2018-09-05 10:35:58 +02:00
|
|
|
include("Projections.jl")
|
2017-06-22 14:12:35 +02:00
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
###############################################################################
|
|
|
|
#
|
|
|
|
# OrbitData
|
|
|
|
#
|
|
|
|
###############################################################################
|
2017-10-09 19:45:28 +02:00
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
struct OrbitData{T<:AbstractArray{Float64, 2}, GEl<:GroupElem, P<:perm}
|
2018-08-20 03:54:03 +02:00
|
|
|
orbits::Vector{Vector{Int}}
|
2018-09-05 09:56:04 +02:00
|
|
|
preps::Dict{GEl, P}
|
2018-08-20 03:54:03 +02:00
|
|
|
Uπs::Vector{T}
|
2018-01-01 14:06:33 +01:00
|
|
|
dims::Vector{Int}
|
2017-06-22 14:12:35 +02:00
|
|
|
end
|
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
function OrbitData(RG::GroupRing, autS::Group)
|
|
|
|
orbs = orbit_decomposition(autS, RG.basis, RG.basis_dict)
|
|
|
|
@assert sum(length(o) for o in orbs) == length(RG.basis)
|
2017-06-22 15:09:46 +02:00
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
autS_mps = Projections.rankOne_projections(GroupRing(autS))
|
2017-06-22 15:09:46 +02:00
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
preps = perm_reps(autS, RG.basis[1:size(RG.pm,1)], RG.basis_dict)
|
|
|
|
mreps = matrix_reps(preps)
|
2017-06-22 15:09:46 +02:00
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
Uπs = [orthSVD(matrix_repr(p, mreps)) for p in autS_mps]
|
2017-06-22 14:12:35 +02:00
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
multiplicities = size.(Uπs,2)
|
|
|
|
dimensions = [Int(p[autS()]*Int(order(autS))) for p in autS_mps]
|
|
|
|
@assert dot(multiplicities, dimensions) == size(RG.pm,1)
|
2017-07-26 10:29:11 +02:00
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
nzros = [i for i in 1:length(Uπs) if size(Uπs[i],2) !=0]
|
2018-01-01 14:06:33 +01:00
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
return OrbitData(orbs, preps, Uπs[nzros], dims[nzros])
|
2017-06-22 14:12:35 +02:00
|
|
|
end
|
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
function compute_OrbitData(RG::GroupRing, autS::Group)
|
2017-08-27 21:23:14 +02:00
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
info("Decomposing E into orbits of $(autS)")
|
|
|
|
@time orbs = orbit_decomposition(autS, RG.basis, RG.basis_dict)
|
|
|
|
@assert sum(length(o) for o in orbs) == length(RG.basis)
|
|
|
|
info("E consists of $(length(orbs)) orbits!")
|
2017-08-27 18:58:01 +02:00
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
info("Action matrices")
|
|
|
|
@time preps = perm_reps(autS, RG.basis[1:size(RG.pm,1)], RG.basis_dict)
|
|
|
|
mreps = matrix_reps(preps)
|
2017-07-26 18:02:21 +02:00
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
info("Projections")
|
|
|
|
@time autS_mps = Projections.rankOne_projections(GroupRing(autS));
|
2018-08-20 04:00:14 +02:00
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
info("Uπs...")
|
|
|
|
@time Uπs = [orthSVD(matrix_repr(p, mreps)) for p in autS_mps]
|
2018-08-20 04:00:14 +02:00
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
multiplicities = size.(Uπs,2)
|
|
|
|
info("multiplicities = $multiplicities")
|
|
|
|
dimensions = [Int(p[autS()]*Int(order(autS))) for p in autS_mps];
|
|
|
|
info("dimensions = $dimensions")
|
|
|
|
@assert dot(multiplicities, dimensions) == size(RG.pm,1)
|
2018-08-20 04:00:14 +02:00
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
return OrbitData(orbs, preps, Uπs, dimensions)
|
2017-06-22 14:12:35 +02:00
|
|
|
end
|
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
function decimate(od::OrbitData)
|
|
|
|
nzros = [i for i in 1:length(od.Uπs) if size(od.Uπs[i],2) !=0]
|
2017-11-05 20:55:53 +01:00
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
Us = map(x -> PropertyT.sparsify!(x, eps(Float64)*1e3, verbose=true), od.Uπs[nzros])
|
|
|
|
#dimensions of the corresponding πs:
|
|
|
|
dims = od.dims[nzros]
|
2017-11-05 20:55:53 +01:00
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
return OrbitData(od.orbits, od.preps, full.(Us), dims);
|
2017-06-22 15:11:14 +02:00
|
|
|
end
|
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
function save_OrbitData(sett::Settings, data::OrbitData)
|
|
|
|
save_preps(filename(prepath(sett), :preps), data.preps)
|
2017-06-22 14:12:35 +02:00
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
save(filename(prepath(sett), :orbits),
|
|
|
|
"orbits", data.orbits)
|
2017-06-22 14:12:35 +02:00
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
save(filename(prepath(sett), :Uπs),
|
|
|
|
"Uπs", data.Uπs,
|
|
|
|
"dims", data.dims)
|
2017-06-22 14:12:35 +02:00
|
|
|
end
|
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
function load_OrbitData(sett::Settings)
|
|
|
|
info("Loading Uπs, dims, orbits...")
