text:
### A Pluto.jl notebook ###
# v0.19.4

using Markdown
using InteractiveUtils

# ╔═╡ 83d05132-b257-4c45-ad70-a24c92c8f8ee
begin
	using QuantumOptics
	using LinearAlgebra
	using SparseArrays
	using PlutoUI
	using Plots
	plotly()
end

# ╔═╡ cd1bc8b0-d5c0-11ec-2a3b-831b0b8d8b3a
md"""
## Šrēdingera vienādojuma risinājumi

Šodien mēs apskatīsimies Šrēdingera vienādojuma risinājumus daļiņai dažādos potenciālos. Strādāsim vienā dimensijā.

Parasti rīkosimies šādi: vispirms risināsim no laika neatkārīgo uzdevumu

``\hat{H}\psi(x)=E \psi(x)``,

kur

``\hat{H} = \frac{\hat{p}^2}{2m} + V(x)``.

``V(x)`` ir potenciālā enerģija, bet ``\hat{p}`` ir kustības daudzuma operators ``\hat{p}=-i\hbar \frac{\partial}{\partial x}``.

Pēc tam pievienosim atkarību no laika:

``\Psi(x,t)=\sum_{n} \psi_n(x)e^{i E_n t/\hbar} ``,

kur ``psi_n(x)`` ir īpašfunkcijas un ``E_n`` ir īpašenerģijas, vai

``\hat{H}\psi_n(x) = E_n \psi_n(x)``.

"""

# ╔═╡ be74a383-df10-463c-92a2-a093b8a2d784
md"""
### Daļiņa bedrē
Lecijas laika tika risināts Šrēdingera vienādojums daļiņai bedrē ar bezgalīgi augšām sieniņām. To var aprakstīt ar potenciālu ``V(x)=0``, kad ``0<=x<=L``, bet ``V(x)=\infty`` citur.

Savukārt ``\psi_n(x)=\sqrt(\frac{2}{L}) sin(n \pi x/L)`` bedrē, bet ``\psi(x)=0`` ārpus bedres.

Mēs izmantosim paketi [QuantumOptics.jl](https://qojulia.org/). Potenciālās funkcijas ar bezgalībām mēs nevaram izmantot, bet varam pētīt, kā risināt bedri ar galīgi augstām sieniņām. Tāds uzdevums nav tik risināms analitiski, tomēr varēsim risināt skaitliski bez lielām problēmām.
"""

# ╔═╡ 5afc4a98-b3cb-49c0-a5a3-acbcd6509ed2
begin
	xmin=-5    # minimalā x-ass vērtība (Nevar būt bezgalīgi garša ass)
	xmax=5     # maximālā x-ass vērtība
 	xstep=0.1  # soļu lielums starp x-vērtībām.
	xrange=xmin:xstep:xmax # iterators ar x-vērtībām.

	basis = PositionBasis(xmin, xmax, length(xrange)) # bāze

	x = position(basis)   # posicijas operators
	p = momentum(basis)   # kustības daudzuma operators

	V0 = 20. # Bedres dziļums
	d = 2.0    # Bedres platums

	# Tagad rakstam funkiju, kas definē poteniālu
	function V_box(x)
	    if x < -d/2 || x > d/2
	        return 0.
	    else
	        return -V0
	    end
	end

	V = potentialoperator(basis, V_box)   # no funkcijas veidojām operatoru

	H = p^2/2 + V   # Hamiltona operators

	Nsols=5   # risinājumu skaits, ko meklējām no Šrēdingera vienādojuma.
	# Ar vienu rindu risinām Šrēdingera vienāojumu:
	energies, states = eigenstates((H+dagger(H))/2, Nsols)
end

# ╔═╡ 9a8b8479-f5a2-46a5-94b7-e66d2d2a3a02
typeof(p)

# ╔═╡ a64c019b-4c80-4f48-8cfa-4646c26c27e6
md"""
Risinājumā ir gan enerģijas ```energies``` un īpašfunkcijas ```states```.
Energijas vērtības ir vektorā. Īpašfunkcijas ir ```Ket``` objektā. Piemēram, enerģija ```energies[1]``` ir saistīts ar īpašfunkciju ```states[1]```.
"""

# ╔═╡ c4b5d3df-2ea1-48c8-9598-48fc1caaba16
energies

# ╔═╡ cef656c7-2cda-41f8-bca1-c17138f35e73
states[1]   # states[1] ir īpašfunkcija, kas atbilst energies[1].

# ╔═╡ 277d6d2c-5ce2-479a-b9b1-006afbd7529b
md"""
Tagad zīmēsim viļņu funkcijas. Zīmējām tikai viļņa funkcijas reālo daļu.(Atcerēsimies, ka varētu būt arī imaginārā daļa - to varētu zīmēt aizvietojot ```real``` ar ```imag```) koda bloka 6. rindā.
"""

# ╔═╡ 8dde5436-b5cc-4ac3-b217-c374d888a345
begin
	xpoints = samplepoints(basis)
	plot(xpoints, V_box.(xpoints),label="V(x)")
	for i=1:length(states)
		label_string="ψ"*string(i)
    	plot!(xpoints, real.(states[i].data)*5 .+ energies[i],label=label_string) # viļņu funkcija ψ reizināta ar 5, lai būtu vieglāk redzama.
	end
	plot!(title="Finite Potential Well",xlabel="Position", ylabel="Energy")
end

