49 changed files with 1177 additions and 1611 deletions
--- a/.gitignore
+++ b/.gitignore
@ -1,3 +1,6 @@
 # probably not recommended
 Project.toml
 # Compiled FORTRAN libraries
 *.so
--- a/EC.jl
+++ b/EC.jl
@ -1,173 +0,0 @@
 using Statistics, SparseArrays, LinearAlgebra, Arpack, Plots
 include("common.jl")
 "EC model for a Hamiltonian family H(c) = H0 + c * H1"
 mutable struct affine_EC
    H0::AbstractMatrix{ComplexF64}
    H1::AbstractMatrix{ComplexF64}
    weights::Vector{ComplexF64}
    trained::Bool
    H0_EC
    H1_EC
    N_EC
    ensemble_size::Int
    H0_EC_ensemble
    H1_EC_ensemble
    N_EC_ensemble
    training_E::Vector{ComplexF64}
    exact_E::Vector{ComplexF64}
    extrapolated_E::Vector{ComplexF64}
    extrapolated_CI::Vector{ComplexF64}
    affine_EC(H0::AbstractMatrix{ComplexF64}, H1::AbstractMatrix{ComplexF64}, weights::Vector{ComplexF64}=ones(ComplexF64, size(H0, 1)); ensemble_size=0) =
        new(H0, H1, weights, false, nothing, nothing, nothing, ensemble_size, Matrix[], Matrix[], Matrix[], ComplexF64[], ComplexF64[], ComplexF64[], ComplexF64[])
 end
 "Train an EC model for a given range of c values.
 If a list is provided for ref_eval, they are used as reference values for picking the closest eigenvalues at each sampling point.
 If a single number is provided for ref_eval, it is used as a reference for the first point, and the previous eigenvalue is used as the reference for each successive point.
 If orthonormalize_threshold > 0, Gram-Schmidt orthonormalization is performed, using this value as the threshold for dropping redundant vectors."
 function train!(EC::affine_EC, c_vals; ref_eval=-10.0, CAEC=false, gram_schmidt_threshold=0, verbose=true, tol=1e-5)
    training_vecs = Vector{ComplexF64}[]
    for c in c_vals
        verbose && println("Training for c = $c")
        global current_E
        if ref_eval isa Number
            current_E = ref_eval
            ref_eval = nothing
        elseif !isnothing(ref_eval)
            current_E = popfirst!(ref_eval)
        end
        H = EC.H0 + c .* EC.H1
        evals, evecs = eigs(H, sigma=current_E, maxiter=5000, tol=tol, ritzvec=true, check=1)
        current_E = nearest(evals, current_E)
        push!(EC.training_E, current_E)
        push!(training_vecs, evecs[:, nearestIndex(evals, current_E)])
    end
    CAEC && append!(training_vecs, conj.(training_vecs))
    (EC.H0_EC, EC.H1_EC, EC.N_EC) = get_reduced_matrices(EC, training_vecs, gram_schmidt_threshold; verbose=true)
    for _ in 1:EC.ensemble_size
        subsample = resample(length(training_vecs))
        if gram_schmidt_threshold > 0
            (H0_EC, H1_EC, N_EC) = get_reduced_matrices(EC, training_vecs, gram_schmidt_threshold, subsample; verbose=false)
            push!(EC.H0_EC_ensemble, H0_EC)
            push!(EC.H1_EC_ensemble, H1_EC)
            push!(EC.N_EC_ensemble, N_EC)
        else
            push!(EC.H0_EC_ensemble, EC.H0_EC[subsample, subsample])
            push!(EC.H1_EC_ensemble, EC.H1_EC[subsample, subsample])
            push!(EC.N_EC_ensemble, EC.N_EC[subsample, subsample])
        end
    end
    EC.trained = true
 end
 function get_reduced_matrices(EC::affine_EC, training_vecs, gram_schmidt_threshold, subsample=1:length(training_vecs); verbose=false)
    vecs = deepcopy(training_vecs[subsample])
    if gram_schmidt_threshold > 0; vecs = gram_schmidt!(vecs, EC.weights, gram_schmidt_threshold; verbose=verbose); end
    EC_basis = hcat(vecs...)
    weights_mat = spdiagm(EC.weights)
    H0_EC = transpose(EC_basis) * weights_mat * EC.H0 * EC_basis
    H1_EC = transpose(EC_basis) * weights_mat * EC.H1 * EC_basis
    N_EC = transpose(EC_basis) * weights_mat * EC_basis
    return (H0_EC, H1_EC, N_EC)
 end
 resample(n::Int) = rand(1:n, n) |> unique |> sort
 "Extrapolate using a trained EC model for a given range of c values
 If a list is provided for ref_eval, they are used as reference values for picking the closest eigenvalues at each point.
 If a single number is provided for ref_eval, it is used as a reference for the first point, and the previous eigenvalue is used as the reference for each successive point.
 If precalculated_exact_E is provided, ref_eval is ignored.
 If pseudo_inv_tol > 0, the GEVP is avoided using Moore-Penrose psuedoinverse, using this value as the relative tolerance for dropping redundant vectors."
 function extrapolate!(EC::affine_EC, c_vals; ref_eval=EC.training_E[end], pseudo_inv_tol=0, verbose=true, tol=1e-5, precalculated_exact_E=nothing)
    @assert EC.trained "EC model must be trained using train() before extrapolation"
    for c in c_vals
        global current_E
        if isnothing(precalculated_exact_E)
            if ref_eval isa Number
                current_E = ref_eval
                ref_eval = nothing
            elseif !isnothing(ref_eval)
                current_E = popfirst!(ref_eval)
            end
            verbose && println("Extact solution for c = $c")
            H = EC.H0 + c .* EC.H1
            evals, _ = eigs(H, sigma=current_E, maxiter=5000, tol=tol, ritzvec=false, check=1)
            current_E = nearest(evals, current_E)
        else
            current_E = popfirst!(precalculated_exact_E)
        end
        push!(EC.exact_E, current_E)
        verbose && println("Extrapolating for c = $c")
        evals = get_extrapolated_evals(EC.H0_EC, EC.H1_EC, EC.N_EC, c, pseudo_inv_tol)
        push!(EC.extrapolated_E, nearest(evals, current_E))
        if EC.ensemble_size > 0
            E_ensemble = zeros(ComplexF64, EC.ensemble_size)
            for i in 1:EC.ensemble_size
                evals = get_extrapolated_evals(EC.H0_EC_ensemble[i], EC.H1_EC_ensemble[i], EC.N_EC_ensemble[i], c, pseudo_inv_tol)
                E_ensemble[i] = nearest(evals, current_E)
            end
            re_CI = std(real.(E_ensemble))
            im_CI = std(imag.(E_ensemble))
            push!(EC.extrapolated_CI, complex(re_CI, im_CI))
        end
    end
 end
 "Solve the GEVP with or without Moore-Penrose psuedoinverse"
 function get_extrapolated_evals(H0_EC, H1_EC, N_EC, c, pseudo_inv_tol)
    H_EC = H0_EC + c .* H1_EC
    if pseudo_inv_tol > 0
        inv_N_EC = pinv(N_EC; atol=pseudo_inv_tol)
        H_EC = inv_N_EC * H_EC
        return eigvals(H_EC)
    else
        return eigvals(H_EC, N_EC)
    end
 end
 "Export EC data as CSV file"
 exportCSV(EC::affine_EC, filename) = exportCSV(filename, (EC.training_E, EC.exact_E, EC.extrapolated_E), ("training", "exact", "extrapolated"))
 "Plot EC data and optionally save figure to a file"
 function plot(EC::affine_EC, save_fig_filename=nothing; basis_points=nothing, basis_contour=nothing, xlims=nothing, ylims=nothing)
    scatter(real.(EC.training_E), imag.(EC.training_E), label="training")
    scatter!(real.(EC.exact_E), imag.(EC.exact_E), label="exact", markercolor=:white)
    if EC.ensemble_size > 0
        scatter!(real.(EC.extrapolated_E), imag.(EC.extrapolated_E), xerror=real.(EC.extrapolated_CI), yerror=imag.(EC.extrapolated_CI), label="extrapolated", m=:x)
    else
        scatter!(real.(EC.extrapolated_E), imag.(EC.extrapolated_E), label="extrapolated", m=:x)
    end
    isnothing(basis_points) || scatter!(real.(basis_points), imag.(basis_points), m=:x, label="basis")
    isnothing(basis_contour) || plot!(real.(basis_contour), imag.(basis_contour), label="contour")
    isnothing(xlims) || xlims!(xlims...)
    isnothing(ylims) || ylims!(ylims...)
    isnothing(save_fig_filename) || savefig(save_fig_filename)
 end
--- a/EC_test.ipynb
+++ b/EC_test.ipynb
@ -0,0 +1,100 @@
 {
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots\n",
    "include(\"p_space.jl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "vertices = [0, 0.4 - 0.15im, 0.8, 6]\n",
    "subdivisions = [128, 128, 128]\n",
    "p, w = get_mesh(vertices, subdivisions)\n",
    "mesh_E = p.*p ./ (2*0.5)\n",
    "\n",
    "# ResonanceEC: Eq. (20)\n",
    "V_system(c) = (p, q) -> c*(-5*g0(sqrt(3), p, q) + 2*g0(sqrt(10), p, q))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "training_points = range(0.75, 0.45, 5)\n",
    "training_E = Vector{ComplexF64}(undef, length(training_points))\n",
    "EC_basis = Matrix{ComplexF64}(undef, length(p), length(training_points))\n",
    "\n",
    "for (j, c) in enumerate(training_points)\n",
    "    evals, evecs = eigen(get_H_matrix(V_system(c), p, w))\n",
    "    i = identify_pole_i(p, evals)\n",
    "    training_E[j] = evals[i]\n",
    "    EC_basis[:, j] = evecs[:, i]\n",
    "end\n",
    "\n",
    "scatter(real.(training_E), imag.(training_E), label=\"training\")\n",
    "plot!(real.(mesh_E), imag.(mesh_E), label=\"contour\")\n",
    "xlims!(0,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "extrapolate_points = range(0.40, 0.25, 5)\n",
    "ref_E = 0.2 - 0.1im\n",
    "\n",
    "exact_E = Vector{ComplexF64}(undef, length(extrapolate_points))\n",
    "extrapolate_E = Vector{ComplexF64}(undef, length(extrapolate_points))\n",
    "\n",
    "EC_basis_w = EC_basis .* w\n",
    "N_EC = transpose(EC_basis_w) * EC_basis\n",
    "\n",
    "for (j, c) in enumerate(extrapolate_points)\n",
    "    exact_E[j] = quick_pole_E(V_system(c))\n",
    "\n",
    "    EC_basis_w = EC_basis .* w\n",
    "    H = get_H_matrix(V_system(c), p, w)\n",
    "    H_EC = transpose(EC_basis_w) * H * EC_basis\n",
    "    evals = eigvals(H_EC, N_EC)\n",
    "    i = argmin(abs.(evals .- ref_E))\n",
    "    ref_E = evals[i]\n",
    "    extrapolate_E[j] = evals[i]\n",
    "end\n",
    "\n",
    "scatter(real.(training_E), imag.(training_E), label=\"training\")\n",
    "scatter!(real.(exact_E), imag.(exact_E), label=\"exact\")\n",
    "scatter!(real.(extrapolate_E), imag.(extrapolate_E), label=\"extrapolated\")\n",
    "plot!(real.(mesh_E), imag.(mesh_E), label=\"contour\")\n",
    "xlims!(0,1)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.10.2",
   "language": "julia",
   "name": "julia-1.10"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.10.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
 }
--- a/Project.toml
+++ b/Project.toml
@ -1,15 +0,0 @@
 [deps]
 Arpack = "7d9fca2a-8960-54d3-9f78-7d1dccf2cb97"
 CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
 DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
 DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa"
 FastGaussQuadrature = "442a2c76-b920-505d-bb47-c5924d526838"
 HDF5 = "f67ccb44-e63f-5c2f-98bd-6dc0ccc4ba2f"
 LRUCache = "8ac3fa9e-de4c-5943-b1dc-09c6b5f20637"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 QuadGK = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
 Roots = "f2b01f46-fcfa-551c-844a-d8ac1e96c665"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
 WignerSymbols = "9f57e263-0b3d-5e2e-b1be-24f2bb48858b"
--- a/berggren.jl
+++ b/berggren.jl
@ -1,22 +1,18 @@
 using SparseArrays
-include("math.jl")
+include("ho_basis.jl")
-"berg_bases1/2 are lists of (1+l_max) matrices containing the eigenbases corresponding to 1st and 2nd DOFs respectively,
+"Basis transformation from HO to momentum space"
-js are a list of tuples (j1, j2) corresponding to 1st and 2nd DOFs respectively,
+function get_W_matrix(basis_p, E_max, Λ, μ1ω1, μ2ω2=μ1ω1; weights=true)
-and ws are the weights needed to evaluate the inner products"
+    Es, n1s, l1s, n2s, l2s = get_2p_basis(E_max, Λ)
-function get_2p_p1p2_matrix(mesh_size, js, Λ, berg_bases1::Vector{Matrix{ComplexF64}}, berg_bases2::Vector{Matrix{ComplexF64}}, ks::Vector{ComplexF64}, ws::Vector{ComplexF64})
+    W = zeros(ComplexF64, length(basis_p), length(Es))
-    # TODO: Cache / precalculate
+    Threads.@threads for idx in CartesianIndices(W)
-    integral1(np, lp, n, l) = sum(ks .* berg_bases1[1 + lp][:, np] .* ws .* berg_bases1[1 + l][:, n])
+        (i1, i2) = Tuple(idx)
-    integral2(np, lp, n, l) = sum(ks .* berg_bases2[1 + lp][:, np] .* ws .* berg_bases2[1 + l][:, n])
+        ((j1, j2), (k1, w1), (k2, w2)) = basis_p[i1]
-
+        if j1 == l1s[i2] && j2 == l2s[i2]
-    basis = iter_prod(js, 1:mesh_size, 1:mesh_size)
+            elem1 = 1/sqrt(sqrt(μ1ω1)) * (-1)^n1s[i2] * ho_basis(j1, n1s[i2], 1/sqrt(μ1ω1) * k1)
-    mat = zeros(ComplexF64, length(basis), length(basis))
+            elem2 = 1/sqrt(sqrt(μ2ω2)) * (-1)^n2s[i2] * ho_basis(j2, n2s[i2], 1/sqrt(μ2ω2) * k2)
-    Threads.@threads for idx in CartesianIndices(mat)
+            W[idx] = elem1 * elem2 * (weights ? w1 * w2 : 1)
-        (ip, i) = Tuple(idx)
+        end
        ((j1p, j2p), n1p, n2p) = basis[ip]
        ((j1, j2), n1, n2) = basis[i]
        val = racahs_reduction_formula(n1p, j1p, n2p, j2p, n1, j1, n2, j2, Λ, integral1, integral2)
        if !(val ≈ 0); mat[idx] = val; end
    end
-    return sparse(mat)
+    return sparse(W)
 end
--- a/berggren_2body.jl
+++ b/berggren_2body.jl
@ -1,5 +1,5 @@
 using SparseArrays, Arpack
-include("common.jl")
+include("helper.jl")
 include("p_space.jl")
 E_target = -0.3919
--- a/berggren_3body.jl
+++ b/berggren_3body.jl
@ -0,0 +1,59 @@
 using LinearAlgebra, SparseArrays, Arpack
 include("helper.jl")
 include("p_space.jl")
 include("berggren.jl")
 println("No of threads = ", Threads.nthreads())
 atol = 10^-5
 maxevals = 10^5
 R_cutoff = 16
 Λ = 0
 m = 1.0
 μ1 = m * 1/2
 μ2 = m * 2/3
 Va = -2
 Ra = 2
 V_of_r(r) = Va * exp(-r^2 / Ra^2)
 V_l(j, k, kp) = Vl_mat_elem(V_of_r, j, k, kp; atol=atol, maxevals=maxevals, R_cutoff=R_cutoff)
 vertices = [0, 0.5 - 0.3im, 1, 4]
 subdivisions = [10, 10, 10]
 ks, ws = get_mesh(vertices, subdivisions)
 jmax = 4
 tri((j1, j2)) = triangle_ineq(j1, j2, Λ)
 js = collect(Iterators.filter(tri, iter_prod(0:jmax, 0:jmax)))
 basis = iter_prod(js, zip(ks, ws), zip(ks, ws)) # basis = ((j1, j2), (k1, w1), (k2, w2))
 basis_size = length(js) * length(ks)^2
@assert length(basis) == basis_size "Something wrong with the basis"
 println("Basis size = $basis_size")
@time "T" begin
    T_blocks = [kron_sum(get_T_matrix(ks, μ1), get_T_matrix(ks, μ2)) for _ in js]
    T = blockdiag(sparse.(T_blocks)...)
 end
@time "V1" begin
    V1_blocks = [kron(get_V_matrix((k, kp) -> V_l(j1, k, kp), ks, ws), I(length(ks))) for (j1, _) in js]
    V1 = blockdiag(sparse.(V1_blocks)...)
