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zQ;S3qv;!aR)ubs8W}qBKcgYR2Obi&aoTTC_2Zfen>6{o?-t`SjhaW|#jR$UM=8I#E zImMejKv)hu3oxa%AeMNZdY4bFEM7GBBo<-Ddm0JHwA(ts*J)jO)I+{|w>I$Aa!i!U zW(Ffeccg`e*zJ48vD-mqaos>~9$Xv#7iNO_|KmJd1E!5P3<=`bI><|x8^{CX`FUk%J2|-ld4A&ZmFCq# z0`mO4jrP0ew=^?5`SB(^FeMO07R(*0VP$4!HIGTWkO1UX2ePfPBf3>Fh>1FZ7F39C z;v1!dfbf$@;36`Z7y6o-F$$yhT|oFJ14;TQBE?Lq04z^nY%E%77?CWP_rVZa1k4F$ j1^{?-lUDxID6VeiE^d!qkmKbM Date: Mon, 13 Jul 2026 14:56:31 +0200 Subject: [PATCH 2/4] Update BuiltinFunctional.jl --- src/physics/exchange correlation/BuiltinFunctional.jl | 10 ++++++++-- 1 file changed, 8 insertions(+), 2 deletions(-) diff --git a/src/physics/exchange correlation/BuiltinFunctional.jl b/src/physics/exchange correlation/BuiltinFunctional.jl index 0a37180..1066898 100644 --- a/src/physics/exchange correlation/BuiltinFunctional.jl +++ b/src/physics/exchange correlation/BuiltinFunctional.jl @@ -6,6 +6,12 @@ implemented to be compared with Libxc.jl and to use higher precision than Float6 """ abstract type BuiltinFunctional end +# Unlike Libxc.OptArray (Union{Ptr{Nothing}, Array{Float64}} -- Libxc calls +# into a Float64-only C library), BuiltinFunctional is pure Julia and must +# accept any real element type to honor the "higher precision than Float64" +# claim above. +const OptRealArray = Union{Ptr{Nothing}, AbstractArray{<:Real}} + function BuiltinFunctional(identifier::Symbol;nspin::Int = 1) nspin in (1, 2) || error("n_spin needs to be 1 or 2") if identifier == :lda_x @@ -60,8 +66,8 @@ end function evaluate_functional!( func::BuiltinFunctional; rho::AbstractArray{<:Real}, - zk::OptArray = C_NULL, - vrho::OptArray = C_NULL) + zk::OptRealArray = C_NULL, + vrho::OptRealArray = C_NULL) if func isa NoFunctional if !(zk == C_NULL) fill!(zk, 0) From 4ae2c86c7dfbc771437b40adc89adaefa83af41f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Th=C3=A9o=20Duez?= <42682941+Theozeud@users.noreply.github.com> Date: Mon, 13 Jul 2026 15:36:36 +0200 Subject: [PATCH 3/4] QuadQK dispatch for handle numerical integration with high precision --- Project.toml | 2 ++ examples/Manifest.toml | 44 +++++++++++++++++++++++++++++++--- src/AtomicKohnSham.jl | 1 + src/fem/integration methods.jl | 17 ++++++++++--- 4 files changed, 58 insertions(+), 6 deletions(-) diff --git a/Project.toml b/Project.toml index e39007c..07fd2cf 100644 --- a/Project.toml +++ b/Project.toml @@ -16,6 +16,7 @@ Libxc = "66e17ffc-8502-11e9-23b5-c9248d0eb96d" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" Optim = "429524aa-4258-5aef-a3af-852621145aeb" Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7" +QuadGK = "1fd47b50-473d-5c70-9696-f719f8f3bcdc" SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" TensorOperations = "6aa20fa7-93e2-5fca-9bc0-fbd0db3c71a2" UnPack = "3a884ed6-31ef-47d7-9d2a-63182c4928ed" @@ -38,6 +39,7 @@ KrylovKit = "0.9.5" Libxc = "0.3.19" Optim = "1.11.0" Printf = "1.11.0" +QuadGK = "2.11.3" julia = "1.9" [extras] diff --git a/examples/Manifest.toml b/examples/Manifest.toml index 9f769c9..caba1b9 100644 --- a/examples/Manifest.toml +++ b/examples/Manifest.toml @@ -145,7 +145,7 @@ uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33" version = "1.11.0" [[deps.AtomicKohnSham]] -deps = ["Arpack", "FastGaussQuadrature", "GenericLinearAlgebra", "HypergeometricFunctions", "Integrals", "JuliaFormatter", "KrylovKit", "Libxc", "LinearAlgebra", "Optim", "Printf", "SparseArrays", "TensorOperations", "UnPack"] +deps = ["Arpack", "FastGaussQuadrature", "GenericLinearAlgebra", "HypergeometricFunctions", "Integrals", "JLD2", "JuliaFormatter", "KrylovKit", "Libxc", "LinearAlgebra", "Optim", "Printf", "QuadGK", "SparseArrays", "TensorOperations", "UnPack"] path = ".." uuid = "2d6a71d3-f4fe-4c59-9782-ebc44d5ef3e9" version = "1.0.0-DEV" @@ -248,6 +248,23 @@ weakdeps = ["SparseArrays"] [deps.ChainRulesCore.extensions] ChainRulesCoreSparseArraysExt = "SparseArrays" +[[deps.ChunkCodecCore]] +git-tree-sha1 = "1a3ad7e16a321667698a19e77362b35a1e94c544" +uuid = "0b6fb165-00bc-4d37-ab8b-79f91016dbe1" +version = "1.0.1" + +[[deps.ChunkCodecLibZlib]] +deps = ["ChunkCodecCore", "Zlib_jll"] +git-tree-sha1 = "d4101e848e8d3f585d61d244c2fe0c80a70e6b3b" +uuid = "4c0bbee4-addc-4d73-81a0-b6caacae83c8" +version = "1.1.0" + +[[deps.ChunkCodecLibZstd]] +deps = ["ChunkCodecCore", "Zstd_jll"] +git-tree-sha1 = "34d9873079e4cb3d0c62926a225136824677073f" +uuid = "55437552-ac27-4d47-9aa3-63184e8fd398" +version = "1.0.0" + [[deps.ColorBrewer]] deps = ["Colors", "JSON"] git-tree-sha1 = "07da79661b919001e6863b81fc572497daa58349" @@ -803,6 +820,11 @@ git-tree-sha1 = "f923f9a774fcf3f5cb761bfa43aeadd689714813" uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566" version = "8.5.1+0" +[[deps.HashArrayMappedTries]] +git-tree-sha1 = "2eaa69a7cab70a52b9687c8bf950a5a93ec895ae" +uuid = "076d061b-32b6-4027-95e0-9a2c6f6d7e74" +version = "0.2.0" + [[deps.HypergeometricFunctions]] deps = ["LinearAlgebra", "OpenLibm_jll", "SpecialFunctions"] git-tree-sha1 = "68c173f4f449de5b438ee67ed0c9c748dc31a2ec" @@ -972,6 +994,16 @@ git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856" uuid = "82899510-4779-5014-852e-03e436cf321d" version = "1.0.0" +[[deps.JLD2]] +deps = ["ChunkCodecLibZlib", "ChunkCodecLibZstd", "FileIO", "MacroTools", "Mmap", "OrderedCollections", "PrecompileTools", "ScopedValues"] +git-tree-sha1 = "9ebadf3f8f0de07031359917549bbdadc23f5dc3" +uuid = "033835bb-8acc-5ee8-8aae-3f567f8a3819" +version = "0.6.5" +weakdeps = ["UnPack"] + + [deps.JLD2.extensions] + UnPackExt = "UnPack" + [[deps.JLLWrappers]] deps = ["Artifacts", "Preferences"] git-tree-sha1 = "0533e564aae234aff59ab625543145446d8b6ec2" @@ -1571,9 +1603,9 @@ version = "1.0.2" [[deps.QuadGK]] deps = ["DataStructures", "LinearAlgebra"] -git-tree-sha1 = "9da16da70037ba9d701192e27befedefb91ec284" +git-tree-sha1 = "5e8e8b0ab68215d7a2b14b9921a946fee794749e" uuid = "1fd47b50-473d-5c70-9696-f719f8f3bcdc" -version = "2.11.2" +version = "2.11.3" [deps.QuadGK.extensions] QuadGKEnzymeExt = "Enzyme" @@ -1785,6 +1817,12 @@ git-tree-sha1 = "607f6867d0b0553e98fc7f725c9f9f13b4d01a32" uuid = "53ae85a6-f571-4167-b2af-e1d143709226" version = "1.10.0" +[[deps.ScopedValues]] +deps = ["HashArrayMappedTries", "Logging"] +git-tree-sha1 = "67a144433c4ce877ee6d1ada69a124d6b1ecf7be" +uuid = "7e506255-f358-4e82-b7e4-beb19740aa63" +version = "1.6.2" + [[deps.Scratch]] deps = ["Dates"] git-tree-sha1 = "9b81b8393e50b7d4e6d0a9f14e192294d3b7c109" diff --git a/src/AtomicKohnSham.jl b/src/AtomicKohnSham.jl index 803eee1..da4a569 100644 --- a/src/AtomicKohnSham.jl +++ b/src/AtomicKohnSham.jl @@ -4,6 +4,7 @@ module AtomicKohnSham using SparseArrays using TensorOperations using FastGaussQuadrature + using QuadGK: gauss as quadgk_gauss using KrylovKit using Arpack using Optim diff --git a/src/fem/integration methods.jl b/src/fem/integration methods.jl index 7d50e1a..9389c70 100644 --- a/src/fem/integration methods.jl +++ b/src/fem/integration methods.jl @@ -16,6 +16,16 @@ Precomputes and caches the quadrature nodes/weights (rescaled to each reference cell and to the full radial domain `[0, Rmax]`), together with the FEM generator polynomials evaluated at the nodes, so that repeated assemblies during the SCF loop avoid recomputing them. + +The nodes/weights are generated at `eltype(basis)` precision: for `Float64` +(the common case) via `FastGaussQuadrature.gausslegendre`, an O(`npoints`) +algorithm that is Float64-only; for any other type (e.g. `Double64`, +`BigFloat`) via `QuadGK.gauss`, a generic-precision O(`npoints`²) +Golub–Welsch implementation. The latter is markedly slower at equal +`npoints` (benchmarked ~1s for `Double64` at `npoints=2000`), but this +constructor only runs once per discretization, not per SCF iteration, so +that one-time cost is worth paying to get genuinely `T`-accurate nodes +rather than nodes that only ever had Float64 accuracy to begin with. """ struct GaussLegendre{T <: Real} <: FEMIntegrationMethod npoints::Int @@ -34,8 +44,9 @@ struct GaussLegendre{T <: Real} <: FEMIntegrationMethod fx2::Matrix{T} function GaussLegendre(basis::FEMBasis, npoints::Int = 1000) @unpack binf, bsup = basis.generators - # GENERATION OF GAUSS POINTS AND WEIGHTS - x, w = gausslegendre(npoints) + T = eltype(basis) + # GENERATION OF GAUSS POINTS AND WEIGHTS ON [-1,1] + x, w = T === Float64 ? gausslegendre(npoints) : quadgk_gauss(T, npoints) # RESCALING ON [0,Rmax] Rmax = last(basis.mesh) y = Rmax/2 .* x .+ Rmax/2 @@ -53,6 +64,6 @@ struct GaussLegendre{T <: Real} <: FEMIntegrationMethod Qgenx = evaluate(basis.cache.prodMG, x) #a = Int(sqrt(size(Qgenx, 1))) #Qgenxreshape = reshape(Qgenx, a, a, size(Qgenx, 2)) - new{eltype(x)}(npoints, x, w, Pgenx, Qgenx, y, wy, shiftx, fx, fy, fx2) + new{T}(npoints, x, w, Pgenx, Qgenx, y, wy, shiftx, fx, fy, fx2) end end From c3997e1ef5b4e744800d3e27f282e0bc0dd5a4ca Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Th=C3=A9o=20Duez?