Update documentation plots to use CompactBases.ShiftAndInvert

[jagot]

Should use built-in functionality instead of duplicating

CompactBases.jl/docs/bspline_plots.jl

Lines 458 to 512 in b022394

	struct ShiftAndInvert{TA,TB,TT}
	A⁻¹::TA
	B::TB
	temp::TT
	end
	Base.size(S::ShiftAndInvert, args...) = size(S.A⁻¹, args...)
	Base.eltype(S::ShiftAndInvert) = eltype(S.A⁻¹)
	function LinearAlgebra.mul!(y,M::ShiftAndInvert,x)
	mul!(M.temp, M.B, x)
	ldiv!(y, M.A⁻¹, M.temp)
	end
	construct_linear_map(A,B,σ=0) =
	ShiftAndInvert(factorize(A-σ*B),B,Vector{eltype(A)}(undef, size(A,1)))
	function bsplines_hydrogen_eigenstates()
	k = 7
	N = 31
	a,b = 0,70
	coulomb(r) = -1/r
	nev = 5
	σ = -0.5
	n = 1:nev
	cfigure("Hydrogen", figsize=(7,9)) do
	for (j,(t,x,tol)) in enumerate([(LinearKnotSet(k, a, b, N),
	range(a, stop=b, length=500)[2:end-1],
	9e-3),
	(ExpKnotSet(k, -1.0, log10(b), N),
	10 .^ range(-1.0, stop=log10(b), length=500)[2:end-1],
	2e-7)])
	B = BSpline(t)[:,2:end-1]
	xx = axes(B, 1)
	S = B'B
	χ = B[x,:]
	D = Derivative(xx)
	∇² = B'*D'*D*B
	T = -∇²/2
	V = B'*QuasiDiagonal(coulomb.(xx))*B
	H = T + V
	schurQR,history = partialschur(construct_linear_map(H, S, σ), nev=nev)