 end
 E_max = 30
 μω_global = 0.5
 μ1ω1 = μω_global * 1/2
 μ2ω2 = μω_global * 2
@time "V2_HO" V2_HO =  get_jacobi_V2_matrix(V_of_r, E_max, Λ, μω_global)
@time "W_right" W_right = get_W_matrix(basis, E_max, Λ, μ1ω1, μ2ω2; weights=true)
@time "W_left" W_left = get_W_matrix(basis, E_max, Λ, μ1ω1, μ2ω2; weights=false)
@time "V2" V2 = W_left * V2_HO * transpose(W_right)
@time "H" H = T + V1 + V2
@time "Eigenvalues" evals, _ = eigs(H, nev=3, ncv=24, which=:SR, maxiter=5000, tol=1e-5, ritzvec=false, check=1)
 display(evals)
--- a/berggren_3body_resonance.jl
+++ b/berggren_3body_resonance.jl
@ -1,7 +1,6 @@
 using LinearAlgebra, SparseArrays, Arpack
-include("common.jl")
+include("helper.jl")
 include("p_space.jl")
 include("ho_basis.jl")
 include("berggren.jl")
 println("No of threads = ", Threads.nthreads())
@ -11,7 +10,8 @@ R_cutoff = 16
 Λ = 0
 m = 1.0
-μ = m/2 # due to simple relative coordinates
+μ1 = m * 1/2
 μ2 = m * 2/3
 target = 4.0766890719636875 - 0.012758927741074495im
@ -31,45 +31,28 @@ basis_size = length(js) * length(ks)^2
@assert length(basis) == basis_size "Something wrong with the basis"
 println("Basis size = $basis_size")
-# generate Berggren bases
+@time "T" begin
-@time "berg_bases" begin
+    T_blocks = [kron_sum(get_T_matrix(ks, μ1), get_T_matrix(ks, μ2)) for _ in js]
-    berg_bases = Vector{Matrix{ComplexF64}}(undef, jmax + 1)
+    T = blockdiag(sparse.(T_blocks)...)
    for j in 0:jmax
        _, berg_basis = eigen(get_H_matrix((k, kp) -> V_l(j, k, kp), ks, ws, μ); permute=false, scale=false)
        N_berg = sum(berg_basis.^2 .* ws, dims=1)
        berg_bases[1 + j] = berg_basis ./ transpose(sqrt.(N_berg))
    end
    to_berg_basis(mat, j) = transpose(berg_bases[1 + j] .* ws) * mat * berg_bases[1 + j]
 end
-@time "U_berggren" begin
+@time "V1" begin
-    U_blocks = [kron(berg_bases[1 + j1], berg_bases[1 + j2]) for (j1, j2) in js]
+    V1_blocks = [kron(get_V_matrix((k, kp) -> V_l(j1, k, kp), ks, ws), I(length(ks))) for (j1, _) in js]
-    U = blockdiag(sparse.(U_blocks)...)
+    V1 = blockdiag(sparse.(V1_blocks)...)
 end
@time "Block diagonal part" begin
    Hb_blocks = [kron_sum(to_berg_basis(get_H_matrix((k, kp) -> V_l(j1, k, kp), ks, ws, μ), j1), to_berg_basis(get_H_matrix((k, kp) -> V_l(j2, k, kp), ks, ws, μ), j2)) for (j1, j2) in js]
    Hb = blockdiag(sparse.(Hb_blocks)...)
 end
@time "T_cross" T_cross = get_2p_p1p2_matrix(length(ks), js, Λ, berg_bases, berg_bases, ks, ws) ./ (2*μ)
 E_max = 30
 μω_global = 0.5
-# due to simple relative coordinates
+μ1ω1 = μω_global * 1/2
-μω = μω_global * 2
+μ2ω2 = μω_global * 2
 μ = m/2
-basis_ho = ho_basis_2B(E_max, Λ)
+@time "V2_HO" V2_HO =  get_jacobi_V2_matrix(V_of_r, E_max, Λ, μω_global)
-@time "V12_HO" V12_HO =  get_src_V12_matrix(V_of_r, basis_ho, μω_global; atol=10^-6, maxevals=10^5)
+@time "W_right" W_right = get_W_matrix(basis, E_max, Λ, μ1ω1, μ2ω2; weights=true)
@time "W_left" W_left = get_W_matrix(basis, E_max, Λ, μ1ω1, μ2ω2; weights=false)
-@time "W" W = get_W_matrix(basis, basis_ho, μω, μω; weights=true)
+@time "V2" V2 = W_left * V2_HO * transpose(W_right)
-
+@time "H" H = T + V1 + V2
@time "V12_p" V12_p = W * V12_HO * transpose(W)
@time "V12" V12 = transpose(U) * V12_p * U
@time "H" H = Hb + T_cross + V12
@time "Eigenvalues" evals, _ = eigs(H, sigma=target, maxiter=5000, tol=1e-5, ritzvec=false, check=1)
 display(evals)
--- a/calculations/2body_data.jl
+++ b/calculations/2body_data.jl
@ -1,33 +0,0 @@
 using Roots, DelimitedFiles
 include("../EC.jl")
 include("../common.jl")
 include("../p_space.jl")
 μ = 0.5
 V_system(c) = (p, q) -> c*(-5*g0(sqrt(3), p, q) + 2*g0(sqrt(10), p, q)) # ResonanceEC: Eq. (20)
 # determining c0 with EC
 temp_c = range(1.1, 0.9, 3)
 p, w = get_mesh([0, 8], [256])
 H0 = get_T_matrix(p, μ)
 V = get_V_matrix(V_system(1), p, w)
 EC = affine_EC(H0, V, w)
 train!(EC, temp_c; ref_eval=-0.2, CAEC=false, verbose=false)
 quick_extrapolate(c) = minimum(abs2, get_extrapolated_evals(EC.H0_EC, EC.H1_EC, EC.N_EC, c, 0))
 c0 = find_zero(quick_extrapolate, 0.85)
 training_c = range(1.2, 0.9, 9) # original: range(1.35, 0.9, 5)
 extrapolating_c = range(0.78, 0.45, 7) # original: range(0.75, 0.40, 8)
 data_c = vcat(training_c, extrapolating_c)
 data_E = [quick_pole_E(V_system(c)) for c in data_c]
 # export to CSV
 file = "temp/2body_data.csv"
 delim = ','
 open(file, "w") do f
    writedlm(f, ["c" "re_E" "im_E"], delim)
    writedlm(f, [c0 0 0], delim) # first entry for the threshold
    writedlm(f, hcat(data_c, real.(data_E), imag.(data_E)), delim)
 end
--- a/calculations/3body_Berggren_B2R_EC.jl
+++ b/calculations/3body_Berggren_B2R_EC.jl
@ -1,40 +1,136 @@
 using Arpack, SparseArrays, LRUCache
 using DelimitedFiles, Plots
 include("../ho_basis.jl")
 include("../p_space.jl")
-include("../EC.jl")
+include("../berggren.jl")
-Λ = 0
+println("No of threads = ", Threads.nthreads())
 m = 1.0
 V_of_r(r) =  2 * exp(-(r-3)^2 / (1.5)^2)
 ϕ = 0.1
 vertices = [0, 4 * exp(-1im * ϕ), 5, 6]
 subdivisions = [40, 12, 15]
 jmax = 6
 E_max = 40
 μω_global = 0.5
 H0, weights = get_3b_H_matrix(jacobi, V_of_r, vertices, subdivisions, jmax, μω_global, E_max, Λ, m)
 # Vp = perturbation to make the state artificially bound
 Vp_of_r(r) = -exp(-(r/3)^2)
 Vp, _ = get_3b_H_matrix(jacobi, Vp_of_r, vertices, subdivisions, jmax, μω_global, E_max, Λ, m, false, true)
 training_c = [2.6, 2.4, 2.2, 2.0, 1.8]
 extrapolating_c = 0.0 : 0.2 : 1.2
 training_ref = -2.22 # complete list not needed because identification is simple
-extrapolating_ref = [4.076662025307587-0.012709842443350328im,
+exact_ref = reverse([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]
+    1.233088227541505-0.0003070320106485624im])
-EC = affine_EC(H0, Vp, weights)
+Λ = 0
-train!(EC, training_c; ref_eval=training_ref, CAEC=true)
+m = 1.0
-extrapolate!(EC, extrapolating_c; ref_eval=extrapolating_ref)
+Va_of_r(r) = 2 * exp(-(r-3)^2 / (1.5)^2)
 Vb_of_r(r) = -exp(-(r/3)^2)
-exportCSV(EC, "temp/Berggren_B2R.csv")
+atol = 10^-5
-plot(EC, "temp/Berggren_B2R.pdf")
+maxevals = 10^5
 R_cutoff = 16
 # due to Jacobi coordinates
 μ1 = m * 1/2
 μ2 = m * 2/3
 vertices = [0, 2 - 0.2im, 3, 4]
 subdivisions = [16, 10, 10]
 ks, ws = get_mesh(vertices, subdivisions)
 jmax = 4
 tri((j1, j2)) = triangle_ineq(j1, j2, Λ)
 js = collect(Iterators.filter(tri, iter_prod(0:jmax, 0:jmax)))
 basis = iter_prod(js, zip(ks, ws), zip(ks, ws)) # basis = ((j1, j2), (k1, w1), (k2, w2))
 basis_size = length(js) * length(ks)^2
 weights_mat = spdiagm(repeat(kron(ws, ws), jmax + 1))
@assert length(basis) == basis_size "Something wrong with the basis"
 println("Basis size = $basis_size")
@time "T" begin
    T_blocks = [kron_sum(get_T_matrix(ks, μ1), get_T_matrix(ks, μ2)) for _ in js]
    T = blockdiag(sparse.(T_blocks)...)
 end
@time "Va1" begin
    Va_l(j, k, kp) = Vl_mat_elem(Va_of_r, j, k, kp; atol=atol, maxevals=maxevals, R_cutoff=R_cutoff)
    Va1_blocks = [kron(get_V_matrix((k, kp) -> Va_l(j1, k, kp), ks, ws), I(length(ks))) for (j1, _) in js]
    Va1 = blockdiag(sparse.(Va1_blocks)...)
 end
@time "Vb1" begin
    Vb_l(j, k, kp) = Vl_mat_elem(Vb_of_r, j, k, kp; atol=atol, maxevals=maxevals, R_cutoff=R_cutoff)
    Vb1_blocks = [kron(get_V_matrix((k, kp) -> Vb_l(j1, k, kp), ks, ws), I(length(ks))) for (j1, _) in js]
    Vb1 = blockdiag(sparse.(Vb1_blocks)...)
 end
 E_max = 40
 μω_global = 0.5
 μ1ω1 = μω_global * 1/2
 μ2ω2 = μω_global * 2
@time "Va2_HO" Va2_HO =  get_jacobi_V2_matrix(Va_of_r, E_max, Λ, μω_global; atol=atol, maxevals=maxevals)
@time "Vb2_HO" Vb2_HO =  get_jacobi_V2_matrix(Vb_of_r, E_max, Λ, μω_global; atol=atol, maxevals=maxevals)
@time "W_right" W_right = get_W_matrix(basis, E_max, Λ, μ1ω1, μ2ω2; weights=true)
@time "W_left" W_left = get_W_matrix(basis, E_max, Λ, μ1ω1, μ2ω2; weights=false)
@time "Va2" Va2 = W_left * Va2_HO * transpose(W_right)
@time "Vb2" Vb2 = W_left * Vb2_HO * transpose(W_right)
@time "Ha" Ha = T + Va1 + Va2
@time "Vb" Vb = Vb1 + Vb2
@time "Eigenvalues" test_evals, _ = eigs(Ha, sigma=exact_ref[end], maxiter=5000, tol=1e-5, ritzvec=false, check=1)
 display(test_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()
 current_E = training_ref
 exact = ComplexF64[]
 training = ComplexF64[]
 extrapolated = ComplexF64[]
 training_vecs = Vector{ComplexF64}[]
 for c in training_c
    println("Training for c = $c")
    H = Ha + c .* Vb
    evals, evecs = eigs(H, sigma=current_E, maxiter=5000, tol=1e-5, ritzvec=true, check=1)
    global current_E = nearest(evals, 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) * weights_mat * EC_basis
 Ha_EC = transpose(EC_basis) * weights_mat * Ha * EC_basis
 Vb_EC = transpose(EC_basis) * weights_mat * Vb * EC_basis
 for c in extrapolating_c
    println("Extrapolating for c = $c")
    global current_E = pop!(exact_ref)
    H = Ha + c .* Vb
    evals, _ = eigs(H, sigma=current_E, maxiter=5000, tol=1e-5, ritzvec=false, check=1)
    global current_E = nearest(evals, 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/Berggren_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/Berggren_B2R.pdf")
--- a/calculations/3body_Berggren_R2R_EC.jl
+++ b/calculations/3body_Berggren_R2R_EC.jl
@ -1,42 +1,134 @@
 using Arpack, SparseArrays, LRUCache
 using DelimitedFiles, Plots
 include("../ho_basis.jl")
 include("../p_space.jl")
-include("../EC.jl")
+include("../berggren.jl")
-Λ = 0
+println("No of threads = ", Threads.nthreads())
 m = 1.0
 V_of_r(r) =  2 * exp(-(r-3)^2 / (1.5)^2)
 vertices = [0, 2 - 0.2im, 3, 4]
 subdivisions = [15, 10, 10]
 jmax = 4
 E_max = 40
 μω_global = 0.5
 H0, weights = get_3b_H_matrix(jacobi, V_of_r, vertices, subdivisions, jmax, μω_global, E_max, Λ, m)
 # Vp = perturbation to make the state artificially bound
 Vp_of_r(r) = -exp(-(r/3)^2)
 Vp, _ = get_3b_H_matrix(jacobi, Vp_of_r, vertices, subdivisions, jmax, μω_global, E_max, Λ, m, false, true)
 training_c = [1.1, 0.9, 0.7, 0.5]
 extrapolating_c = 0.0 : 0.2 : 1.2
-training_ref = [1.4750633616275919 - 0.0003021770706749637im
+training_ref = reverse([1.4750633616275919 - 0.0003021770706749637im
    1.9567078295375822 - 0.0007646829108872369im
    2.4351117758403076 - 0.001281037843108658im
-    2.9096543462392357 - 0.002962488527470604im]
+    2.9096543462392357 - 0.002962488527470604im])
-extrapolating_ref = [4.076662025307587-0.012709842443350328im,
+exact_ref = reverse([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]
+    1.233088227541505-0.0003070320106485624im])
-EC = affine_EC(H0, Vp, weights)
+Λ = 0
-train!(EC, training_c; ref_eval=training_ref, CAEC=false)
+m = 1.0
-extrapolate!(EC, extrapolating_c; ref_eval=extrapolating_ref)
+Va_of_r(r) = 2 * exp(-(r-3)^2 / (1.5)^2)
 Vb_of_r(r) = -exp(-(r/3)^2)
-exportCSV(EC, "temp/Berggren_R2R.csv")
+atol = 10^-5
-plot(EC, "temp/Berggren_R2R.pdf")
+maxevals = 10^5
 R_cutoff = 16
 # due to Jacobi coordinates
 μ1 = m * 1/2
 μ2 = m * 2/3
 vertices = [0, 2 - 0.1im, 3, 4]
 subdivisions = [16, 10, 10]
 ks, ws = get_mesh(vertices, subdivisions)
 jmax = 4
 tri((j1, j2)) = triangle_ineq(j1, j2, Λ)
 js = collect(Iterators.filter(tri, iter_prod(0:jmax, 0:jmax)))
 basis = iter_prod(js, zip(ks, ws), zip(ks, ws)) # basis = ((j1, j2), (k1, w1), (k2, w2))
 basis_size = length(js) * length(ks)^2
 weights_mat = spdiagm(repeat(kron(ws, ws), jmax + 1))
@assert length(basis) == basis_size "Something wrong with the basis"
 println("Basis size = $basis_size")
@time "T" begin
    T_blocks = [kron_sum(get_T_matrix(ks, μ1), get_T_matrix(ks, μ2)) for _ in js]
    T = blockdiag(sparse.(T_blocks)...)
 end
@time "Va1" begin
    Va_l(j, k, kp) = Vl_mat_elem(Va_of_r, j, k, kp; atol=atol, maxevals=maxevals, R_cutoff=R_cutoff)
    Va1_blocks = [kron(get_V_matrix((k, kp) -> Va_l(j1, k, kp), ks, ws), I(length(ks))) for (j1, _) in js]
    Va1 = blockdiag(sparse.(Va1_blocks)...)
 end
@time "Vb1" begin
    Vb_l(j, k, kp) = Vl_mat_elem(Vb_of_r, j, k, kp; atol=atol, maxevals=maxevals, R_cutoff=R_cutoff)
    Vb1_blocks = [kron(get_V_matrix((k, kp) -> Vb_l(j1, k, kp), ks, ws), I(length(ks))) for (j1, _) in js]
    Vb1 = blockdiag(sparse.(Vb1_blocks)...)
 end
 E_max = 40
 μω_global = 0.5
 μ1ω1 = μω_global * 1/2
 μ2ω2 = μω_global * 2
@time "Va2_HO" Va2_HO =  get_jacobi_V2_matrix(Va_of_r, E_max, Λ, μω_global; atol=atol, maxevals=maxevals)
@time "Vb2_HO" Vb2_HO =  get_jacobi_V2_matrix(Vb_of_r, E_max, Λ, μω_global; atol=atol, maxevals=maxevals)
@time "W_right" W_right = get_W_matrix(basis, E_max, Λ, μ1ω1, μ2ω2; weights=true)
@time "W_left" W_left = get_W_matrix(basis, E_max, Λ, μ1ω1, μ2ω2; weights=false)
@time "Va2" Va2 = W_left * Va2_HO * transpose(W_right)
@time "Vb2" Vb2 = W_left * Vb2_HO * transpose(W_right)
@time "Ha" Ha = T + Va1 + Va2
@time "Vb" Vb = Vb1 + Vb2
@time "Eigenvalues" test_evals, _ = eigs(Ha, sigma=exact_ref[end], maxiter=5000, tol=1e-5, ritzvec=false, check=1)
 display(test_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()
 exact = ComplexF64[]
 training = ComplexF64[]
 extrapolated = ComplexF64[]
 training_vecs = Vector{ComplexF64}[]
 for c in training_c
    println("Training for c = $c")
    global current_E = pop!(training_ref)
    H = Ha + c .* Vb
    evals, evecs = eigs(H, sigma=current_E, maxiter=5000, tol=1e-5, ritzvec=true, check=1)
    global current_E = nearest(evals, current_E)
    push!(training, current_E)
    push!(training_vecs, evecs[:, nearestIndex(evals, current_E)])
 end
 EC_basis = hcat(training_vecs...)