= <42682941+Theozeud@users.noreply.github.com> Date: Mon, 13 Jul 2026 16:35:04 +0200 Subject: [PATCH 4/4] example of densities --- .../atomic density comparison/densities.pdf | Bin 0 -> 270074 bytes examples/atomic density comparison/run.jl | 83 ++++++++ examples/density computations/densities.pdf | Bin 284375 -> 0 bytes .../density computations.jl | 61 ------ examples/maximum ionization/graphics.jl | 0 examples/maximum ionization/run.jl | 197 ------------------ 6 files changed, 83 insertions(+), 258 deletions(-) create mode 100644 examples/atomic density comparison/densities.pdf create mode 100644 examples/atomic density comparison/run.jl delete mode 100644 examples/density computations/densities.pdf delete mode 100644 examples/density computations/density computations.jl delete mode 100644 examples/maximum ionization/graphics.jl delete mode 100644 examples/maximum ionization/run.jl diff --git a/examples/atomic density comparison/densities.pdf 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b/examples/atomic density comparison/run.jl @@ -0,0 +1,83 @@ +cd(@__DIR__) +using Pkg +Pkg.activate(joinpath(@__DIR__, "..")) +using AtomicKohnSham +using CairoMakie +using Libxc + +# Ground-state radial densities for a handful of atoms, overlaid on one +# plot. No log.txt/results.txt here -- just solve and plot. + +# ===================== STEP 1 : PARAMETERS =====================# +Zs = [3, 16, 17, 18, 20, 26] # Li, S, Cl, Ar, Ca, Fe + +# DISCRETIZATION : P1IntLegendreBasis + expmesh (same for every atom) +Rmax = 1000 +Nmesh = 30 +ordermax = 10 + +# ALGORITHM : ODA + Optimized Aufbau +# scftol=1e-10 with the default adaptive line-search mixing (tinit=0.4, +# frozen_t=false) is enough on its own to bring the density tail down to +# its Float64-precision floor (~1e-31, i.e. eps(Float64)^2 -- checked +# directly: eval_density(argon, r=50) with these exact settings reaches +# 4.4e-31 in just 26 iterations). A *looser* scftol leaks numerical noise +# from the density matrix straight into the quadratic form eval_density +# evaluates: at scftol=1e-8, rho(50) floors around 6e-19 and then +# *increases* with r past that, which isn't physics. +# +# Iron alone needs different handling: its 3d/4s near-degeneracy makes this +# adaptive mixing oscillate indefinitely (checked: stopping criterion +# bounces between 1e-9 and 1e-7 for hundreds of iterations, regardless of +# scftol). frozen_t=true with a fixed, fairly strong tinit tames that. Only +# apply that fix to iron, though -- tried it on every atom first, and a +# frozen mixing throttles each iteration's step enough that the *easy* +# atoms can satisfy the stopping criterion (successive-iterate difference +# below scftol) well before their density is actually converged, a false +# positive that looked identical to real convergence until checked