text:
md"""
# Searching for an optimal cut sequence
"""

struct SearchState
    # panels are removed from wanten once they are finished.
    wanted::Panels{AbstractWantedPanel}
    bought::Panels{BoughtPanel}
    finished::Panels{FinishedPanel}
    scrapped::Panels{ScrappedPanel}
    working::Panels{CuttablePanel}
    accumulated_cost::MoneyType

    function SearchState(;
                         wanted=Panels{AbstractWantedPanel}([]),
                         bought=Panels{BoughtPanel}([]),
                         finished=Panels{FinishedPanel}([]),
                         scrapped=Panels{ScrappedPanel}([]),
                         working=Panels{CuttablePanel}([]),
                         accumulated_cost=money(0))
	newstate = new(wanted, bought, finished, scrapped, working, accumulated_cost)
	panels = AllOf(finished, scrapped, working)
	for i in 1:length(panels)
	    for j in i+1:length(panels)
		errIfOverlap(panels[i], panels[j], newstate)
	    end
	end
        return newstate
    end
end

# Constructor for the initial search state:
function SearchState(want::Vector{<:AbstractWantedPanel})
    SearchState(; wanted=Panels{
        AbstractWantedPanel}(sort(want; lt=smaller, rev=true)))
end

# A constructor for successor states that enforces critical invariants
function SearchState(precursor::SearchState, cost,
		     finished::Union{Nothing, FinishedPanel},
                     used::Union{Nothing, CuttablePanel},
		     offcuts::CuttablePanel...)
    ### This will not catch a newly bought panel that left no off-cut
    newly_bought = filter(x -> x isa BoughtPanel, offcuts)
    bought = if length(newly_bought) == 0
	precursor.bought
    else
	Panels{BoughtPanel}([precursor.bought..., newly_bought...])
    end
    wanted = if finished == nothing
        precursor.wanted
    else
        filter(precursor.wanted) do w
	    !wantsmatch(w, finished.wanted)
        end
    end
    newlyscrapped=[]
    working=[]
    for p in [offcuts...,
              precursor.working...]
        if p == used
            # We just cut this panel, it's gone now.
            continue
        end
        if any((w) -> fitsin(w, p), wanted)
	    push!(working, p)
        else
            # p can't fit any remaining AbstractWantedPanel, scrap it:
	    push!(newlyscrapped, ScrappedPanel(was=p))
        end
    end
    state = SearchState(;
		        wanted=wanted,
		        bought=bought,
		        finished=if finished == nothing
                            precursor.finished
                        else
                            Panels{FinishedPanel}(
			        union((finished,),
				      precursor.finished))
                        end,
		        scrapped=Panels{ScrappedPanel}(
			    union(newlyscrapped, precursor.scrapped)),
		        working=Panels{CuttablePanel}(working),
		        accumulated_cost=precursor.accumulated_cost + cost)
    # println("precursor: ", precursor, "\n      new: ", state)
    return state
end

function doneness(state::SearchState)::Real
    a = (x) -> reduce(+, area.(x); init=0u"inch^2")
    finished = a(state.finished)
    return finished / (finished + a(state.wanted))
end

export SearchState, doneness

md"""
## Priority

For A* Search we need to assign a priority to each state in the state
space we are searching through.  A SearchState with **lower** priority
will be considered **ahead** of one with higher priority.
"""

SearchPriority = Real

function priority(state::SearchState)::SearchPriority
    # Priority should get worse as the cost increases but should get better
    # as we approach completion.
    (1 - doneness(state)) * unmoney(state.accumulated_cost)
end

export SearchPriority, priority

md"""
 ## Searching

This Searcher implements A* search using a PriorityQueue.

One could implement other searchers to implement, for example, depth or breadth first search.
"""

mutable struct Searcher
    supplier::Supplier
    wanted::Vector{<:AbstractWantedPanel}
    states::PriorityQueue{SearchState, SearchPriority}
    finished_states::Set{SearchState}
    cheapest::Union{SearchState, Nothing}
    # For debugging:
    considered_states::Vector{SearchState}

    function Searcher(supplier::Supplier,
                       want::Vector{<:AbstractWantedPanel})
        initial_state = SearchState(want)
        new(supplier, uniqueWantedPanels(want),
            PriorityQueue{SearchState, SearchPriority}(
                initial_state => priority(initial_state)),
            Set{SearchState}(),
	    nothing,
	    Vector{SearchState}())
    end
end

function enqueue(searcher::Searcher, state::Union{SearchState, Nothing})::Nothing
    if state == Nothing
        return nothing
    end
    if isempty(state.wanted)
        push!(searcher.finished_states, state)
        if searcher.cheapest == nothing
            searcher.cheapest = state
        elseif state.accumulated_cost < searcher.cheapest.accumulated_cost
            searcher.cheapest = state
        end
    else
        enqueue!(searcher.states, state => priority(state))
    end
    nothing
end

function search(searcher::Searcher)
    while !isempty(searcher.states)
        s = dequeue!(searcher.states)
        progress(searcher, s)
    end
end

function progress(searcher::Searcher, state::SearchState)::Nothing
    if searcher.cheapest != nothing &&
        searcher.cheapest.accumulated_cost <= state.accumulated_cost
        # No improvement possible.  Prune this search branch:
        return nothing
    end
    push!(searcher.considered_states, state)
    if isempty(state.wanted)
        return nothing
    end
    successors = 0
    # Try cutting the first wanted panel from each of the working panels
    function cutWanted(wanted)
        for working in state.working
            if !fitsin(wanted, working)
                continue
            end
            for axis_ in subtypes(Axis)
                axis = axis_()
                cuts = cut(working, axis, distance(wanted, axis);
			   kerf=searcher.supplier.kerf,
			   cost=searcher.supplier.cost_per_cut)
                if length(cuts) == 0
	            continue
                end
                @assert distance(cuts[1], axis) == distance(wanted, axis)
                if distance(cuts[1], other(axis)) == distance(wanted, other(axis))
	            enqueue(searcher, SearchState(state, searcher.supplier.cost_per_cut,
				                  FinishedPanel(cuts[1], wanted),
                                                  working,
						  cuts[2:end]...))
		    successors += 1
	            continue
                end
                cuts2 = cut(cuts[1], other(axis), distance(wanted, other(axis));
                            kerf=searcher.supplier.kerf,
			    cost=searcher.supplier.cost_per_cut)
                if length(cuts2) == 0
	            continue
                end
                @assert distance(cuts2[1], other(axis)) == distance(wanted, other(axis))
                enqueue(searcher, SearchState(state, 2 * searcher.supplier.cost_per_cut,
				              FinishedPanel(cuts2[1], wanted),
                                              working,
					      cuts[2:end]..., cuts2[2:end]...))
		successors += 1
            end
        end
        return nothing
    end
    wanted = state.wanted[1]
    cutWanted(wanted)
    # For FlippedPanel we consider both the flipped and original shapes:
    if wanted isa FlippedPanel
        cutWanted(wanted.was)
    end
    # If there are still WantedPanels remaininig but no progress was
    # made, buy more stock.
    if successors == 0 && !isempty(state.wanted)
        for p in searcher.supplier.available_stock
            if fitsin(state.wanted[1], p)
                new_state = SearchState(state, p.cost, nothing,
                                        nothing, BoughtPanel(p))
	        enqueue(searcher, new_state)
            end
        end
    end
end

function allstates(searcher::Searcher)
    union(searcher.finished_states,
	  keys(searcher.states))
end

export Searcher, enqueue, search, progress, allstates


text:
using Plots, JLD2
include(pwd()*"/src/SFFM.jl")
include(pwd()*"/examples/meNumerics/discontinuitiesModelDef.jl")

t = 10.2 # 4.2, 1.2, 1
@load pwd()*"/examples/meNumerics/discontinuitiesModelSims_t_"*string(t)*".jld2" sims_Psi sims_1

## mesh set up
orders = [1;3;5;7;11;13;15;21]
errors_1 = []
errors_Psi = []
errors_Pi = []
Δtemp = 1.0# the grid size; must have kΔ = 1 for some k due to discontinuity in r at 1
nodes = collect(0:Δtemp:bounds[1,2])
# for order in orders
order = 3
    println("order = "*string(order))
    dgmesh = SFFM.DGMesh(
        model,
        nodes,
        order;
        Basis = "lagrange",
    )
    frapmesh = SFFM.FRAPMesh(
        model,
        nodes,
        order,
    )
    fvmesh = SFFM.FVMesh(
        model,
        collect(0:Δtemp/order:bounds[1,2]),
        order
    )
    simmesh = SFFM.FVMesh(
        model,
        nodes,
        1,
    )

