3-body XZ in p-space (not working)

EC.jl

@@ -156,11 +156,11 @@ exportCSV(EC::affine_EC, filename) = exportCSV(filename, (EC.training_E, EC.exac
 "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")
+    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")
+        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")
+        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")

Project.toml

@@ -1,5 +1,7 @@
 [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"

calculations/2body_data.jl

@@ -0,0 +1,33 @@
+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

calculations/3body_HO_B2R_ACCC.jl

@@ -0,0 +1,68 @@
+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")

calculations/ACCC.jl

@@ -13,14 +13,14 @@ 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)
+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 = new_sqrt.(2μ .* training_E)
+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]
@@ -28,7 +28,7 @@ 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) = complex(c - c0)^(i/2)
+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]
@@ -37,14 +37,11 @@ a = sol[1:order+1]
 b = [1; sol[order+2:end]]
 
 # Pade approximant
-polynomial(a, c) = sum(i -> a[i+1] * complex(c - c0)^(i/2), 0:order)
+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])
-if real.(extrapolated_k[end]) < 0 # flip if following anti-resonance
-    extrapolated_k = -conj.(extrapolated_k)
-end
 extrapolated_E = (extrapolated_k .^ 2) / (2μ)
 
 # Plotting

calculations/PMM.jl

@@ -1,71 +0,0 @@
-using LinearAlgebra, Random, Plots
-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)
-
-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)
-
-# calculate training data
-data_c = training_c
-data_E = [quick_pole_E(V_system(c)) for c in data_c]
-
-# hyperparameters
-N = 9
-
-# initialize random Hamiltonians
-H0 = randn(ComplexF64, N, N)
-H0 = H0 + transpose(H0) # symmetric
-H1 = randn(ComplexF64, N, N)
-H1 = H1 + transpose(H1) # symmetric
-
-# training
-Es = ComplexF64[]
-ψs = Vector{ComplexF64}[]
-
-lr = 0.05
-epochs = 100000
-for epoch in 1:epochs
-    empty!(Es)
-    empty!(ψs)
-    for (c, E) in zip(data_c, data_E)
-        H = H0 + c * H1
-        evals, evecs = eigen(H)
-        i = nearestIndex(evals, E) # TODO: more robust way to identify the eigenvector
-        push!(Es, evals[i])
-        push!(ψs, evecs[:, i])
-    end
-
-    if epoch % 1000 == 0
-        loss = sum(abs2, Es .- data_E)
-        println("Epoch:$epoch/$epochs \t Loss: $loss")
-    end
-
-    # gradient of the loss function
-    function grad(c_order=0)
-        out = zeros(ComplexF64, N, N)
-        for (c, E_target, ψ, E) in zip(data_c, data_E, ψs, Es)
-            out .+= (c^c_order * conj(E - E_target)) .* (ψ * transpose(ψ))
-        end
-        return 2 .* real.(out)
-    end
-    H0 .-= lr .* grad(0) # update H0
-    H1 .-= lr .* grad(1) # update H1    
-end
-
-# evaluate for all points
-all_c = vcat(training_c, extrapolating_c)
-exact_E = [quick_pole_E(V_system(c)) for c in all_c]
-extrapolated_E = ComplexF64[]
-for c in all_c
-    H = H0 + c * H1
-    evals, evecs = eigen(H)
-    evals = vcat(evals, conj.(evals)) # include complex conjugates
-    push!(extrapolated_E, nearest(evals, exact_E[end]))
-end
-
-# plot results
-scatter(real.(data_E), imag.(data_E), label="training", title="PMM", xlabel="Re E", ylabel="Im E")
-scatter!(real.(exact_E), imag.(exact_E), label="exact", m=:+)
-scatter!(real.(extrapolated_E), imag.(extrapolated_E), label="predicted", m=:x)

calculations/PMM.py

@@ -0,0 +1,81 @@
+#%%
+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()
+
+# %%

calculations/XZ/2body_HO.jl

@@ -0,0 +1,39 @@
+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")

calculations/XZ/2body_p_space.jl

@@ -0,0 +1,50 @@
+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")

calculations/XZ/3body_HO.jl

@@ -0,0 +1,36 @@
+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")

calculations/XZ/3body_p_space.jl

@@ -0,0 +1,45 @@
+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.

calculations/XZ/p_space_vs_HO.jl

@@ -0,0 +1,71 @@
+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")

calculations/XZ_technique.jl

@@ -1,30 +0,0 @@
-include("../EC.jl")
-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)
-
-near_E = 0.2 + 0.2im
-
-EC = affine_EC(T, V)
-train!(EC, train_cs; ref_eval=near_E, CAEC=false)
-extrapolate!(EC, target_cs)
-
-plot(EC, "temp/XZ.pdf"; xlims=(-0.2,0.3), ylims=(-0.3,0.3))

common.jl

@@ -2,8 +2,8 @@ using LinearAlgebra, DelimitedFiles, SparseArrays
 
 @enum coordinate_system jacobi src
 
-"Square root function with the branch cut along the postive real axis"
+"Square root function with the branch cut along the postive imaginary axis"
-new_sqrt(x::Number)::ComplexF64 = im * sqrt(complex(-x))
+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