# ╔═╡ a4bc121f-9002-46d5-a688-e2c865726af3
md"""
#### Uzdevums 1. Daļiņa bedrē ar galīgi augstām sienām.

a. Kad bedres dzilms ```V0=20``` un bedres platums ```d=2```.

i)  cik daudz saistīto viļņu funkcijas varam dabūt?

ii) Salīdziniet iegūtos saistītā stāvokļa enerģijas vērtībām ar attiecīgām enerģijas vērtībām bedrē ar bezgalīgi augstām sieniņām.

b. Raksturojiet viļņu funkcijas.

i) Raksturojiet funkcijas, kas apraksta viļņu funkciju bedrē, t.i.,  kad ``-d<x<d``

ii) Raksturojiet funkcijas, kas apraksta viļņu funkciju āprus bedres, t.i., kad ``x>d`` vai ``x<-d``.

iii) Kāda ir attiecība starp mezgļu punktu skaitu un viļņu funkcijas kvantu skaitli ``n``? (Mezglu punkts ir punkts, kur ``\psi_n(x)=0``.)

c. Paspēlējiet ar parametriem ```V0```, ```d``` un ```Nsols```.

i) Kā saistīto viļņu funkciju skaits ir atkarīgi no parametra ```V0```. (Varbūt noderēs zīmēt kādu grafiku. Pietiek ar kvalitatīvo aprakstu. )

ii) Kā saistīto viļņu funkciju skaits ir atkarīgi no parametra ```d```.

iii) Vai ir kāds platums vai dziļums, kuram neatbilst saistītā stāvokļa?
"""

# ╔═╡ 612f9b30-f156-40cd-8835-f5b0ce7865fa
md"""
### Varbūtība atrast daļiņu

Viļņu funkcija apraksta daļiņas dinamiku, bet to nevaram novērot tieši. Varam novērot daļiņas varbūtības sadaļijumu ``P(x)=|\psi(x)|^2=\psi^{\star}(x)\psi(x)``, kur ``\psi^{\star}(x)`` ir viļņu funkcijas kompleksais saistītais. (Piemēram, ja ``\psi(x)=e^{ix}``, tad ``\psi^{\star}(x)=e^{-ix}``.)

Tagad zīmēsim varbūtības sadalījumus.

"""

# ╔═╡ 8338eac7-9dab-4343-9b71-b4b71fb9848e
begin
	plot(xpoints, V_box.(xpoints),label="V(x)")
	for i=1:length(states)
		label_string2="|ψ"*string(i)*"|²"
    	plot!(xpoints, abs2.(states[i].data)*30 .+ energies[i],label=label_string2) # |ψ|² reizināts ar 30, lai būtu vieglāk redzams.
	end
	plot!(title="Finite Potential Well",xlabel="Position", ylabel="Energy")
end

# ╔═╡ 1e6a2be5-8f21-4d89-9050-c64bc7509be4
md"""
## Viļņu funkcijas evolūcija laikā
Tagad varam skatīties, kā viļņu funkcija attīstās laikā.
"""

# ╔═╡ 775f9389-8040-42c4-9b3f-cd55cd7ba013
begin
	gr()
	x0box = 0
	p0box = 1.5
	sigma0box = 0.25
	Ψ0box = gaussianstate(basis, x0box, p0box, sigma0box);
	boxAnimation=Animation()
	#Ψ0box=states[1]+states[2] # Sāksim ar stāvokli, kuru veido divi no īpašstāvokļiem.

	# Time evolution
	Trange = [0:0.05:50;]     # iterators ar laika vērtībām
	toutBox, ΨtBox = timeevolution.schroedinger(Trange, Ψ0box, H);

	# Animācijas veidošana
	for i=1:length(Trange)
	    Ψbox = ΨtBox[i]
	    n2 = abs2.(Ψbox.data)
		plot(xpoints, V_box.(xpoints),xlabel="x",ylabel="|Ψ(t)|^2",ylim=(-50,50))
	    plt=plot!(xpoints, 100*n2)# , "C0", alpha=0.9*(float(i)/length(T))^8+0.1)
		frame(boxAnimation,plt)
	end

	gif(boxAnimation)
end

# ╔═╡ 5165e0bd-8196-4a58-97b6-2bff9d920185
md"""
## Daļiņa harmoniskā oscilatora potenciālā

Tagad apskatīsimies daļiņas viļņu funkcijas harmoniskajā oscilātora potenciālā.

Hamiltona operators ir

``\hat{H}=\frac{\hat{p}^2}{2 m} + \frac{1}{2}k \hat{x}^2 = \frac{\hat{p}^2}{2 m} + \frac{1}{2}m \omega^2 \hat{x}^2,``

kur ``k`` ir atsperes konstante, ``m`` ir daļiņas masa, un ``\omega = \sqrt{\frac{k}{m}}``.

No lekcijām zinām, ka enerģijas ``E_n=(n+\frac{1}{2})\hbar \omega``.