    # simulated distributions
    simprobs_Psi = SFFM.Sims2Dist(
        model,
        simmesh,
        sims_Psi,
        SFFM.SFFMProbability,
    )
    simdensity_Psi = SFFM.Sims2Dist(
        model,
        simmesh,
        sims_Psi,
        SFFM.SFFMDensity,
    )
    simprobs_1 = SFFM.Sims2Dist(
        model,
        simmesh,
        sims_1,
        SFFM.SFFMProbability,
    )
    simdensity_1 = SFFM.Sims2Dist(
        model,
        simmesh,
        sims_1,
        SFFM.SFFMDensity
    )

    # DG
    B_DG = SFFM.MakeFullGenerator(model, dgmesh)
    #ME
    me = SFFM.MakeME(SFFM.CMEParams[order], mean = 1)
    B_ME = SFFM.MakeFullGenerator(model, frapmesh)
    # Erlang (this is the erlang which is equivalent to DG)
    erlang = SFFM.MakeErlang(order, mean = 1)
    B_Erlang = SFFM.MakeFullGenerator(model, frapmesh, erlang)
    # meph (this is the erlang treated as an ME)
    meph = SFFM.ME(erlang.a, erlang.S, erlang.s; D = SFFM.erlangDParams[string(order)])
    B_MEPH = SFFM.MakeFullGenerator(model, frapmesh, meph)
    # FVM
    B_FV = SFFM.MakeFullGenerator(model, fvmesh)

    # construct initial condition
    point = 0+eps()
    pointIdx = convert(Int,ceil(point/Δtemp))
    begin
        V = SFFM.vandermonde(order)
        theNodes = SFFM.CellNodes(dgmesh)[:,pointIdx]
        basisValues = zeros(length(theNodes))
        for n in 1:length(theNodes)
            basisValues[n] = prod(point.-theNodes[[1:n-1;n+1:end]])./prod(theNodes[n].-theNodes[[1:n-1;n+1:end]])
        end
        initpm = [
            zeros(sum(model.C.<=0)) # LHS point mass
            zeros(sum(model.C.>=0)) # RHS point mass
        ]
        initprobs = zeros(Float64,SFFM.NBases(dgmesh),SFFM.NIntervals(dgmesh),SFFM.NPhases(model))
        initprobs[:,pointIdx,1] = basisValues'*V.V*V.V'.*2/Δtemp
        initdist = SFFM.SFFMDensity(
            initpm,
            initprobs,
            SFFM.CellNodes(dgmesh),
        ) # convert to a distribution object so we can apply Dist2Coeffs
        # convert to Coeffs α in the DG context
        x0_DG = SFFM.Dist2Coeffs(model, dgmesh, initdist)
    end
    begin
        initpm = [
            zeros(sum(model.C.<=0)) # LHS point mass
            zeros(sum(model.C.>=0)) # RHS point mass
        ]
        initprobs = zeros(Float64,SFFM.NBases(frapmesh),SFFM.NIntervals(frapmesh),SFFM.NPhases(model))
        initprobs[:,pointIdx,1] = me.a
        initdist = SFFM.SFFMDensity(
            initpm,
            initprobs,
            SFFM.CellNodes(frapmesh),
        ) # convert to a distribution object so we can apply Dist2Coeffs
        # convert to Coeffs α in the DG context
        x0_ME = SFFM.Dist2Coeffs( model, frapmesh, initdist)
    end
    begin
        initpm = [
            zeros(sum(model.C.<=0)) # LHS point mass
            zeros(sum(model.C.>=0)) # RHS point mass
        ]
        initprobs = zeros(Float64,SFFM.NBases(frapmesh),SFFM.NIntervals(frapmesh),SFFM.NPhases(model))
        initprobs[1,pointIdx,1] = 1
        initdist = SFFM.SFFMDensity(
            initpm,
            initprobs,
            SFFM.CellNodes(frapmesh),
        ) # convert to a distribution object so we can apply Dist2Coeffs
        # convert to Coeffs α in the DG context
        x0_Erlang = SFFM.Dist2Coeffs( model, frapmesh, initdist)
    end
    begin
        initpm = [
            zeros(sum(model.C.<=0)) # LHS point mass
            zeros(sum(model.C.>=0)) # RHS point mass
        ]
        initprobs = zeros(Float64,SFFM.NBases(fvmesh),SFFM.NIntervals(fvmesh),SFFM.NPhases(model))
        initprobs[1,pointIdx,1] = 1 ./SFFM.Δ(fvmesh)[1]
        initdist = SFFM.SFFMDensity(
            initpm,
            initprobs,
            SFFM.CellNodes(fvmesh),
        ) # convert to a distribution object so we can apply Dist2Coeffs
        # convert to Coeffs α in the DG context
        x0_FV = SFFM.Dist2Coeffs( model, fvmesh, initdist)
    end

    euler(B,x0) = SFFM.EulerDG( B, t, x0, h = 0.001)
    x1_DG = euler(B_DG, x0_DG)
    x1_ME = euler(B_ME, x0_ME)
    x1_Erlang = euler(B_Erlang, x0_Erlang)
    x1_MEPH = euler(B_MEPH, x0_Erlang)
    x1_FV = euler(B_FV, x0_FV)

#     x1_DG = SFFM.Coeffs2Dist(
#         model,
#         dgmesh,
#         x1_DG,
#         SFFM.SFFMProbability,
#     )
#     x1_ME = SFFM.Coeffs2Dist(
#         model,
#         frapmesh,
#         x1_ME,
#         SFFM.SFFMProbability,
#     )
#     x1_Erlang = SFFM.Coeffs2Dist(
#         model,
#         frapmesh,
#         x1_Erlang,
#         SFFM.SFFMProbability,
#     )
#     x1_MEPH = SFFM.Coeffs2Dist(
#         model,
#         frapmesh,
#         x1_MEPH,
#         SFFM.SFFMProbability,
#     )

#     # # reshape x1_FV to same size as DG/FRAP
#     # N₋ = sum(model.C.<=0)
#     # N₊ = sum(model.C.>=0)
#     # nCells = (length(x1_FV)-N₋-N₊)÷order
#     # temp = sum( reshape( x1_FV[(N₋+1):(end-N₊)], order, nCells), dims=1)
#     # x1_FV = [x1_FV[1:N₋]' temp x1_FV[(end-N₊+1):end]']

#     x1_FV = SFFM.Coeffs2Dist(
#         model,
#         frapmesh,
#         x1_FV,
#         SFFM.SFFMProbability,
#     )

#     errVec_1 = (
#         SFFM.starSeminorm(x1_DG, simprobs_1),
#         SFFM.starSeminorm(x1_ME, simprobs_1),
#         SFFM.starSeminorm(x1_Erlang, simprobs_1),
#         SFFM.starSeminorm(x1_MEPH, simprobs_1),
#         SFFM.starSeminorm(x1_FV, simprobs_1),
#     )
#     push!(errors_1, errVec_1)

#     p = SFFM.plot(model, dgmesh, x1_DG,
#         color = 1, label = "DG")
#     p = SFFM.plot!(p, model, frapmesh, x1_ME,
#         color = 2, label = "ME")
#     SFFM.plot!(p, model, frapmesh, x1_Erlang,
#         color = 3, label = "Erlang")
#     SFFM.plot!(p, model, frapmesh, simprobs_1,
#         color = 4, label = "Sim")
#     SFFM.plot!(p, model, frapmesh, x1_MEPH,
#         color = 5, label = "ME-PH")
#     SFFM.plot!(p, model, fvmesh, x1_FV,
#         color = 7, label = "FV")
#     p = plot!(title = "approx dist at t=t; order = "*string(order), subplot = 1)
#     display(p)

#     # the initial condition on Ψ is restricted to + states so find the + states
#     plusIdx = [
#         dgmesh.Fil["p+",:];
#         repeat(dgmesh.Fil["+",:]', SFFM.NBases(dgmesh), 1)[:];
#         dgmesh.Fil["q+",:];
#     ]
#     plusIdxFV = [
#         fvmesh.Fil["p+",:];
#         repeat(fvmesh.Fil["+",:]', SFFM.NBases(fvmesh), 1)[:];
#         fvmesh.Fil["q+",:];
#     ]
#     # get the elements of x0_DG in + states only
#     x0_Psi_DG = x0_DG[plusIdx]'
#     x0_Psi_ME = x0_ME[plusIdx]'
#     x0_Psi_Erlang = x0_Erlang[plusIdx]'
#     x0_Psi_FV = x0_FV[plusIdxFV]'
#     # check that it is equal to 1 (or at least close)
#     # println(sum(x0_Psi_DG))
#     # println(sum(x0_Psi_ME))
#     # println(sum(x0_Psi_Erlang))

#     ## Psi paths
#     R = SFFM.MakeR( model, dgmesh, approxType = "interpolation")
#     R_FV = SFFM.MakeR( model, fvmesh, approxType = "interpolation")

