Standarize w/ separate package all eliminationOrdering methods

[dehann]

see new package https://github.com/JuliaRobotics/VariableEliminationOrderings.jl

Background

• https://www.coursera.org/lecture/probabilistic-graphical-models-2-inference/finding-elimination-orderings-ckOIz
• Local Caesar.jl Wiki page of known references
• Papers and thesis Caesar literature page
• https://en.wikipedia.org/wiki/Variable_elimination

Existing Usage in IncrementalInference

IncrementalInference.jl/src/FactorGraph.jl

Lines 1138 to 1167 in 870e518

	# Get the sparse adjacency matrix, variable, and factor labels
	adjMat, permuteds, permutedsf = DFG.getBiadjacencyMatrix(dfg, solvable=solvable)
	# adjMat, permuteds, permutedsf = DFG.getAdjacencyMatrixSparse(dfg, solvable=solvable)
	# Create dense adjacency matrix
	p = Int[]
	if ordering==:chol
	# hack for dense matrix....
	A = adjMat
	p = cholesky(Matrix(A'A),Val(true)).piv
	@warn "check that cholesky ordering is not reversed -- basically how much fill in (separator size) are you seeing??? Long skinny chains in tree is bad."
	elseif ordering==:qr
	# hack for dense matrix....
	A = Array(adjMat)
	# this is the default
	q,r,p = qr(A, Val(true))
	p .= p |> reverse
	elseif ordering==:ccolamd
	cons = zeros(SuiteSparse_long, length(adjMat.colptr) - 1)
	cons[findall(x->x in constraints, permuteds)] .= 1
	p = Ccolamd.ccolamd(adjMat, cons)
	@warn "Ccolamd is experimental in IIF at this point in time."
	else
	prtslperr("getEliminationOrder -- cannot do the requested ordering $(ordering)")
	end
	# Return the variable ordering that we should use for the Bayes map
	# reverse order checked in #475 and #499
	return permuteds[p]

And the new RCS package to be included:
https://discourse.julialang.org/t/implementing-cuthill-mckee/9268/31

---

Also see discussion at (pending license):

• Consolidate CCOLAMD wrapper from IncrementalInference.jl? JuliaSmoothOptimizers/AMD.jl#36

One solution might be to have JuliaRobotics/VariableEliminationOrderings.jl provides a mechanism to include more methods depending on the desired license restrictions.