Attiecīgās īpašfunkcijas ir

``\psi_n(x)=\frac{1}{\sqrt{2^n n!} \left(\frac{m \omega}{\pi \hbar} \right)} e^{\frac{m \omega x^2}{2 \hbar}}H_n \left(\sqrt{\frac{m \omega}{\hbar}} \right)``,

kur ``H_n`` ir [Hermīta polinomiāli](https://en.wikipedia.org/wiki/Hermite_polynomials).
"""

# ╔═╡ c710d71c-62f9-4a3e-abf0-c1338f3d0c5f
begin
	basis_position_HO = PositionBasis(-5, 5, 100)
	basis_momentum_HO = MomentumBasis(basis_position_HO)
	xHO = position(basis_position_HO)
	pHO = momentum(basis_position_HO)

	m=1.0 # daļiņas masa
	ω=0.5 # oscilātora potenciāla stiprums

	HHO = pHO^2/(2*m) + 0.5*m*ω^2*xHO^2
	energiesHO, statesHO = eigenstates((HHO+dagger(HHO))/2, 5);
end

# ╔═╡ 5ce6769e-2eea-49c7-99cf-01fff2a8a193
begin
	X = samplepoints(basis_position_HO)
	plot(X, 2*X.^2)
	for i=1:length(statesHO)
		labelHO="|ψ"*string(i)*"|²"
	    plot!(X, abs2.(statesHO[i].data).*200 .+ 20*energiesHO[i],label=labelHO)
	end
	plot!(title="Harmonic Oscillator",xlabel="Position", ylabel="Energy")
end

# ╔═╡ 21bc8a72-5790-4e81-b420-d6d47047a24a
md"""
### Uzdevums 2. Harmoniskais oscilātors.

a. Kāda ir attiecībā starp kvantu skaitli ``n`` un mezgļu punktu skaitu?

b. Kāpēc viļņu funkciju telpiskā perioda pie augstākām enerģijām ir mazākā? Ar kādu fizikālo lielumu tas ir saistīts?

c. Kāpēc viļņu funkciju telpiskā perioda pie oscilātora potenciāla malām ir lielākā? Kāpēc tur amplitūda ir lielākā? Kā šis novērojums saistās ar klasisko oscilātoru?

"""

# ╔═╡ 42b3c114-ece5-47bf-8ae5-498e3d517ec4
md"""
Arī harmonisko oscilātoru viļņu funkcijām varam pievienot laika atkarību. Vispirms definēsim Furjē transformāciju no pozīcijas bāzes uz kustības daudzuma bāzi.
"""

# ╔═╡ 20f36616-c2fd-4ba0-93a5-a8fdf95d0619
begin
	# Transforms a state multiplied from the right side from real space
	# to momentum space.
	T_px = transform(basis_momentum_HO, basis_position_HO)
end

# ╔═╡ 204c3f78-deca-4547-a2f5-ed8d3d69b7e3
md"""
Varam arī definēt transforāciju otrā virzienā.
md"""

# ╔═╡ 74bed55e-3150-4b75-a087-11ba127143fb
begin
	T_xp = dagger(T_px)   # Transformācija no p-bāzes uz x-bāzi.

	x_HO2 = position(basis_position_HO)   # x-bāzes definīcja
	p_HO2 = momentum(basis_momentum_HO)   # b-bāzes definīcija

	H_kin_HO2 = LazyProduct(T_xp, p_HO2^2/2m, T_px)  # Hamiltona operatora kinētiskā daļa
	V_HO2 = ω*x_HO2^2  # Hamiltona operatora potenciālā daļa
	H_HO2 = LazySum(H_kin_HO2, V_HO2)  # Hamiltona operators
end

# ╔═╡ fa269ca9-01fc-4a6d-bf35-4e1ba561a7ba
md"""
### Gausa viļņa pakete Harmoniskā oscilatora potenciālā

Tagad definēsim Gausa viļņu pakete Harmoniskā oscilatora potenciālā un novērosim laika evolūciju.

Interesanti ir tas, ka viļņu pakete patur savu formu laikā: nenotiek dispersija. Tādu stāvokli sauc par koherentu stāvokli.
"""

# ╔═╡ 1341e7a1-ee6e-4e60-b46b-8b392f1989b5
begin
	# Initial state
	gr()
	HOanimation=Animation()

	x0 = 1.5
	p0 = 0
	sigma0 = 0.6
	Ψ0 = gaussianstate(basis_position_HO, x0, p0, sigma0);

	# Time evolution
	T = [0:0.1:6;]
	tout, Ψt = timeevolution.schroedinger(T, Ψ0, H_HO2);

	# Plot dynamics of particle density
	x_points = samplepoints(basis_position_HO)

	n = abs.(Ψ0.data).^2
	##V = ω*x_points.^2
	VV=diag(V_HO2.data)    # get diagonal elements of sparse operator as matrix
	C = maximum(abs.(VV))/maximum(n)

	plt_bg=plot(x_points, (abs.(VV).-3)./C,xlabel="x",ylabel="|Ψ(t)|^2") #, "k--")

	for i=1:length(T)
	    Ψ = Ψt[i]
	    n = abs.(Ψ.data).^2
		plot(x_points, (abs.(VV).-3)./C,xlabel="x",ylabel="|Ψ(t)|^2",ylim=(-0.03,0.1),label="V(x)")
	    plt=plot!(x_points, n,label="|Ψ(x,t)|²")
		frame(HOanimation,plt)
	end

	gif(HOanimation,fps=10)
end

# ╔═╡ 8609b62a-66a7-4186-bd3e-0db3794fd8d5
md"""
#### Uzdevums 3. Elektrons bedre ar bezgalīgi augstām sieniņām
Elektrons atrodas bezgalīgi dziļa bedrē (``0<x<L``). Pieņemiet, ka elektrons atrodas pamatstāvoklī. Aprēķiniet varbūtību, ka elektrons atrodas starp ``x=0`` un ``x=L/4``.
"""