#     ΨFun(B) = SFFM.MakeD(dgmesh, B, R) |> D -> SFFM.PsiFun(D)
#     Ψ_DG = ΨFun(B_DG)
#     Ψ_ME = ΨFun(B_ME)
#     Ψ_Erlang = ΨFun(B_Erlang)
#     Ψ_MEPH = ΨFun(B_MEPH)
#     Ψ_FV = SFFM.MakeD(fvmesh, B_FV, R_FV) |> D -> SFFM.PsiFun(D)

#     w_DG = x0_Psi_DG*Ψ_DG
#     w_ME = x0_Psi_ME*Ψ_ME
#     w_Erlang = x0_Psi_Erlang*Ψ_Erlang
#     w_MEPH = x0_Psi_Erlang*Ψ_MEPH
#     w_FV = x0_Psi_FV*Ψ_FV

#     minusIdx = [
#         dgmesh.Fil["p-",:];
#         repeat(dgmesh.Fil["-",:]', SFFM.NBases(dgmesh), 1)[:];
#         dgmesh.Fil["q-",:];
#     ]
#     minusIdxFV = [
#         fvmesh.Fil["p-",:];
#         repeat(fvmesh.Fil["-",:]', SFFM.NBases(fvmesh), 1)[:];
#         fvmesh.Fil["q-",:];
#     ]
#     z_DG = zeros(
#         Float64,
#         SFFM.NBases(dgmesh)*SFFM.NIntervals(dgmesh) * SFFM.NPhases(model) +
#             sum(model.C.<=0) + sum(model.C.>=0)
#     )
#     z_ME = zeros(
#         Float64,
#         SFFM.NBases(dgmesh)*SFFM.NIntervals(dgmesh) * SFFM.NPhases(model) +
#             sum(model.C.<=0) + sum(model.C.>=0)
#     )
#     z_Erlang = zeros(
#         Float64,
#         SFFM.NBases(dgmesh)*SFFM.NIntervals(dgmesh) * SFFM.NPhases(model) +
#             sum(model.C.<=0) + sum(model.C.>=0)
#     )
#     z_MEPH = zeros(
#         Float64,
#         SFFM.NBases(dgmesh)*SFFM.NIntervals(dgmesh) * SFFM.NPhases(model) +
#             sum(model.C.<=0) + sum(model.C.>=0)
#     )
#     z_FV = zeros(
#         Float64,
#         SFFM.NBases(fvmesh)*SFFM.NIntervals(fvmesh) * SFFM.NPhases(model) +
#             sum(model.C.<=0) + sum(model.C.>=0)
#     )

#     z_DG[minusIdx] = w_DG
#     z_ME[minusIdx] = w_ME
#     z_Erlang[minusIdx] = w_Erlang
#     z_MEPH[minusIdx] = w_MEPH
#     z_FV[minusIdxFV] = w_FV

#     # # reshape z_FV to same size as DG/FRAP
#     # nCells = (length(z_FV)-N₋-N₊)÷order
#     # temp = sum( reshape( z_FV[(N₋+1):(end-N₊)], order, nCells), dims=1)
#     # z_FV = [z_FV[1:N₋]' temp z_FV[(end-N₊+1):end]']

#     returnDist_DG =  SFFM.Coeffs2Dist(
#         model,
#         frapmesh,
#         z_DG,
#         SFFM.SFFMProbability,
#     )
#     returnDist_ME =  SFFM.Coeffs2Dist(
#         model,
#         frapmesh,
#         z_ME,
#         SFFM.SFFMProbability,
#     )
#     returnDist_Erlang =  SFFM.Coeffs2Dist(
#         model,
#         frapmesh,
#         z_Erlang,
#         SFFM.SFFMProbability,
#     )
#     returnDist_MEPH =  SFFM.Coeffs2Dist(
#         model,
#         frapmesh,
#         z_MEPH,
#         SFFM.SFFMProbability,
#     )
#     returnDist_FV =  SFFM.Coeffs2Dist(
#         model,
#         frapmesh,
#         z_FV,
#         SFFM.SFFMProbability,
#     )

#     errVec_Psi = (
#         SFFM.starSeminorm(returnDist_DG, simprobs_Psi),
#         SFFM.starSeminorm(returnDist_ME, simprobs_Psi),
#         SFFM.starSeminorm(returnDist_Erlang, simprobs_Psi),
#         SFFM.starSeminorm(returnDist_MEPH, simprobs_Psi),
#         SFFM.starSeminorm(returnDist_FV, simprobs_Psi),
#     )
#     push!(errors_Psi, errVec_Psi)

#     # p = SFFM.plot(model, dgmesh, returnDist_DG,
#     #     color = 1, label = "DG")
#     # p = SFFM.plot!(p, model, dgmesh, returnDist_ME,
#     #     color = 2, label = "ME")
#     # p = SFFM.plot!(p, model, frapmesh, returnDist_Erlang,
#     #     color = 3, label = "Erlang")
#     # p = SFFM.plot!(p, model, frapmesh, simprobs_Psi,
#     #     color = 4, label = "Sim")
#     # p = SFFM.plot!(p, model, frapmesh, returnDist_MEPH,
#     #     color = 5, label = "MEPH")
#     # p = SFFM.plot!(p, model, fvmesh, returnDist_FV,
#     #     color = 7, label = "FV")
#     # p = plot!(title = "approx Ψ; order = "*string(order), subplot = 1)
#     # display(p)
# # end

# # simmesh = SFFM.FVMesh(
# #     model,
# #     collect(model.Bounds[1,1]:0.1:model.Bounds[1,2]),
# # )

# # simdensity_Psi = SFFM.Sims2Dist(
# #     model,
# #     simmesh,
# #     sims_Psi,
# #     SFFM.SFFMProbability,
# # )
# # q = SFFM.plot(model, simmesh, simdensity_Psi)
# # display(q)

# # q = plot(xlabel = "order", ylabel = "log10 error", title = "error for Psi")
# # methodNames = ["DG";"ME";"Er";"Er as ME"; "FV"]
# # shapes = [:circle, :utriangle, :x, :+, :square]
# # for whichOrder in 2:length(orders)
# # # order = 3
# #     for whichMethod in 1:length(methodNames)
# #         plot!(
# #             q,
# #             [orders[whichOrder-1];orders[whichOrder]],
# #             [
# #                 log10(errors_Psi[whichOrder-1][whichMethod]);
# #                 log10(errors_Psi[whichOrder][whichMethod])
# #             ],
# #             label = whichOrder == 2 && methodNames[whichMethod],
# #             colour = whichMethod,
# #             markershape = shapes[whichMethod],
# #         )
# #     end
# # end
# # display(q)

# # simdensity_1 = SFFM.Sims2Dist(
# #     model,
# #     simmesh,
# #     sims_1,
# #     SFFM.SFFMProbability,
# # )
# # q = SFFM.plot(model, simmesh, simdensity_1)
# # display(q)

# # q = plot(
# #     xlabel = "order",
# #     ylabel = "log10 error",
# #     title = "error for t="*string(t),
# #     legend = :bottomleft
# # )
# # for whichOrder in 2:length(orders)
# # # order = 3
# #     for whichMethod in 1:length(methodNames)
# #         plot!(
# #             q,
# #             [orders[whichOrder-1];orders[whichOrder]],
# #             [
# #                 log10(errors_1[whichOrder-1][whichMethod]);
# #                 log10(errors_1[whichOrder][whichMethod])
# #             ],
# #             label = whichOrder == 2 && methodNames[whichMethod],
# #             colour = whichMethod,
# #             markershape = shapes[whichMethod],
# #         )
# #     end
# # end
# # display(q)

# lzB = SFFM.MakeLazyGenerator(model,dgmesh)

# lzB

# sum(abs.(lzB-B_DG))

# # using BenchmarkTools

# # @btime  SFFM.EulerDG( lzB, t, x0_DG, h = 0.0001)

ext: jl

max_stars_repo_name: angus-lewis/SFFM

max_issues_repo_name: angus-lewis/SFFM

max_forks_repo_name: angus-lewis/SFFM


text:
"""
	solve_particle_scattering_FMM(k0, kin, P, sp::ScatteringProblem, u::Einc, opt::FMMoptions; plot_res = false, get_inner = true, verbose = true) -> result, inner

Solve the scattering problem `sp` with outer wavenumber `k0`, inner wavenumber
`kin`, `2P+1` cylindrical harmonics per inclusion and incident TM field
`u`. Utilizes FMM with options `opt` to solve multiple-scattering equation.
Returns the cylindrical harmonics basis `beta` along with convergence data in
`result`. `inner` contains potential densities (in case of arbitrary inclusion)
or inner cylindrical coefficients (in case of circular).