 N_EC = transpose(EC_basis) * weights_mat * EC_basis
 Ha_EC = transpose(EC_basis) * weights_mat * Ha * EC_basis
 Vb_EC = transpose(EC_basis) * weights_mat * Vb * EC_basis
 for c in extrapolating_c
    println("Extrapolating for c = $c")
    global current_E = pop!(exact_ref)
    H = Ha + c .* Vb
    evals, _ = eigs(H, sigma=current_E, maxiter=5000, tol=1e-5, ritzvec=false, check=1)
    global current_E = nearest(evals, 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
 scatter(real.(training),imag.(training), label="training")
 scatter!(real.(exact),imag.(exact), label="exact")
 scatter!(real.(extrapolated),imag.(extrapolated), label="extrapolated")
 savefig("temp/Berggren_R2R.pdf")
--- a/calculations/3body_CSM_B2R_EC.jl
+++ b/calculations/3body_CSM_B2R_EC.jl
@ -1,40 +0,0 @@
 include("../p_space.jl")
 include("../EC.jl")
 Λ = 0
 m = 1.0
 V_of_r(r) =  2 * exp(-(r-3)^2 / (1.5)^2)
 ϕ = 0.1
 vertices = [0, 6 * exp(-1im * ϕ)]
 subdivisions = [50]
 jmax = 4
 E_max = 40
 μω_global = 0.5
 H0, weights = get_3b_H_matrix(jacobi, V_of_r, vertices, subdivisions, jmax, μω_global, E_max, Λ, m)
 # Vp = perturbation to make the state artificially bound
 Vp_of_r(r) = -exp(-(r/3)^2)
 Vp, _ = get_3b_H_matrix(jacobi, Vp_of_r, vertices, subdivisions, jmax, μω_global, E_max, Λ, m, false, true)
 training_c = [2.6, 2.4, 2.2, 2.0, 1.8]
 extrapolating_c = 0.0 : 0.2 : 1.2
 training_ref = -2.22 # complete list not needed because identification is simple
 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 = affine_EC(H0, Vp, weights)
 train!(EC, training_c; ref_eval=training_ref, CAEC=true)
 extrapolate!(EC, extrapolating_c; precalculated_exact_E=exact_E)
 exportCSV(EC, "temp/CSM_B2R.csv")
 plot(EC, "temp/CSM_B2R.pdf")
--- a/calculations/3body_HO_B2R_ACCC.jl
+++ b/calculations/3body_HO_B2R_ACCC.jl
@ -1,68 +0,0 @@
 using Roots, LinearAlgebra, Plots
 include("../EC.jl")
 include("../common.jl")
 include("../ho_basis.jl")
 V_of_r(r) = 2 * exp(-(r-3)^2 / (1.5)^2)
 Λ = 0
 m = 1.0
 ϕ = 0.1
 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)
 training_ref = -2.22
 extrapolating_ref = [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]
 training_c = range(2.8, 1.8, 5)
 extrapolating_c = 0.0 : 0.2 : 1.2
 EC = affine_EC(H0, Vp)
 train!(EC, training_c; ref_eval=training_ref, CAEC=true)
 extrapolate!(EC, extrapolating_c; ref_eval=extrapolating_ref)
 # determining c0 with EC
 approx_c0 = 1.5
 quick_extrapolate(c) = minimum(abs2, get_extrapolated_evals(EC.H0_EC, EC.H1_EC, EC.N_EC, c, 1e-14))
 c0 = find_zero(quick_extrapolate, approx_c0)
 order::Int = ceil((length(training_c) - 1) / 2) # order of the Pade approximant
 # Solve coefficients as a linear system
 training_k = alt_sqrt.(EC.training_E)
 M_left_element(c, i) = alt_sqrt(c - c0)^i
 M_left = M_left_element.(training_c, (0:order)')
 M_right = -training_k .* M_left[:, 2:end] # remove the first column
 M = hcat(M_left, M_right) # M = [M_left | M_right]
 sol = M \ training_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.([extrapolating_c; training_c])
 extrapolated_E = extrapolated_k .^ 2
 # Plotting
 scatter(real.(EC.training_E), imag.(EC.training_E), label="training")
 scatter!(real.(EC.exact_E), imag.(EC.exact_E), label="exact")
 scatter!(real.(EC.extrapolated_E), imag.(EC.extrapolated_E), label="CAEC", m=:x)
 scatter!(real.(extrapolated_E), imag.(extrapolated_E), label="ACCC", m=:+)
 title!("3-body extrapolation with $(length(training_c)) training points")
 savefig("temp/3body_HO_B2R_ACCC-$(length(training_c)).pdf")
--- a/calculations/3body_HO_B2R_EC.jl
+++ b/calculations/3body_HO_B2R_EC.jl
@ -1,36 +1,93 @@
 using Arpack, SparseArrays, LRUCache
 using DelimitedFiles, Plots
 include("../ho_basis.jl")
 include("../EC.jl")
 V_of_r(r) = 2 * exp(-(r-3)^2 / (1.5)^2)
 Λ = 0
 m = 1.0
 Va_of_r(r) = 2 * exp(-(r-3)^2 / (1.5)^2)
 Vb_of_r(r) = -exp(-(r/3)^2)
 ϕ = 0.1
 μω_global = 0.5 * exp(-2im * ϕ)
 E_max = 40
 μω_global = 0.5 * exp(-2im * pi / 9)
-H0 = get_3b_H_matrix(jacobi, V_of_r, μω_global, E_max, Λ, m, true, true)
+# due to Jacobi coordinates
 μ1ω1 = μω_global * 1/2
 μ2ω2 = μω_global * 2
 μ1 = m * 1/2
 μ2 = m * 2/3
-# Vp = perturbation to make the state artificially bound
+println("No of threads = ", Threads.nthreads())
 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)
-training_ref = -2.22
+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')
-extrapolating_ref = [4.076662025307587-0.012709842443350328im,
+println("Basis size = ", length(Es))
    3.613318119833891-0.007335804709990623im,
    3.1453431847006783-0.004030580410326795im,
    2.672967129943755-0.00211498327461944im,
    2.196542557810288-0.0010719835443437104im,
    1.7164583929199813-0.0005455212208182736im,
    1.233088227541505-0.0003070320106485624im]
-training_c = [2.6, 2.4, 2.2, 2.0, 1.8]
+@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_V_matrix(Va_of_r, E_max, Λ, μ1ω1, μω_global)
@time "Va" Vb = get_jacobi_V_matrix(Vb_of_r, E_max, Λ, μ1ω1, μω_global)
@time "Ha" Ha = T1 + T2 + Va
@time "Eigenvalues" target_evals, _ = eigs(Ha, nev=5, ncv=50, which=:LI, 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()
 current_E = -0.72763
 training_c = [2.0, 1.9, 1.8]
 extrapolating_c = 0.0 : 0.2 : 1.2
-EC = affine_EC(H0, Vp)
+exact = ComplexF64[]
-train!(EC, training_c; ref_eval=training_ref, CAEC=true)
+training = ComplexF64[]
-extrapolate!(EC, extrapolating_c; ref_eval=extrapolating_ref)
+extrapolated = ComplexF64[]
 training_vecs = Vector{ComplexF64}[]
-exportCSV(EC, "temp/HO_B2R.csv")
+for c in training_c
-plot(EC, "temp/HO_B2R.pdf")
+    println("Training for c = $c")
    H = Ha + c .* Vb
    evals, evecs = eigs(H, nev=3, ncv=24, which=:LI, maxiter=5000, tol=1e-5, ritzvec=true, check=1)
    global current_E = nearest(evals, 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 = 4.0766890719636635 - 0.01275892774109674im
 for c in extrapolating_c
    println("Extrapolating for c = $c")
    H = Ha + c .* Vb
    evals, evecs = eigs(H, nev=3, ncv=24, which=:LI, maxiter=5000, tol=1e-5, ritzvec=true, check=1)
    global current_E = nearest(evals, 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/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/HO_B2R.pdf")
--- a/calculations/3body_HO_R2R_EC.jl
+++ b/calculations/3body_HO_R2R_EC.jl
@ -1,24 +1,54 @@
-include("../ho_basis.jl")
+using DelimitedFiles, Plots
-include("../EC.jl")
+include("../ho_basis_3body_resonance.jl")
-V_of_r(r) = 2 * exp(-(r-3)^2 / (1.5)^2)
+current_E = 5.9673 - 0.0006im
 Λ = 0
 m = 1.0
 μω_global = 0.5 * exp(-2im * pi / 9)
 E_max = 40
 T = get_3b_H_matrix(src, V_of_r, μω_global, E_max, Λ, m, true, false)
 V = get_3b_H_matrix(src, V_of_r, μω_global, E_max, Λ, m, false, true)
 ref_E = 5.9673 - 0.0006im
 training_c = 2.0 : -0.2 : 1.2
 extrapolating_c = 1.05 .- [0.0 : 0.1 : 0.4; 0.45 : 0.05 : 0.60]
-EC = affine_EC(T, V)
+@time "H0" H0 = T1 + T2
 train!(EC, training_c; ref_eval=ref_E, CAEC=false)
 extrapolate!(EC, extrapolating_c)
-exportCSV(EC, "temp/HO_R2R.csv")
+# free memory
-plot(EC, "temp/HO_R2R.pdf")
+Es = n1s = l1s = n2s = l2s = mask1 = mask2 = T1 = T2 = V1_cache = V_relative_cache = V1 = V_relative = U = V2 = nothing
 GC.gc()
 exact = ComplexF64[]
 training = ComplexF64[]
 extrapolated = ComplexF64[]
 training_vecs = Vector{ComplexF64}[]
 for c in training_c
    println("Training for c = $c")
    local H = H0 + c .* V
    local evals, evecs = eigs(H, nev=3, ncv=24, which=:LI, maxiter=5000, tol=1e-5, ritzvec=true, check=1)
    global current_E = nearest(evals, current_E)
    push!(training, current_E)
    push!(training_vecs, evecs[:, nearestIndex(evals, current_E)])
 end
 EC_basis = hcat(training_vecs...)
 N_EC = transpose(EC_basis) * EC_basis
 H0_EC = transpose(EC_basis) * H0 * EC_basis
 V_EC = transpose(EC_basis) * V * EC_basis
 for c in extrapolating_c
    println("Extrapolating for c = $c")
    local H = H0 + c .* V
    local evals, evecs = eigs(H, nev=3, ncv=24, which=:LI, maxiter=5000, tol=1e-5, ritzvec=true, check=1)
    global current_E = nearest(evals, current_E)
    push!(exact, current_E)
    # extrapolation
    H_EC = H0_EC + c .* V_EC
    evals = eigvals(H_EC, N_EC)
    push!(extrapolated, nearest(evals, current_E))
 end
 exportCSV("temp/NCSM.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/NCSM.pdf")
--- a/calculations/3body_dis_CSM_EC.jl
+++ b/calculations/3body_dis_CSM_EC.jl
@ -1,77 +0,0 @@
 include("../p_space.jl")
 include("../EC.jl")
 Λ = 0
 m = 1.0
 # Distinguishable particles: V12 = bound and V13 & V23 = resonant
 Vsubsystem_of_r(r) = -2 * exp(-r^2/4)
 Vdecay_of_r(r) = -exp(-r^2 / 3) + exp(-r^2 / 10)
 ϕ = 0.1
 vertices = [0, 6 * exp(-1im * ϕ)]
 subdivisions = [50]
 jmax = 4
 E_max = 40
 μω_global = 0.4
 # Jacobi coordinates
 μ1ω1 = μω_global * 1/2
 μ2ω2 = μω_global * 2
 μ1 = m * 1/2
 μ2 = m * 2/3
 atol=10^-5; maxevals=10^5; R_cutoff=16; verbose=true;
 ###########
 verbose && println("No of threads = ", Threads.nthreads())
 V_l(j, k, kp) = Vl_mat_elem(Vsubsystem_of_r, j, k, kp; atol=atol, maxevals=maxevals, R_cutoff=R_cutoff)
 ks, ws = get_mesh(vertices, subdivisions)
 weights = repeat(kron(ws, ws), jmax + 1)
 block_size = length(ks)
 tri((j1, j2)) = triangle_ineq(j1, j2, Λ)
 js = collect(Iterators.filter(tri, iter_prod(0:jmax, 0:jmax)))
 basis = iter_prod(js, zip(ks, ws), zip(ks, ws)) # basis = ((j1, j2), (k1, w1), (k2, w2))
 basis_size = length(js) * length(ks)^2
@assert length(basis) == basis_size "Something wrong with the basis"
 verbose && println("Basis size = $basis_size")
@time "Block diagonal part" begin
    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]
    Ha = blockdiag(sparse.(blocks)...)
 end
 basis_ho = ho_basis_2B(E_max, Λ)
 verbose && println("HO basis size = ", basis_ho.dim)
@time "V2_HO" V2_HO =  get_jacobi_V2_matrix(Vdecay_of_r, basis_ho, μω_global)
@time "W_right" W_right = get_W_matrix(basis, basis_ho, μ1ω1, μ2ω2; weights=true)
@time "W_left" W_left = get_W_matrix(basis, basis_ho, μ1ω1, μ2ω2; weights=false)
@time "V2" Vb = W_left * V2_HO * transpose(W_right)
 ###########
 training_c = [-0.55, -0.7, -0.85, -1, -1.2]
 extrapolating_c = [0.2, 0.1, 0.0, -0.1, -0.2, -0.3]
 ref_E = -0.5173809356244544
 exact_ref = [-0.31360746615280954-0.07689284936870341im
    -0.3233372403877718-0.06011323914565665im
    -0.339615582074795-0.04239442037174759im
    -0.36333816534241997-0.02648721825958402im
    -0.39376650561322885-0.014382935339817332im	
    -0.4299479825535172-0.006510710745123606im]
 EC = affine_EC(Ha, Vb)
 train!(EC, training_c; ref_eval=ref_E, CAEC=true)
 extrapolate!(EC, extrapolating_c; precalculated_exact_E=exact_ref)
 exportCSV(EC, "temp/dis_CSM_B2R.csv")
 plot(EC, "temp/dis_CSM_B2R.pdf")
--- a/calculations/3body_dis_HO_EC.jl
+++ b/calculations/3body_dis_HO_EC.jl
@ -1,52 +0,0 @@
 include("../ho_basis.jl")
 include("../EC.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())
 basis = ho_basis_2B(E_max, Λ)
 println("Basis size = ", basis.dim)
@time "T1" T1 = get_sp_T_matrix(basis.n1s, basis.l1s, [basis.n2s, basis.l2s]; μω_gen=μ1ω1, μ=μ1)
@time "T2" T2 = get_sp_T_matrix(basis.n2s, basis.l2s, [basis.n1s, basis.l1s]; μω_gen=μ2ω2, μ=μ2)
@time "Va" Va = get_jacobi_V1_matrix(Va_of_r, basis, μ1ω1)
@time "Vb" Vb = get_jacobi_V2_matrix(Vb_of_r, basis, 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)
 training_c = [-0.55, -0.7, -0.85, -1, -1.2]
 extrapolating_c = [0.2, 0.1, 0.0, -0.1, -0.2, -0.3]
 ref_E = -0.5173809356244544
 exact_ref = [-0.3136074661528041-0.07689284936868852im
    -0.323337240387771-0.06011323914564878im
    -0.33961558207479553-0.04239442037174764im
    -0.3633381653424224-0.026487218259589693im
    -0.393766505613234-0.014382935339825854im
    -0.42994798255352606-0.006510710745131777im]
 EC = affine_EC(Ha, Vb)
 train!(EC, training_c; ref_eval=ref_E, CAEC=true) # try CAEC=false !!!
