Notebooks -> Scripts
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EC_test.ipynb
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EC_test.ipynb
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@ -1,100 +0,0 @@
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"using Plots\n",
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"include(\"p_space.jl\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"vertices = [0, 0.4 - 0.15im, 0.8, 6]\n",
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"subdivisions = [128, 128, 128]\n",
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"p, w = get_mesh(vertices, subdivisions)\n",
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"mesh_E = p.*p ./ (2*0.5)\n",
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"\n",
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"# ResonanceEC: Eq. (20)\n",
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"V_system(c) = (p, q) -> c*(-5*g0(sqrt(3), p, q) + 2*g0(sqrt(10), p, q))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"training_points = range(0.75, 0.45, 5)\n",
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"training_E = Vector{ComplexF64}(undef, length(training_points))\n",
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"EC_basis = Matrix{ComplexF64}(undef, length(p), length(training_points))\n",
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"\n",
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"for (j, c) in enumerate(training_points)\n",
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" evals, evecs = eigen(get_H_matrix(V_system(c), p, w))\n",
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" i = identify_pole_i(p, evals)\n",
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" training_E[j] = evals[i]\n",
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" EC_basis[:, j] = evecs[:, i]\n",
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"end\n",
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"\n",
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"scatter(real.(training_E), imag.(training_E), label=\"training\")\n",
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"plot!(real.(mesh_E), imag.(mesh_E), label=\"contour\")\n",
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"xlims!(0,1)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"extrapolate_points = range(0.40, 0.25, 5)\n",
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"ref_E = 0.2 - 0.1im\n",
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"\n",
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"exact_E = Vector{ComplexF64}(undef, length(extrapolate_points))\n",
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"extrapolate_E = Vector{ComplexF64}(undef, length(extrapolate_points))\n",
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"\n",
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"EC_basis_w = EC_basis .* w\n",
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"N_EC = transpose(EC_basis_w) * EC_basis\n",
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"\n",
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"for (j, c) in enumerate(extrapolate_points)\n",
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" exact_E[j] = quick_pole_E(V_system(c))\n",
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"\n",
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" EC_basis_w = EC_basis .* w\n",
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" H = get_H_matrix(V_system(c), p, w)\n",
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" H_EC = transpose(EC_basis_w) * H * EC_basis\n",
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" evals = eigvals(H_EC, N_EC)\n",
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" i = argmin(abs.(evals .- ref_E))\n",
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" ref_E = evals[i]\n",
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" extrapolate_E[j] = evals[i]\n",
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"end\n",
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"\n",
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"scatter(real.(training_E), imag.(training_E), label=\"training\")\n",
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"scatter!(real.(exact_E), imag.(exact_E), label=\"exact\")\n",
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"scatter!(real.(extrapolate_E), imag.(extrapolate_E), label=\"extrapolated\")\n",
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"plot!(real.(mesh_E), imag.(mesh_E), label=\"contour\")\n",
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"xlims!(0,1)"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Julia 1.10.2",
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"language": "julia",
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"name": "julia-1.10"
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},
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"language_info": {
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"file_extension": ".jl",
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"mimetype": "application/julia",
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"name": "julia",
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"version": "1.10.2"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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using Plots
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include("../p_space.jl")
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# contour
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vertices = [0, 0.4 - 0.15im, 0.8, 6]
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subdivisions = [128, 128, 128]
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p, w = get_mesh(vertices, subdivisions)
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mesh_E = p.*p ./ (2*0.5)
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# ResonanceEC: Eq. (20)
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V_system(c) = (p, q) -> c*(-5*g0(sqrt(3), p, q) + 2*g0(sqrt(10), p, q))
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training_points = range(0.75, 0.45, 5)
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training_E = Vector{ComplexF64}(undef, length(training_points))
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EC_basis = Matrix{ComplexF64}(undef, length(p), length(training_points))
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for (j, c) in enumerate(training_points)
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evals, evecs = eigen(get_H_matrix(V_system(c), p, w))
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i = identify_pole_i(p, evals)
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training_E[j] = evals[i]
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EC_basis[:, j] = evecs[:, i]
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end
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extrapolate_points = range(0.40, 0.25, 5)
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ref_E = 0.2 - 0.1im
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exact_E = Vector{ComplexF64}(undef, length(extrapolate_points))
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extrapolate_E = Vector{ComplexF64}(undef, length(extrapolate_points))
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EC_basis_w = EC_basis .* w
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N_EC = transpose(EC_basis_w) * EC_basis
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for (j, c) in enumerate(extrapolate_points)
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exact_E[j] = quick_pole_E(V_system(c))
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H = get_H_matrix(V_system(c), p, w)
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H_EC = transpose(EC_basis_w) * H * EC_basis
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evals = eigvals(H_EC, N_EC)
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i = argmin(abs.(evals .- ref_E))
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global ref_E = evals[i]
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extrapolate_E[j] = evals[i]
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end
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scatter(real.(training_E), imag.(training_E), label="training")
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scatter!(real.(exact_E), imag.(exact_E), label="exact")
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scatter!(real.(extrapolate_E), imag.(extrapolate_E), label="extrapolated")