# ╔═╡ feb57b20-7c4e-4d60-9a63-35b76c341a01
md"""
#### Uzdevums 4. Spiediens bedrē.
Daļiņa atrodas viendimensiju potenciālā bedrē ar bezgalīgi augstām sienām. Bedres platums ``L``. Nosakiet daļiņas spiediena spēku uz bedres sieniņām, ja daļiņai ir minimālā enerģija. [Saspiežot kasti nepieciešams padarīt darbu, kas pāriet daļiņas iekšējā enerģijā.]
"""

# ╔═╡ 46310bf4-b49e-42de-a18a-d2e34093c6cb
md"""
#### Uzdevums 5. ``\delta-``funkcijas potenciāls.

Izskatiet potenciālu ``V(x) = −aV_0 \delta(x)``.

(Atcerēsimies, ka ``\delta(x-x_0)=\infty``, kad ``x=x_0``, bet 0 citur.

``\int_{-\infty}^{\infty} \delta(x-x_0) \mathrm{dx} = 1``.)

a. Pierādiet, ka potenciālam ir saistīts stāvoklis ar enerģiju ``E=ma^2 V_0^2/2\hbar^2``.

b. Atrodiet normēto viļņu funkciju.

Varbūt noder atcerēties:
1. ``\lim_{\epsilon \rightarrow 0}[\psi'(\epsilon)-\psi'(\epsilon)] = \lim_{\epsilon \rightarrow 0} \int_{-\epsilon}^{\epsilon} \psi''(x) \mathrm{dx}``.

2. ``\int_{-\infty}^{\infty} f(x)\delta(x-x_0) \mathrm{dx} = f(x_0)``.
"""

# ╔═╡ d0d9ee0b-b1db-4e47-8788-37bf879167b9
md"""
#### Uzdevums 6. Bedre, kas pekšņi palielināsies
Daļiņa atrodas bezgalīgi dziļas bedres pamatstāvoklī. Bedres platums ir ``L``.  Pēkšņi bedres platums palielinās divas reizes uz ``2L``, nemainot daļiņas viļņu funkciju. Pierādiet, ka varbūtība, ka daļiņa palīks jaunās bedres pamatstāvoklī ir ``(8/3\pi)^2``.

Varbūt noder atcerēties:

1. ``\psi(x)=\sum_{n=1}^{n=\infty} a_n \phi_n(x)``,

kur ``\phi_n(x)`` ir konkrētā Hamiltoniāna ``\hat{H}`` īpašfunkcijas.

2. ``\int_{-\infty}^{\infty} \phi_n(x) \phi_m(x) \mathrm{dx} = \delta_{mn}``

3. ``a_n = \int_{-\infty}^{\infty} \psi(x) \phi_n(x) \mathrm{dx} = \int_{-infty}^{\infty} \left(\sum_{m=1}^{m=\infty}\phi_m(x) \right)  \phi_n(x) \mathrm{dx} ``
"""

# ╔═╡ 00000000-0000-0000-0000-000000000001
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"""

# ╔═╡ Cell order:
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# ╟─00000000-0000-0000-0000-000000000002


text:
import Pkg
using Test
using Base: ImmutableDict
using BangBang
using BangBang: implements
using StaticArrays: SVector

"""
    ==ₜ(x, y)

Check that _type_ and value of `x` and `y` are equal.
"""
==ₜ(_, _) = false
==ₜ(x::T, y::T) where T = x == y

macro test_error(ex)
    quote
        let err = nothing
            try
                $(esc(ex))
            catch err
            end
            @test err isa Exception
            err
        end
    end
end

macro test_inferred(ex)
    esc(:($Test.@test (($Test.@inferred $ex); true)))
end

"""
    @test_returns_first f(x, ...) ==′ rhs

It is transformed
    @test f((tmp = x; tmp), ...) === tmp ==′ rhs
"""
macro test_returns_first(ex)
    Meta.isexpr(ex, :call, 3) || error("need `lhs cmp rhs`; got:\n$ex")
    c, l, r = ex.args
    (Meta.isexpr(l, :call) && length(l.args) > 1)|| error("lhs should be a call; got:\n$l")
    a = l.args[2]
    @gensym x
    l.args[2] = quote
        $x = $a
        $x
    end
    cmp = Expr(:comparison, l, :(===), x, c, r)
    quote
        $Test.@test $cmp
    end |> esc
end

versionof(pkg::Module) = versionof(Base.PkgId(pkg))
if isdefined(Pkg, :dependencies)
    versionof(pkg::Base.PkgId) = Pkg.dependencies()[pkg.uuid].version
else
    versionof(pkg::Base.PkgId) = Pkg.installed()[pkg.name]
end

ext: jl


text:
function exportdensematrix(A::GBMatrix{T};
    desc::Descriptor = Descriptors.NULL
) where {T}
    nrows = Ref{libgb.GrB_Index}(size(A,1))
    ncols = Ref{libgb.GrB_Index}(size(A,2))
    Csize = Ref{libgb.GrB_Index}(length(A) * sizeof(T))
    Cx = Ptr{T}(Libc.malloc(length(A) * sizeof(T)))
    CRef = Ref{Ptr{Cvoid}}(Cx)
    isuniform = Ref{Bool}(false)
    libgb.GxB_Matrix_export_FullC(
        Ref(A.p),
        Ref(toGrB_Type(T).p),
        nrows,
        ncols,
        CRef,
        Csize,
        isuniform,
        desc
    )
    C = Matrix{T}(undef, nrows[], ncols[])
    unsafe_copyto!(pointer(C), Ptr{T}(CRef[]), length(C))
    return C
end