`plot_res` controls plotting of the residual. Inner coefficients are calculated
only if `get_inner` is true, and timing is printed if `verbose` is true.
"""
function solve_particle_scattering_FMM(k0, kin, P, sp::ScatteringProblem, u::Einc, opt::FMMoptions; plot_res = false, get_inner = true, verbose = true)
	@assert opt.FMM "opt.FMM is disabled, set to true"
	shapes = sp.shapes;	ids = sp.ids; centers = sp.centers; φs = sp.φs
    Ns = size(sp)
    groups, boxSize = divideSpace(centers, opt)
    P2, Q = FMMtruncation(opt.acc, boxSize, k0)
    verbose && println("FMM solution timing:")
    dt0 = @elapsed begin
    	mFMM = FMMbuildMatrices(k0, P, P2, Q, groups, centers, boxSize, tri=true)
    end

    dt1 = @elapsed begin
    	scatteringMatrices,innerExpansions = particleExpansion(k0, kin, shapes, P, ids)
    end

    dt2 = @elapsed begin
	    #construct rhs
	    rhs = u2α(k0, u, centers, P)
	    for ic = 1:Ns
	        rng = (ic-1)*(2*P+1) .+ (1:2*P+1)
	        #see if there is a faster alternative
	        if φs[ic] == 0.0
	            rhs[rng] = scatteringMatrices[ids[ic]]*rhs[rng]
	        else
	            #rotate without matrix
	            rotateMultipole!(view(rhs,rng),-φs[ic],P)
	            rhs[rng] = scatteringMatrices[ids[ic]]*rhs[rng]
	            rotateMultipole!(view(rhs,rng),φs[ic],P)
	        end
	    end
	end

    pre_agg_buffer = zeros(Complex{Float64},Q,length(groups))
    trans_buffer = Array{Complex{Float64}}(undef, Q)
    dt3 = @elapsed begin
	    MVP = LinearMap{eltype(rhs)}((output_, x_) -> FMM_mainMVP_pre!(output_,
									x_, scatteringMatrices, φs, ids, P, mFMM,
									pre_agg_buffer, trans_buffer), Ns*(2*P+1),
									Ns*(2*P+1), ismutating = true)
	    result = gmres(MVP, rhs, restart = Ns*(2*P+1), tol = opt.tol, log = true) #no restart, preconditioning
    end

    if get_inner
        #recover full incoming expansion - in sigma_mu terms for parametrized shape,
        #in multipole expansion for circle
        dt4 = @elapsed begin
	        #find LU factorization once for each shape
	        scatteringLU = [lu(scatteringMatrices[i]) for i = 1:length(shapes)]
	        inner = Array{Vector{Complex{Float64}}}(undef, Ns)
	        α_c = Array{Complex{Float64}}(undef, 2*P+1)
	    	for ic = 1:Ns
	    		rng = (ic-1)*(2*P+1) .+ (1:2*P+1)
	            if typeof(shapes[ids[ic]]) == ShapeParams
	                if φs[ic] == 0.0
	                    α_c[:] = scatteringLU[ids[ic]]\result[1][rng]
	                else
	                    rotateMultipole!(α_c, view(result[1],rng), -φs[ic], P)
	                    ldiv!(scatteringLU[ids[ic]], α_c)
	                end
	        		inner[ic] = innerExpansions[ids[ic]]*α_c
	            else
	                inner[ic] = innerExpansions[ids[ic]]*result[1][rng]
	            end
	    	end
        end
    end

    if plot_res
        residual_ = MVP*result[1] - rhs
        println("last residual is empirically: $(norm(residual_)), but result[2].residuals[end] = $(result[2].residuals[end])")
        figure()
        semilogy(transpose(result[2].residuals))
    end
    if verbose
        println("FMM matrix construction: $dt0 s")
        println("Scattering matrix solution: $dt1 s")
        println("RHS construction: $dt2 s")
        println("Iterative process: $dt3 s")
        get_inner && println("Retrieving inner coefficients: $dt4 s")
    end
    get_inner ? (return result, inner) : (return result)
end


text:
"""
    Construct{T <: Number} <: Number

An abstract Cayley-Dickson construct.
"""
abstract type Construct{T <: Number} <: Number end

"""
    array(z::Construct) -> Array

Return an array with all the `Real` components of `z`.
"""
function array(z::Construct)
    vcat(real(z), unreal(z))
end

"""
    iszero(z::Construct) -> Bool

Return `true` if all `Real` components of `z` are zero.
"""
function iszero(z::Construct)
    iszero(array(z))
end

"""
    isreal(z::Construct) -> Bool

Return `true` if the unreal part of `z` is zero.
"""
function isreal(z::Construct)
    iszero(unreal(z))
end

"""
    (+)(z::Construct)

The identity operation on Cayley-Dickson constructs.
"""
function (+)(z::Construct)
    z
end

"""
    commutator(x::Construct, y::Construct)

Measure the failure of commutativity of the multiplication operation:
```julia
    (x * y) - (y * x)
```
If `commutator(x, y)` is zero, then the multiplication operation is commutative.
"""
function commutator(x::Construct, y::Construct)
    (x * y) - (y * x)
end

"""
    anti_commutator(x::Construct, y::Construct)

Measure the failure of anti-commutativity of the multiplication operation:
```julia
    (x * y) + (y * x)
```
If `anti_commutator(x, y)` is zero, then the multiplication operation is anti-commutative.
"""
function anti_commutator(x::Construct, y::Construct)
    (x * y) + (y * x)
end

"""
    associator(x::Construct, y::Construct, z::Construct)

Measure the failure of associativity of the multiplication operation:
```julia
    ((x * y) * z) - (x * (y * z))
```
If `associator(x, y, z)` is zero, then the multiplication operation is associative.
"""
function associator(x::Construct, y::Construct, z::Construct)
    ((x * y) * z) - (x * (y * z))
end

"""
    anti_associator(x::Construct, y::Construct, z::Construct)

Measure the failure of anti-associativity of the multiplication operation:
```julia
    ((x * y) * z) + (x * (y * z))
```
If `anti_associator(x, y, z)` is zero, then the multiplication operation is anti-associative.
"""
function anti_associator(x::Construct, y::Construct, z::Construct)
    ((x * y) * z) + (x * (y * z))
end

"""
    jacobiator(x::Construct, y::Construct, z::Construct)

Measure the failure of the multiplication operation to satisfy the Jacobi identity:
```julia
    ((x * y) * z) + ((z * x) * y) + ((y * z) * x)
```
If `jacobiator(x, y, z)` is zero, then the multiplication operation satisfies the Jacobi
identity.
"""
function jacobiator(x::Construct, y::Construct, z::Construct)
    ((x * y) * z) + ((z * x) * y) + ((y * z) * x)
end

"""
    alternatorL(x::Construct, y::Construct)

Measure the failure of the multiplication operation to be left-alternative:
```julia
    ((x * x) * y) - (x * (x * y))
```
If `alternatorL(x, y)` is zero, then the multiplication operation is left-alternative.
"""
function alternatorL(x::Construct, y::Construct)
    associator(x, x, y)
end

"""
    anti_alternatorL(x::Construct, y::Construct)

Measure the failure of the multiplication operation to be anti-left-alternative:
```julia
    ((x * x) * y) + (x * (x * y))
```
If `anti_alternatorL(x, y)` is zero, then the multiplication operation is anti-left-alternative.
"""
function anti_alternatorL(x::Construct, y::Construct)
    anti_associator(x, x, y)
end

"""
    alternatorR(x::Construct, y::Construct)

Measure the failure of the multiplication operation to be right-alternative:
```julia
    ((x * y) * y) - (x * (y * y))
```
If `alternatorR(x, y)` is zero, then the multiplication operation is right-alternative.
"""
function alternatorR(x::Construct, y::Construct)
    associator(x, y, y)
end

"""
    anti_alternatorR(x::Construct, y::Construct)

Measure the failure of the multiplication operation to be anti-right-alternative:
```julia
    ((x * y) * y) + (x * (y * y))
```
If `anti_alternatorR(x, y)` is zero, then the multiplication operation is anti-right-alternative.
"""
function anti_alternatorR(x::Construct, y::Construct)
    anti_associator(x, y, y)
end

"""
    flexator(x::Construct, y::Construct)

Measure the failure of the multiplication operation to be flexible:
```julia
    ((x * y) * x) - (x * (y * x))
```
If `flexator(x, y)` is zero, then the multiplication operation is flexible.
"""
function flexator(x::Construct, y::Construct)
    associator(x, y, x)
end

"""
    anti_flexator(x::Construct, y::Construct)

Measure the failure of the multiplication operation to be anti-flexible:
```julia
    ((x * y) * x) + (x * (y * x))
```
If `anti_flexator(x, y)` is zero, then the multiplication operation is anti-flexible.
"""
function anti_flexator(x::Construct, y::Construct)
    anti_associator(x, y, x)
end

"""
    inv(z::Construct)

Return the multiplicative inverse of a Cayley-Dickson construct.
If `z` is a zero divisor, then an `ErrorException` is thrown.
"""
function inv(z::Construct)
    if iszerodivisor(z)
        error(ZeroDivisorInverse)
    end

    conj(z) / quadrance(z)
end

"""
    (/)(x::Construct, y::Construct)