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plot!(real.(mesh_E), imag.(mesh_E), label="contour")
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xlims!(0,1)
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@ -1,62 +0,0 @@
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"using Plots\n",
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"include(\"helper.jl\")\n",
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"include(\"p_space.jl\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"vertices = [0, 1 - 0.5im, 2, 6]\n",
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"subdivisions = [64, 64, 64]\n",
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"p, w = get_mesh(vertices, subdivisions)\n",
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"\n",
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"scatter(real.(p), imag.(p))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# ComplexScaling-FV: Eq. (54)\n",
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"V_pq(p, q) = -10 * g1(1, p, q)\n",
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"\n",
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"H = get_H_matrix(V_pq, p, w)\n",
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"evals = eigen(H).values\n",
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"\n",
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"E_target = 0.258 - 0.164im\n",
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"E = nearest(evals, E_target)\n",
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"\n",
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"print(\"E = $E\")\n",
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"scatter(real.(evals), imag.(evals), xlim = (0,1))"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Julia 1.9.0",
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"language": "julia",
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"name": "julia-1.9"
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},
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"language_info": {
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"file_extension": ".jl",
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"mimetype": "application/julia",
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"name": "julia",
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"version": "1.9.0"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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@ -1,70 +0,0 @@
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"using Plots\n",
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"include(\"helper.jl\")\n",
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"include(\"p_space.jl\")"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"vertices = [0, 0.5 - 0.3im, 1, 6]\n",
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"subdivisions = [64, 64, 64]\n",
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"p, w = get_mesh(vertices, subdivisions)\n",
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"\n",
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"# resonance example from my thesis\n",
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"V_basis(p, q) = 2*g0(4, p, q) - 3*g0(2, p, q)\n",
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"\n",
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"basis_eig = eigen(get_H_matrix(V_basis, p, w))\n",
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"basis = basis_eig.vectors .* w\n",
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"\n",
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"evals = basis_eig.values\n",
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"E_target = 0.7\n",
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"E = include(\"helper.jl\")\n",
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"\n",
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"print(\"E = $E\")\n",
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"scatter(real.(evals), imag.(evals), xlim = (0,2))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"# ResonanceEC: Eq. (20)\n",
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"V_system(c) = (p, q) -> c*(-5*g0(sqrt(3), p, q) + 2*g0(sqrt(10), p, q))\n",
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"\n",
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"H = get_H_matrix(V_system(0.45), p, w)\n",
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"H_berggren = transpose(basis) * H * basis\n",
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"\n",
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"evals = eigvals(H)\n",
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"scatter(real.(evals), imag.(evals), xlim = (0, 0.5))"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Julia 1.10.2",
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"language": "julia",
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"name": "julia-1.10"
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},
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"language_info": {
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"file_extension": ".jl",
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"mimetype": "application/julia",
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"name": "julia",
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"version": "1.10.2"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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using Plots
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include("../helper.jl")
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include("../p_space.jl")
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vertices = [0, 1 - 0.5im, 2, 6]
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subdivisions = [64, 64, 64]
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p, w = get_mesh(vertices, subdivisions)
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scatter(real.(p), imag.(p))
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# ComplexScaling-FV: Eq. (54)
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V_pq(p, q) = -10 * g1(1, p, q)
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H = get_H_matrix(V_pq, p, w)
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evals = eigen(H).values
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E_target = 0.258 - 0.164im
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E = nearest(evals, E_target)
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print("E = $E")
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scatter(real.(evals), imag.(evals), xlim = (0,1))
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using Plots
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include("../helper.jl")
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include("../p_space.jl")
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vertices = [0, 0.5 - 0.3im, 1, 6]
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subdivisions = [64, 64, 64]
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p, w = get_mesh(vertices, subdivisions)
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# resonance example from my thesis
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V_basis(p, q) = 2*g0(4, p, q) - 3*g0(2, p, q)
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basis_eig = eigen(get_H_matrix(V_basis, p, w))
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basis = basis_eig.vectors .* w
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basis_evals = basis_eig.values
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E_target = 0.7
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E = nearest(basis_evals, E_target)
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print("pole E = $E")
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# ResonanceEC: Eq. (20)
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V_system(c) = (p, q) -> c*(-5*g0(sqrt(3), p, q) + 2*g0(sqrt(10), p, q))
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H = get_H_matrix(V_system(0.45), p, w)
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H_berggren = transpose(basis) * H * basis
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evals = eigvals(H)
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scatter(real.(evals), imag.(evals), label="E")
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scatter!(real.(basis_evals), imag.(basis_evals), label="basis", markershape=:x)
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xlims!((0, 1))
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