function toJL(A::GBMatrix)
    return exportdensematrix(A)
end

function exportdensevec(
    n::Integer, v::Vector{T};
    desc::Descriptor = Descriptors.NULL
) where {T}
    w = Ref{libgb.GrB_Vector}()
    n = libgb.GrB_Index(n)
    vsize = libgb.GrB_Index(sizeof(v))

    vx = Ptr{T}(Libc.malloc(vsize))
    unsafe_copyto!(vx, pointer(v), length(v))
    libgb.GxB_Vector_export_Full(
        w,
        toGrB_Type(T),
        n,
        Ref{Ptr{Cvoid}}(vx),
        vsize,
        false,
        desc
    )
    return GBVector{T}(w[])
end

function toGB(v::Vector)
    return exportdensevec(size(v)..., v)
end


text:
ENV["GKSwstype"] = "nul"  # For StatsPlots

import Pkg; Pkg.activate(joinpath(@__DIR__, "../../../"))
using CSV, DataFrames
using CytofDensityEstimation
const CDE = CytofDensityEstimation
using Distributions
import Random
using BSON
using StatsPlots

using RCall
@rimport stats as rstats

function postprocess(chain, laststate, summarystats, yC, yT, imgdir;
                     bw_postpred=0.2, density_legend_pos=:best,
                     ygrid=collect(range(-8, 8, length=1000)))
  # Print KS Statistic.
  ks_fit = rstats.ks_test(yC, yT)
  println("KS-test p-value: ", ks_fit["p.value"][1])
  flush(stdout)

  # Print summary statistics.
  CDE.Model.printsummary(chain, summarystats)
  flush(stdout)

  # Plot results.
  @time CDE.Model.plotpostsummary(chain, summarystats, yC, yT, imgdir,
                                  bw_postpred=bw_postpred, ygrid=ygrid,
                                  density_legend_pos=density_legend_pos)
  flush(stdout)
end

function defaults(yC, yT, K; seed=nothing)
  seed == nothing || Random.seed!(seed)

  data = CDE.Model.Data(yC, yT)
  prior = CDE.Model.Prior(K, mu=CDE.Model.compute_prior_mu(data),
                          nu=LogNormal(1.6, 0.4), p=Beta(100, 100),
                          omega=InverseGamma(.1, .1), psi=Normal(-1, 1))
  state = CDE.Model.State(data, prior)
  tuners = CDE.Model.Tuners(K, 0.1)
  return (state=state, data=data, prior=prior, tuners=tuners)
end

function run(config)
  resultsdir = config[:resultsdir]
  mkpath(resultsdir)
  path_to_log = joinpath(resultsdir, "log.txt")
  CDE.Util.redirect_stdout_to_file(path_to_log) do
    _run(config)
  end
end

function _run(config)
  println("pid: $(getpid())"); flush(stdout)

  resultsdir = config[:resultsdir]
  awsbucket = config[:awsbucket]
  yC = config[:yC]
  yT = config[:yT]
  K = config[:K]
  nsamps = config[:nsamps]
  nburn = config[:nburn]

  # Make image path id needed.
  imgdir = joinpath(resultsdir, "img")
  mkpath(imgdir)

  # Create initial state, data, prior, and tuners objects.
  state, data, prior, tuners = defaults(yC, yT, K, seed=0)
  println("Priors:")
  foreach(fn -> println(fn, " => ", getfield(prior, fn)),
          fieldnames(CDE.Model.Prior))

  # Run analysis.
  println("Run Chain ..."); flush(stdout)
  @time chain, laststate, summarystats = CDE.Model.fit(
      state, data, prior, tuners, nsamps=[nsamps], nburn=nburn, thin=1,
      rep_aux=10, rep_beta_flipped=50)
  flush(stdout)

  # Save results
  BSON.bson("$(resultsdir)/results.bson",
            Dict(:chain=>chain, :laststate=>laststate, :data=>data,
                 :prior=>prior, :summarystats=>summarystats))

  # Load data:
  out = BSON.load("$(resultsdir)/results.bson")

  # Post process
  postprocess(out[:chain], out[:laststate], out[:summarystats], out[:data].yC,
              out[:data].yT, imgdir; bw_postpred=0.2,
              ygrid=collect(range(-8, 8, length=1000)),
              density_legend_pos=:topleft)

  # Send results
  if awsbucket != nothing
    CDE.Util.s3sync(from=resultsdir, to=awsbucket, tags=`--exclude '*.nfs'`)
  end

  # Print done.
  println("Done!"); flush(stdout)
end

max_stars_repo_name: luiarthur/CytofDensityEstimation

max_issues_repo_name: luiarthur/CytofDensityEstimation

max_forks_repo_name: luiarthur/CytofDensityEstimation


text:
# This file is a part of Julia. License is MIT: https://julialang.org/license

module CoreLogging

import Base: isless, +, -, convert, show

export
    AbstractLogger,
    LogLevel,
    NullLogger,
    @debug,
    @info,
    @warn,
    @error,
    @logmsg,
    with_logger,
    current_logger,
    global_logger,
    disable_logging,
    SimpleLogger

#-------------------------------------------------------------------------------
# The AbstractLogger interface
"""
A logger controls how log records are filtered and dispatched.  When a log
record is generated, the logger is the first piece of user configurable code
which gets to inspect the record and decide what to do with it.
"""
abstract type AbstractLogger ; end

"""
    handle_message(logger, level, message, _module, group, id, file, line; key1=val1, ...)

