p-space systems refactored
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@ -1,5 +1,23 @@
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include("../p_space.jl")
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include("../EC.jl")
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Λ = 0
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m = 1.0
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V_of_r(r) = 2 * exp(-(r-3)^2 / (1.5)^2)
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vertices = [0, 2 - 0.2im, 3, 4]
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subdivisions = [15, 10, 10]
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jmax = 4
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E_max = 40
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μω_global = 0.5
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H0, weights = get_3b_H_matrix(jacobi, V_of_r, vertices, subdivisions, jmax, μω_global, E_max, Λ, m)
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# Vp = perturbation to make the state artificially bound
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Vp_of_r(r) = -exp(-(r/3)^2)
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Vp, _ = get_3b_H_matrix(jacobi, Vp_of_r, vertices, subdivisions, jmax, μω_global, E_max, Λ, m, false, true)
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training_c = [2.6, 2.4, 2.2, 2.0, 1.8]
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extrapolating_c = 0.0 : 0.2 : 1.2
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@ -13,24 +31,6 @@ extrapolating_ref = [4.076662025307587-0.012709842443350328im,
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1.7164583929199813-0.0005455212208182736im,
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1.233088227541505-0.0003070320106485624im]
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include("../p_space_3body_resonance.jl")
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H0 = H
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# Vp = perturbation to make the state artificially bound
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Vp_of_r(r) = -exp(-(r/3)^2)
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Vp_l(j, k, kp) = Vl_mat_elem(Vp_of_r, j, k, kp; atol=atol, maxevals=maxevals, R_cutoff=R_cutoff)
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@time "Vp block diagonal part" begin
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Vpb_blocks = [kron_sum(get_V_matrix((k, kp) -> Vp_l(j1, k, kp), ks, ws), spzeros(length(ks), length(ks))) for (j1, _) in js]
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Vpb = blockdiag(sparse.(Vpb_blocks)...)
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end
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@time "Vp2_HO" Vp2_HO = get_jacobi_V2_matrix(Vp_of_r, basis_ho, μω_global; atol=atol, maxevals=maxevals)
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@time "Vp2" Vp2 = W_left * Vp2_HO * transpose(W_right)
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@time "Vp" Vp = Vpb + Vp2
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weights = repeat(kron(ws, ws), jmax + 1)
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EC = affine_EC(H0, Vp, weights)
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train!(EC, training_c; ref_eval=training_ref, CAEC=true)
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extrapolate!(EC, extrapolating_c; ref_eval=extrapolating_ref)
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@ -1,5 +1,23 @@
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include("../p_space.jl")
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include("../EC.jl")
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Λ = 0
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m = 1.0
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V_of_r(r) = 2 * exp(-(r-3)^2 / (1.5)^2)
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vertices = [0, 2 - 0.2im, 3, 4]
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subdivisions = [15, 10, 10]
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jmax = 4
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E_max = 40
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μω_global = 0.5
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H0, weights = get_3b_H_matrix(jacobi, V_of_r, vertices, subdivisions, jmax, μω_global, E_max, Λ, m)
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# Vp = perturbation to make the state artificially bound
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Vp_of_r(r) = -exp(-(r/3)^2)
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Vp, _ = get_3b_H_matrix(jacobi, Vp_of_r, vertices, subdivisions, jmax, μω_global, E_max, Λ, m, false, true)
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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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@ -16,24 +34,6 @@ extrapolating_ref = [4.076662025307587-0.012709842443350328im,
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1.7164583929199813-0.0005455212208182736im,
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1.233088227541505-0.0003070320106485624im]
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include("../p_space_3body_resonance.jl")
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H0 = H
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# Vp = perturbation to make the state artificially bound
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Vp_of_r(r) = -exp(-(r/3)^2)
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Vp_l(j, k, kp) = Vl_mat_elem(Vp_of_r, j, k, kp; atol=atol, maxevals=maxevals, R_cutoff=R_cutoff)
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@time "Vp block diagonal part" begin
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Vpb_blocks = [kron_sum(get_V_matrix((k, kp) -> Vp_l(j1, k, kp), ks, ws), spzeros(length(ks), length(ks))) for (j1, _) in js]
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Vpb = blockdiag(sparse.(Vpb_blocks)...)