 extrapolate!(EC, extrapolating_c, precalculated_exact_E = exact_ref)
 exportCSV(EC, "temp/dis_HO_B2R.csv")
 plot(EC, "temp/dis_HO_B2R.pdf")
--- a/calculations/ACCC.jl
+++ b/calculations/ACCC.jl
@ -1,50 +0,0 @@
 using Roots, LinearAlgebra, Plots
 include("../EC.jl")
 include("../common.jl")
 include("../p_space.jl")
 μ = 0.5
 V_system(c) = (p, q) -> c*(-5*g0(sqrt(3), p, q) + 2*g0(sqrt(10), p, q)) # ResonanceEC: Eq. (20)
 # determining c0 with EC
 temp_c = range(1.1, 0.9, 3)
 p, w = get_mesh([0, 8], [256])
 H0 = get_T_matrix(p, μ)
 V = get_V_matrix(V_system(1), p, w)
 EC = affine_EC(H0, V, w)
 train!(EC, temp_c; ref_eval=-0.2, CAEC=false, verbose=false)
 quick_extrapolate(c) = minimum(abs2, get_extrapolated_evals(EC.H0_EC, EC.H1_EC, EC.N_EC, c, 0))
 c0 = find_zero(quick_extrapolate, 0.85)
 # Calculation of training and extrapolating E
 training_c = range(1.2, 0.9, 9) # original: range(1.35, 0.9, 5)
 training_E = [quick_pole_E(V_system(c)) for c in training_c]
 training_k = alt_sqrt.(2μ .* training_E)
 extrapolating_c = range(0.78, 0.45, 7) # original: range(0.75, 0.40, 8)
 exact_E = [quick_pole_E(V_system(c)) for c in extrapolating_c]
 order::Int = ceil((length(training_c) - 1) / 2) # 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.(training_c, (0:order)')
 M_right = -training_k .* M_left[:, 2:end] # remove the first column
 M = hcat(M_left, M_right) # M = [M_left | M_right]
 sol = M \ training_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.([training_c; extrapolating_c])
 extrapolated_E = (extrapolated_k .^ 2) / (2μ)
 # Plotting
 scatter(real.(training_E), imag.(training_E), label="training")
 scatter!(real.(exact_E), imag.(exact_E), label="exact")
 scatter!(real.(extrapolated_E), imag.(extrapolated_E), label="extrapolated", m=:star5)
--- a/calculations/B2R_Berggren_poles.jl
+++ b/calculations/B2R_Berggren_poles.jl
@ -1,12 +1,12 @@
-include("../EC.jl")
+using Plots
-include("../common.jl")
+include("../helper.jl")
 include("../p_space.jl")
 # contour
 p, w = get_mesh([0, 0.4 - 0.15im, 0.8, 6], [128, 128, 128])
-μ = 0.5
+# ResonanceEC: Eq. (20)
-V_system(c) = (p, q) -> c*(-5*g0(sqrt(3), p, q) + 2*g0(sqrt(10), p, q)) # ResonanceEC: Eq. (20)
+V_system(c) = (p, q) -> c*(-5*g0(sqrt(3), p, q) + 2*g0(sqrt(10), p, q))
 # generating a Berggren basis with a pole using the same system
 basis_c = 0.6
@ -16,18 +16,48 @@ N_berg = sqrt.(diag(transpose(berg_basis .* w) * berg_basis))
 berg_basis = berg_basis ./ transpose(N_berg)
 berg_basis_w = berg_basis .* w
-H0 = transpose(berg_basis_w) * get_T_matrix(p, μ) * berg_basis
+training_points = range(1.1, 0.9, 5) # original: range(1.35, 0.9, 5)
 V = transpose(berg_basis_w) * get_V_matrix(V_system(1), p, w) * berg_basis
-training_c = range(1.1, 0.9, 5) # original: range(1.35, 0.9, 5)
+training_E = Vector{ComplexF64}(undef, length(training_points))
-extrapolating_c = range(0.78, 0.45, 7) # original: range(0.75, 0.40, 8)
+EC_basis = Matrix{ComplexF64}(undef, length(p), length(training_points))
-training_ref = -0.26
+# training
-extrapolating_ref = [quick_pole_E(V_system(c)) for c in extrapolating_c]
+for (j, c) in enumerate(training_points)
    H = get_H_matrix(V_system(c), p, w)
    H_berg = transpose(berg_basis_w) * H * berg_basis
    evals, evecs = eigen(H_berg)
    i = argmin(real.(evals))
 #    i = identify_pole_i(basis_p, evals)
    training_E[j] = evals[i]
    EC_basis[:, j] = evecs[:, i]
 end
-EC = affine_EC(H0, V)
+EC_basis = hcat(EC_basis, conj.(EC_basis)) # CA-EC
-train!(EC, training_c; ref_eval=training_ref, CAEC=true)
+N_EC = transpose(EC_basis) * EC_basis
 extrapolate!(EC, extrapolating_c; ref_eval=extrapolating_ref)
-exportCSV(EC, "temp/2b_GSM_B2R.csv")
+extrapolate_points = range(0.78, 0.45, 7) # original: range(0.75, 0.40, 8)
-plot(EC, "temp/2b_GSM_B2R.pdf"; basis_points=basis_E, xlims=(0, 0.3), ylims=(-0.120, 0.020))
+
 exact_E = Vector{ComplexF64}(undef, length(extrapolate_points))
 extrapolate_E = Vector{ComplexF64}(undef, length(extrapolate_points))
 # extrapolating
 for (j, c) in enumerate(extrapolate_points)
    exact_E[j] = quick_pole_E(V_system(c))
    H = get_H_matrix(V_system(c), p, w)
    H_berg = transpose(berg_basis_w) * H * berg_basis
    H_EC = transpose(EC_basis) * H_berg * EC_basis
    evals = eigvals(H_EC, N_EC)
    i = argmin(abs.(evals .- exact_E[j]))
    extrapolate_E[j] = evals[i]
 end
 exportCSV("temp/2b_GSM_B2R.csv", (training_E, exact_E, extrapolate_E), ("training", "exact", "extrapolated"))
 scatter(real.(training_E), imag.(training_E), label="training")
 scatter!(real.(exact_E), imag.(exact_E), label="exact")
 scatter!(real.(extrapolate_E), imag.(extrapolate_E), label="extrapolated")
 scatter!(real.(basis_E), imag.(basis_E), m=:x, label="Berggren basis")
 xlims!(0,0.3)
 ylims!(-0.120,0.020)
 savefig("temp/2b_GSM_B2R.pdf")
--- a/calculations/B2R_comparison.jl
+++ b/calculations/B2R_comparison.jl
@ -1,30 +1,51 @@
-include("../EC.jl")
+using Plots
 include("../common.jl")
 include("../p_space.jl")
 berggren_mesh = get_mesh([0, 0.4 - 0.15im, 0.8, 6], [128, 128, 128])
 csm_mesh = get_mesh([0, 8 - 3im], [512])
-for (mesh, name) in zip((berggren_mesh, csm_mesh), ("beggren", "csm"))
+for mesh in (berggren_mesh, csm_mesh)
    p, w = mesh
    mesh_E = p.*p ./ (2*0.5)
-    μ = 0.5
+    # ResonanceEC: Eq. (20)
-    V_system(c) = (p, q) -> c*(-5*g0(sqrt(3), p, q) + 2*g0(sqrt(10), p, q)) # ResonanceEC: Eq. (20)
+    V_system(c) = (p, q) -> c*(-5*g0(sqrt(3), p, q) + 2*g0(sqrt(10), p, q))
    H0 = get_T_matrix(p, μ)
    V = get_V_matrix(V_system(1), p, w)
    training_c = range(1.1, 0.9, 5) # original: range(1.35, 0.9, 5)
    extrapolating_c = range(0.78, 0.45, 7) # original: range(0.75, 0.40, 8)
-    training_ref = [quick_pole_E(V_system(c)) for c in training_c]
+    training_points = range(1.1, 0.9, 5) # original: range(1.35, 0.9, 5)
-    exact_E = [quick_pole_E(V_system(c)) for c in extrapolating_c]
+    training_E = Vector{ComplexF64}(undef, length(training_points))
    EC_basis = Matrix{ComplexF64}(undef, length(p), length(training_points))
-    EC = affine_EC(H0, V, w)
+    for (j, c) in enumerate(training_points)
-    train!(EC, training_c; ref_eval=training_ref, CAEC=true)
+        evals, evecs = eigen(get_H_matrix(V_system(c), p, w))
-    extrapolate!(EC, extrapolating_c; precalculated_exact_E=exact_E)
+        i = identify_pole_i(p, evals)
-    
+        training_E[j] = evals[i]
-    #exportCSV(EC, "temp/2b_comparison_$name.csv")
+        EC_basis[:, j] = evecs[:, i]
-    plot(EC, "temp/2b_comparison_$name.pdf"; basis_contour=mesh_E, xlims=(-0.3,0.3), ylims=(-0.120,0.020))
+    end
    EC_basis = hcat(EC_basis, conj.(EC_basis)) # CA-EC
    EC_basis_w = EC_basis .* w
    N_EC = transpose(EC_basis_w) * EC_basis
    extrapolate_points = range(0.78, 0.45, 7) # original: range(0.75, 0.40, 8)
    exact_E = Vector{ComplexF64}(undef, length(extrapolate_points))
    extrapolate_E = Vector{ComplexF64}(undef, length(extrapolate_points))
    for (j, c) in enumerate(extrapolate_points)
        exact_E[j] = quick_pole_E(V_system(c))
        H = get_H_matrix(V_system(c), p, w)
        H_EC = transpose(EC_basis_w) * H * EC_basis
        evals = eigvals(H_EC, N_EC)
        i = argmin(abs.(evals .- exact_E[j]))
        extrapolate_E[j] = evals[i]
    end
    scatter(real.(training_E), imag.(training_E), label="training")
    scatter!(real.(exact_E), imag.(exact_E), label="exact")
    scatter!(real.(extrapolate_E), imag.(extrapolate_E), label="extrapolated")
    plot!(real.(mesh_E), imag.(mesh_E), label="contour")
    xlims!(-0.3,0.3)
    ylims!(-0.120,0.020)
    savefig("temp/" * string(rand(UInt16)) * ".pdf")
 end
--- a/calculations/PMM.py
+++ b/calculations/PMM.py
@ -1,81 +0,0 @@
 #%%
 import pandas as pd
 import torch
 import numpy as np
 #%%
 df = pd.read_csv('../temp/2body_data.csv').sort_values(by='c')
 df['E'] = df['re_E'] + 1j * df['im_E']
 train_data = df[df['re_E'] < 0]
 target_data = df[df['re_E'] > 0]
 train_cs = train_data['c'].to_numpy()
 train_Es = torch.tensor(train_data['E'].to_numpy(), dtype=torch.complex128)
 #%%
 # hyperparameters
 N = 9
 # initialize random Hamiltonians
 H0 = torch.randn(N, N, dtype=torch.complex128)
 H0 = (H0 + torch.transpose(H0, 0, 1)).requires_grad_() # symmetric
 H1 = torch.randn(N, N, dtype=torch.complex128)
 H1 = (H1 + torch.transpose(H1, 0, 1)).requires_grad_() # symmetric
 #%%
 # training
 # generate a set of c values to follow by subdividing the training cs
 subdivisions = 3
 c_steps = np.concatenate([np.linspace(start, stop, subdivisions, endpoint=False) for (start, stop) in zip(train_cs, train_cs[1:])])
 c_steps = np.append(c_steps, train_cs[-1])
 lr = 0.05
 epochs = 100000
 for epoch in range(epochs):
    Es = torch.empty(len(train_data), dtype=torch.complex128)
    current_E = 0.0 # start at the threshold
    for c in c_steps:
        H = H0 + c * H1
        evals = torch.linalg.eigvals(H)
        current_E = evals[torch.argmin(torch.abs(evals - current_E))]
        if np.any(c == train_cs):
            index = np.where(c == train_cs)[0][0]
            Es[index] = current_E
    loss = ((Es - train_Es).abs() ** 2).sum()
    if epoch % 1000 == 0:
        print(f"Training {(epoch+1)/epochs:.1%} \t Loss: {loss}")
    if H0.grad is not None:
        H0.grad.zero_()
    if H1.grad is not None:
        H1.grad.zero_()
    loss.backward()
    with torch.no_grad():
        H0 -= lr * H0.grad
        H1 -= lr * H1.grad
 # %%
 # evaluate for all points
 all_c = torch.tensor(df['c'].values, dtype=torch.float64)
 exact_E = torch.tensor(df['E'].values, dtype=torch.complex128)
 pred_Es = torch.empty(len(df), dtype=torch.complex128)
 with torch.no_grad():
    for (index, (c, E)) in enumerate(zip(all_c, exact_E)):
        H = H0 + c * H1
        evals = torch.linalg.eigvals(H)
        i = torch.argmin(torch.abs(evals - E)) # TODO: more robust way to identify the eigenvector
        pred_Es[index]= evals[i]
 # %%
 # plot the results
 import matplotlib.pyplot as plt
 plt.scatter(train_data['re_E'], train_data['im_E'], label='training')
 plt.scatter(target_data['re_E'], target_data['im_E'], label='target')
 plt.scatter(pred_Es.real, pred_Es.imag, marker='x', label='predicted')
 plt.legend()
 # %%
--- a/calculations/R2R_Berggren.jl
+++ b/calculations/R2R_Berggren.jl
@ -1,28 +0,0 @@
 include("../EC.jl")
 include("../common.jl")
 include("../p_space.jl")
 # contour
 vertices = [0, 0.4 - 0.15im, 0.8, 6]
 subdivisions = [128, 128, 128]
 p, w = get_mesh(vertices, subdivisions)
 mesh_E = p.*p ./ (2*0.5)
 μ = 0.5
 V_system(c) = (p, q) -> c*(-5*g0(sqrt(3), p, q) + 2*g0(sqrt(10), p, q)) # ResonanceEC: Eq. (20)
 H0 = get_T_matrix(p, μ)
 V = get_V_matrix(V_system(1), p, w)
 training_c = range(0.75, 0.45, 5)
 extrapolating_c = range(0.40, 0.25, 5)
 training_ref = [quick_pole_E(V_system(c)) for c in training_c]
 exact_E = [quick_pole_E(V_system(c)) for c in extrapolating_c]
 EC = affine_EC(H0, V, w)
 train!(EC, training_c; ref_eval=training_ref, CAEC=false)
 extrapolate!(EC, extrapolating_c; precalculated_exact_E=exact_E)
 #exportCSV(EC, "temp/2b_R2R.csv")
 plot(EC, "temp/2b_R2R.pdf"; basis_contour=mesh_E, xlims=(0, 1))
--- a/calculations/R2R_Berggren_poles.jl
+++ b/calculations/R2R_Berggren_poles.jl
@ -1,33 +1,66 @@
-include("../EC.jl")
+using Plots
-include("../common.jl")
+include("../helper.jl")
 include("../p_space.jl")
 # contour
-p, w = get_mesh([0, 0.4 - 0.15im, 0.8, 6], [128, 128, 128])
+p, w = get_mesh([0, 0.4 - 0.08im, 0.8, 6], [128, 128, 128])
 contour_E = p.^2
-μ = 0.5
+# ResonanceEC: Eq. (20)
-V_system(c) = (p, q) -> c*(-5*g0(sqrt(3), p, q) + 2*g0(sqrt(10), p, q)) # ResonanceEC: Eq. (20)
+V_system(c) = (p, q) -> c*(-5*g0(sqrt(3), p, q) + 2*g0(sqrt(10), p, q))
 # generating a Berggren basis with a pole using the same system
 basis_c = 0.6
 basis_E, berg_basis = eigen(get_H_matrix(V_system(basis_c), p, w); permute=false, scale=false)
 pole_E = quick_pole_E(V_system(basis_c)) # basis only has 1 pole
 basis_p = sqrt.(basis_E)
 N_berg = sqrt.(diag(transpose(berg_basis .* w) * berg_basis))
 berg_basis = berg_basis ./ transpose(N_berg)
 berg_basis_w = berg_basis .* w
-H0 = transpose(berg_basis_w) * get_T_matrix(p, μ) * berg_basis
+training_points = range(0.79, 0.66, 4) # original: range(1.35, 0.9, 5)
 V = transpose(berg_basis_w) * get_V_matrix(V_system(1), p, w) * berg_basis
-training_c = range(0.79, 0.66, 4) # original: range(1.35, 0.9, 5)
+training_E = Vector{ComplexF64}(undef, length(training_points))
-extrapolating_c = range(0.62, 0.40, 6) # original: range(0.75, 0.40, 8)
+EC_basis = Matrix{ComplexF64}(undef, length(p), length(training_points))
-training_ref = [quick_pole_E(V_system(c)) for c in training_c]
+# training
-extrapolating_ref = [quick_pole_E(V_system(c)) for c in extrapolating_c]
+for (j, c) in enumerate(training_points)