Naive right quotient of two Cayley-Dickson constructs.
Equivalent to multiplying `x` on the right by the inverse of `y`.
"""
function (/)(x::Construct, y::Construct)
    x * inv(y)
end

"""
    (\\)(y::Construct, x::Construct)

Naive left quotient of two Cayley-Dickson constructs.
Equivalent to multiplying `x` on the left by the inverse of `y`.
"""
function (\)(y::Construct, x::Construct)
    inv(y) * x
end

"""
    (/)(a::Real, z::Construct)

Equivalent to multiplying the inverse of `z` by `a`.
"""
function (/)(a::Real, z::Construct)
    a * inv(z)
end

"""
    (\\)(z::Construct, a::Real)

Equivalent to multiplying the inverse of `z` by `a`.
"""
function (\)(z::Construct, a::Real)
    inv(z) * a
end

"""
    convert(::Type{T}, z::Construct) where T <: Real

Convert a Cayley-Dickson construct to a real number.
If `z` is not real (i.e. has non-zero unreal part), then an `InexactError` is
thrown.
"""
function convert(::Type{T}, z::Construct) where T <: Real
    if !isreal(z)
        throw(InexactError())
    end

    convert(T, real(z))
end

"""
    convert(::Type{T}, z::T) where T <: Construct

The trivial conversion. Equivalent to the identity operation.
"""
function convert(::Type{T}, z::T) where T <: Construct
    z
end

"""
    convert(::Type{T}, a::Real) where T <: Construct

Convert a real number into a Cayley-Dickson construct.
"""
function convert(::Type{T}, a::Real) where T <: Construct
    T(a)
end


text:
for (func, elty) in [(:CLBlastSscal, Float32), (:CLBlastDscal, Float64),
                     (:CLBlastCscal, ComplexF32), (:CLBlastZscal, ComplexF64)]
    #TODO: (:CLBlastHscal, Float16)

    @eval function $func(n::Integer, alpha::$elty,
                         x_buffer::cl.CL_mem, x_offset::Integer, x_inc::Integer,
                         queue::cl.CmdQueue, event::cl.Event)
        err = ccall(
            ($(string(func)), libCLBlast),
            cl.CL_int,
            (Csize_t, $elty, Ptr{Cvoid}, Csize_t, Csize_t, Ptr{Cvoid}, Ptr{Cvoid}),
            n, alpha, x_buffer, x_offset, x_inc, Ref(queue), Ref(event)
        )
        if err != cl.CL_SUCCESS
            println(stderr, "Calling function $(string($func)) failed!")
            throw(cl.CLError(err))
        end
        return err
    end

    @eval function scal!(n::Integer, α::Number,
                         x::cl.CLArray{$elty}, x_inc::Integer;
                         queue::cl.CmdQueue=cl.queue(x))
        # output event
        event::cl.Event = cl.Event(C_NULL)
        alpha = convert($elty, α)

        $func(Csize_t(n), alpha,
              pointer(x), Csize_t(0), Csize_t(x_inc),
              queue, event)

        # wait for kernel
        cl.wait(event)

        x
    end

    @eval function scal!(α::Number,
                         x::cl.CLArray{$elty};
                         queue::cl.CmdQueue=cl.queue(x))
        scal!(length(x), α, x, 1, queue=queue)
    end

end


text:
const echo2 =  raw"""
       /==!/======ECHO==,==.==#
       |   |
$==>==@/==@/==<==#"""

@enum Direction left up right down

function snusp(datalength, progstring)
    stack = Vector{Tuple{Int, Int, Direction}}()
    data = zeros(datalength)
    dp = ipx = ipy = 1
    direction = right    # default to go to right at beginning

    lines = split(progstring, "\n")
    lmax = maximum(map(length, lines))
    lines = map(x -> rpad(x, lmax), lines)
    for (y, li) in enumerate(lines)
        if (x = findfirst("\$", li)) != nothing
            (ipx, ipy) = (x[1], y)
        end
    end

    instruction = Dict([('>', ()-> dp += 1),
        ('<', ()-> (dp -= 1; if dp < 0 running = false end)), ('+', ()-> data[dp] += 1),
        ('-', ()-> data[dp] -= 1), (',', ()-> (data[dp] = read(stdin, UInt8))),
        ('.', ()->print(Char(data[dp]))),
        ('/', ()-> (d = Int(direction); d += (iseven(d) ? 3 : 5); direction = Direction(d % 4))),
        ('\\', ()-> (d = Int(direction); d += (iseven(d) ? 1 : -1); direction = Direction(d))),
        ('!', () -> ipnext()), ('?', ()-> if data[dp] == 0 ipnext() end),
        ('@', ()-> push!(stack, (ipx, ipy, direction))),
        ('#', ()-> if length(stack) > 0 (ipx, ipy, direction) = pop!(stack) end),
        ('\n', ()-> (running = false))])

    inboundsx(plus) = (plus ? (ipx < lmax) : (ipx > 1)) ? true : exit(data[dp])
    inboundsy(plus) = (plus ? (ipy < length(lines)) : (ipy > 1)) ? true : exit(data[dp])
    function ipnext()
        if direction == right && inboundsx(true)     ipx += 1
        elseif direction == left && inboundsx(false) ipx -= 1
        elseif direction == down && inboundsy(true)  ipy += 1
        elseif direction == up && inboundsy(false)   ipy -= 1
        end
    end

    running = true
    while running
        cmdcode = lines[ipy][ipx]
        if haskey(instruction, cmdcode)
            instruction[cmdcode]()
        end
        ipnext()
    end
    exit(data[dp])
end

snusp(100, echo2)

max_stars_repo_name: ethansaxenian/RosettaDecode

max_issues_repo_name: ethansaxenian/RosettaDecode

max_forks_repo_name: ethansaxenian/RosettaDecode


text:
module RationalApproximations

import GenericSVD: svd!
#import GenericLinearAlgebra: qr, eigen
import LinearAlgebra: norm, Diagonal, qr, eigen
import Optim: optimize

export aaa_v1, aaa_v2, locate_extrema_idx, minimax

"""
Represents a rational function of type `(m,m)` in barycentric form.
"""
struct RationalFunc{T<:AbstractFloat}
    α::Vector{T}
    β::Vector{T}
    supp_pt::Vector{T}
end # module

function (r::RationalFunc{T})(x::T) where T <: AbstractFloat
    numer = zero(T)
    denom = zero(T)
    for k = 1:length(r.α)
        δ = x - r.supp_pt[k]
        if abs(δ) ≤ eps(x)
            numer = r.α[k]
            denom = r.β[k]
            break
        else
            numer += r.α[k] / δ
            denom += r.β[k] / δ
        end
    end
    return numer / denom
end

"""
    aaa_v1(F, S, max_m, tol) -> r, err

Adaptive Antoulas-Anderson algorithm computes rational approximations `r[m]`of
type `(m,m)` to a real function `f(x)` based on sample values `F[i] = f(S[i])`.
Stops if `err[m] < tol * norm(F, Inf)` or when `m` reaches `max_m`.

This is version 1 of the algorithm, for which `r[m]` interpolates `f` at the
support points based on `m` weights `w[m]` with `α[j] = w[j] * F[j]` and
`β[j] = w[j]`.
"""
function aaa_v1(F::Vector{T}, S::AbstractVector{T},
                    max_m::Integer, tol::T) where T <: AbstractFloat
    K = length(F)
    if length(S) ≠ K
        throw(DimensionMismatch("F and S must have the same length"))
    end
    avg_F = sum(F) / K
    R = fill(avg_F, K)
    J = collect(1:K)
    supp_pt = T[]
    f = T[]
    w = T[]
    err = T[]
    r = RationalFunc[]
    for m = 1:max_m
        val, i = findmax(abs.(F[J]-R[J]))
        j = J[i]
        push!(supp_pt, S[j])
        push!(f, F[j])
        J = remove(J, i)
        A = T[ (F[J[i]]-f[j])/(S[J[i]]-supp_pt[j]) for i=1:K-m, j=1:m ]
        Fact = svd!(A)
        w = Fact.V[:,m]
        α = w .* f
        β = w
        push!(r, RationalFunc(α, β, copy(supp_pt)))
        R[J] .= r[m].(S[J])
        push!(err, norm(F[J] - R[J], Inf))
        if err[m] < tol * norm(F, Inf)
            r = r[1:m]
            err = err[1:m]
            break
        end
    end
    return r, err
end

"""
    remove(J, i)

Returns the vector obtained from `J` by removing the `i`th element.
"""
function remove(J::Vector, i::Integer)
    m = length(J)
    if i ≤ 0 || i ≥ m+1
        throw(BoundsError(J, i))
    end
    return [J[1:i-1]; J[i+1:m]]
end

"""
    aaa_v1(F, S, max_m, tol) -> r, err

Adaptive Antoulas-Anderson algorithm computes rational approximations `r[m]`of
type `(m,m)` to a real function `f(x)` based on sample values `F[i] = f(S[i])`.
Stops if `err[m] < tol * norm(F, Inf)` or when `m` reaches `max_m`.