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end
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@time "Vp2_HO" Vp2_HO = get_jacobi_V2_matrix(Vp_of_r, basis_ho, μω_global; atol=atol, maxevals=maxevals)
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@time "Vp2" Vp2 = W_left * Vp2_HO * transpose(W_right)
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@time "Vp" Vp = Vpb + Vp2
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weights = repeat(kron(ws, ws), jmax + 1)
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EC = affine_EC(H0, Vp, weights)
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train!(EC, training_c; ref_eval=training_ref, CAEC=false)
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extrapolate!(EC, extrapolating_c; ref_eval=extrapolating_ref)
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54
p_space.jl
54
p_space.jl
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@ -1,5 +1,6 @@
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using LinearAlgebra
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using SpecialFunctions, FastGaussQuadrature, QuadGK
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include("ho_basis.jl")
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function gausslegendre_shifted(a, b, n)
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scale = (b - a) / 2
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@ -59,3 +60,56 @@ function Vl_mat_elem(V_of_r, l, p, q; atol=0, maxevals=10^7, R_cutoff=Inf)
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(integral, _) = quadgk(integrand, 0, R_cutoff; atol=atol, maxevals=maxevals)
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return (2 / pi) * integral
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end
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"Return the Hamiltonian matrix (and the array of weights) for the given system."
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function get_3b_H_matrix(coord_system::coordinate_system, V_of_r, vertices, subdivisions, jmax, μω_global, E_max, Λ, m=1.0, kinetic_part=true, potential_part=true; atol=10^-5, maxevals=10^5, R_cutoff=16, verbose=true)
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if coord_system == jacobi
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μ1ω1 = μω_global * 1/2
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μ2ω2 = μω_global * 2
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μ1 = m * 1/2
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μ2 = m * 2/3
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else
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error("Only Jacobi coordinates are implemented")
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end
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verbose && println("No of threads = ", Threads.nthreads())
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V_l(j, k, kp) = Vl_mat_elem(V_of_r, j, k, kp; atol=atol, maxevals=maxevals, R_cutoff=R_cutoff)
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ks, ws = get_mesh(vertices, subdivisions)
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weights = repeat(kron(ws, ws), jmax + 1)
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block_size = length(ks)
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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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@assert length(basis) == basis_size "Something wrong with the basis"
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verbose && println("Basis size = $basis_size")
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out = spzeros(basis_size, basis_size)
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@time "Block diagonal part" begin
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if kinetic_part & potential_part
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Hb_blocks = [kron_sum(get_H_matrix((k, kp) -> V_l(j1, k, kp), ks, ws, μ1), get_T_matrix(ks, μ2)) for (j1, _) in js]
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elseif kinetic_part
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Hb_blocks = [kron_sum(get_T_matrix(ks, μ1), get_T_matrix(ks, μ2)) for _ in js]
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elseif potential_part
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Hb_blocks = [kron_sum(get_V_matrix((k, kp) -> V_l(j1, k, kp), ks, ws), spzeros(block_size, block_size)) for (j1, _) in js]
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end
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out += blockdiag(sparse.(Hb_blocks)...)
