Temp commit

calculations/EC+ACCC.jl

@@ -1,74 +0,0 @@
-using Roots, LinearAlgebra, Plots
-
-include("../ho_basis.jl")
-include("../EC.jl")
-include("../common.jl")
-
-V_of_r(r) = 2 * exp(-(r-3)^2 / (1.5)^2)
-Λ = 0
-m = 1.0
-
-ϕ = 0.0
-μω_global = 0.5 * exp(-2im * ϕ)
-E_max = 40
-
-H0 = get_3b_H_matrix(jacobi, V_of_r, μω_global, E_max, Λ, m, true, true)
-
-# Vp = perturbation to make the state artificially bound
-Vp_of_r(r) = -exp(-(r/3)^2)
-@time "Vp" Vp = get_3b_H_matrix(jacobi, Vp_of_r, μω_global, E_max, Λ, m, false, true)
-
-ref_E = -2.22
-training_c = [3.0, 2.6, 2.2, 1.8]
-
-EC = affine_EC(H0, Vp)
-train!(EC, training_c; ref_eval=ref_E, CAEC=false)
-training_E = EC.training_E
-
-quick_extrapolate(c) = argmin(real, get_extrapolated_evals(EC.H0_EC, EC.H1_EC, EC.N_EC, c, 0))
-
-n_EC = 30
-EC_c = (1.8 .+ rand(n_EC)) .+ 0.001im .* (-2 .+ 4 * rand(n_EC))
-
-target_c = 0.0 : 0.2 : 1.2
-exact_E = [4.076662025307587-0.012709842443350328im,
-    3.613318119833891-0.007335804709990623im,
-    3.1453431847006783-0.004030580410326795im,
-    2.672967129943755-0.00211498327461944im,
-    2.196542557810288-0.0010719835443437104im,
-    1.7164583929199813-0.0005455212208182736im,
-    1.233088227541505-0.0003070320106485624im]
-
-EC_E = [quick_extrapolate(c) for c in EC_c]
-
-# determining c0 with EC
-c0 = find_zero(c -> abs2(quick_extrapolate(c)), 0.85)
-println("Estimated c0 = ", c0)
-
-EC_k = alt_sqrt.(EC_E)
-
-order::Int = 5 # order of the Pade approximant
-
-# Solve coefficients as a linear system
-M_left_element(c, i) = alt_sqrt(c - c0)^i
-M_left = M_left_element.(EC_c, (0:order)')
-M_right = -EC_k .* M_left[:, 2:end] # remove the first column
-M = hcat(M_left, M_right) # M = [M_left | M_right]
-sol = M \ EC_k
-a = sol[1:order+1]
-b = [1; sol[order+2:end]]
-
-# Pade approximant
-polynomial(a, c) = sum(i -> a[i+1] * alt_sqrt(c - c0)^i, 0:order)
-pade_approx(c) = polynomial(a, c) / polynomial(b, c)
-
-# Extrapolate
-extrapolated_k = pade_approx.([EC_c; target_c])
-extrapolated_E = (extrapolated_k .^ 2)
-
-# Plotting
-scatter(real.(training_E), imag.(training_E), label="training")
-scatter!(real.(exact_E), imag.(exact_E), label="exact")
-scatter!(real.(EC_E), imag.(EC_E), label="EC", m=:star5)
-scatter!(real.(extrapolated_E), imag.(extrapolated_E), label="ACCC", m=:x)
-savefig("temp/EC+ACCC.pdf")

calculations/He_cluster.jl

@@ -0,0 +1,38 @@
+using Arpack
+include("../ho_basis.jl")
+
+coord_system = jacobi
+atol = 10 ^ -5
+maxevals = 10 ^ 5
+
+Λ = 0
+m = 1.0 / 43.281307
+V_of_r(r) = -1.2343566 * exp(-r^2 / 100)
+
+# three-body potential V3b = V3b_of_r(r12) * V3b_of_r(r23) * V3b_of_r(r31)
+V3b_of_r(r) = 0.43 * exp(-(2/3) * r^2 / 100)
+
+E_max = 30
+μω_global = 0.1
+
+μ1ω1 = μω_global * 1/2
+basis = ho_basis_2B(E_max, Λ)
+
+V1_elem(l, n1, n2) = V_numerical(V3b_of_r, l, n1, n2; μω_gen=μ1ω1, atol=atol, maxevals=maxevals)
+@time "V1" V1 = get_sp_V_matrix(V1_elem, basis.n1s, basis.l1s, [basis.n2s, basis.l2s]; dtype=ComplexF64, E_max=basis.E_max)
+
+V_relative_elem(l, n1, n2) = V_numerical(V3b_of_r, l, n1, n2; μω_gen=μω_global, atol=atol, maxevals=maxevals)
+V_relative_cache = prealloc_V_cache(basis.E_max, ComplexF64)
+
+V_relative_1 = get_sp_V_matrix(V_relative_elem, basis.n1s, basis.l1s, [basis.n2s, basis.l2s]; dtype=ComplexF64, cache=V_relative_cache)
+V_relative_2 = get_sp_V_matrix(V_relative_elem, basis.n2s, basis.l2s, [basis.n1s, basis.l1s]; dtype=ComplexF64, cache=V_relative_cache)
+@time "V_relative" V_relative = V_relative_1 * V_relative_2 # commutative?
+U = Moshinsky_transform(basis)
+@time "V2" V2 =  transpose(U) * V_relative * U
+
+@time "V3b" V3b = V2 * V1 # commutative?
+
+H = get_3b_H_matrix(coord_system, V_of_r, μω_global, E_max, Λ, m) + V3b
+
+@time "Eigenvalues" evals, _ = eigs(H, nev=3, ncv=30, which=:SR, maxiter=5000, tol=1e-5, ritzvec=false, check=1)
+display(evals)

ho_space_3body_V3b.jl

@@ -0,0 +1,31 @@
+using Arpack
+include("ho_basis.jl")
+
+coord_system = src
+atol = 10 ^ -5
+maxevals = 10 ^ 5
+
+Λ = 0
+m = 1.0
+V_of_r(r) = -2 * exp(-r^2 / 4)
+
+# three-body potential V3b = V3b_of_r(r12) * V3b_of_r(r23) * V3b_of_r(r31)
+V3b_of_r(r) = -1 * exp(-r^2 / 4)
+
+E_max = 40
+μω_global = 0.3
+
+# compute three-body potential matrix elements
+μω = μω_global * 2
+basis = ho_basis_2B(E_max, Λ)
+V3b_elem(l, n1, n2) = V_numerical(V3b_of_r, l, n1, n2; μω_gen=μω, atol=atol, maxevals=maxevals)
+V_cache = prealloc_V_cache(basis.E_max, ComplexF64)
+@time "V1" V1 = get_sp_V_matrix(V3b_elem, basis.n1s, basis.l1s, [basis.n2s, basis.l2s]; dtype=ComplexF64, cache=V_cache)
+@time "V2" V2 = get_sp_V_matrix(V3b_elem, basis.n2s, basis.l2s, [basis.n1s, basis.l1s]; dtype=ComplexF64, cache=V_cache)
+@time "V12" V12 = get_src_V12_matrix(V3b_of_r, basis, μω_global; atol=atol, maxevals=maxevals)
+@time "V3b" V3b = (V1 * V2) * V12 # commutative?
+
+H = get_3b_H_matrix(coord_system, V_of_r, μω_global, E_max, Λ, m) + V3b
+
+@time "Eigenvalues" evals, _ = eigs(H, nev=3, ncv=30, which=:SR, maxiter=5000, tol=1e-5, ritzvec=false, check=1)
+display(evals)