tupui

"""Halton low discrepancy sequence.

This snippet implements the Halton sequence following the generalization of
a sequence of *Van der Corput* in n-dimensions.

---------------------------

MIT License

Copyright (c) 2017 Pamphile Tupui ROY

tupui

"""Discrepancy of a sample.

Compute the centered discrepancy on a given sample.
It is a measure of the uniformity of the points in the parameter space.
The lower the value is, the better the coverage of the parameter space is.

---------------------------
MIT License
Copyright (c) 2017 Pamphile Tupui ROY
Permission is hereby granted, free of charge, to any person obtaining a copy

tupui

"""Get info about Cryptocurrency wallets.

Gather information about the market and you own wallet. Using transactions
file, it also compare your investment with the available capital.

Transactions are to be stored in JSON files formated as:

{
    "2018_01_15": {
        "rate": 1.505,

tupui

"""Quantile dotplot.

Based on R code from https://github.com/mjskay/when-ish-is-my-bus/blob/master/quantile-dotplots.md

Reference:

Matthew Kay, Tara Kola, Jessica Hullman, Sean Munson. When (ish) is My Bus?
User-centered Visualizations of Uncertainty in Everyday, Mobile Predictive Systems.
CHI 2016. DOI: 10.1145/2858036.2858558

tupui

"""Proper Orthogonal Decomposition.

Demonstrate how to use it.

---------------------------

MIT License

Copyright (c) 2018 Pamphile Tupui ROY

tupui

"""Sobol' indices.

Compute Sobol' variance based sensitivity indices.
Use formulations from Saltelli2010.

Reference:

Saltelli et al. Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index,
Computer Physics Communications, 2010. DOI: 10.1016/j.cpc.2009.09.018

tupui

"""Minimum Spanning Tree.

MST is used here as a discrepancy criterion.
Comparing two different designs: the higher the mean, the better the design is
in terms of space filling.

---------------------------

MIT License

tupui

"""Cosine transformation sensitivity indices.

Using a Discrete Cosine Transformation (DCT), it is possible to compute
first order sensitivity indices.

Reference:

Plischke E., How to compute variance-based sensitivity indicators with your
spreadsheet software, Environmental Modelling & Software,
2012. DOI: 10.1016/j.envsoft.2012.03.004

tupui

r"""Visual explanation of Sobol' indices.

Sobol' indices are metrics to express sensitivity of the output from
perturbations comming from input parameters. First order indices write

.. math:: S_{x_i} = \frac{\mathbb{V}_i(Y)}{\mathbb{V}[Y]} =
          \frac{\mathbb{\mathbb{V}}[\mathbb{E}(Y|x_i)]}{\mathbb{V}[Y]}

The following is using the Ishigami function

tupui

r"""Visual explanation of Moment independent sensitivity analysis.

Moment-based method are based on the whole PDF to mitigate these
issues (Borgonovo2007). Based on the unconditional PDF, a conditional PDF per
parameter is computed. The more the conditional PDF deviates from the
unconditional PDF, the more the parameter has an impact on the quantity of
interest. The same procedure can be done using the Empirical Cumulative
Density Function (ECDF), respectively with the unconditional ECDF.
This visually shows this procedure. Bins of samples (red circles) are used to
compute a conditional PDF of the output. This PDF is compared to the