This is version 2 of the algorithm, for which the coefficients `α[j]` and `β[j]`
vary independently.
"""
function aaa_v2(F::Vector{T}, S::AbstractVector{T},
                    max_m::Integer, tol::T) where T <: AbstractFloat
    K = length(F)
    if length(S) ≠ K
        throw(DimensionMismatch("F and S must have the same length"))
    end
    avg_F = sum(F) / K
    R = fill(avg_F, K)
    J = collect(1:K)
    supp_pt = T[]
    supp_pt_idx = fill(-1, K)
    resid = F - R
    f = T[]
    w = T[]
    err = T[]
    r = RationalFunc[]
    buffer = Vector{T}(undef, K*2*max_m)
    for m = 1:max_m
        val, l = findmax(abs.(resid[1:K-m+1]))
        i = 0
        for i1 = 1:l
            i += 1
            if supp_pt_idx[i] ≥ 0
                i += 1
            end
        end
        supp_pt_idx[i] = m
        push!(supp_pt, S[i])
        push!(f, F[i])
        A = reshape(view(buffer, 1:(K-m)*2*m), K-m, 2m)
        for j = 1:m
            i1 = 0
            for i = 1:K
                if supp_pt_idx[i] ≤ 0
                    i1 += 1
                    A[i1,j]   = -1 / ( S[i] - supp_pt[j] )
                    A[i1,m+j] =  F[i] / ( S[i] - supp_pt[j] )
                end
            end
        end
        Fact = svd!(A)
        α = Fact.V[1:m,2m]
        β = Fact.V[m+1:2m,2m]
        push!(r, RationalFunc(α, β, copy(supp_pt)))
        i1 = 0
        for i = 1:K
            if supp_pt_idx[i] ≤ 0
                i1 += 1
                resid[i1] = F[i] - r[m](S[i])
            end
        end
        push!(err, norm(resid[1:K-m], Inf))
        if err[m] ≤ tol * norm(F, Inf)
            break
        end
    end
    return r, err
end

"""
    minimax(f, x, supp_pt, Interval, max_iterations, clamp) -> r, zmin, zmax
"""
function minimax(f::Function, x::Vector{T}, supp_pt::Vector{T},
                 Interval::Tuple{T,T}, max_iterations::Integer,
                 clamp=:no) where T <: AbstractFloat
    N = length(supp_pt)
    if length(x) ≠ 2N
        throw(DimensionMismatch("x must be twice as long as supp_pt"))
    end
    α = Vector{T}(undef, N)
    β = similar(α)
    δ = one(T)
    zmax = Vector{T}(undef, max_iterations)
    zmin = similar(zmax)
    r = Vector{RationalFunc{T}}(undef, max_iterations)
    for i = 1:max_iterations
        α, β, λ = equioscillation!(f, x, supp_pt, clamp)
        r[i] = RationalFunc(α, β, supp_pt)
        zmin[i], zmax[i] = locate_extrema!(x, Interval) do t
            return f(t) - r[i](t)
        end
        δ = zmax[i] - zmin[i]
        if δ ≤ 10*eps(zmax[i])
            zmax = zmax[1:i]
            zmin = zmin[1:i]
            r = r[1:i]
            break
        end
    end
    return r, zmin, zmax
end

"""
    locate_extrema_idx(resid, m)
"""
function locate_extrema_idx(resid::Vector{T},
                            m::Integer) where T <: AbstractFloat
    K = length(resid)
    idx = Int64[]
    push!(idx, 1)
    fwd = resid[2] - resid[1]
    σ = sign(fwd)
    for k = 2:K-1
        fwd = resid[k+1] - resid[k]
        if σ * sign(fwd) == -1.0
            push!(idx, k)
            σ = -σ
        end
    end
    push!(idx, K)
    len_idx = length(idx)
    if len_idx < 2m
        error("Found only $len_idx extrema; need $(2m)")
    elseif len_idx > 2m
        var = abs.(diff(resid[idx]))
        I = sortperm(var, rev=true)
        new_idx = [ idx[I[1:2m-1]]; idx[end] ]
        idx = sort(new_idx)
    end
    return idx
end

"""
    equioscillation!(f, x, supp_pt, clamp) -> α, β, λ
"""
function equioscillation!(f::Function, x::Vector{T},
                         supp_pt::Vector{T},
                         clamp::Symbol) where T <: AbstractFloat
    N = length(supp_pt)
    if length(x) ≠ 2N
        throw(DimensionMismatch("x must be twice as long as supp_pt"))
    end
    M = Matrix{T}(undef, 2N, N)
    for k = 1:N
        for l = 1:2N
            Mlk = one(T)
            for p = 1:k-1
                Mlk *= x[l] - supp_pt[p]
            end
            for p = k+1:N
                Mlk *= x[l] - supp_pt[p]
            end
            M[l,k] = Mlk
        end
    end
    d = Vector{T}(undef, 2N)
    for l = 1:2N
        Dl = one(T)
        for p = 1:l-1
            Dl *= x[l] - x[p]
        end
        for p = l+1:2N
            Dl *= x[l] - x[p]
        end
        d[l] = 1/sqrt(abs(Dl))
    end
    D = Diagonal(d)
    Fact = qr(D*M)
    Q1, R = Matrix(Fact.Q), Fact.R
    sgn = Vector{T}(undef, 2N)
    sgn[1] = -one(T)
    for l = 2:2N
        sgn[l] = -sgn[l-1]
    end
    S = Diagonal(sgn)
    F = Diagonal(f.(x))
    A = Q1' * ( S * F ) * Q1
    if clamp == :no
        EFact = eigen(A)
    else
        I0 = Diagonal(ones(2N))
        if clamp == :left
            I0[1,1] = zero(T)
        elseif clamp == :right
            I0[2N,2N] = zero(T)
        elseif clamp == :both
            I0[1,1] = zero(T)
            I0[2N,2N] = zero(T)
        else
            error("illegal value $clamp for argument clamp")
        end
        B = Q1' * I0 * Q1
        EFact = eigen(A, B)
    end
    y = EFact.vectors
    Q1y = Q1 * y
    q = D \ Q1y
    k_no_root = -1
    check_count = 0
    for k = 1:N
        no_root = true
        for l = 2:2N
            if sign(q[l,k]) != sign(q[1,k])
                no_root = false
            end
        end
        if no_root
            k_no_root = k
            check_count += 1
        end
    end
    if check_count ≠ 1
        error("Failed to find unique eigenpair with q≠0")
    end
    λ = EFact.values[k_no_root]
    if clamp == :no
        α = R \ ( Q1' * F * Q1y[:,k_no_root] )
    else
        α = R \ ( Q1' * (F-λ*I0*S) * Q1y[:,k_no_root] )
    end
    β = R \ y[:,k_no_root]
    return α, β, λ
end

"""
    locate_extrema!(resid, x, Interval) -> zmin, zmax
"""
function locate_extrema!(resid::Function, x::Vector{Float64},
                         Interval::Tuple{Float64,Float64})
    n = length(x)
    if resid(x[1]) < resid(x[2])
        sgn = 1
    else
        sgn = -1
    end
    res = optimize(Interval[1], x[2]) do t
        return sgn * resid(t)
    end
    x[1] = res.minimizer
    zmax = zmin = abs(resid(x[1]))
    for l = 2:n-1
        sgn = -sgn
        res = optimize(x[l-1], x[l+1]) do t
            return sgn * resid(t)
        end
        x[l] = res.minimizer
        zmax = max(zmax, abs(resid(x[l])))
        zmin = min(zmin, abs(resid(x[l])))
    end
    sgn = -sgn
    res = optimize(x[n-1], Interval[2]) do t
        return sgn * resid(t)
    end
    x[n] = res.minimizer
    zmax = max(zmax, abs(resid(x[n])))
    zmin = min(zmin, abs(resid(x[n])))
    return zmin, zmax
end

end # module

max_stars_repo_name: billmclean/RationalApproximations

max_issues_repo_name: billmclean/RationalApproximations

max_forks_repo_name: billmclean/RationalApproximations


text:
using ModelTES, Interpolations

type InterpolatedRIT{T} <: ModelTES.AbstractRIT
  interpolator::T
end

T = collect((100:0.1:106)/1000)
slopes = ones(length(T)-1)
slopes[1:2]=0
# slopes[4:5]=1.1
slopes[17:20]=1.3
R = cumsum(slopes.*diff(T))
push!(R,R[end])
R*=0.01/R[end]
a=interpolate((T,),R,Gridded(Linear()))