Log a message to `logger` at `level`.  The logical location at which the
message was generated is given by module `_module` and `group`; the source
location by `file` and `line`. `id` is an arbitrary unique [`Symbol`](@ref) to be used
as a key to identify the log statement when filtering.
"""
function handle_message end

"""
    shouldlog(logger, level, _module, group, id)

Return true when `logger` accepts a message at `level`, generated for
`_module`, `group` and with unique log identifier `id`.
"""
function shouldlog end

"""
    min_enabled_level(logger)

Return the maximum disabled level for `logger` for early filtering.  That is,
the log level below or equal to which all messages are filtered.
"""
function min_enabled_level end

"""
    catch_exceptions(logger)

Return true if the logger should catch exceptions which happen during log
record construction.  By default, messages are caught

By default all exceptions are caught to prevent log message generation from
crashing the program.  This lets users confidently toggle little-used
functionality - such as debug logging - in a production system.

If you want to use logging as an audit trail you should disable this for your
logger type.
"""
catch_exceptions(logger) = true

"""
    NullLogger()

Logger which disables all messages and produces no output - the logger
equivalent of /dev/null.
"""
struct NullLogger <: AbstractLogger; end

min_enabled_level(::NullLogger) = AboveMaxLevel
shouldlog(::NullLogger, args...) = false
handle_message(::NullLogger, args...; kwargs...) =
    error("Null logger handle_message() should not be called")

#-------------------------------------------------------------------------------
# Standard log levels
"""
    LogLevel(level)

Severity/verbosity of a log record.

The log level provides a key against which potential log records may be
filtered, before any other work is done to construct the log record data
structure itself.
"""
struct LogLevel
    level::Int32
end

LogLevel(level::LogLevel) = level

isless(a::LogLevel, b::LogLevel) = isless(a.level, b.level)
+(level::LogLevel, inc::Integer) = LogLevel(level.level+inc)
-(level::LogLevel, inc::Integer) = LogLevel(level.level-inc)
convert(::Type{LogLevel}, level::Integer) = LogLevel(level)

const BelowMinLevel = LogLevel(-1000001)
const Debug         = LogLevel(   -1000)
const Info          = LogLevel(       0)
const Warn          = LogLevel(    1000)
const Error         = LogLevel(    2000)
const AboveMaxLevel = LogLevel( 1000001)

function show(io::IO, level::LogLevel)
    if     level == BelowMinLevel  print(io, "BelowMinLevel")
    elseif level == Debug          print(io, "Debug")
    elseif level == Info           print(io, "Info")
    elseif level == Warn           print(io, "Warn")
    elseif level == Error          print(io, "Error")
    elseif level == AboveMaxLevel  print(io, "AboveMaxLevel")
    else                           print(io, "LogLevel($(level.level))")
    end
end

#-------------------------------------------------------------------------------
# Logging macros

_logmsg_docs = """
    @debug message  [key=value | value ...]
    @info  message  [key=value | value ...]
    @warn  message  [key=value | value ...]
    @error message  [key=value | value ...]

    @logmsg level message [key=value | value ...]

Create a log record with an informational `message`.  For convenience, four
logging macros `@debug`, `@info`, `@warn` and `@error` are defined which log at
the standard severity levels `Debug`, `Info`, `Warn` and `Error`.  `@logmsg`
allows `level` to be set programmatically to any `LogLevel` or custom log level
types.

`message` should be an expression which evaluates to a string which is a human
readable description of the log event.  By convention, this string will be
formatted as markdown when presented.

The optional list of `key=value` pairs supports arbitrary user defined
metadata which will be passed through to the logging backend as part of the
log record.  If only a `value` expression is supplied, a key representing the
expression will be generated using [`Symbol`](@ref). For example, `x` becomes `x=x`,
and `foo(10)` becomes `Symbol("foo(10)")=foo(10)`.  For splatting a list of
key value pairs, use the normal splatting syntax, `@info "blah" kws...`.

There are some keys which allow automatically generated log data to be
overridden:

  * `_module=mod` can be used to specify a different originating module from
    the source location of the message.
  * `_group=symbol` can be used to override the message group (this is
    normally derived from the base name of the source file).
  * `_id=symbol` can be used to override the automatically generated unique
    message identifier.  This is useful if you need to very closely associate
    messages generated on different source lines.
  * `_file=string` and `_line=integer` can be used to override the apparent
    source location of a log message.

There's also some key value pairs which have conventional meaning:

  * `maxlog=integer` should be used as a hint to the backend that the message
    should be displayed no more than `maxlog` times.
  * `exception=ex` should be used to transport an exception with a log message,
    often used with `@error`. An associated backtrace `bt` may be attached
    using the tuple `exception=(ex,bt)`.

