Some undone task that could be be useful to add. Any help is welcome.
Please create a Github issue if you want to claim a task.
Difficulty: easy
Quadrature works best when done on the unscaled random variables. In other
words, instead of making quadrature directly on e.g.
chaospy.Uniform(1000, 1001), create the quadrature on the variable
chaospy.Uniform(-1, 1) and scale the samples to the correct interval
afterwards. This is a much more accurate approach than what is currently
implemented.
In practice there are only three edgecases that needs to be dealt with:
chaospy.Add, chaospy.Mul and chaospy.J. All three can be
intercepted in the chaospy.quadrature.frontend:generate_quadrature with
isinstance(dist, chaospy.{Add,Mul,J}).
Difficulty: easy
Canonical orthogonal polynomial expansion from literature usually come in two
variants: Physisist and Probabilist variant. The difference between the two is
usually only a constant. See e.g.
`https://en.wikipedia.org/wiki/Hermite_polynomials`_.
In chaospy the latter is supported.
However, there isn't a good reason not to support both. To do so, one could e.g. add an extra method to each distribution that returns the constant multiplier at each order. This could by default have the form:
@staticmethod def physisists_constant(order): return 1
Or in the case of the Normal distribution (aka Hermite):
@staticmethod def physisists_constant(order): return 2**order
This function can then be read by functions in chaospy.orthogonal if an
extra argument is provided by the user asking for it.
Difficulty: easy
Currently if a distribution don't implement moment calculations,
in chaospy.Distribution._get_mom, a switch to numerical
integration using the probability density function. If density is missing as
well (which is the case for all Copulas), this estimation will be slow.
In practice, calculating moments usually don't come alone (like orth_ttr,
orth_chol, etc.), making the whole procedure computationally prohibitively
expensive.
This can be optimized quite a bit, as the density evaluations are the same for every moments. So as a simple solution is to let the approximation function to: * Cache the moments evaluations with some form lru_cache for the ._mom
method.
- Store density evaluations related to moment approximations to the density, which can be reused for every moment estimation.
The approximation function can be found at
chaospy.distributions.approximation.
Difficulty: medium
There is support for converting data into a sample distribution. It would be nice to display how a good data-driven analysis can be performed.
Difficulty: medium
Leja is completely nested. A example that shows how to do analysis iterative without re-evaluating the model function would be nice.
Difficulty: medium
Kronrod and Gaussian quadrature is linked in the sense that at each quadrature order, all Gaussian nodes are nested in the Kronrod samples. A common strategy to evaluate that polynomial chaos expansion has converged, is to repeat the analysis done with optimal Gaussian, also holds true when expanded to the Kronrod example.
Difficulty: easy
Currently two discrete distributions are supported: chaospy.DescreteUniform
and chaospy.Binomial. Use these as templates and the literature to extend
chaospy.distribution.collection with the thee distributions:
Hyper-geometric, Negative-Binomial and Poisson. If other distributions also
makes sense, add as one sees fit.
Difficulty: medium
Current Lagrange polynomial implementation is rudimentary and can be improved upon quite a bit.
This does not require re-inventing the wheel, as there are others who have solve it before. For examples, it should be possible to get inspired/copy from: `https://people.sc.fsu.edu/~jburkardt/m_src/lagrange_nd/lagrange_nd.html`_ `https://sandialabs.github.io/pyapprox/tensor_product_lagrange_interpolation.html`_