ModelTES.R(I, T, RIT::InterpolatedRIT, Tc, Rn) = RIT.interpolator[T,I]
ModelTES.transitionwidth(RIT::InterpolatedRIT) = std(T)
p = ModelTES.TESParams(
3.3, #n
mean(T), #Tc
0.07, #Tbath
3.5e-9, #k
10e-13, #C
1.5e-7, #L
0.00035, #Rl
0.0, #Rp
R[end], #Rn
InterpolatedRIT(a), #RIT
)

bt = BiasedTES(p, p.Rn*0.15)
ih = ModelTES.IrwinHiltonTES(bt)

function alpha(p::ModelTES.TESParams, T)
  f(x) = ModelTES.R(0, x[1], bt.p)
  r = ModelTES.R(0,T,bt.p)
  drdt = ForwardDiff.gradient(f, [T])
  alpha = drdt[1]*T/r
end

using PyPlot
Ts = linspace(bt.T0,maximum(T),100)
plot(Ts, [alpha(bt.p,t) for t in Ts])
plot(bt.T0, ih.alpha,"o")
xlabel("T (K)")
ylabel("α")
function pulsefb(energy, bt=bt)
  r=ModelTES.rk8(40000,1e-7,bt,energy,100)
  fb = -(r.I-r.I[1])
  fb
end
# function maxt(energy, bt=bt)
#   r=ModelTES.pulse(4000,1e-6,bt,energy,100)
#   maximum(r.T)
# end
energies = 1:100:10000
pulses = pulsefb.(energies)
# maxts = maxt.(energies)
tstarts = bt.T0+(energies./p.C*ModelTES.J_per_eV)
alphas = [alpha(bt.p,t) for t in tstarts]
av = mean(pulses)
fv = [dot(av,pulse) for pulse in pulses]

figure()
for j = 10:10:100
  plot(pulses[j])
end
""

using HDF5
h5 = h5open("out","w")
h5["energies"]=collect(energies)
h5["filt_value"]=fv
close(h5)


text:
using Filetimes
using Test
using Dates

filetime()

@test filetime(Dates.DateTime(1601, 1, 1)) == 0
@test filetime(Dates.DateTime(1601, 1, 2)) == convert(UInt64, 24 * 60 * 60 * 1000 * 1000 * 10)

@test Dates.year(Filetimes.datetime(131259265027478363)) == 2016

x = now()
@test Dates.year(Filetimes.datetime(Filetimes.filetime(x))) == Dates.year(x)


text:
# ------------------------------------------------------------------
# Licensed under the MIT License. See LICENSE in the project root.
# ------------------------------------------------------------------

"""
    BallPartition(radius; metric=Euclidean())

A method for partitioning spatial objects into balls of a given
`radius` using a `metric`.
"""
struct BallPartition{T,M} <: SPredicatePartitionMethod
  radius::T
  metric::M
end

BallPartition(radius::T; metric::M=Euclidean()) where {T,M} =
  BallPartition{T,M}(radius, metric)

(p::BallPartition)(x, y) = evaluate(p.metric, x, y) < p.radius


text:
using LCIO
using StatsPlots

kaonTimes = Float64[]
pionTimes = Float64[]
LCIO.open("ssReco_1000.slcio") do reader
	for (iEvent, event) in enumerate(reader)
    	coll = getCollection(event, "ECalBarrelHits")
		decode = CellIDDecoder(coll)
        for hit in coll
			layer = decode(hit)["layer"]
			if layer != 0
				continue
			end
			for i=1:LCIO.getNMCContributions(hit)
				pdgID = abs(getPDG(LCIO.getParticleCont(hit, i)))
				if pdgID == 321
					push!(kaonTimes, LCIO.getTimeCont(hit, i))
				elseif pdgID == 211
					push!(pionTimes, LCIO.getTimeCont(hit, i))
				end
			end
		end
		if iEvent % 500 == 0
			println("processed ", iEvent, " events")
		end
	end
end

plot(kaonTimes, seriestype=:stephist, label="K", bins=0:0.1:10, normalize=true)
plot!(pionTimes, seriestype=:stephist, label="pi", bins=0:0.1:10, normalize=true)
savefig("layer0times.png")

max_stars_repo_name: jstrube/LCTutorials

max_issues_repo_name: jstrube/LCTutorials

max_forks_repo_name: jstrube/LCTutorials


text:
using Clang.Generators
using Clang.LibClang.Clang_jll

cd(@__DIR__)

const INCLUDE_DIR = normpath(Clang_jll.artifact_dir, "include")
const CLANG_C_DIR = joinpath(INCLUDE_DIR, "clang-c")

options = load_options(joinpath(@__DIR__, "generator.toml"))

# add compiler flags
args = get_default_args()
push!(args, "-I$INCLUDE_DIR")

headers = detect_headers(CLANG_C_DIR, args)

# add extra definition
@add_def time_t AbstractJuliaSIT JuliaCtime_t Ctime_t

# create context
ctx = create_context(headers, args, options)

# build without printing so we can do custom rewriting
build!(ctx, BUILDSTAGE_NO_PRINTING)

# custom rewriter
function rewrite!(e::Expr)
    Meta.isexpr(e, :function) || return e
    # Add deprecated warning to some functions
    #   ref: [Remove unused CompilationDatabase::MappedSources](https://reviews.llvm.org/D32351)
    fname = e.args[1].args[1]
    deprecated_func = [
        # :clang_CompileCommand_getNumMappedSources, # not export
        :clang_CompileCommand_getMappedSourcePath,
        :clang_CompileCommand_getMappedSourceContent,
    ]

    if e.head == :function && fname in deprecated_func
        msg = """
        `$fname` Left here for backward compatibility.
        No mapped sources exists in the C++ backend anymore.
        This function just return Null `CXString`.
        See:
        - [Remove unused CompilationDatabase::MappedSources](https://reviews.llvm.org/D32351)
        """
        insert!(e.args[2].args, 1, Expr(:macrocall, Symbol("@warn"), :Base, msg))
    end
    return e
end

function rewrite!(dag::ExprDAG)
    for node in get_nodes(dag)
        for expr in get_exprs(node)
            rewrite!(expr)
        end
    end
end

rewrite!(ctx.dag)

# print
build!(ctx, BUILDSTAGE_PRINTING_ONLY)


text:
using DirectDetections, Distributions
using MCMCChains

# Create a function mapping (age_Myr, mass_Mjup) -> temp_K
const cooling_tracks = sonora_cooling_interpolator()

# Create functions mapping (temp_K, mass_Mjup) -> absolute magnitude
const sonora_temp_mass_Z = sonora_photometry_interpolator(:MKO_Z)
const sonora_temp_mass_J = sonora_photometry_interpolator(:MKO_J)
const sonora_temp_mass_L = sonora_photometry_interpolator(:Keck_L′)

##
@named f = DirectDetections.Planet(
    Priors(
        τ = Uniform(0, 1),
    ),
    # Flux will be calculated from planet mass and system age
    Derived(
        e = Returns(0),
        i = Returns(deg2rad(30)),
        ω = Returns(0),
        Ω = Returns(deg2rad(90)),
        a = (sys,pl) -> ∛((0.5sys.P1)^2),
        mass = (sys,pl) -> sys.mass,
    ),
)

@named e = DirectDetections.Planet(
    Priors(
        τ = Uniform(0, 1),
    ),
    # Flux will be calculated from planet mass and system age
    Derived(
        e = Returns(0),
        i = Returns(deg2rad(30)),
        ω = Returns(0),
        Ω = Returns(deg2rad(90)),
        a = (sys,pl) -> ∛(sys.P1^2),
        mass = (sys,pl) -> sys.mass,
    ),
)

@named d = DirectDetections.Planet(
    Priors(
        τ = Uniform(0, 1),
    ),
    # Flux will be calculated from planet mass and system age
    Derived(
        e = Returns(0),
        i = Returns(deg2rad(30)),
        ω = Returns(0),
        Ω = Returns(deg2rad(90)),
        a = (sys,pl) -> ∛((2sys.P1)^2),
        mass = (sys,pl) -> sys.mass,
    ),
)

@named c = DirectDetections.Planet(
    Priors(
        τ = Uniform(0, 1),
    ),
    # Flux will be calculated from planet mass and system age
    Derived(
        e = Returns(0),
        i = Returns(deg2rad(30)),
        ω = Returns(0),
        Ω = Returns(deg2rad(90)),
        a = (sys,pl) -> ∛((4sys.P1)^2),
        mass = (sys,pl) -> sys.mass,
    ),
)

@named b = DirectDetections.Planet(
    Priors(
        τ = Uniform(0, 1),
    ),
    # Flux will be calculated from planet mass and system age
    Derived(
        e = Returns(0),
        i = Returns(deg2rad(30)),
        ω = Returns(0),
        Ω = Returns(deg2rad(90)),
        a = (sys,pl) -> ∛((8sys.P1)^2),
        mass = (sys,pl) -> 0.5*sys.mass,
    ),
)