|
|
|
|
Uπs = load(filename(prepath(sett), :Uπs), "Uπs")
|
|
|
|
nzros = [i for i in 1:length(Uπs) if size(Uπs[i],2) !=0]
|
2017-06-22 14:12:35 +02:00
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
Uπs = map(x -> sparsify!(x, sett.tol/100, verbose=true), Uπs)
|
|
|
|
#dimensions of the corresponding πs:
|
|
|
|
dims = load(filename(prepath(sett), :Uπs), "dims")
|
2017-08-27 19:06:17 +02:00
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
orbits = load(filename(prepath(sett), :orbits), "orbits")
|
2018-08-20 04:00:58 +02:00
|
|
|
preps = load_preps(filename(prepath(sett), :preps), sett.autS)
|
|
|
|
|
2018-09-05 09:56:04 +02:00
|
|
|
return OrbitData(orbits, preps, Uπs, dims)
|
2017-06-22 14:12:35 +02:00
|
|
|
end
|
|
|
|
|
2018-07-31 10:21:54 +02:00
|
|
|
function load_preps(fname::String, G::Group)
|
2017-11-08 09:33:00 +01:00
|
|
|
lded_preps = load(fname, "perms_d")
|
|
|
|
permG = PermutationGroup(length(first(lded_preps)))
|
|
|
|
@assert length(lded_preps) == order(G)
|
|
|
|
return Dict(k=>permG(v) for (k,v) in zip(elements(G), lded_preps))
|
|
|
|
end
|
|
|
|
|
|
|
|
function save_preps(fname::String, preps)
|
|
|
|
autS = parent(first(keys(preps)))
|
2018-08-20 04:02:44 +02:00
|
|
|
save(fname, "perms_d", [preps[elt].d for elt in elements(autS)])
|
2017-11-08 09:33:00 +01:00
|
|
|
end
|
|
|
|
|
2018-08-20 03:57:33 +02:00
|
|
|
|
2018-09-05 09:10:58 +02:00
|
|
|
###############################################################################
|
|
|
|
#
|
|
|
|
# Sparsification
|
|
|
|
#
|
|
|
|
###############################################################################
|
|
|
|
|
|
|
|
dens(M::SparseMatrixCSC) = nnz(M)/length(M)
|
|
|
|
dens(M::AbstractArray) = countnz(M)/length(M)
|
2018-01-02 03:19:57 +01:00
|
|
|
|
2018-09-05 09:10:58 +02:00
|
|
|
function sparsify!{Tv,Ti}(M::SparseMatrixCSC{Tv,Ti}, eps=eps(Tv); verbose=false)
|
2018-09-05 09:06:00 +02:00
|
|
|
|
2018-09-05 09:10:58 +02:00
|
|
|
densM = dens(M)
|
|
|
|
for i in eachindex(M.nzval)
|
|
|
|
if abs(M.nzval[i]) < eps
|
|
|
|
M.nzval[i] = zero(Tv)
|
|
|
|
end
|
|
|
|
end
|
|
|
|
dropzeros!(M)
|
2018-09-05 09:06:00 +02:00
|
|
|
|
2018-09-05 09:10:58 +02:00
|
|
|
if verbose
|
|
|
|
info("Sparsified density:", rpad(densM, 20), " → ", rpad(dens(M), 20), " ($(nnz(M)) non-zeros)")
|
2018-01-02 03:19:57 +01:00
|
|
|
end
|
2018-01-01 14:06:33 +01:00
|
|
|
|
2018-09-05 09:10:58 +02:00
|
|
|
return M
|
|
|
|
end
|
2018-01-01 14:06:33 +01:00
|
|
|
|
2018-09-05 09:10:58 +02:00
|
|
|
function sparsify!{T}(M::AbstractArray{T}, eps=eps(T); verbose=false)
|
|
|
|
densM = dens(M)
|
|
|
|
if verbose
|
|
|
|
info("Sparsifying $(size(M))-matrix... ")
|
2018-01-01 14:06:33 +01:00
|
|
|
end
|
|
|
|
|
2018-09-05 09:10:58 +02:00
|
|
|
for n in eachindex(M)
|
|
|
|
if abs(M[n]) < eps
|
|
|
|
M[n] = zero(T)
|
|
|
|
end
|
|
|
|
end
|
2018-01-01 14:06:33 +01:00
|
|
|
|
2018-09-05 09:10:58 +02:00
|
|
|
if verbose
|
|
|
|
info("$(rpad(densM, 20)) → $(rpad(dens(M),20))), ($(countnz(M)) non-zeros)")
|
|
|
|
end
|
2018-01-01 14:06:33 +01:00
|
|
|
|
2018-09-05 09:10:58 +02:00
|
|
|
return sparse(M)
|
2017-06-22 14:12:35 +02:00
|
|
|
end
|
2018-09-05 09:10:58 +02:00
|
|
|
|
|
|
|
sparsify{T}(U::AbstractArray{T}, tol=eps(T); verbose=false) = sparsify!(deepcopy(U), tol, verbose=verbose)
|