Way to get the weights and nodes for an expectation operator?

[jlperla]

It is very convenient to do the following

E = expectation(Normal(0.0, 1.0))
E(x-> x^2)

However, sometimes you would prefer to instead directly get the nodes and weights for the expectation operator (which is then a linear operator).

Because of this, instead of expectation(...) returning a function, perhaps it should return an operator "type" which is callable (and hence can act as a function) but has other methods. In particular,

E = expectation(Normal(0.0, 1.0))
E(x-> x^2)
nodes(E) #returns a vector of the underlying nodes associated with the operator
weights(E) #returns the weights.

[arnavs]

Makes sense. Is there any distinction (in CS-land) between an operator and a function f(x::Function)::Function?

[jlperla]

Well, I meant to use operator in the mathematical sense, but this is how you make an object callable https://docs.julialang.org/en/v0.6.0/manual/methods/#Function-like-objects-1
Where the argument would be a function.

The only thing to keep in mind with the design of the types is that nodes and weights do not apply to all quadrature algorithms. For example, with adaptive quadrature it doesn't make any sense, so we would need to have the type returned from the expectation have different super-types depending on the algorithm. But we can design those parts of the interface later.

[arnavs]

Gotcha. Thanks for the link; could easily see myself struggling with that. And makes sense re different algos.

[arnavs]

This issue is now implemented; e.g.

# Callable behavior for the object. Parameters because we cannot add methods to an abstract type. 
function (e::IterableExpectation{NT, WT})(f::Function; kwargs...) where {NT, WT}
    applicable(f, rand([e.nodes...])) || throw(MethodError("The function doesn't accept elements from the distribution's support."))
    return dot(f.(e.nodes), e.weights; kwargs...) 
end