correct reconstruction of the original solution

Orb_AutFN.jl

@@ -130,13 +130,6 @@ function addconstraints!(m::JuMP.Model, data::OrbitData, l::Int=length(data.lapl
     end
 end
 
-function reconstructP(m::JuMP.Model, data::OrbitData)
-    computedPs = [getvalue(P) for P in data.Ps]
-    return sum(
-      data.dims[π]*transform(data.Us[π]',computedPs[π], sparse=false)
-      for π in 1:endof(data.Ps))
-end
-
 function create_SDP_problem(name::String; upper_bound=Inf)
    info(PropertyT.logger, "Loading data....")
    t = @timed SDP_problem, orb_data = init_OrbitData(name);
@@ -158,11 +151,43 @@ function λandP(m::JuMP.Model, data::OrbitData)
    info(PropertyT.logger, "Solving SDP problem...")
    varλ = m[:λ]
    varP = data.Ps
-   λ, P = PropertyT.λandP(data.name, m, varλ, varP)
+   λ, Ps = PropertyT.λandP(data.name, m, varλ, varP)
+   return λ, Ps
+end
+
+function matrix_reps{T<:GroupElem}(G::Group, S::Vector{T}, AutS::Group, radius::Int)
+   Id = (isa(G, Nemo.Ring) ? one(G) : G())
+   E2, _ = Groups.generate_balls(S, Id, radius=radius)
+   Edict = GroupRings.reverse_dict(E2)
+
+   mreps = Dict(g => matrix_repr(g, E2, Edict) for g in elements(AutS))
+   return mreps
+end
+
+function reconstruct(mreps::Dict, Us::Vector, Ps::Vector, dims::Vector)
+   recP = zeros(size(Us[1],1), size(Us[1],1))
+
+   for g in keys(mreps)
+      for π in 1:endof(Us)
+         recP .+= dims[π] .* mreps[g]*transform(Us[π]', Ps[π])*mreps[inv(g)]
+      end
+   end
+   recP .*= 1/length(collect(keys(mreps)))
+
+   return recP
+end
+
+function λandP(m::JuMP.Model, data::OrbitData, sett::Settings)
+   info(PropertyT.logger, "Solving SDP problem...")
+   λ, Ps = λandP(m, data)
+
+   info(PropertyT.logger, "Reconstructing P...")
+   mreps = matrix_reps(sett.G, sett.S, sett.AutS, sett.radius)
+
+   recP = reconstruct(mreps, data.Us, Ps, data.dims)
 
-   recP = reconstructP(m, data)
    fname = PropertyT.λSDPfilenames(data.name)[2]
-   save(fname, "origP", P, "P", recP)
+   save(fname, "origP", Ps, "P", recP)
    return λ, recP
 end
 
@@ -193,7 +218,8 @@ function orbit_check_propertyT(logger, sett::Settings)
       info(logger, "Creating SDP problem...")
       SDP_problem, orb_data = create_SDP_problem(sett.name, upper_bound=sett.upper_bound)
       JuMP.setsolver(SDP_problem, sett.solver)
-      λ, P = λandP(SDP_problem, orb_data)
+
+      λ, P = λandP(SDP_problem, orb_data, sett)
    end
 
    info(logger, "λ = $λ")