Tillmann Muehlpfordt

Add adaptive sparse polynomial chaos

2

see [this paper](https://www.sciencedirect.com/science/article/pii/S0021999110006856) and the section on it in the [UQLab manual](http://docs.wixstatic.com/ugd/0f4bf0_cce5f6946fd14c7aa848f5f8670dc6fd.pdf).

Inverse transform sampling

2

It would be helpful to transpile the inverse transform sampling method from [here](https://github.com/dlfivefifty/InverseTransformSampling) to our package. Yes, I am aware that there is a working implementation withing [`ApproxFun.jl`](https://github.com/JuliaApproximation/ApproxFun.jl#sampling), but we...

jldoctests are tested when building the documentation with `Documenter.jl`. This should be favored to ```@example``` or its friends.

__This issue can be tackled as soon as there is a new version of `Pkg.jl`:__ [https://github.com/JuliaLang/Pkg.jl/issues/876](https://github.com/JuliaLang/Pkg.jl/issues/876) As we need certain packages only for testing, we should specify this in `project.toml`,...

For instance, `op = OrthoPoly("gaussian",10)` could be `op = @gaussian 10`. This really needs to be thought through -- what should be the syntax to distinguish between `OrthoPoly` and `OrthoPolyQ`?...

Construct bases for rates other than 1? This is currently a kind-of severe limitation.

non-exhaustive list of things that would be interesting to plot: ``` plot(w::Function,dom::Tuple(Float64,Float64)) plot(m::Measure) histogram(x::Vector{Float64},op::Union{OrthoPolyQ, MultiOrthoPoly}) histogram(op::Union{OrthoPolyQ, MultiOrthoPoly) ``` This should be done with `Plots.jl` and recipes. caveat: when plotting the...

probably needs `IterTools` or something comparable for an elegant solution.

Starting from a linear time-invariant *ODE* $\dot{x}(t) = A(\theta) x(t) + B(\theta) u(t)$ with initial condition $x(0) = x_0(\theta)$ and a random parameter $\theta$, auto-generate the Galerkin-projected ODE in terms...