against +# the density values directly. +default_alg(aufbau) = ODA(tinit = 0.4, aufbau = aufbau, scftol = 1e-10) +iron_alg(aufbau) = ODA(tinit = 0.15, frozen_t = true, aufbau = aufbau, scftol = 1e-12) + +default_maxiter = 100 +# Iron plateaus around stopping~2e-9 rather than cleanly reaching scftol, +# so it reports MAXITERS below -- reported honestly rather than loosened +# away, since even without satisfying the criterion exactly its density +# still reaches ~1e-30, far better than a falsely-"successful" run would. +iron_maxiter = 800 + +# PLOT +X = AtomicKohnSham.exprange(1e-3, 99.9, 10000; s = 1.5) + +# ===================== STEP 2 : BUILD & SOLVE =====================# +""" +Angular momentum cutoff and orbitals-per-channel, scaled with Z so heavier +atoms (which need d orbitals, more radial nodes) get a big enough basis +without over-paying for light ones. +""" +basis_size(Z) = (lh = min(ceil(Int, Z / 20), 3), nh = clamp(Z, 2, 10)) + +sols = KSESolution[] +for Z in Zs + lh, nh = basis_size(Z) + + ex = Functional(:lda_x; n_spin = 1) + ec = NoFunctional(1) + model = KSEModel(; Z = Z, N = Z, ex = ex, ec = ec) + + mesh = expmesh(0, Rmax, Nmesh; s = 1.2) + basis = P1IntLegendreBasis(mesh; ordermax = ordermax) + dis = KSEDiscretization(basis, model; lh = lh, nh = nh, + fem_integration_method = GaussLegendre(basis, 1000)) + + aufbau = OptimizedAufbau(tol = 1e-2) + alg = Z == 26 ? iron_alg(aufbau) : default_alg(aufbau) + maxiter = Z == 26 ? iron_maxiter : default_maxiter + + sol = groundstate(model, dis, alg; maxiter = maxiter) + println(sol.name, ": ", sol.success, " in ", sol.niter, " iterations") + push!(sols, sol) +end + +# ===================== STEP 3 : PLOT =====================# +save("densities.pdf", plot_density(sols, X)) diff --git a/examples/density computations/densities.pdf b/examples/density computations/densities.pdf deleted file mode 100644 index ceaa647e10d0d1c6c844dc4a52cddfb2f72de18e..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 284375 zcmV)tK$pKIP((&8F)lX>CAICY`wBE5Fd%PYY6?6&ATLa1ZfA68AT=N`AW{k-ARsSB zX>4?5av(28Y+-a|L}g=dWMv9IJ_>Vma%Ev{3V581z00m_&61_npHH!yMI%>*-`yod z0|_A^(Ev^l(LfYgsC2SXNrTrXY>Z*UW5ut$WGYYY^_>|$efrhh%-pQ}dA>i=Rg1P|9t)V&;RcePyExL-P_L^?|=S1|2g0P_xCs8|NnpV zTq%`L;U7`x-&Od1<{zIj`p@`N>Yp?A`yXq+{`~X*{pK&!=YRbl-|sGXcf9ETd*lD< z{eS=E`QQJKKd+zHpa1lfpLYrCRsQ_XfBx&Af*U({r%7X z_UC_j{_^~6{ip1%=ku?B`T6o%ub=iB`GWlOU-<>TcAoiDCYq?U{Oe!+#dwXMIcokS z|NK{f)5`cMedKTQ&wuqdrS_lMR{kdc)maC`={qW{^LKq{vlrXw|{*8!$1EwfBP>_TR-}7{EI&>d%fS+`>cO7W*IM3neOEC4XWxIWKmYLip}v0F 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DoubleFloats -using AtomicKohnSham -using Libxc - -# LOG CONFIG -logconfig = LogConfig(; orbitals_energy = false, - orbitals = false, - density = false, - occupation_number = false - ) - -function density(Z::AbstractVector) - - Sols = [] - for z ∈ Z - - # CREATION OF THE PROBLEM - lh = Int(min(ceil(z/20),3)) - nh = min(max(z,2),10) - problem = AtomProblem(; - T =Float64, - z = z, - N = z, - hartree = 1, - ex = Functional(:lda_x, n_spin = 1),#NoFunctional(1), #Functional(:lda_x, n_spin = 1), - ec = NoFunctional(1),#Functional(:lda_c_pw, n_spin = 2), - lh = lh, - nh = nh, - Nmesh = 30, - Rmax = 1000, - typemesh = expmesh, - optsmesh = (s = 1.2,), - typebasis = P1IntLegendreBasis, - optsbasis = (ordermax = 10,), - integration_method = GaussLegendre, - optsintegration = (npoints = 1000,), - alg = ODA(0.4), - scftol = 1e-10, - maxiter = 100, - degen_tol = 1e-2, - logconfig = logconfig, - verbose = 0) - - # RESOLUTION - @time sol = groundstate(problem); - push!(Sols, sol) - - end - - return Sols - - -end - -Sols = density([3, 16, 17, 18, 20, 26]) - -X = AtomicKohnSham.exprange(0.001,99.9, 10000; s = 1.5) -fig = plot_density(Sols, X) -save("./examples/density computations/densities.pdf",fig) diff --git a/examples/maximum ionization/graphics.jl b/examples/maximum ionization/graphics.jl deleted file mode 100644 index e69de29..0000000 diff --git a/examples/maximum ionization/run.jl b/examples/maximum ionization/run.jl deleted file mode 100644 index 9a6c8b5..0000000 --- a/examples/maximum ionization/run.jl +++ /dev/null @@ -1,197 +0,0 @@ -cd("./examples") -using Pkg -Pkg.activate(".") -using AtomicKohnSham -using Libxc - -# ===================== STEP 0 : LOG =====================# -VERBOSE = 3 -WRITE_LOG = true -LOGFILE = joinpath(@__DIR__, "scf.log") - -# ===================== STEP 1 : PARAMETERS =====================# -# MODEL -Z = 11 -N = 11 -ex = Functional(:lda_x; n_spin=2) -ec = Functional(:lda_c_pw, n_spin=2) - -# DISCRETIZATION : P1IntLegendreBasis + expmesh -Rmax = 500 -Nmesh = 60 -ordermax = 10 -lh = 2 - -# ALGORITHM : ODA + Optimized Aufbau -maxiter = 100 -degen_tol = 1e-1 -scftol = 1e-9 - -# PLOT -Rmax_plot = 100 -N_plot = 10000 -lplot = lh - -# ===================== STEP 2 : SOLVE =====================# -function run_solve(Z::Real, N::Real, ex::TEX, ec::TEC, - Rmax::Real, Nmesh::Int, ordermax::Int, lh::Int, - maxiter::Int, degen_tol::Real, scftol::Real) where {TEX, TEC} - # Creation of the model - model = KSEModel(; Z = Z, N = N, ex = ex, ec = ec) - - # Creation of the mesh - mesh = expmesh(0, Rmax, Nmesh; s = 1.2) - - # Creation of the Basis - basis = P1IntLegendreBasis(mesh; ordermax = ordermax) - - # Creation of the discretization - dis = KSEDiscretization(basis, model; lh = lh, nh=10, fem_integration_method=GaussLegendre(basis, 2000)) - - # Creation of the algorithm - aufbau = OptimizedAufbau(max_degen = 2, tol = degen_tol) - alg = ODA(tinit = 0.6, aufbau = aufbau, scftol = scftol) - - # Resolution of the problem - sol = if WRITE_LOG - open(LOGFILE, "w") do io - redirect_stdout(io) do - groundstate(model, dis, alg; maxiter = maxiter, verbose = VERBOSE) - end - end - else - sol = groundstate(model, dis, alg; maxiter = maxiter, verbose = VERBOSE) - end - return sol -end - -sol = run_solve(Z, N,ex, ec, Rmax, Nmesh, ordermax, lh, maxiter, degen_tol, scftol) - -# ===================== STEP 3 : EVALUATION =====================# - -# Evaluation of occupied orbitals -X = LinRange(0.001,Rmax_plot, N_plot) - - - -#= -function compute_potentials(solver, lmax::Int, Rmax_plot::Real, N_plot::Int) - @unpack N,Z = solver.model - X = LinRange(0.001,Rmax_plot, N_plot) - # Hartree - @unpack cache, basis, Rmax = solver.discretization - Vhart = evaluate(basis, cache.tmp_C, X)./ X .+ N/Rmax - # Kinetic Potential - Vl = zeros(length(X),lmax+1) - for l ∈ 0:lmax - @views Vl_l = Vl[:,l+1] - @. Vl_l = l*(l+1)/(2*X^2) - end - # Nucleous-Electrons Potential - Vnuc = @. - z/X - # Total Potential - V = zeros(length(X),lmax+1) - for l ∈ 0:lmax - @views V_l = V[:,l+1] - @views Vl_l = Vl[:,l+1] - @. V_l = Vhart + Vl_l + Vnuc - end - Vhart, Vnuc, Vl, V -end - -Vhart, Vnuc, Vl, V = compute_potentials(solver, lmax, Rmax_plot, N_plot) - -function compute_orbitals(sol, Rmax_plot::Real, N_plot::Int) - X = LinRange(0,Rmax_plot, N_plot) - u = zeros(length(X), length(sol.occupation_number)) - for (i,orb) ∈ enumerate(sol.occupation_number) - idx = orb[1] - u[:,i] = eigenvector(sol, idx, X) - M = max(u[:,i]...) - m = min(u[:,i]...) - if abs(M) > abs(m) - u[:,i] .*= sign(M) - else - u[:,i] .*= sign(m) - end - end - u -end - -u = compute_orbitals(sol, Rmax_plot, N_plot) -=# -# ===================== STEP 4 : MAKE GRAPHICS =====================# - - - -#= -function make_figure(u::AbstractMatrix{<:Real}, V::AbstractMatrix{<:Real}, lplot::Int, - Rmax_plot::Real, N_plot::Int) - X = LinRange(0,Rmax_plot, N_plot) - fig = Figure(size = (1000, 800), fontsize = 30) - - Energies = sol.datas.orbitals_energy[:,lplot+1] - min_E = min(Energies...) - - ax = Axis(fig[1, 1], - xlabel = L"\text{r}", - #yscale = log10, - #xscale = log10, - xticklabelsize = 40, - yticklabelsize = 40, - xlabelsize = 50, - ylabelsize = 50, - - ) - ylims!(ax, min_E*1.2, 2) - plots = [] - labels = [] - - # Plot Potential - V_l = V[:,lplot+1] - li = lines!(ax, X, V_l; linewidth = 4) - push!(plots, li) - push!(labels, "V") - - # Plots Orbitals - Colors = [:green, :orange, :purple, :yellow, :cyan] - jc = 0 - for (i,orb) ∈ enumerate(sol.occupation_number) - idx = orb[1] - l = findfirst(x->x==idx[2],L_QUANTUM_LABELS) - 1 - if l == lplot - jc += 1 - E = orb[2] - hlines!(ax, E, linewidth=4, linestyle=:dash, label="E", color=Colors[jc]) - ui = u[:,i] .+ E - li = lines!(ax, X, ui; linewidth = 4, color=Colors[jc]) - push!(plots, li) - push!(labels, idx) - end - end - - Legend( - fig[1, 1], - plots, - labels, - halign = :right, - valign = :top, - tellheight = false, - tellwidth = false, - margin = (20, 20, 20, 20), - orientation = :vertical, - labelsize = 50, - patchsize = (20, 20) - ) - - return fig -end -=# -X = LinRange(0.001,Rmax_plot, N_plot) -#= -CairoMakie.activate!() -for l ∈ 0:lmax - fig = make_figure(u, V, l, Rmax_plot, N_plot) - save("./dev/ionization conjecture/fig_l=$l.pdf", fig) -end -=#