Integral of (basis) functions

[jagot]

What would be a sensible interface for computing integrals? If 'B' is a Basis (or suitable QuasiMatrix), c the expansion coefficients of a function, and f = B*c the function expanded over B, I'm thinking

• integral(f) would give me the integral of the function,
• integral(B) would give me an adjoint vector with the integral of each individual basis function, which I can dot with c to get the same as integral(f),
• integral(B[Inclusion(a..b),:]) would integrate the basis functions on a subinterval a..b,
• integral(B*QuasiDiagonal(f.(axes(B,1))) would integrate each basis function, weighted by the function f(x).

Instead of integral, I guess sum would be a good name, but that's already taken for something I am not completely sure what it does (maybe exactly this?).

In any case, it tells me I need to Override for ContinuumArrays.BasisLayout(). If this is what I want, what is the canonical way to do this?

[dlfivefifty]

sum and sum(B; dims=1) is what you want