# Examples

```
@debug "Verbose debugging information.  Invisible by default"
@info  "An informational message"
@warn  "Something was odd.  You should pay attention"
@error "A non fatal error occurred"

x = 10
@info "Some variables attached to the message" x a=42.0

@debug begin
    sA = sum(A)
    "sum(A) = \$sA is an expensive operation, evaluated only when `shouldlog` returns true"
end

for i=1:10000
    @info "With the default backend, you will only see (i = \$i) ten times"  maxlog=10
    @debug "Algorithm1" i progress=i/10000
end
```
"""

# Get (module,filepath,line) for the location of the caller of a macro.
# Designed to be used from within the body of a macro.
macro _sourceinfo()
    esc(quote
        (__module__,
         __source__.file === nothing ? "?" : String(__source__.file),
         __source__.line)
    end)
end

macro logmsg(level, exs...) logmsg_code((@_sourceinfo)..., esc(level), exs...) end
macro debug(exs...) logmsg_code((@_sourceinfo)..., :Debug, exs...) end
macro  info(exs...) logmsg_code((@_sourceinfo)..., :Info,  exs...) end
macro  warn(exs...) logmsg_code((@_sourceinfo)..., :Warn,  exs...) end
macro error(exs...) logmsg_code((@_sourceinfo)..., :Error, exs...) end

# Logging macros share documentation
@eval @doc $_logmsg_docs :(@logmsg)
@eval @doc $_logmsg_docs :(@debug)
@eval @doc $_logmsg_docs :(@info)
@eval @doc $_logmsg_docs :(@warn)
@eval @doc $_logmsg_docs :(@error)

_log_record_ids = Set{Symbol}()
# Generate a unique, stable, short, somewhat human readable identifier for a
# logging *statement*. The idea here is to have a key against which log events
# can be filtered and otherwise manipulated. The key should uniquely identify
# the source location in the originating module, but ideally should be stable
# across versions of the originating module, provided the log generating
# statement itself doesn't change.
function log_record_id(_module, level, message, log_kws)
    modname = _module === nothing ?  "" : join(fullname(_module), "_")
    # Use an arbitriraly chosen eight hex digits here. TODO: Figure out how to
    # make the id exactly the same on 32 and 64 bit systems.
    h = UInt32(hash(string(modname, level, message, log_kws)) & 0xFFFFFFFF)
    while true
        id = Symbol(modname, '_', string(h, base = 16, pad = 8))
        # _log_record_ids is a registry of log record ids for use during
        # compilation, to ensure uniqueness of ids.  Note that this state will
        # only persist during module compilation so it will be empty when a
        # precompiled module is loaded.
        if !(id in _log_record_ids)
            push!(_log_record_ids, id)
            return id
        end
        h += 1
    end
end

# Generate code for logging macros
function logmsg_code(_module, file, line, level, message, exs...)
    id = Expr(:quote, log_record_id(_module, level, message, exs))
    group = nothing
    kwargs = Any[]
    for ex in exs
        if ex isa Expr && ex.head === :(=) && ex.args[1] isa Symbol
            k,v = ex.args
            if !(k isa Symbol)
                throw(ArgumentError("Expected symbol for key in key value pair `$ex`"))
            end
            k = ex.args[1]
            # Recognize several special keyword arguments
            if k == :_id
                # id may be overridden if you really want several log
                # statements to share the same id (eg, several pertaining to
                # the same progress step).  In those cases it may be wise to
                # manually call log_record_id to get a unique id in the same
                # format.
                id = esc(v)
            elseif k == :_module
                _module = esc(v)
            elseif k == :_line
                line = esc(v)
            elseif k == :_file
                file = esc(v)
            elseif k == :_group
                group = esc(v)
            else
                # Copy across key value pairs for structured log records
                push!(kwargs, Expr(:kw, k, esc(v)))
            end
        elseif ex isa Expr && ex.head === :...
            # Keyword splatting
            push!(kwargs, esc(ex))
        else
            # Positional arguments - will be converted to key value pairs
            # automatically.
            push!(kwargs, Expr(:kw, Symbol(ex), esc(ex)))
        end
    end

    if group === nothing
        group = if isdefined(Base, :basename) && isa(file, String)
            # precompute if we can
            QuoteNode(splitext(basename(file))[1])
        else
            # memoized run-time execution
            ref = Ref{Symbol}()
            :(isassigned($ref) ? $ref[]
                               : $ref[] = Symbol(splitext(basename(something($file, "")))[1]))
        end
    end

    quote
        level = $level
        std_level = convert(LogLevel, level)
        if std_level >= getindex(_min_enabled_level)
            group = $group
            _module = $_module
            logger = current_logger_for_env(std_level, group, _module)
            if !(logger === nothing)
                id = $id
                # Second chance at an early bail-out (before computing the message),
                # based on arbitrary logger-specific logic.
                if shouldlog(logger, level, _module, group, id)
                    file = $file
                    line = $line
                    try
                        msg = $(esc(message))
                        handle_message(logger, level, msg, _module, group, id, file, line; $(kwargs...))
                    catch err
                        logging_error(logger, level, _module, group, id, file, line, err)
                    end
                end
            end
        end
        nothing
    end
end

# Report an error in log message creation (or in the logger itself).
@noinline function logging_error(logger, level, _module, group, id,
                                 filepath, line, @nospecialize(err))
    if !catch_exceptions(logger)
        rethrow(err)
    end
    try
        msg = "Exception while generating log record in module $_module at $filepath:$line"
        handle_message(logger, Error, msg, _module, :logevent_error, id, filepath, line; exception=(err,catch_backtrace()))
    catch err2
        try
            # Give up and write to stderr, in three independent calls to
            # increase the odds of it getting through.
            print(stderr, "Exception handling log message: ")
            println(stderr, err)
            println(stderr, "  module=$_module  file=$filepath  line=$line")
            println(stderr, "  Second exception: ", err2)
        catch
        end
    end
    nothing
end