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end
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if potential_part
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basis_ho = ho_basis_2B(E_max, Λ)
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verbose && println("HO basis size = ", basis_ho.dim)
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@time "V2_HO" V2_HO = get_jacobi_V2_matrix(V_of_r, basis_ho, μω_global)
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@time "W_right" W_right = get_W_matrix(basis, basis_ho, μ1ω1, μ2ω2; weights=true)
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@time "W_left" W_left = get_W_matrix(basis, basis_ho, μ1ω1, μ2ω2; weights=false)
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@time "V2" out += W_left * V2_HO * transpose(W_right)
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end
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return (out, weights)
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end
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@ -1,56 +1,18 @@
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using LinearAlgebra, SparseArrays, Arpack
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include("common.jl")
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using Arpack
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include("p_space.jl")
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include("ho_basis.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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Λ = 0
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m = 1.0
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μ1 = m * 1/2
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μ2 = m * 2/3
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Va = -2
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Ra = 2
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V_of_r(r) = Va * exp(-r^2 / Ra^2)
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V_l(j, k, kp) = Vl_mat_elem(V_of_r, j, k, kp; atol=atol, maxevals=maxevals, R_cutoff=R_cutoff)
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V_of_r(r) = -2 * exp(-r^2 / 4)
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vertices = [0, 0.5 - 0.3im, 1, 4]
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subdivisions = [10, 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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@assert length(basis) == basis_size "Something wrong with the basis"
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println("Basis size = $basis_size")
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@time "Block diagonal part" begin
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Hb_blocks = [kron_sum(get_H_matrix((k, kp) -> V_l(j1, k, kp), ks, ws, μ1), get_T_matrix(ks, μ2)) for (j1,_ ) in js]
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Hb = blockdiag(sparse.(Hb_blocks)...)
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end
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E_max = 30
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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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basis_ho = ho_basis_2B(E_max, Λ)
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@time "V2_HO" V2_HO = get_jacobi_V2_matrix(V_of_r, basis_ho, μω_global)
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@time "W_right" W_right = get_W_matrix(basis, basis_ho, μ1ω1, μ2ω2; weights=true)
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@time "W_left" W_left = get_W_matrix(basis, basis_ho, μ1ω1, μ2ω2; weights=false)
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@time "V2" V2 = W_left * V2_HO * transpose(W_right)
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@time "H" H = Hb + V2
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H, _ = get_3b_H_matrix(jacobi, V_of_r, vertices, subdivisions, jmax, μω_global, E_max, Λ, m)
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@time "Eigenvalues" evals, _ = eigs(H, nev=3, ncv=24, which=:SR, maxiter=5000, tol=1e-5, ritzvec=false, check=1)
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display(evals)
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@ -1,55 +1,20 @@
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using LinearAlgebra, SparseArrays, Arpack
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include("common.jl")
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using Arpack
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include("p_space.jl")
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include("ho_basis.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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Λ = 0
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m = 1.0
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μ1 = m * 1/2
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μ2 = m * 2/3
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target = 4.0766890719636875 - 0.012758927741074495im
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Λ = 0
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m = 1.0
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V_of_r(r) = 2 * exp(-(r-3)^2 / (1.5)^2)
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V_l(j, k, kp) = Vl_mat_elem(V_of_r, j, k, kp; atol=atol, maxevals=maxevals, R_cutoff=R_cutoff)
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vertices = [0, 2 - 0.2im, 3, 4]
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subdivisions = [15, 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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@assert length(basis) == basis_size "Something wrong with the basis"
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println("Basis size = $basis_size")
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@time "Block diagonal part" begin
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Hb_blocks = [kron_sum(get_H_matrix((k, kp) -> V_l(j1, k, kp), ks, ws, μ1), get_T_matrix(ks, μ2)) for (j1,_ ) in js]
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Hb = blockdiag(sparse.(Hb_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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basis_ho = ho_basis_2B(E_max, Λ)
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@time "V2_HO" V2_HO = get_jacobi_V2_matrix(V_of_r, basis_ho, μω_global; atol=atol, maxevals=maxevals)
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@time "W_right" W_right = get_W_matrix(basis, basis_ho, μ1ω1, μ2ω2; weights=true)
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@time "W_left" W_left = get_W_matrix(basis, basis_ho, μ1ω1, μ2ω2; weights=false)
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@time "V2" V2 = W_left * V2_HO * transpose(W_right)
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@time "H" H = Hb + V2
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H, _ = get_3b_H_matrix(jacobi, V_of_r, vertices, subdivisions, jmax, μω_global, E_max, Λ, m)
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@time "Eigenvalues" evals, _ = eigs(H, sigma=target, maxiter=5000, tol=1e-5, ritzvec=false, check=1)
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display(evals)
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