Bound subsystem

calculations/3body_dis_HO_EC.jl

@@ -0,0 +1,97 @@
+using Arpack, SparseArrays, LRUCache
+using DelimitedFiles, Plots
+include("../ho_basis.jl")
+
+Λ = 0
+m = 1.0
+
+# Distinguishable particles: V12 = bound and V13 & V23 = resonant
+Va_of_r(r) = -2 * exp(-r^2/4)
+Vb_of_r(r) = -exp(-r^2 / 3) + exp(-r^2 / 10)
+
+E_max = 40
+μω_global = 0.4 * exp(-2im * pi / 9)
+
+# due to Jacobi coordinates
+μ1ω1 = μω_global * 1/2
+μ2ω2 = μω_global * 2
+μ1 = m * 1/2
+μ2 = m * 2/3
+
+println("No of threads = ", Threads.nthreads())
+
+Es, n1s, l1s, n2s, l2s = get_2p_basis(E_max, Λ)
+l_max = max(maximum(l1s), maximum(l2s))
+n_max = max(maximum(n1s), maximum(n2s))
+mask1 = (n2s .== n2s') .&& (l2s .== l2s')
+mask2 = (n1s .== n1s') .&& (l1s .== l1s')
+
+println("Basis size = ", length(Es))
+
+@time "T1" T1 = get_sp_T_matrix(n1s, l1s; mask=mask1, μω_gen=μ1ω1, μ=μ1)
+@time "T2" T2 = get_sp_T_matrix(n2s, l2s; mask=mask2, μω_gen=μ2ω2, μ=μ2)
+
+@time "Va" Va = get_jacobi_V1_matrix(Va_of_r, E_max, Λ, μ1ω1)
+@time "Vb" Vb = get_jacobi_V2_matrix(Vb_of_r, E_max, Λ, μω_global)
+
+@time "Ha" Ha = T1 + T2 + Va
+@time "Eigenvalues" target_evals, _ = eigs(Ha, nev=5, ncv=50, which=:SR, maxiter=5000, tol=1e-5, ritzvec=false, check=1)
+
+display(target_evals)
+
+# free memory
+Es = n1s = l1s = n2s = l2s = mask1 = mask2 = T1 = T2 = V1_cache = V_relative_cache = V1 = V_relative = U = V2 = nothing
+GC.gc()
+
+training_c = [-0.5, -0.65, -0.8, -1, -1.2]
+extrapolating_c = [0.8, 0.6, 0.4, 0.2, 0.1, 0.0, -0.1, -0.2, -0.3]
+
+current_E = -0.5173809356244544
+
+exact = ComplexF64[]
+training = ComplexF64[]
+extrapolated = ComplexF64[]
+training_vecs = Vector{ComplexF64}[]
+
+for c in training_c
+    print("Training for c = $c: ")
+    H = Ha + c .* Vb
+    evals, evecs = eigs(H, nev=3, ncv=24, which=:SR, maxiter=5000, tol=1e-5, ritzvec=true, check=1)
+
+    global current_E = nearest(evals, current_E)
+    println(current_E)
+    push!(training, current_E)
+    push!(training_vecs, evecs[:, nearestIndex(evals, current_E)])
+end
+
+# CA-EC
+training_vecs = vcat(training_vecs, conj(training_vecs))
+
+EC_basis = hcat(training_vecs...)
+N_EC = transpose(EC_basis) * EC_basis
+Ha_EC = transpose(EC_basis) * Ha * EC_basis
+Vb_EC = transpose(EC_basis) * Vb * EC_basis
+
+current_E = -0.3005521915662689 - 0.13612069020686351im
+
+for c in extrapolating_c
+    print("Extrapolating for c = $c: ")
+    H = Ha + c .* Vb
+    evals, evecs = eigs(H, nev=3, ncv=24, which=:SR, maxiter=5000, tol=1e-5, ritzvec=true, check=1)
+
+    global current_E = nearest(evals, current_E)
+    println(current_E)
+    push!(exact, current_E)
+
+    # extrapolation
+    H_EC = Ha_EC + c .* Vb_EC
+    evals = eigvals(H_EC, N_EC)
+    push!(extrapolated, nearest(evals, current_E))
+end
+
+# exportCSV("temp/dis_HO_B2R.csv", (training, exact, extrapolated), ("training", "exact", "extrapolated"))
+
+scatter(real.(training),imag.(training), label="training")
+scatter!(real.(exact),imag.(exact), label="exact")
+scatter!(real.(extrapolated),imag.(extrapolated), label="extrapolated")
+savefig("temp/dis_HO_B2R.pdf")

ho_basis.jl

@@ -141,6 +141,12 @@ function pick_Moshinsky_bracket(BRAC, n1′, l1′, n2′, l2′, n1, l1, n2, l2
 end
 
 function get_jacobi_V_matrix(V_of_r, E_max, Λ, μ1ω1, μω_global; atol=10^-6, maxevals=10^5)
+    V1 = get_jacobi_V1_matrix(V_of_r, E_max, Λ, μ1ω1; atol=atol, maxevals=maxevals)
+    V2 =  get_jacobi_V2_matrix(V_of_r, E_max, Λ, μω_global; atol=atol, maxevals=maxevals)
+    return V1 + V2
+end
+
+function get_jacobi_V1_matrix(V_of_r, E_max, Λ, μ1ω1; atol=10^-6, maxevals=10^5)
     _, n1s, l1s, n2s, l2s = get_2p_basis(E_max, Λ)
     l_max = max(maximum(l1s), maximum(l2s))
     n_max = max(maximum(n1s), maximum(n2s))
@@ -150,9 +156,7 @@ function get_jacobi_V_matrix(V_of_r, E_max, Λ, μ1ω1, μω_global; atol=10^-6,
     V1_cache = LRU{Tuple{UInt8, UInt8, UInt8}, ComplexF64}(maxsize=(1+l_max)*(1+n_max)^2)
     V1 = get_sp_V_matrix(V1_elem, n1s, l1s; mask=mask1, dtype=ComplexF64, cache=V1_cache)
 
-    V2 =  get_jacobi_V2_matrix(V_of_r, E_max, Λ, μω_global; atol=atol, maxevals=maxevals)
+    return V1
-
-    return V1 + V2
 end
 
 function get_jacobi_V2_matrix(V_of_r, E_max, Λ, μω_global; atol=10^-6, maxevals=10^5)