# Log a message. Called from the julia C code; kwargs is in the format
# Any[key1,val1, ...] for simplicity in construction on the C side.
function logmsg_shim(level, message, _module, group, id, file, line, kwargs)
    real_kws = Any[(kwargs[i],kwargs[i+1]) for i in 1:2:length(kwargs)]
    @logmsg(convert(LogLevel, level), message,
            _module=_module, _id=id, _group=group,
            _file=String(file), _line=line, real_kws...)
end

# Global log limiting mechanism for super fast but inflexible global log
# limiting.
const _min_enabled_level = Ref(Debug)

# LogState - a concretely typed cache of data extracted from the logger, plus
# the logger itself.
struct LogState
    min_enabled_level::LogLevel
    logger::AbstractLogger
end

LogState(logger) = LogState(LogLevel(min_enabled_level(logger)), logger)

function current_logstate()
    logstate = current_task().logstate
    return (logstate !== nothing ? logstate : _global_logstate)::LogState
end

# helper function to get the current logger, if enabled for the specified message type
@noinline function current_logger_for_env(std_level::LogLevel, group, _module)
    logstate = current_logstate()
    if std_level >= logstate.min_enabled_level || env_override_minlevel(group, _module)
        return logstate.logger
    end
    return nothing
end

function with_logstate(f::Function, logstate)
    t = current_task()
    old = t.logstate
    try
        t.logstate = logstate
        f()
    finally
        t.logstate = old
    end
end

#-------------------------------------------------------------------------------
# Control of the current logger and early log filtering

"""
    disable_logging(level)

Disable all log messages at log levels equal to or less than `level`.  This is
a *global* setting, intended to make debug logging extremely cheap when
disabled.
"""
function disable_logging(level::LogLevel)
    _min_enabled_level[] = level + 1
end

let _debug_groups = Symbol[],
    _debug_str::String = ""
global function env_override_minlevel(group, _module)
    debug = get(ENV, "JULIA_DEBUG", "")
    if !(debug === _debug_str)
        _debug_str = debug
        empty!(_debug_groups)
        for g in split(debug, ',')
            isempty(g) && continue
            if g == "all"
                empty!(_debug_groups)
                push!(_debug_groups, :all)
                break
            end
            push!(_debug_groups, Symbol(g))
        end
    end
    if isempty(_debug_groups)
        return false
    end
    if _debug_groups[1] == :all
        return true
    end
    if isa(group, Symbol) && group in _debug_groups
        return true
    end
    if isa(_module, Module)
        if nameof(_module) in _debug_groups
            return true
        end
        if nameof(Base.moduleroot(_module)) in _debug_groups
            return true
        end
    end
    return false
end
end

"""
    global_logger()

Return the global logger, used to receive messages when no specific logger
exists for the current task.

    global_logger(logger)

Set the global logger to `logger`, and return the previous global logger.
"""
global_logger() = _global_logstate.logger

function global_logger(logger::AbstractLogger)
    prev = _global_logstate.logger
    global _global_logstate = LogState(logger)
    prev
end

"""
    with_logger(function, logger)

Execute `function`, directing all log messages to `logger`.

# Example

```julia
function test(x)
    @info "x = \$x"
end

with_logger(logger) do
    test(1)
    test([1,2])
end
```
"""
with_logger(f::Function, logger::AbstractLogger) = with_logstate(f, LogState(logger))

"""
    current_logger()

Return the logger for the current task, or the global logger if none is
attached to the task.
"""
current_logger() = current_logstate().logger

#-------------------------------------------------------------------------------
# SimpleLogger
"""
    SimpleLogger(stream=stderr, min_level=Info)

Simplistic logger for logging all messages with level greater than or equal to
`min_level` to `stream`.
"""
struct SimpleLogger <: AbstractLogger
    stream::IO
    min_level::LogLevel
    message_limits::Dict{Any,Int}
end
SimpleLogger(stream::IO=stderr, level=Info) = SimpleLogger(stream, level, Dict{Any,Int}())

shouldlog(logger::SimpleLogger, level, _module, group, id) =
    get(logger.message_limits, id, 1) > 0

min_enabled_level(logger::SimpleLogger) = logger.min_level

catch_exceptions(logger::SimpleLogger) = false

function handle_message(logger::SimpleLogger, level, message, _module, group, id,
                        filepath, line; maxlog=nothing, kwargs...)
    if maxlog !== nothing && maxlog isa Integer
        remaining = get!(logger.message_limits, id, maxlog)
        logger.message_limits[id] = remaining - 1
        remaining > 0 || return
    end
    buf = IOBuffer()
    iob = IOContext(buf, logger.stream)
    levelstr = level == Warn ? "Warning" : string(level)
    msglines = split(chomp(string(message)), '\n')
    println(iob, "┌ ", levelstr, ": ", msglines[1])
    for i in 2:length(msglines)
        println(iob, "│ ", msglines[i])
    end
    for (key, val) in kwargs
        println(iob, "│   ", key, " = ", val)
    end
    println(iob, "└ @ ", something(_module, "nothing"), " ",
            something(filepath, "nothing"), ":", something(line, "nothing"))
    write(logger.stream, take!(buf))
    nothing
end

_global_logstate = LogState(SimpleLogger(Core.stderr, CoreLogging.Info))

end # CoreLogging

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