    H = get_H_matrix(V_system(c), p, w)
    H_berg = transpose(berg_basis_w) * H * berg_basis
    evals, evecs = eigen(H_berg)
    i = identify_pole_i(basis_p, evals)
    training_E[j] = evals[i]
    EC_basis[:, j] = evecs[:, i]
 end
-EC = affine_EC(H0, V)
+N_EC = transpose(EC_basis) * EC_basis
 train!(EC, training_c; ref_eval=training_ref, CAEC=false)
 extrapolate!(EC, extrapolating_c; ref_eval=extrapolating_ref)
-exportCSV(EC, "temp/2b_GSM_R2R.csv")
+extrapolate_points = range(0.62, 0.40, 6) # original: range(0.75, 0.40, 8)
-plot(EC, "temp/2b_GSM_R2R.pdf"; basis_points=basis_E, xlims=(0, 0.3), ylims=(-0.120, 0.020))
+
 exact_E = Vector{ComplexF64}(undef, length(extrapolate_points))
 extrapolate_E = Vector{ComplexF64}(undef, length(extrapolate_points))
 # extrapolating
 for (j, c) in enumerate(extrapolate_points)
    exact_E[j] = quick_pole_E(V_system(c))
    H = get_H_matrix(V_system(c), p, w)
    H_berg = transpose(berg_basis_w) * H * berg_basis
    H_EC = transpose(EC_basis) * H_berg * EC_basis
    evals = eigvals(H_EC, N_EC)
    i = argmin(abs.(evals .- exact_E[j]))
    extrapolate_E[j] = evals[i]
 end
 exportCSV("temp/2b_GSM_R2R.csv", (training_E, exact_E, extrapolate_E, [pole_E]), ("training", "exact", "extrapolated", "basis"))
 contour_E_export = contour_E[real.(contour_E) .< 1] # to trim unnecessary data outside axis limits
 exportCSV("temp/2b_GSM_R2R_contour.csv", contour_E_export)
 scatter(real.(training_E), imag.(training_E), label="training")
 scatter!(real.(exact_E), imag.(exact_E), label="exact")
 scatter!(real.(extrapolate_E), imag.(extrapolate_E), label="extrapolated")
 scatter!(real.(basis_E), imag.(basis_E), m=:x, label="Berggren basis")
 xlims!(0,0.3)
 ylims!(-0.120,0.020)
 savefig("temp/2b_GSM_R2R.pdf")
--- a/calculations/XZ/2body_HO.jl
+++ b/calculations/XZ/2body_HO.jl
@ -1,39 +0,0 @@
 using Plots
 include("../../EC.jl")
 include("../../ho_basis.jl")
 include("../../p_space.jl")
 angle = 0.25 * pi # DOESN'T WORK WITHOUT ROTATION
 μω_gen = 0.5 * exp(-2im * angle)
 μ = 0.5
 l = 0
 V1 = -5
 R1 = sqrt(3)
 V2 = 2
 R2 = sqrt(10)
 n_max = 15
 ns = collect(0:n_max)
 ls = fill(l, n_max + 1)
 T = get_sp_T_matrix(ns, ls; μω_gen=μω_gen, μ=μ)
 V = V1 .* V_Gaussian.(R1, l, ns, transpose(ns); μω_gen=μω_gen) + V2 .* V_Gaussian.(R2, l, ns, transpose(ns); μω_gen=μω_gen)
 n_EC = 8
 train_cs = (0.7 .+ 0.05 * randn(n_EC)) - 1im * (0.2 .+ 0.05 * randn(n_EC))
 target_cs = [0.5]
 near_E = 0.2 + 0.2im
 exact_E = [0.20845136860234303 - 0.07100640993695649im]
 EC = affine_EC(T, V; ensemble_size=32)
 train!(EC, train_cs; ref_eval=near_E, CAEC=false)
 extrapolate!(EC, target_cs; precalculated_exact_E=exact_E)
 plot(EC; xlims=(0,0.3), ylims=(-0.3,0.3))
 hline!([0], color=:red, label="continuum")
 xlabel!("Re(E)")
 ylabel!("Im(E)")
 plot!(legend=:bottomleft)
 savefig("temp/2b_HO_XZ.pdf")
--- a/calculations/XZ/2body_p_space.jl
+++ b/calculations/XZ/2body_p_space.jl
@ -1,50 +0,0 @@
 using Plots
 include("../../EC.jl")
 include("../../ho_basis.jl")
 include("../../p_space.jl")
 # paramters of the system
 angle = 0.0
 μ = 0.5
 l = 0
 V1 = -5
 R1 = sqrt(3)
 V2 = 2
 R2 = sqrt(10)
 n_EC = 8
 train_cs = (0.7 .+ 0.03 * randn(n_EC)) - 1im * (0.2 .+ 0.03 * randn(n_EC))
 near_E = 0.2 + 0.2im
 target_c = 0.5
 exact_E = 0.20845136860234303 - 0.07100640993695649im
 vertices = [0, 4 * exp(-1im * angle)]
 subdivisions = [256]
 ks, ws = get_mesh(vertices, subdivisions)
 V_of_r(r) = V1 * exp(-r^2 / R1^2) + V2 * exp(-r^2 / R2^2)
 V_mat_elem(k, kp) = Vl_mat_elem(V_of_r, l, k, kp; atol=10^-5, maxevals=10^5, R_cutoff=16)
 V = get_V_matrix(V_mat_elem, ks, ws)
 T = get_T_matrix(ks, μ)
 EC_p_space = affine_EC(T, V)
 train!(EC_p_space, train_cs; ref_eval=near_E, CAEC=false)
 extrapolate!(EC_p_space, [target_c]; precalculated_exact_E=[exact_E])
 # Plotting
 theme(:dark) # Set the global theme to dark
 scatter([real(exact_E)], [imag(exact_E)], label="exact", marker=:circle, markercolor=:white, bg = :black) # black background
 scatter!(real.(EC_p_space.training_E), imag.(EC_p_space.training_E), label="training", marker=:circle, color=:blue)
 scatter!(real.(EC_p_space.extrapolated_E), imag.(EC_p_space.extrapolated_E), label="extrapolated", marker=:x, color=:green)
 hline!([0], color=:red, label="continuum")
 plot!(legend=:bottomleft)
 xlabel!("Re(E)")
 ylabel!("Im(E)")
 xlims!(0, 0.3)
 ylims!(-0.3, 0.3)
 savefig("temp/2body_p_space.pdf")
--- a/calculations/XZ/3body_HO.jl
+++ b/calculations/XZ/3body_HO.jl
@ -1,36 +0,0 @@
 include("../../ho_basis.jl")
 include("../../EC.jl")
 V_of_r(r) = 2 * exp(-(r-3)^2 / (1.5)^2)
 Λ = 0
 m = 1.0
 ϕ = 0.1 # DOESN'T WORK WITHOUT ROTATION
 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)
 training_ref = 2 + 0.5im
 exact_E = [4.076642792419057-0.012998408352259658im,
    3.6129849325287-0.007397677539402868im,
    3.145212908643357-0.0038660337822150753im,	
    2.6729225739451596-0.0021090370393881063im,	
    2.196385760253282-0.0010430088245526555im,	
    1.7162659936896967-0.0004515351140200029,	
    1.2329926791785895-0.00017698044022813525im]
 training_c = [0.6 - 0.16im] .+ 0.04 .* (randn(8) .+ 0.5im * randn(8))
 extrapolating_c = 0.0 : 0.2 : 1.2
 EC = affine_EC(H0, Vp)
 train!(EC, training_c; ref_eval=training_ref, CAEC=false)
 extrapolate!(EC, extrapolating_c; precalculated_exact_E=exact_E)
 exportCSV(EC, "temp/3b_HO_XZ.csv")
 plot(EC, "temp/3b_HO_XZ.pdf")
--- a/calculations/XZ/3body_p_space.jl
+++ b/calculations/XZ/3body_p_space.jl
@ -1,45 +0,0 @@
 include("../../p_space.jl")
 include("../../EC.jl")
 using Arpack
 # target = 4.0766890719636875 - 0.012758927741074495im
 Λ = 0
 m = 1.0
 V_of_r(r) =  2 * exp(-(r-3)^2 / (1.5)^2)
 vertices = [0, 2 - 0.2im, 3, 4] # TODO: real contour instead of Berggren basis
 subdivisions = [15, 10, 10]
 jmax = 4
 E_max = 40
 μω_global = 0.5
@time "H0" H0, _ = get_3b_H_matrix(jacobi, V_of_r, vertices, subdivisions, jmax, 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, vertices, subdivisions, jmax, μω_global, E_max, Λ, m, false, true)
 training_ref = 2 + 0.5im
 exact_E = [4.076642792419057-0.012998408352259658im,
    3.6129849325287-0.007397677539402868im,
    3.145212908643357-0.0038660337822150753im,	
    2.6729225739451596-0.0021090370393881063im,	
    2.196385760253282-0.0010430088245526555im,	
    1.7162659936896967-0.0004515351140200029,	
    1.2329926791785895-0.00017698044022813525im]
 training_c = [-1.5 - 0.5im] .+ (randn(8) .+ 0.05im * randn(8))
 extrapolating_c = 0.0 : 0.2 : 1.2
 EC = affine_EC(H0, Vp)
 train!(EC, training_c; ref_eval=training_ref, CAEC=false)
 extrapolate!(EC, extrapolating_c; precalculated_exact_E=exact_E)
 exportCSV(EC, "temp/3b_p_space_XZ.csv")
 plot(EC, "temp/3b_p_space_XZ.pdf")
 # Results: training points are all over the place, and extrapolated values are garbage.
--- a/calculations/XZ/p_space_vs_HO.jl
+++ b/calculations/XZ/p_space_vs_HO.jl
@ -1,71 +0,0 @@
 using Plots
 include("../../EC.jl")
 include("../../ho_basis.jl")
 include("../../p_space.jl")
 # paramters of the system
 angle = 0.0 * pi
 μ = 0.5
 l = 0
 V1 = -5
 R1 = sqrt(3)
 V2 = 2
 R2 = sqrt(10)
 n_EC = 8
 train_cs = (0.7 .+ 0.03 * randn(n_EC)) - 1im * (0.2 .+ 0.03 * randn(n_EC))
 near_E = 0.2 + 0.2im
 target_c = 0.5
 exact_E = 0.20845136860234303 - 0.07100640993695649im
 # HO basis
 global EC_HO
 begin
    println("HO basis calculation")
    μω_gen = 0.5 * exp(-1im * angle)
    n_max = 40
    ns = collect(0:n_max)
    ls = fill(l, n_max + 1)
    T = get_sp_T_matrix(ns, ls; μω_gen=μω_gen, μ=μ)
    V = V1 .* V_Gaussian.(R1, l, ns, transpose(ns); μω_gen=μω_gen) + V2 .* V_Gaussian.(R2, l, ns, transpose(ns); μω_gen=μω_gen)
    global EC_HO = affine_EC(T, V)
    train!(EC_HO, train_cs; ref_eval=near_E, CAEC=false)
    extrapolate!(EC_HO, [target_c]; precalculated_exact_E=[exact_E])
 end
 # p-space
 global EC_p_space
 begin
    println("p-space calculation")
    vertices = [0, 4 * exp(-1im * angle)]
    subdivisions = [256]
    ks, ws = get_mesh(vertices, subdivisions)
    V_of_r(r) = V1 * exp(-r^2 / R1^2) + V2 * exp(-r^2 / R2^2)
    V_mat_elem(k, kp) = Vl_mat_elem(V_of_r, l, k, kp; atol=10^-5, maxevals=10^5, R_cutoff=16)
    V = get_V_matrix(V_mat_elem, ks, ws)
    T = get_T_matrix(ks, μ)
    global EC_p_space = affine_EC(T, V)
    train!(EC_p_space, train_cs; ref_eval=near_E, CAEC=false)
    extrapolate!(EC_p_space, [target_c]; precalculated_exact_E=[exact_E])
 end
 # Plotting
 scatter([real(exact_E)], [imag(exact_E)], label="Exact", marker=:circle, markercolor=:white)
 scatter!(real.(EC_HO.training_E), imag.(EC_HO.training_E), label="HO basis training", marker=:circle, color=:blue)
 scatter!(real.(EC_HO.extrapolated_E), imag.(EC_HO.extrapolated_E), label="HO basis extrapolated", marker=:x, color=:blue)
 scatter!(real.(EC_p_space.training_E), imag.(EC_p_space.training_E), label="p-space training", marker=:circle, color=:red)
 scatter!(real.(EC_p_space.extrapolated_E), imag.(EC_p_space.extrapolated_E), label="p-space extrapolated", marker=:x, color=:red)
 plot!(legend=:bottomleft)
 xlabel!("Re(E)")
 ylabel!("Im(E)")
 savefig("temp/2b_p_space_vs_HO.pdf")
--- a/calculations/XZ_technique.jl
+++ b/calculations/XZ_technique.jl
@ -0,0 +1,55 @@
 using LinearAlgebra, Plots
 include("../ho_basis.jl")
 include("../p_space.jl")
 μω_gen = 0.5 * exp(-1im * 0.47 * pi)
 μ = 0.5
 l = 0
 V1 = -5
 R1 = sqrt(3)
 V2 = 2
 R2 = sqrt(10)
 n_max = 15
 ns = collect(0:n_max)
 ls = fill(l, n_max + 1)
 T = get_sp_T_matrix(ns, ls; μω_gen=μω_gen, μ=μ)
 V = V1 .* V_Gaussian.(R1, l, ns, transpose(ns); μω_gen=μω_gen) + V2 .* V_Gaussian.(R2, l, ns, transpose(ns); μω_gen=μω_gen)
 n_EC = 8
 train_cs = (0.7 .+ 0.05 * randn(n_EC)) - 1im * (0.2 .+ 0.05 * randn(n_EC))
 target_cs = range(0.77, 0.22, 6)
 train_E = zeros(ComplexF64, n_EC)
 EC_basis = zeros(ComplexF64, (n_max + 1, length(train_cs)))
 exact_E = zeros(ComplexF64, length(target_cs))
 extrapolate_E = similar(exact_E)
 near_E = 0.2 + 0.2im
 for (j, c) in enumerate(train_cs)
    H = T + c .* V
    evals, evecs = eigen(H)
    i = argmin(abs.(evals .- near_E))
    train_E[j] = evals[i]
    EC_basis[:, j] = evecs[:, i]
 end
 N_EC = transpose(EC_basis) * EC_basis
 for (j, c) in enumerate(target_cs)
    exact_E[j] = quick_pole_E((p, q) -> c*(V1*g0(R1, p, q) + V2*g0(R2, p, q)), μ; cs_angle=0.5)
    H = T + c .* V
    H_EC = transpose(EC_basis) * H * EC_basis
    evals = eigvals(H_EC, N_EC)
    i = argmin(abs.(evals .- exact_E[j]))
    extrapolate_E[j] = evals[i]
 end
 scatter(real.(train_E), imag.(train_E), label="training")
 scatter!(real.(exact_E), imag.(exact_E), label="exact")
 scatter!(real.(extrapolate_E), imag.(extrapolate_E), label="extrapolated")
 xlims!(-0.2,0.3)
 ylims!(-0.3,0.3)
--- a/common.jl
+++ b/common.jl
@ -1,106 +0,0 @@
 using LinearAlgebra, DelimitedFiles, SparseArrays
@enum coordinate_system jacobi src
 "Square root function with the branch cut along the postive imaginary axis"
 alt_sqrt(x::Number)::ComplexF64 = sqrt(im * x) / sqrt(im)
 "Sum over array while minimizing catastrophic cancellation as much as possible"
 function better_sum(arr::Array{T}) where T<:Real
    pos_arr = arr[arr .> 0]
    neg_arr = arr[arr .< 0]
    sort!(pos_arr)
    sort!(neg_arr, rev=true)
    return sum(pos_arr) + sum(neg_arr)
 end
 better_sum(arr::Array{ComplexF64}) = better_sum(real.(arr)) + 1im * better_sum(imag.(arr))
 "The triangle inequality for angular momenta"
 triangle_ineq(l1, l2, L) = abs(l1 - l2) ≤ L && L ≤ (l1 + l2)
 "Index of the nearest value in a list to a given reference point"
 nearestIndex(list::Array, ref) = argmin(norm.(list .- ref))
 "Nearest value in a list to a given reference point"
 nearest(list::Array, ref) = list[nearestIndex(list, ref)]
 "Simple implementation of the Kronecker sum"
 function kron_sum(A::AbstractMatrix, B::AbstractMatrix)
    @assert size(A, 1) == size(A, 2) && size(B, 1) == size(B, 2) "Matrices should be square"
    return kron(A, I(size(B, 1))) + kron(I(size(A, 1)), B)
 end
 "Flattened vector version of Iterators.product(...) with index hierachy reversed -- leftmost index has the highest hierachy"
 iter_prod(args...) = reverse.(collect(Iterators.product(reverse(args)...))[:])
 "Export CSV data for a scatter plot taking in data as a list of complex vectors (x=Re, y=Im), and a list of corresponding labels, typically used for EC results"
 function exportCSV(file::String, data, labels=nothing)
    columns = ["x" "y" "label"]
    if isnothing(labels)
        columns[end] = ""
        labels = fill("", length(data))
    end
    open(file, "w") do f
        writedlm(f, columns)
        for (d, label) in zip(data, labels)
            l = fill(label, length(d))
            writedlm(f, hcat(reim(d)..., l))
        end
    end
 end
 "In-place c-orthogonalization via (modified) Gram-Schmidt. Only significant vectors are returned (c-normalized).
