tssos_tests.jl

using TSSOS, DynamicPolynomials, LinearAlgebra
## from Constrained Polynomial Optimization section of TSSOS' README
@polyvar x[1:3]
f = 1 + x[1]^4 + x[2]^4 + x[3]^4 + x[1]*x[2]*x[3] + x[2]
g = 1 - x[1]^2 - 2*x[2]^2
h = x[2]^2 + x[3]^2 - 1
pop = [f, g]
d = 2 # set the relaxation order
opt,sol,data = cs_tssos_first(pop, x, d, numeq=0, TS="MD", CS="MD", Gram=true, solve=false);
show_blocks(data, include_constraints=true)
##
# *********************************** TSSOS ***********************************
# TSSOS is launching...
# -----------------------------------------------------------------------------
# The clique sizes of varibles:
# [list of different sizes of cliques]
# [list of how many cliques have the sizes displayed]
# -----------------------------------------------------------------------------
## list of (list of variables in clique)
data.cliques
## = p in book notation = length(data.cliques)
data.cql
## inequality constraints in each clique
data.I
## equality constraints in each clique
data.J
## J' from book - only non empty when deg(g_j) = deg(f) = 2r for all j
data.ncc
##
data.GramMat
##
data.GramMat[1]
##
data.GramMat[1][1]
## list of supports of pop data [f; g; h]
# where the support of each polynomial = a list of (term = list of variables)
data.supp
##
show_blocks(data, include_constraints=true)
##basis[clique][constraint]
data.basis[1]
##blocks[clique][constraint][block] -> indices of basis[clique][constraint] that appear in this block 
data.blocks[1][1]
## what is the ts graph?
opt,sol,data = cs_tssos_higher!(data, TS="MD", solve=false)
show_blocks(data, include_constraints=true)
## plot correlative sparsity
using Graphs, GLMakie, GraphMakie
function cs_graph(pop, x, d; numeq, cs_alg="NC")
    opt,sol,data = cs_tssos_first(pop, x, d, numeq=numeq, CS=cs_alg, solve=false, solution=false);

    cs_graph(data), data
end

function cs_graph(data::TSSOS.mcpop_data)
    GCSP = SimpleGraph(length(data.x))
    for l = 1:data.cql
        TSSOS.add_clique!(GCSP, data.cliques[l])
    end
    GCSP
end
## compute & plot CS graph of problem (after chordal extension)
function node_drag_action_p(p, state, idx, event, axis)
    p[:node_pos][][idx] = event.data
    p[:node_pos][] = p[:node_pos][]
end

function plot_draggable(G; kwargs...)
    f, ax, p = graphplot(G; kwargs...)