134 lines
4.3 KiB
Julia
134 lines
4.3 KiB
Julia
using Arpack, SparseArrays, LRUCache
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using DelimitedFiles, Plots
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include("../ho_basis.jl")
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include("../p_space.jl")
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include("../berggren.jl")
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println("No of threads = ", Threads.nthreads())
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atol = 10^-5
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maxevals = 10^5
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R_cutoff = 16
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training_c = [1.1, 0.9, 0.7, 0.5]
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extrapolating_c = 0.0 : 0.2 : 1.2
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training_ref = reverse([1.4750633616275919 - 0.0003021770706749637im
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1.9567078295375822 - 0.0007646829108872369im
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2.4351117758403076 - 0.001281037843108658im
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2.85])
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exact_ref = reverse([4.076662025307587-0.012709842443350328im,
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3.613318119833891-0.007335804709990623im,
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3.1453431847006783-0.004030580410326795im,
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2.672967129943755-0.00211498327461944im,
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2.196542557810288-0.0010719835443437104im,
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1.7164583929199813-0.0005455212208182736im,
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1.233088227541505-0.0003070320106485624im])
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Λ = 0
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m = 1.0
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Va_of_r(r) = 2 * exp(-(r-3)^2 / (1.5)^2)
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Vb_of_r(r) = -exp(-(r/3)^2)
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# due to Jacobi coordinates
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μ1 = m * 1/2
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μ2 = m * 2/3
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vertices = [0, 2 - 0.1im, 3, 4]
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subdivisions = [16, 10, 10]
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ks, ws = get_mesh(vertices, subdivisions)
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jmax = 4
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tri((j1, j2)) = triangle_ineq(j1, j2, Λ)
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js = collect(Iterators.filter(tri, iter_prod(0:jmax, 0:jmax)))
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basis = iter_prod(js, zip(ks, ws), zip(ks, ws)) # basis = ((j1, j2), (k1, w1), (k2, w2))
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basis_size = length(js) * length(ks)^2
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weights_mat = spdiagm(repeat(kron(ws, ws), jmax + 1))
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@assert length(basis) == basis_size "Something wrong with the basis"
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println("Basis size = $basis_size")
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@time "T" begin
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T_blocks = [kron_sum(get_T_matrix(ks, μ1), get_T_matrix(ks, μ2)) for _ in js]
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T = blockdiag(sparse.(T_blocks)...)
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end
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@time "Va1" begin
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Va_l(j, k, kp) = Vl_mat_elem(Va_of_r, j, k, kp; atol=atol, maxevals=maxevals, R_cutoff=R_cutoff)
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Va1_blocks = [kron(get_V_matrix((k, kp) -> Va_l(j1, k, kp), ks, ws), I(length(ks))) for (j1, _) in js]
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Va1 = blockdiag(sparse.(Va1_blocks)...)
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end
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@time "Vb1" begin
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Vb_l(j, k, kp) = Vl_mat_elem(Vb_of_r, j, k, kp; atol=atol, maxevals=maxevals, R_cutoff=R_cutoff)
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Vb1_blocks = [kron(get_V_matrix((k, kp) -> Vb_l(j1, k, kp), ks, ws), I(length(ks))) for (j1, _) in js]
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Vb1 = blockdiag(sparse.(Vb1_blocks)...)
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end
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E_max = 40
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μω_global = 0.5
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μ1ω1 = μω_global * 1/2
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μ2ω2 = μω_global * 2
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@time "Va2_HO" Va2_HO = get_jacobi_V2_matrix(Va_of_r, E_max, Λ, μω_global; atol=atol, maxevals=maxevals)
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@time "Vb2_HO" Vb2_HO = get_jacobi_V2_matrix(Vb_of_r, E_max, Λ, μω_global; atol=atol, maxevals=maxevals)
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@time "W_right" W_right = get_W_matrix(basis, E_max, Λ, μ1ω1, μ2ω2; weights=true)
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@time "W_left" W_left = get_W_matrix(basis, E_max, Λ, μ1ω1, μ2ω2; weights=false)
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@time "Va2" Va2 = W_left * Va2_HO * transpose(W_right)
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@time "Vb2" Vb2 = W_left * Vb2_HO * transpose(W_right)
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@time "Ha" Ha = T + Va1 + Va2
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@time "Vb" Vb = Vb1 + Vb2
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@time "Eigenvalues" test_evals, _ = eigs(Ha, sigma=exact_ref[end], maxiter=5000, tol=1e-5, ritzvec=false, check=1)
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display(test_evals)
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# free memory
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Es = n1s = l1s = n2s = l2s = mask1 = mask2 = T1 = T2 = V1_cache = V_relative_cache = V1 = V_relative = U = V2 = nothing
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GC.gc()
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exact = ComplexF64[]
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training = ComplexF64[]
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extrapolated = ComplexF64[]
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training_vecs = Vector{ComplexF64}[]
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for c in training_c
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println("Training for c = $c")
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global current_E = pop!(training_ref)
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H = Ha + c .* Vb
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evals, evecs = eigs(H, sigma=current_E, maxiter=5000, tol=1e-5, ritzvec=true, check=1)
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global current_E = nearest(evals, current_E)
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push!(training, current_E)
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push!(training_vecs, evecs[:, nearestIndex(evals, current_E)])
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end
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EC_basis = hcat(training_vecs...)
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N_EC = transpose(EC_basis) * weights_mat * EC_basis
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Ha_EC = transpose(EC_basis) * weights_mat * Ha * EC_basis
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Vb_EC = transpose(EC_basis) * weights_mat * Vb * EC_basis
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for c in extrapolating_c
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println("Extrapolating for c = $c")
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global current_E = pop!(exact_ref)
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H = Ha + c .* Vb
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evals, _ = eigs(H, sigma=current_E, maxiter=5000, tol=1e-5, ritzvec=false, check=1)
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global current_E = nearest(evals, current_E)
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push!(exact, current_E)
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# extrapolation
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H_EC = Ha_EC + c .* Vb_EC
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evals = eigvals(H_EC, N_EC)
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push!(extrapolated, nearest(evals, current_E))
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end
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scatter(real.(training),imag.(training), label="training")
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scatter!(real.(exact),imag.(exact), label="exact")
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scatter!(real.(extrapolated),imag.(extrapolated), label="extrapolated")
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savefig("temp/Berggren_R2R.pdf") |