 The number of significant vectors to return are determined by the original singular values (compared to the threshold)."
 function gram_schmidt!(vecs::Vector{Vector{T}}, ws=ones(length(vecs[1])), threshold=1e-5; verbose=false) where T<: Number
    c_product(i, j) = sum(vecs[i] .* ws .* vecs[j])
    norm(i) = c_product(i, i)
    proj(i, j) = (c_product(i, j) / norm(i)) .* vecs[i] # component of vec[i] in vec[j]
    # initial normalization
    for i in eachindex(vecs)
        vecs[i] ./= sqrt(norm(i))
    end
    verbose && println("Absolute singular values = $(round.(c_singular_values(vecs, ws); sigdigits=1))")
    target_dim = c_rank(vecs, ws, threshold)
    verbose && println("Target dimensionality = $target_dim")
    selected_vecs_i = Integer[]
    while length(selected_vecs_i) < target_dim
        i = argmax(i -> abs(norm(i)), setdiff(eachindex(vecs), selected_vecs_i)) # find the largest vector from the remaining
        push!(selected_vecs_i, i)
        for j in setdiff(eachindex(vecs), selected_vecs_i)
            vecs[j] .-= proj(i, j)
        end
    end
    verbose && println("Absolute norms of selected vectors = $(round.(selected_vecs_i .|> norm .|> abs; sigdigits=1))")
    verbose && println("Absolute norms of dropped vectors = $(round.(setdiff(eachindex(vecs), selected_vecs_i) .|> norm .|> abs; sigdigits=1))")
    # final normalization
    for i in selected_vecs_i
        vecs[i] ./= sqrt(norm(i))
    end
    return vecs[selected_vecs_i]
 end
 "Same as above but the basis is provided as a matrix instead of an array of vectors"
 gram_schmidt!(vecs::Matrix{T}, ws=ones(size(vecs, 1)), threshold=1e-5; verbose=false) where T<: Number = hcat(gram_schmidt!([vecs[:, i] for i in axes(vecs, 2)], ws, threshold; verbose=verbose)...)
 "Rank of a basis set (pre-normalized) under c-product"
 c_rank(vecs, ws, threshold=1e-8) = count(c_singular_values(vecs, ws) .> threshold)
 "Singular values (magnitudes) of a basis set (pre-normalized) under c-product"
 function c_singular_values(vecs, ws)
    basis = hcat(vecs...)
    N = transpose(basis) * spdiagm(ws) * basis
    singular_values = eigvals(N) .|> abs .|> sqrt
    return singular_values
 end
--- a/helper.jl
+++ b/helper.jl
@ -0,0 +1,50 @@
 using LinearAlgebra, DelimitedFiles
 "Sum over array while minimizing catastrophic cancellation as much as possible"
 function better_sum(arr::Array{T}) where T<:Real
    pos_arr = arr[arr .> 0]
    neg_arr = arr[arr .< 0]
    sort!(pos_arr)
    sort!(neg_arr, rev=true)
    return sum(pos_arr) + sum(neg_arr)
 end
 better_sum(arr::Array{ComplexF64}) = better_sum(real.(arr)) + 1im * better_sum(imag.(arr))
 "The triangle inequality for angular momenta"
 triangle_ineq(l1, l2, L) = abs(l1 - l2) ≤ L && L ≤ (l1 + l2)
 "Index of the nearest value in a list to a given reference point"
 nearestIndex(list::Array, ref) = argmin(norm.(list .- ref))
 "Nearest value in a list to a given reference point"
 nearest(list::Array, ref) = list[nearestIndex(list, ref)]
 "Simple implementation of the Kronecker sum"
 function kron_sum(A::AbstractMatrix, B::AbstractMatrix)
    @assert size(A, 1) == size(A, 2) && size(B, 1) == size(B, 2) "Matrices should be square"
    return kron(A, I(size(B, 1))) + kron(I(size(A, 1)), B)
 end
 "Flattened vector version of Iterators.product(...) with index hierachy reversed -- leftmost index has the highest hierachy"
 iter_prod(args...) = reverse.(collect(Iterators.product(reverse(args)...))[:])
 "Export CSV data for a scatter plot taking in data as a list of complex vectors (x=Re, y=Im), and a list of corresponding labels, typically used for EC results"
 function exportCSV(file::String, data, labels=nothing)
    columns = ["x" "y" "label"]
    if isnothing(labels)
        columns[end] = ""
        labels = fill("", length(data))
    end
    open(file, "w") do f
        writedlm(f, columns)
        for (d, label) in zip(data, labels)
            l = fill(label, length(d))
            writedlm(f, hcat(reim(d)..., l))
        end
    end
 end
--- a/ho_basis.jl
+++ b/ho_basis.jl
@ -1,74 +1,65 @@
 using SparseArrays
 using QuadGK
 using LRUCache
-include("common.jl")
+include("helper.jl")
 include("math.jl")
-"2-body HO basis (used for 3-body systems without the CM DOF)"
+function V_numerical(V_of_r, l, n1, n2; μω_gen=1.0, atol=0, maxevals=10^7)
-struct ho_basis_2B
+    integrand(r) = sqrt(μω_gen) * ho_basis(l, n1, sqrt(μω_gen) * r) * ho_basis(l, n2, sqrt(μω_gen) * r) * V_of_r(r)
-    E_max::Int
+    (integral, _) = quadgk(integrand, 0, Inf; atol=atol, maxevals=maxevals)
-    Λ::Int
+    return integral
-    dim::Int # dimensionality of the basis
+end
    Es::Vector{Int}
    n1s::Vector{Int}
    l1s::Vector{Int}
    n2s::Vector{Int}
    l2s::Vector{Int}
-    function ho_basis_2B(E_max, Λ=-1)
+function get_sp_basis(E_max)
-        Es = Int[]
+    Es = Int[]
-        n1s = Int[]
+    ns = Int[]
-        l1s = Int[]
+    ls = Int[]
        n2s = Int[]
        l2s = Int[]
-        # E = 2*n1 + l1 + 2*n2 + l2
+    # E = 2*n + l
-        for E in E_max : -2 : 0 # same parity states only
+    for E in 0 : E_max
-            for n1 in 0 : E ÷ 2
+        for n in 0 : E ÷ 2
-                for n2 in 0 : (E - 2*n1) ÷ 2
+            l = E - 2*n
-                    for l1 in 0 : (E - 2*n1 - 2*n2)
+            push!(Es, E)
-                        l2 = E - 2*n1 - 2*n2 - l1
+            push!(ns, n)
-                        if Λ≥0 && !triangle_ineq(l1, l2, Λ); continue; end
+            push!(ls, l)
-                        push!(Es, E)
+        end
-                        push!(n1s, n1)
+    end
-                        push!(l1s, l1)
+
-                        push!(n2s, n2)
+    return (Es, ns, ls)
-                        push!(l2s, l2)
+end
-                    end
+
 function get_2p_basis(E_max, Λ=-1)
    Es = Int[]
    n1s = Int[]
    l1s = Int[]
    n2s = Int[]
    l2s = Int[]
    # E = 2*n1 + l1 + 2*n2 + l2
    for E in E_max : -2 : 0 # same parity states only
        for n1 in 0 : E ÷ 2
            for n2 in 0 : (E - 2*n1) ÷ 2
                for l1 in 0 : (E - 2*n1 - 2*n2)
                    l2 = E - 2*n1 - 2*n2 - l1
                    if Λ≥0 && !triangle_ineq(l1, l2, Λ); continue; end
                    push!(Es, E)
                    push!(n1s, n1)
                    push!(l1s, l1)
                    push!(n2s, n2)
                    push!(l2s, l2)
                end
            end
        end
        return new(E_max, Λ, length(Es), Es, n1s, l1s, n2s, l2s)
    end
    return (Es, n1s, l1s, n2s, l2s)
 end
-"Number of possible distinct matrix elements for a given l."
+function get_sp_T_matrix(ns, ls; mask=trues(length(ns),length(ns)), μω_gen=1.0, μ=1.0)
 function cache_size_l(E_max::Int, l::Int)::Int
    n_max = (E_max - l) ÷ 2
    return (n_max * (n_max + 1)) ÷ 2
 end
 "Number of possible distinct matrix elements for all l."
 cache_size(E_max::Int)::Int = sum(l -> cache_size_l(E_max, l), 0 : E_max)
 "Preallocation of cache for PE matrix elements."
 prealloc_V_cache(E_max::Int, dtype::DataType=Float64) = LRU{Tuple{UInt8, UInt8, UInt8}, dtype}(maxsize=cache_size(E_max))
 function V_numerical(V_of_r, l, n1, n2; μω_gen=1.0, atol=0, maxevals=10^7)
    const_part = sqrt(μω_gen) * ho_basis_const(l, n1) * ho_basis_const(l, n2)
    integrand(r) = ho_basis_func(l, n1, sqrt(μω_gen) * r) * ho_basis_func(l, n2, sqrt(μω_gen) * r) * V_of_r(r)
    (integral, _) = quadgk(integrand, 0, Inf; atol=atol, maxevals=maxevals)
    return const_part * integral
 end
 "KE matrix for a single DOF. Set kron_deltas=[other quantum numbers] for other DOFs which the operator does not act on.
    E.g. get_sp_T_matrix(n1s, l1s, kron_deltas=[n2s l2s])"
 function get_sp_T_matrix(ns, ls, kron_deltas=[]; μω_gen=1.0, μ=1.0)
    mat = spzeros(length(ns), length(ns))
    for idx in CartesianIndices(mat)
        if !mask[idx]; continue; end
        (i, j) = Tuple(idx)
        all(arr -> arr[i]==arr[j], kron_deltas) || continue # check if all Kronecker deltas are non-zero
        if ls[i] == ls[j]
            if ns[i] == ns[j]
                mat[idx] = ns[j] + ls[i]/2 + 3/4
@ -81,14 +72,11 @@ function get_sp_T_matrix(ns, ls, kron_deltas=[]; μω_gen=1.0, μ=1.0)
    return (μω_gen / μ) .* mat
 end
-"PE matrix for a single DOF. Set kron_deltas=[other quantum numbers] for other DOFs which the operator does not act on.
+function get_sp_V_matrix(V_l, ns, ls; mask=trues(length(ns),length(ns)), dtype=Float64, cache=LRU{Tuple{UInt8, UInt8, UInt8}, dtype}(maxsize=(1+maximum(ns))^2))
    E.g. get_sp_V_matrix(n1s, l1s, kron_deltas=[n2s l2s])
    Providing a preallocated cache is optional. Otherwise, provided E_max value is used to initialize one (defaults to 100)."
 function get_sp_V_matrix(V_l, ns, ls, kron_deltas=[]; dtype=Float64, E_max=100, cache=prealloc_V_cache(E_max, dtype))
    mat = zeros(dtype, length(ns), length(ns))
    Threads.@threads for idx in CartesianIndices(mat) 
        if !mask[idx]; continue; end
        (i, j) = Tuple(idx)
        all(arr -> arr[i]==arr[j], kron_deltas) || continue # check if all Kronecker deltas are non-zero
        if ls[i] == ls[j]
            l = UInt8(ls[i])
            n1, n2 = UInt8.(minmax(ns[i], ns[j])) # assuming transpose symmetry
@ -98,12 +86,12 @@ function get_sp_V_matrix(V_l, ns, ls, kron_deltas=[]; dtype=Float64, E_max=100,
    return sparse(mat)
 end
-function Moshinsky_transform(basis::ho_basis_2B)
+function Moshinsky_transform(Es, n1s, l1s, n2s, l2s, Λ)
-    NQMAX = maximum(basis.Es)
+    NQMAX = maximum(Es)
-    @assert all(mod.(basis.Es, 2) .== mod(NQMAX, 2)) "Can only admit basis states with same parity"
+    @assert all(mod.(Es, 2) .== mod(NQMAX, 2)) "Can only admit basis states with same parity"
-    LMIN = basis.Λ
+    LMIN = Λ
-    LMAX = basis.Λ
+    LMAX = Λ
    CO = 1/sqrt(2)
    SI = 1/sqrt(2)
@ -111,15 +99,15 @@ function Moshinsky_transform(basis::ho_basis_2B)
    BRAC = zeros(Float64, 1 + LMAX, 1 + (NQMAX - LMIN) ÷ 2, 1 + (NQMAX - LMIN) ÷ 2, 1 + (NQMAX - LMIN) ÷ 2, 1 + (NQMAX - LMIN) ÷ 2, 1 + LMAX, 1 + (NQMAX-LMIN) ÷ 2, 1 + LMAX-LMIN)
    @ccall "../OSBRACKETS/allosbrac.so".allosbrac_(NQMAX::Ref{Int32},LMIN::Ref{Int32},LMAX::Ref{Int32},CO::Ref{Float64},SI::Ref{Float64},BRAC::Ptr{Array{Float64}})::Cvoid
-    mat = zeros(basis.dim, basis.dim)
+    mat = zeros(length(Es), length(Es))
-    s = hcat(basis.Es, basis.n1s, basis.l1s, basis.n2s, basis.l2s)
+    s = hcat(Es, n1s, l1s, n2s, l2s)
    Threads.@threads for idx in CartesianIndices(mat)
        (i, j) = Tuple(idx)
        (Elhs, N, L, n, l) = s[i, :]
        (Erhs, n1, l1, n2, l2) = s[j, :]
-        if Elhs == Erhs && triangle_ineq(L, l, basis.Λ) && triangle_ineq(l1, l2, basis.Λ)
+        if Elhs == Erhs && triangle_ineq(L, l, Λ) && triangle_ineq(l1, l2, Λ)
-            mat[i, j] = (-1)^(n1 + n2 + N + n) * pick_Moshinsky_bracket(BRAC, n1, l1, n2, l2, N, L, n, l, basis.Λ)
+            mat[i, j] = (-1)^(n1 + n2 + N + n) * pick_Moshinsky_bracket(BRAC, n1, l1, n2, l2, N, L, n, l, Λ)
        end
    end
@ -137,115 +125,78 @@ function pick_Moshinsky_bracket(BRAC, n1′, l1′, n2′, l2′, n1, l1, n2, l2
    return BRAC[1 + NP, 1 + n1′, 1 + MP, 1 + n1, 1 + n2, 1 + N, 1 + M, 1]
 end
-function get_jacobi_V_matrix(V_of_r, basis::ho_basis_2B, μ1ω1, μω_global; atol=10^-6, maxevals=10^5)
+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, basis, μ1ω1; atol=atol, maxevals=maxevals)
+    _, n1s, l1s, n2s, l2s = get_2p_basis(E_max, Λ)
-    V2 = get_jacobi_V2_matrix(V_of_r, basis, μω_global; atol=atol, maxevals=maxevals)
+    l_max = max(maximum(l1s), maximum(l2s))
    n_max = max(maximum(n1s), maximum(n2s))
    mask1 = (n2s .== n2s') .&& (l2s .== l2s')
    V1_elem(l, n1, n2) = V_numerical(V_of_r, l, n1, n2; μω_gen=μ1ω1, atol=atol, maxevals=maxevals)
    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 + V2
 end
-function get_jacobi_V1_matrix(V_of_r, basis::ho_basis_2B, μ1ω1; atol=10^-6, maxevals=10^5)
+function get_jacobi_V2_matrix(V_of_r, E_max, Λ, μω_global; atol=10^-6, maxevals=10^5)
-    V1_elem(l, n1, n2) = V_numerical(V_of_r, l, n1, n2; μω_gen=μ1ω1, atol=atol, maxevals=maxevals)
+    Es, n1s, l1s, n2s, l2s = get_2p_basis(E_max, Λ)
-    V1 = get_sp_V_matrix(V1_elem, basis.n1s, basis.l1s, [basis.n2s, basis.l2s]; dtype=ComplexF64, E_max=basis.E_max)
+    l_max = max(maximum(l1s), maximum(l2s))
-    return V1
+    n_max = max(maximum(n1s), maximum(n2s))
-end
+    mask1 = (n2s .== n2s') .&& (l2s .== l2s')
-
+    mask2 = (n1s .== n1s') .&& (l1s .== l1s')
-function get_jacobi_V2_matrix(V_of_r, basis::ho_basis_2B, μω_global; atol=10^-6, maxevals=10^5)    
+    
    V_relative_elem(l, n1, n2) = V_numerical(V_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_cache = LRU{Tuple{UInt8, UInt8, UInt8}, ComplexF64}(maxsize=(1+l_max)*(1+n_max)^2)
-    V_relative = get_sp_V_matrix(V_relative_elem, basis.n1s, basis.l1s, [basis.n2s, basis.l2s]; dtype=ComplexF64, cache=V_relative_cache) + get_sp_V_matrix(V_relative_elem, basis.n2s, basis.l2s, [basis.n1s, basis.l1s]; dtype=ComplexF64, cache=V_relative_cache)
+    V_relative = get_sp_V_matrix(V_relative_elem, n1s, l1s; mask=mask1, dtype=ComplexF64, cache=V_relative_cache) + get_sp_V_matrix(V_relative_elem, n2s, l2s; mask=mask2, dtype=ComplexF64, cache=V_relative_cache)
-    U = Moshinsky_transform(basis)
+    U = Moshinsky_transform(Es, n1s, l1s, n2s, l2s, Λ)
-    V2 =  transpose(U) * V_relative * U
+    V2 =  U' * V_relative * U
    return V2
 end
-function get_2p_p1p2_matrix(basis::ho_basis_2B, μ1ω1, μ2ω2; dtype=Float64)
