
}

@article{loukrezis2019assessing,
author  = {Dimitrios Loukrezis and Ulrich  Römer and Herbert  De Gersem},
title   = {Assessing the performance of Leja and Clenshaw-Curtis collocation for 
           computational electromagnetics with random input data},
journal = {International Journal for Uncertainty Quantification},
issn    = {2152-5080},
year    = {2019},
volume  = {9},
number  = {1},
pages   = {33--57}
}

@article{loukrezis2019interpolPCE,
author = {{Loukrezis}, Dimitrios and {De Gersem}, Herbert},
title = "{Adaptive Sparse Polynomial Chaos Expansions via Leja Interpolation}",
journal = {arXiv e-prints},
year = "2019",
eprint={1911.08312}
}

@article{georg2018uncertainty,
author = {{Georg}, Niklas and {Loukrezis}, Dimitrios and {R{\"o}mer}, Ulrich and 
          {Sch{\"o}ps}, Sebastian},
title = "{Uncertainty quantification for an optical grating coupler with an 
          adjoint-based Leja adaptive collocation method}",
journal = {arXiv e-prints},
year = "2018",
eid = {arXiv:1807.07485},
}

In accordance to ethical scientific practice, we kindly ask you to cite at least 
one of these works, in case you use DALI for your own research.
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The present software and the related examples rely partially on the Chaospy 
Python toolbox (https://github.com/jonathf/chaospy). 

The extension to Polynomial Chaos Expansions makes use of the OpenTURNS 
C++/Python library (http://openturns.github.io/openturns/master/index.html).

Please note that using DALI implies that the user respects the corresponding 
copyright notices, licenses, and disclaimers of warranty of the aforementioned 
software libraries as well.  
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