Inverse problems #12
Description
I managed to get some of the basis inversions to work, but not all:
using FiniteDifferencesQuasi
using LinearAlgebra
using Test
R = FiniteDifferences(20,0.2)
R⁻¹ = pinv(R)
# # Actually, we want
# R⁻¹ = inv(R)
# # but then we get
# # ERROR: LoadError: MethodError: no method matching ContinuumArrays.AlephInfinity{1}(::Int64)
u = R*rand(size(R,2))
v = R*rand(size(R,2))
uvc = [u.args[2] v.args[2]]
uv = R*uvc
ut = u'
@test R⁻¹*R == I
@test R*R⁻¹ == I
@test R⁻¹*u === u.args[2]
@test R⁻¹*uv === uvc
# # We also want this to work
# @test ut*R⁻¹' === ut.args[1]
# # ERROR: MethodError: no method matching axes(::UniformScaling{Float64}, ::Int64)
M = Diagonal(2ones(size(R,2)))
# # Finally, we'd like to write operators as
# O = R*M*R⁻¹
# # but alas
# # ERROR: LoadError: MethodError: no method matching ContinuumArrays.AlephInfinity{1}(::Int64)
# @test R⁻¹*O*u == M*R⁻¹*uI've not yet figured out why inv does not work, to me it seems most things are mirrored compared to pinv in e.g. inv.jl.