+function get_2p_p1p2_matrix(n1s, l1s, n2s, l2s, Λ, μ1ω1, μ2ω2; dtype=Float64)
-    # TODO: Cache for integrals
+    mat = zeros(dtype, length(n1s), length(n1s))
    integral1(np, lp, n, l) = integral_HO(np, lp, n, l, μ1ω1)
    integral2(np, lp, n, l) = integral_HO(np, lp, n, l, μ2ω2)
    mat = zeros(dtype, basis.dim, basis.dim)
    Threads.@threads for idx in CartesianIndices(mat)
        (i, j) = Tuple(idx)
-        val = racahs_reduction_formula(basis.n1s[i], basis.l1s[i], basis.n2s[i], basis.l2s[i], basis.n1s[j], basis.l1s[j], basis.n2s[j], basis.l2s[j], basis.Λ, integral1, integral2)
+        val = racahs_reduction_formula(n1s[i], l1s[i], n2s[i], l2s[i], n1s[j], l1s[j], n2s[j], l2s[j], Λ, μ1ω1, μ2ω2)
        if !(val ≈ 0); mat[idx] = val; end
    end
    return sparse(mat)
 end
-function get_src_V_matrix(V_of_r, basis::ho_basis_2B, μω, μω_global; atol=10^-6, maxevals=10^5)    
+function get_src_V_matrix(V_of_r, E_max, Λ, μω, μω_global; 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))
    mask1 = (n2s .== n2s') .&& (l2s .== l2s')
    mask2 = (n1s .== n1s') .&& (l1s .== l1s')
    V_elem(l, n1, n2) = V_numerical(V_of_r, l, n1, n2; μω_gen=μω, atol=atol, maxevals=maxevals)
-    V_cache = prealloc_V_cache(basis.E_max, ComplexF64)
+    V_cache = LRU{Tuple{UInt8, UInt8, UInt8}, ComplexF64}(maxsize=(1+l_max)*(1+n_max)^2)
-    V1 = get_sp_V_matrix(V_elem, basis.n1s, basis.l1s, [basis.n2s, basis.l2s]; dtype=ComplexF64, cache=V_cache)
+    V1 = get_sp_V_matrix(V_elem, n1s, l1s; mask=mask1, dtype=ComplexF64, cache=V_cache)
-    V2 = get_sp_V_matrix(V_elem, basis.n2s, basis.l2s, [basis.n1s, basis.l1s]; dtype=ComplexF64, cache=V_cache)
+    V2 = get_sp_V_matrix(V_elem, n2s, l2s; mask=mask2, dtype=ComplexF64, cache=V_cache)
-    V12 = get_src_V12_matrix(V_of_r, basis, μω_global; atol=atol, maxevals=maxevals)
+    V12 =  get_src_V12_matrix(V_of_r, E_max, Λ, μω_global; atol=atol, maxevals=maxevals)
    return V1 + V2 + V12
 end
-function get_src_V12_matrix(V_of_r, basis::ho_basis_2B, μω_global; atol=10^-6, maxevals=10^5)
+function get_src_V12_matrix(V_of_r, E_max, Λ, μω_global; atol=10^-6, maxevals=10^5)
    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')
    V_relative_elem(l, n1, n2) = V_numerical(V_of_r, l, n1, n2; μω_gen=μω_global, atol=atol, maxevals=maxevals)
-    V_relative = get_sp_V_matrix(V_relative_elem, basis.n1s, basis.l1s, [basis.n2s, basis.l2s]; dtype=ComplexF64, E_max=basis.E_max)
+    V_relative_cache = LRU{Tuple{UInt8, UInt8, UInt8}, ComplexF64}(maxsize=(1+l_max)*(1+n_max)^2)
-    U = Moshinsky_transform(basis)
+    V_relative = get_sp_V_matrix(V_relative_elem, n1s, l1s; mask=mask1, dtype=ComplexF64, cache=V_relative_cache)
-    V12 =  transpose(U) * V_relative * U
+    U = Moshinsky_transform(Es, n1s, l1s, n2s, l2s, Λ)
    V12 =  U' * V_relative * U
    return V12
 end
 "Basis transformation from HO to momentum space"
 function get_W_matrix(basis_p, basis::ho_basis_2B, μ1ω1, μ2ω2=μ1ω1; weights=true)
    W = zeros(ComplexF64, length(basis_p), basis.dim)
    Threads.@threads for idx in CartesianIndices(W)
        (i1, i2) = Tuple(idx)
        ((j1, j2), (k1, w1), (k2, w2)) = basis_p[i1]
        if j1 == basis.l1s[i2] && j2 == basis.l2s[i2]
            elem1 = 1/sqrt(sqrt(μ1ω1)) * (-1)^basis.n1s[i2] * ho_basis(j1, basis.n1s[i2], 1/sqrt(μ1ω1) * k1)
            elem2 = 1/sqrt(sqrt(μ2ω2)) * (-1)^basis.n2s[i2] * ho_basis(j2, basis.n2s[i2], 1/sqrt(μ2ω2) * k2)
            W[idx] = elem1 * elem2 * (weights ? w1 * w2 : 1)
        end
    end
    return sparse(W)
 end
 function get_3b_H_matrix(coord_system::coordinate_system, V_of_r, μω_global, E_max, Λ, m=1.0, kinetic_part=true, potential_part=true; atol=10^-5, maxevals=10^5, verbose=true)
    if coord_system == jacobi
        μ1ω1 = μω_global * 1/2
        μ2ω2 = μω_global * 2
        μ1 = m * 1/2
        μ2 = m * 2/3        
    elseif coord_system == src
        μ1ω1 = μ2ω2 = μω = μω_global * 2
        μ1 = μ2 = μ = m/2
    end
    verbose && println("No of threads = ", Threads.nthreads())
    @time "Basis" basis = ho_basis_2B(E_max, Λ)
    verbose && println("Basis size = ", basis.dim)
    out = spzeros(basis.dim, basis.dim)
    if kinetic_part
        verbose && println("Constructing KE matrices")
        @time "T1" out += get_sp_T_matrix(basis.n1s, basis.l1s, [basis.n2s, basis.l2s]; μω_gen=μ1ω1, μ=μ1)
        @time "T2" out += get_sp_T_matrix(basis.n2s, basis.l2s, [basis.n1s, basis.l1s]; μω_gen=μ2ω2, μ=μ2)
        if coord_system == src
            @time "T_cross" out += get_2p_p1p2_matrix(basis, μ1ω1, μ2ω2; dtype=ComplexF64) ./ (2*μ)
        end
    end
    if potential_part
        verbose && println("Constructing PE matrices")
        if coord_system == jacobi
            @time "V" out += get_jacobi_V_matrix(V_of_r, basis, μ1ω1, μω_global; atol=atol, maxevals=maxevals)
        elseif coord_system == src
            @time "V" out += get_src_V_matrix(V_of_r, basis, μω, μω_global; atol=atol, maxevals=maxevals)
        end
    end
    return out
 end
--- a/ho_basis_2body.jl
+++ b/ho_basis_2body.jl
@ -0,0 +1,30 @@
 using Arpack, SparseArrays
 include("ho_basis.jl")
 E_max = 30
 μω_gen = 0.2
 Λ = 0
 m = 1.0
 Va = -2
 Ra = 2
 μ1 = m * 1/2
 println("No of threads = ", Threads.nthreads())
 Es, n1s, l1s = get_sp_basis(E_max)
 println("Basis size = ", length(Es))
 println("Constructing KE matrices")
@time "T1" T1 = get_sp_T_matrix(n1s, l1s; μω_gen=μω_gen, μ=μ1)
 println("Constructing PE matrices")
 V1_elem(l, n1, n2) = Va * V_Gaussian(Ra, l, n1, n2; μω_gen=μω_gen)
@time "V1" V1 = get_sp_V_matrix(V1_elem, n1s, l1s)
 println("Calculating spectrum")
@time "H" H = T1 + V1
@time "Eigenvalues" evals, _ = eigs(H, nev=3, ncv=30, which=:SR, maxiter=5000, tol=1e-5, ritzvec=false, check=1)
 display(evals)
--- a/ho_basis_3body.jl
+++ b/ho_basis_3body.jl
@ -1,14 +1,44 @@
-using Arpack
+using Arpack, SparseArrays
 include("ho_basis.jl")
 Λ = 0
 m = 1.0
-V_of_r(r) = -2 * exp(-r^2 / 4)
+Va = -2
 Ra = 2
 E_max = 40
 μω_global = 0.3
-H = get_3b_H_matrix(src, V_of_r, μω_global, E_max, Λ, m)
+# due to simple relative coordinates
 μω = μω_global * 2
 μ = m/2
 println("No of threads = ", Threads.nthreads())
@time "Basis" begin
    Es, n1s, l1s, n2s, l2s = get_2p_basis(E_max, Λ)
    mask1 = (n2s .== n2s') .&& (l2s .== l2s')
    mask2 = (n1s .== n1s') .&& (l1s .== l1s')
 end
 println("Basis size = ", length(Es))
 println("Constructing KE matrices")
@time "T1" T1 = get_sp_T_matrix(n1s, l1s; mask=mask1, μω_gen=μω, μ=μ)
@time "T2" T2 = get_sp_T_matrix(n2s, l2s; mask=mask2, μω_gen=μω, μ=μ)
@time "T_cross" T_cross = get_2p_p1p2_matrix(n1s, l1s, n2s, l2s, Λ, μω, μω) ./ (2*μ)
 println("Constructing PE matrices")
 V_elem(l, n1, n2) = Va * V_Gaussian(Ra, l, n1, n2; μω_gen=μω)
 V_relative_elem(l, n1, n2) = Va * V_Gaussian(Ra, l, n1, n2; μω_gen=μω_global)
@time "V1" V1 = get_sp_V_matrix(V_elem, n1s, l1s; mask=mask1)
@time "V2" V2 = get_sp_V_matrix(V_elem, n2s, l2s; mask=mask2)
@time "V relative" V_relative = get_sp_V_matrix(V_relative_elem, n1s, l1s; mask=mask1)
@time "Moshinsky brackets" U = Moshinsky_transform(Es, n1s, l1s, n2s, l2s, Λ)
@time "V12" V12 =  U' * V_relative * U
 println("Calculating spectrum")
@time "H" H = T1 + T2 + T_cross + V1 + V2 + V12
@time "Eigenvalues" evals, _ = eigs(H, nev=3, ncv=30, which=:SR, maxiter=5000, tol=1e-5, ritzvec=false, check=1)
 display(evals)
--- a/ho_basis_3body_resonance.jl
+++ b/ho_basis_3body_resonance.jl
@ -1,15 +1,41 @@
-using Arpack
+using Arpack, SparseArrays, LRUCache
 include("ho_basis.jl")
 target_E = 4.07656088827514 - 0.012743522750966718im
 V_of_r(r) = 2 * exp(-(r-3)^2 / (1.5)^2)
 Λ = 0
 m = 1.0
 V_of_r(r) = 2 * exp(-(r-3)^2 / (1.5)^2)
 μω_global = 0.5 * exp(-2im * pi / 9)
 E_max = 30
 μω_global = 0.5 * exp(-2im * pi / 9)
-H = get_3b_H_matrix(src, V_of_r, μω_global, E_max, Λ, m)
+# due to simple relative coordinates
 μω = μω_global * 2
 μ = m/2
 println("No of threads = ", Threads.nthreads())
@time "Basis" begin
    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')
 end
 println("Basis size = ", length(Es))
 println("Constructing KE matrices")
@time "T1" T1 = get_sp_T_matrix(n1s, l1s; mask=mask1, μω_gen=μω, μ=μ)
@time "T2" T2 = get_sp_T_matrix(n2s, l2s; mask=mask2, μω_gen=μω, μ=μ)
@time "T_cross" T_cross = get_2p_p1p2_matrix(n1s, l1s, n2s, l2s, Λ, μω, μω; dtype=ComplexF64) ./ (2*μ)
 println("Constructing PE matrices")
@time "V" V = get_src_V_matrix(V_of_r, E_max, Λ, μω, μω_global)
 println("Calculating spectrum")
@time "H" H = T1 + T2 + T_cross + V
@time "Eigenvalues" evals, _ = eigs(H, nev=5, ncv=50, which=:LI, maxiter=5000, tol=1e-5, ritzvec=false, check=1)
@time "Eigenvalues" evals, _ = eigs(H, nev=5, ncv=50, sigma=target_E, maxiter=5000, tol=1e-5, ritzvec=false, check=1)
 display(evals)
--- a/ho_basis_3body_wf.jl
+++ b/ho_basis_3body_wf.jl
@ -0,0 +1,30 @@
 using HDF5
 include("ho_basis_3body.jl")
@time "Eigenvectors" evals, evecs = eigs(H, nev=1, ncv=10, which=:SR, maxiter=5000, tol=1e-8, ritzvec=true, check=1)
 idx = argmin(real.(evals))
 E = evals[idx]
@assert imag(E) ≈ 0 "Energy is not real"
 E = real(E)
 println("Exporting E = $E")
 wf = real.(evecs[:, idx])
@assert all(imag.(wf) .≈ 0) "Wave function is not real"
 wf = real.(wf)
 h5open("temp/HO_3b.h5", "w") do fid
    write_attribute(fid, "E", E)
    write_attribute(fid, "Λ", Λ)
    write_attribute(fid, "μ1ω1", μ1ω1)
    write_attribute(fid, "μ2ω2", μ2ω2)
    write_attribute(fid, "μ1", μ1)
    write_attribute(fid, "μ2", μ2)
    write_dataset(fid, "n1", n1s)
    write_dataset(fid, "l1", l1s)
    write_dataset(fid, "n2", n2s)
    write_dataset(fid, "l2", l2s)
    write_dataset(fid, "wf", wf)
 end
--- a/test/ho_basis_test.jl
+++ b/test/ho_basis_test.jl
@ -1,5 +1,5 @@
 using LinearAlgebra
-include("../ho_basis.jl")
+include("ho_basis.jl")
 l = 0
 V0 = -10
--- a/math.jl
+++ b/math.jl
@ -1,5 +1,5 @@
 using SpecialFunctions, WignerSymbols
-include("common.jl")
+include("helper.jl")
 # Gaussian potentials in HO space
 inv_factorial(n) = Iterators.prod(inv.(1:n))
@ -12,36 +12,27 @@ V_Gaussian(R, l, n1, n2; μω_gen=1.0) = (-1)^(n1 + n2) * better_sum([N_lnk(l, n
 sqrt_double_factorial(n) = Iterators.prod(sqrt.(n:-2:1))
 sqrt_sqrt_pi = sqrt(sqrt(pi))
 laguerre(l, n, x) = gamma(n + l + 3/2) * better_sum([(-x * x)^k / gamma(k + l + 3/2) * inv_factorial(n - k) * inv_factorial(k)  for k in 0:n])
-ho_basis_const(l, n) = (-1)^n / sqrt_sqrt_pi * (2.0)^((n + l + 2) / 2) * sqrt_factorial(n) / sqrt_double_factorial(2*n + 2*l + 1)
+ho_basis(l, n, x) = (-1)^n / sqrt_sqrt_pi * 2^((n + l + 2) / 2) * sqrt_factorial(n) / sqrt_double_factorial(2*n + 2*l + 1) * x^(l + 1) * exp(-x^2 / 2) * laguerre(l, n, x)
 ho_basis_func(l, n, x) = x^(l + 1) * exp(-x^2 / 2) * laguerre(l, n, x)
 ho_basis(l, n, x) = ho_basis_const(l, n) * ho_basis_func(l, n, x)
 # for implementation of simple relative coordinates
 double_factorial(n::Int) = Iterators.prod(big, n:-2:1)
 "Gaussian integral for n ∈ Integers (Ref: Wolfram MathWorld + simplifications)"
-gauss_int(a, n) = double_factorial(n - 1) / (2.0 * a)^((n + 1)/2) * (iseven(n) ? sqrt(π / 2) : 1)
+gauss_int(a, n) = double_factorial(n - 1) / (2 * a)^((n + 1)/2) * (iseven(n) ? sqrt(π / 2) : 1)
-"Gives ∫dp p u' u where u' and u are HO functions with different l (Ref: worked out in Mathematica)"
+"Gives ∫dp p u' u where u' and u' may have different l (Ref: worked out in Mathematica)"
-function integral_HO(np, lp, n, l, μω)
+function integral(np, lp, n, l, μω)
    s = [(-1)^(m + mp) * gauss_int(1, 2 * m + 2 * mp + l + lp + 3) * N_lnk(l, n, m) * N_lnk(lp, np, mp) for (m, mp) in Iterators.product(0:n, 0:np)]
    return 2 * sqrt(μω) * better_sum(s)
 end
-"Gives <n' l'|| p ||n l> for the HO basis, where integral(np, lp, n, l) is a function that returns ∫dp p u' u"
+"Gives <n' l'|| p ||n l> for the HO basis"
-function reduced_matrix_element(np, lp, n, l, integral)::ComplexF64
+reduced_matrix_element(np, lp, n, l, μω) = (-1)^lp * sqrt(2*lp + 1) * sqrt(2*l + 1) * wigner3j(Float64, lp, 1, l, 0, 0, 0) * integral(np, lp, n, l, μω)
    wig::Float64 = wigner3j(Float64, lp, 1, l, 0, 0, 0)
    if wig == 0
        return 0
    else
        return (-1)^lp * sqrt(2*lp + 1) * sqrt(2*l + 1) * wig * integral(np, lp, n, l)
    end
 end
-"Matrix element <n1p l1p n2p l2p| p1⋅p2 |n1 l1 n2 l2> (Ref: de-Shalit & Talmi, Eq 15.5), where integral(np, lp, n, l) is a function that returns ∫dp p u' u"
+"Matrix element <n1p l1p n2p l2p| p1⋅p2 |n1 l1 n2 l2> (Ref: de-Shalit & Talmi, Eq 15.5)"
-function racahs_reduction_formula(n1p, l1p, n2p, l2p, n1, l1, n2, l2, Λ, integral1, integral2)
+function racahs_reduction_formula(n1p, l1p, n2p, l2p, n1, l1, n2, l2, Λ, μ1ω1, μ2ω2)
    val = wigner6j(Float64, l1p, l2p, Λ, l2, l1, 1)
-    if val != 0; val *= reduced_matrix_element(n1p, l1p, n1, l1, integral1); end
+    if val != 0; val *= reduced_matrix_element(n1p, l1p, n1, l1, μ1ω1); end
-    if val != 0; val *= reduced_matrix_element(n2p, l2p, n2, l2, integral2); end
+    if val != 0; val *= reduced_matrix_element(n2p, l2p, n2, l2, μ2ω2); end
    return (-1)^(l1 + l2p + Λ) * val
 end
--- a/p_space.jl
+++ b/p_space.jl
@ -1,6 +1,5 @@
 using LinearAlgebra
 using SpecialFunctions, FastGaussQuadrature, QuadGK
 include("ho_basis.jl")
 function gausslegendre_shifted(a, b, n)
    scale = (b - a) / 2
@ -60,56 +59,3 @@ function Vl_mat_elem(V_of_r, l, p, q; atol=0, maxevals=10^7, R_cutoff=Inf)
    (integral, _) = quadgk(integrand, 0, R_cutoff; atol=atol, maxevals=maxevals)
    return (2 / pi) * integral
 end
 "Return the Hamiltonian matrix (and the array of weights) for the given system."
 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)
    if coord_system == jacobi
        μ1ω1 = μω_global * 1/2
        μ2ω2 = μω_global * 2
        μ1 = m * 1/2
        μ2 = m * 2/3
    else
        error("Only Jacobi coordinates are implemented")
    end
    verbose && println("No of threads = ", Threads.nthreads())
    V_l(j, k, kp) = Vl_mat_elem(V_of_r, j, k, kp; atol=atol, maxevals=maxevals, R_cutoff=R_cutoff)
    ks, ws = get_mesh(vertices, subdivisions)
    weights = repeat(kron(ws, ws), jmax + 1)
    block_size = length(ks)
    tri((j1, j2)) = triangle_ineq(j1, j2, Λ)
    js = collect(Iterators.filter(tri, iter_prod(0:jmax, 0:jmax)))
    basis = iter_prod(js, zip(ks, ws), zip(ks, ws)) # basis = ((j1, j2), (k1, w1), (k2, w2))
    basis_size = length(js) * length(ks)^2
    @assert length(basis) == basis_size "Something wrong with the basis"
    verbose && println("Basis size = $basis_size")
    out = spzeros(basis_size, basis_size)
    @time "Block diagonal part" begin
        if kinetic_part & potential_part
            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]
        elseif kinetic_part
            Hb_blocks = [kron_sum(get_T_matrix(ks, μ1), get_T_matrix(ks, μ2)) for _ in js]
        elseif potential_part
            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]
        end
        out += blockdiag(sparse.(Hb_blocks)...)
    end
    if potential_part
        basis_ho = ho_basis_2B(E_max, Λ)
        verbose && println("HO basis size = ", basis_ho.dim)
        @time "V2_HO" V2_HO =  get_jacobi_V2_matrix(V_of_r, basis_ho, μω_global)
        @time "W_right" W_right = get_W_matrix(basis, basis_ho, μ1ω1, μ2ω2; weights=true)
        @time "W_left" W_left = get_W_matrix(basis, basis_ho, μ1ω1, μ2ω2; weights=false)
        @time "V2" out += W_left * V2_HO * transpose(W_right)
    end
    return (out, weights)
 end
--- a/p_space_3body.jl
+++ b/p_space_3body.jl
@ -1,18 +0,0 @@
 using Arpack
 include("p_space.jl")
 Λ = 0
 m = 1.0
 V_of_r(r) = -2 * exp(-r^2 / 4)
 vertices = [0, 0.5 - 0.3im, 1, 4]
 subdivisions = [10, 10, 10]
 jmax = 4
 E_max = 30
 μω_global = 0.5
 H, _ = get_3b_H_matrix(jacobi, V_of_r, vertices, subdivisions, jmax, μω_global, E_max, Λ, m)
@time "Eigenvalues" evals, _ = eigs(H, nev=3, ncv=24, which=:SR, maxiter=5000, tol=1e-5, ritzvec=false, check=1)
 display(evals)
--- a/p_space_3body_resonance.jl
+++ b/p_space_3body_resonance.jl
@ -1,20 +0,0 @@
 using Arpack
 include("p_space.jl")
 target = 4.0766890719636875 - 0.012758927741074495im
 Λ = 0
 m = 1.0
 V_of_r(r) =  2 * exp(-(r-3)^2 / (1.5)^2)
 vertices = [0, 2 - 0.2im, 3, 4]
 subdivisions = [15, 10, 10]
 jmax = 4
 E_max = 40
 μω_global = 0.5
 H, _ = get_3b_H_matrix(jacobi, V_of_r, vertices, subdivisions, jmax, μω_global, E_max, Λ, m)
@time "Eigenvalues" evals, _ = eigs(H, sigma=target, maxiter=5000, tol=1e-5, ritzvec=false, check=1)
 display(evals)
--- a/p_space_test.ipynb
+++ b/p_space_test.ipynb
@ -0,0 +1,62 @@
 {
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots\n",
    "include(\"helper.jl\")\n",
    "include(\"p_space.jl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "vertices = [0, 1 - 0.5im, 2, 6]\n",
    "subdivisions = [64, 64, 64]\n",
    "p, w = get_mesh(vertices, subdivisions)\n",
    "\n",
    "scatter(real.(p), imag.(p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ComplexScaling-FV: Eq. (54)\n",
    "V_pq(p, q) = -10 * g1(1, p, q)\n",
    "\n",
    "H = get_H_matrix(V_pq, p, w)\n",
    "evals = eigen(H).values\n",
    "\n",
    "E_target = 0.258 - 0.164im\n",
    "E = nearest(evals, E_target)\n",
    "\n",
    "print(\"E = $E\")\n",
    "scatter(real.(evals), imag.(evals), xlim = (0,1))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.9.0",
   "language": "julia",
   "name": "julia-1.9"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.9.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
 }
--- a/simple_berggren.ipynb
+++ b/simple_berggren.ipynb
@ -0,0 +1,70 @@
 {
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots\n",
    "include(\"helper.jl\")\n",
    "include(\"p_space.jl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "vertices = [0, 0.5 - 0.3im, 1, 6]\n",
    "subdivisions = [64, 64, 64]\n",
    "p, w = get_mesh(vertices, subdivisions)\n",
    "\n",
    "# resonance example from my thesis\n",
    "V_basis(p, q) = 2*g0(4, p, q) - 3*g0(2, p, q)\n",
    "\n",
    "basis_eig = eigen(get_H_matrix(V_basis, p, w))\n",
    "basis = basis_eig.vectors .* w\n",
    "\n",
    "evals = basis_eig.values\n",
    "E_target = 0.7\n",
    "E = include(\"helper.jl\")\n",
    "\n",
    "print(\"E = $E\")\n",
    "scatter(real.(evals), imag.(evals), xlim = (0,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ResonanceEC: Eq. (20)\n",
    "V_system(c) = (p, q) -> c*(-5*g0(sqrt(3), p, q) + 2*g0(sqrt(10), p, q))\n",
    "\n",
    "H = get_H_matrix(V_system(0.45), p, w)\n",
    "H_berggren = transpose(basis) * H * basis\n",
    "\n",
    "evals = eigvals(H)\n",
    "scatter(real.(evals), imag.(evals), xlim = (0, 0.5))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.10.2",
   "language": "julia",
   "name": "julia-1.10"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.10.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
 }
--- a/test/3body_Berggren_orthogonality.jl
+++ b/test/3body_Berggren_orthogonality.jl
@ -1,4 +1,4 @@
-include("../p_space_3body_resonance.jl")
+include("../berggren_3body_resonance.jl")
@time "Eigenvectors" evals, evecs = eigs(H, sigma=target, maxiter=5000, tol=1e-5, ritzvec=true, check=1)
--- a/test/misc.jl
+++ b/test/misc.jl
@ -1,65 +0,0 @@
 using SparseArrays, LinearAlgebra
 include("../common.jl")
 #### gram_schmidt ####
 n = 64
 N = 8
 vecs = [rand(n) + 1im .* rand(n) for _ in 1:N]
 ws = rand(n)
 ws_mat = spdiagm(ws)
 basis = hcat(vecs...)
 H = rand(n, n)
 H += transpose(H) # complex symmetric
 H_EC = transpose(basis) * ws_mat * H * ws_mat * basis
 N_EC = transpose(basis) * ws_mat * basis
 evals = eigvals(H_EC, N_EC)
 println("Eigenvalues with GEVP:")
 display(evals)
 ortho_basis = hcat(gram_schmidt!(vecs, ws)...)
 N_ortho = transpose(ortho_basis) * ws_mat * ortho_basis
 println("Norm matrix after Gram-Schmidt:")
 display(round.(N_ortho; digits=2)) # should be ≈I
@assert N_ortho ≈ I(N) "Gram-Schmidt did not yield an orthogonal basis"
 H_EC_ortho = transpose(ortho_basis) * ws_mat * H * ws_mat * ortho_basis
 evals_ortho = eigvals(H_EC_ortho)
 println("Eigenvalues after Gram-Schmidt:")
 display(evals_ortho)
@assert evals ≈ evals_ortho "Gram-Schmidt did not preserve the eigenvalues"
 ############
 println("\nRepeat with a redundant basis\n")
 println("Original dimensionality = $(length(vecs))")
 for pow in 6:9
    noise = rand(n) ./ 10^pow
    new_vec = vecs[1] + noise
    push!(vecs, new_vec)
 end
 println("Dimensionality before Gram-Schmidt = $(length(vecs))")
 ortho_vecs = gram_schmidt!(vecs, ws; verbose=true)
 ortho_basis = hcat(ortho_vecs...)
 println("Dimensionality after Gram-Schmidt = $(length(ortho_vecs))")
 H_EC_ortho = transpose(ortho_basis) * ws_mat * H * ws_mat * ortho_basis
 evals_ortho = eigvals(H_EC_ortho)
 println("Eigenvalues after Gram-Schmidt:")
 display(evals_ortho)
@assert isapprox(evals, evals_ortho; atol=1e-3) "Gram-Schmidt did not approximately preserve the eigenvalues"
 ######################
--- a/test/moshinsky.jl
+++ b/test/moshinsky.jl
@ -1,4 +1,4 @@
-println("### Test: transpose(U) * U == identity")
+println("### Test: U' * U == identity")
 using LinearAlgebra
@ -9,13 +9,13 @@ E_max = 30
 println("No of threads = ", Threads.nthreads())
-@time "Basis" basis = ho_basis_2B(E_max, Λ)
+@time "Basis" Es, n1s, l1s, n2s, l2s = get_2p_basis(E_max, Λ)
-println("Basis size = ", basis.dim)
+println("Basis size = ", length(Es))
-@time "Moshinsky brackets" U = Moshinsky_transform(basis)
+@time "Moshinsky brackets" U = Moshinsky_transform(Es, n1s, l1s, n2s, l2s, Λ)
-check = transpose(U) * U - I
+check = U' * U - I
 println("Maximum = ", maximum(abs.(check)))
 println("Norm = ", sum(check .* conj(check)))
--- a/test/p1p2_matrix.jl
+++ b/test/p1p2_matrix.jl
@ -1,57 +0,0 @@
 using LinearAlgebra, SparseArrays, Plots
 include("../p_space.jl")
 include("../ho_basis.jl")
 include("../berggren.jl")
 println("No of threads = ", Threads.nthreads())
 atol = 10^-5
 maxevals = 10^5
 R_cutoff = 16
 Λ = 0
 m = 1.0
 μ = m/2 # due to simple relative coordinates
 vertices = [0, 2 - 0.2im, 3, 4]
 subdivisions = [15, 10, 10]
 ks, ws = get_mesh(vertices, subdivisions)
 jmax = 4
 tri((j1, j2)) = triangle_ineq(j1, j2, Λ)
 js = collect(Iterators.filter(tri, iter_prod(0:jmax, 0:jmax)))
 basis = iter_prod(js, zip(ks, ws), zip(ks, ws)) # basis = ((j1, j2), (k1, w1), (k2, w2))
 basis_size = length(js) * length(ks)^2
@assert length(basis) == basis_size "Something wrong with the basis"
 println("Basis size = $basis_size")
 V_of_r(r) =  2 * exp(-(r-3)^2 / (1.5)^2)
 V_l(j, k, kp) = Vl_mat_elem(V_of_r, j, k, kp; atol=atol, maxevals=maxevals, R_cutoff=R_cutoff)
 # generate p-space bases (actually identity matrices)
@time "p-space bases" ps_bases = [Matrix(spdiagm(1 ./ sqrt.(ws))) for _ in 0:jmax]
 # generate Berggren bases
@time "Berggren bases" begin
    berg_bases = Vector{Matrix{ComplexF64}}(undef, jmax + 1)
    for j in 0:jmax
        _, berg_basis = eigen(get_H_matrix((k, kp) -> V_l(j, k, kp), ks, ws, μ); permute=false, scale=false)
        N_berg = sum(berg_basis.^2 .* ws, dims=1)
        berg_bases[1 + j] = berg_basis ./ transpose(sqrt.(N_berg))
    end
 end
@time "BB tranform matrix" begin
    U_blocks = [kron(berg_bases[1 + j1] .* ws, berg_bases[1 + j2] .* ws) for (j1, j2) in js]
    U = blockdiag(sparse.(U_blocks)...)
 end
@time "In p-space" T_cross_PS = get_2p_p1p2_matrix(length(ks), js, Λ, ps_bases, ps_bases, ws)
@time "In BB" T_cross_BB = get_2p_p1p2_matrix(length(ks), js, Λ, berg_bases, berg_bases, ws)
@time "Basis transform" T_cross_transformed = transpose(U) * T_cross_PS * U
 diff = abs.(T_cross_transformed .- T_cross_BB)
 println("Max error = $(maximum(diff))")
 #@time "In in HO" T_cross_HO = get_2p_p1p2_matrix(n1s, l1s, n2s, l2s, Λ, μω, μω; dtype=ComplexF64)
--- a/test/p_space_basic.jl
+++ b/test/p_space_basic.jl
@ -1,21 +0,0 @@
 using Plots
 include("../common.jl")
 include("../p_space.jl")
 vertices = [0, 1 - 0.5im, 2, 6]
 subdivisions = [64, 64, 64]
 p, w = get_mesh(vertices, subdivisions)
 scatter(real.(p), imag.(p))
 # ComplexScaling-FV: Eq. (54)
 V_pq(p, q) = -10 * g1(1, p, q)
 H = get_H_matrix(V_pq, p, w)
 evals = eigen(H).values
 E_target = 0.258 - 0.164im
 E = nearest(evals, E_target)
 print("E = $E")
 scatter(real.(evals), imag.(evals), xlim = (0,1))
--- a/test/simple_berggren.jl
+++ b/test/simple_berggren.jl
@ -1,30 +0,0 @@
 using Plots
 include("../common.jl")
 include("../p_space.jl")
 vertices = [0, 0.5 - 0.3im, 1, 6]
 subdivisions = [64, 64, 64]
 p, w = get_mesh(vertices, subdivisions)
 # resonance example from my thesis
 V_basis(p, q) = 2*g0(4, p, q) - 3*g0(2, p, q)
 basis_eig = eigen(get_H_matrix(V_basis, p, w))
 basis = basis_eig.vectors .* w
 basis_evals = basis_eig.values
 E_target = 0.7
 E = nearest(basis_evals, E_target)
 print("pole E = $E")
 # ResonanceEC: Eq. (20)
 V_system(c) = (p, q) -> c*(-5*g0(sqrt(3), p, q) + 2*g0(sqrt(10), p, q))
 H = get_H_matrix(V_system(0.45), p, w)
 H_berggren = transpose(basis) * H * basis
 evals = eigvals(H)
 scatter(real.(evals), imag.(evals), label="E")
 scatter!(real.(basis_evals), imag.(basis_evals), label="basis", markershape=:x)
 xlims!((0, 1))
`@ -1,4 +1,4 @@`
	`include("../p_space_3body_resonance.jl")`	`include("../berggren_3body_resonance.jl")`

	`@time "Eigenvectors" evals, evecs = eigs(H, sigma=target, maxiter=5000, tol=1e-5, ritzvec=true, check=1)`	`@time "Eigenvectors" evals, evecs = eigs(H, sigma=target, maxiter=5000, tol=1e-5, ritzvec=true, check=1)`