@named HR8799 = System(
    Priors(
        # age = TruncatedNormal(40, 15, 5, Inf),
        # age = Uniform(5, 100),
        μ = Normal(1.5, 0.05),
        plx = gaia_plx(gaia_id=2832463659640297472),
        # mass = Uniform(0.6, 75),
        mass = TruncatedNormal(7,1,0,Inf),
        P1 = Uniform(40, 100)
    ),
    ProperMotionAnomHGCA(gaia_id=2832463659640297472),
    f, e, d, c, b
)

##
chains = DirectDetections.hmc(
    HR8799, 0.85,
    MCMCThreads(),
    num_chains=4,
    adaptation =   1_000,
    iterations = 30_000,
)

##

# Histograms
margin_hist(chains, "e[a]", "e[τ]"; color=:grey)

##
margin_hist(chains, "d[a]", "mass"; color=:grey)

##
margin_hist(chains, "e[a]", "mass"; color=:grey)
margin_hist(chains, "d[a]", "mass"; color=:grey)

##

fig =  Figure(resolution=(700,700))
ax_hist = Axis(
    fig[1,1],
    ylabel="posterior density",
    xlabel="e[a]",
)
hideydecorations!(ax_hist)
hist_prop!(ax_hist, chains["e[a]"], color=:black, label="e[a]")
hist_prop!(ax_hist, chains["f[a]"], color=:red, label="f[a]")
Legend(fig[1,2], ax_hist)
xlims!(ax_hist, low=0)
fig
##
plot_all(chains)


text:
using ConstructionBase
using Test

struct Empty end
struct AB{A,B}
    a::A
    b::B
end

@testset "constructorof" begin
    @test constructorof(Empty)() === Empty()
    @inferred constructorof(AB{Int, Int})
    @test constructorof(AB{Int, Int})(1, 2) === AB(1,2)
    @test constructorof(AB{Int, Int})(1.0, 2) === AB(1.0,2)
    @test constructorof(typeof((a=1, b=2)))(1.0, 2) === (a=1.0, b=2)
    @test constructorof(NamedTuple{(:a, :b)})(1.0, 2) === (a=1.0, b=2)
    @test constructorof(Tuple)(1.0, 2) === (1.0, 2)
    @test constructorof(Tuple{Nothing, Missing})(1.0, 2) === (1.0, 2)
end

@testset "setproperties" begin
    o = AB(1,2)
    @test setproperties(o, (a=2, b=3))   === AB(2,3)
    @test setproperties(o, (a=2, b=3.0)) === AB(2,3.0)
    @test setproperties(o, a=2, b=3.0) === AB(2,3.0)

    res = @test_throws ArgumentError setproperties(o, (a=2, this_field_does_not_exist=3.0))
    msg = sprint(showerror, res.value)
    @test occursin("this_field_does_not_exist", msg)
    @test occursin("overload", msg)
    @test occursin("ConstructionBase.setproperties", msg)

    res = @test_throws ArgumentError setproperties(o, a=2, this_field_does_not_exist=3.0)
    msg = sprint(showerror, res.value)
    @test occursin("this_field_does_not_exist", msg)
    @test occursin("overload", msg)
    @test occursin("ConstructionBase.setproperties", msg)

    @test setproperties(Empty(), NamedTuple()) === Empty()
    @test setproperties(Empty()) === Empty()

    @test setproperties((a=1, b=2), (a=1.0,)) === (a=1.0, b=2)
    @test setproperties((a=1, b=2), a=1.0) === (a=1.0, b=2)

    @inferred setproperties(o, a=2, b=3.0)
    @inferred setproperties(Empty(), NamedTuple())
    @inferred setproperties((a=1, b=2), a=1.0)
    @inferred setproperties((a=1, b=2), (a=1.0,))
end


text:
using Blio

"""
    subarray_name(grh::GuppiRaw.Header)

Get subarray name from Header, default to "array_1" if missing.
"""
function subarray_name(grh::GuppiRaw.Header)
    get(grh, :subarray, "array_1")
end

"""
    starttime(grh::GuppiRaw.Header)

Calculate starttime from Header in seconds since the Unix epoch.
"""
function starttime(grh::GuppiRaw.Header)
    # Calc seconds per block
    secs_per_blk = grh[:tbin] * ntime(grh)

    # Calc seconds per PKTIDX
    secs_per_pktidx = secs_per_blk / grh[:piperblk]

    # Calc seconds from SYNCTIME to PKTSTART
    secs_since_synctime = grh[:pktstart] * secs_per_pktidx

    # Return seconds from UNIX epoch to PKTSTART
    grh[:synctime] + secs_since_synctime
end

"""
    obsid(grh::GuppiRaw.Header, telescope)

Get OBSID from `grh`, using `telescope` as the telescope component.
"""
function obsid(grh::GuppiRaw.Header, telescope)
    subname = subarray_name(grh)
    timestamp = Libc.strftime("%Y%m%dT%H%M%SZ", starttime(grh))
    join((telescope, subname, timestamp), ':')
end

"""
    obsid(grh::GuppiRaw.Header)

Get OBSID from `grh`.
"""
function obsid(grh::GuppiRaw.Header)
    telescope = lowercase(get(grh, :telescop, "MeerKAT"))
    obsid(grh, telescope)
end

"""
    instrument(grh::GuppiRaw.Header)

Get instrumwnt from `grh[:instrmnt]`, defaulting to "bluse" if missing.
"""
function instrument(grh::GuppiRaw.Header)
    get(grh, :instrmnt, "bluse")
end

"""
    fch1(grh::guppiraw.header)

Get frequency of first channel of entire band (not just grh's sub-band) in GHz.
"""
function fch1(grh::GuppiRaw.Header)
    (chanfreq(grh, 1) - grh[:schan] * grh[:chan_bw]) / 1e3
end

"""
    fch1(grh::guppiraw.header)

Get coarse channel frequency step size (aka width) in GHz.
"""
function foff(grh::GuppiRaw.Header)
    grh[:chan_bw] / 1e3
end

"""
    ra(grh::guppiraw.header)

Get right ascension from `grh` in radians.
"""
function ra(grh::GuppiRaw.Header)
    deg2rad(grh[:ra])
end

"""
    dec(grh::guppiraw.header)

Get declination from `grh` in radians.
"""
function dec(grh::GuppiRaw.Header)
    deg2rad(grh[:dec])
end


text:
printstyled(stdout,"  show\n", color=:light_green)

# SeisChannel show
S = SeisData()
C = randSeisChannel()
C.fs = 100.0
nx = (1, 2, 3, 4, 5, 10, 100, 10000)
C.t = Array{Int64,2}(undef, 0, 2)
C.x = Float32[]
push!(S, C)
redirect_stdout(out) do
  for i in nx
    C.t = [1 0; i 0]
    C.x = randn(Float32, i)
    show(C)
    push!(S, C)
  end
  show(S)
end

redirect_stdout(out) do
  # show
  show(breaking_seis())
  show(randSeisData(1))
  show(SeisChannel())
  show(SeisData())
  show(randSeisChannel())
  show(randSeisData(10, c=1.0))

  # summary
  summary(randSeisChannel())
  summary(randSeisData())

  # invoke help-only functions
  seed_support()
  mseed_support()
  dataless_support()
  resp_wont_read()
  @test web_chanspec() == nothing
end


text:
using GameOfLife
using Test

@testset "rules.jl" begin
    A = GameOfLife.default_state()

    @test GameOfLife.neighborhood(A, CartesianIndex(62, 62)) == [1 1 0; 0 1 1; 0 1 0]

    @test GameOfLife.liferule(A, CartesianIndex(62, 62)) == 0

    @test GameOfLife.liferule([1 1 1; 0 0 1; 0 1 1], CartesianIndex(2, 2)) == 0

    @test GameOfLife.next(A) == (
        B = GameOfLife.default_state(); B[61:63, 61:63] = [1 1 1; 0 0 1; 0 1 1;];
        B
    )
end

max_stars_repo_name: VasanthManiVasi/Conways-Game-of-Life

max_issues_repo_name: VasanthManiVasi/Conways-Game-of-Life

max_forks_repo_name: VasanthManiVasi/Conways-Game-of-Life


text:
### A Pluto.jl notebook ###
# v0.17.1

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
        el
    end
end

# ╔═╡ c29521d1-6563-4c9f-9d06-656eb8b98a6f
begin
	using PlutoUI # user-interface do Pluto.jl
	using Plots   # Julia package para gráficos

end

# ╔═╡ c0e4d750-b9a4-11eb-2e0c-edaeaaf3f36a
html"<button onclick='present()'>present</button>"

# ╔═╡ 606ac8d7-7cd6-4da3-b83f-9889f6883190
md"""
# Máquina síncrona trifásica
Máquina síncrona sobre rede de potência infinita, (**pólos lisos**)
## Exercício sobre curvas "V" (curvas de Mordey)
"""

# ╔═╡ 4c9ce872-1164-4c7f-9a26-3af89b345c41
md"""
É dado um alternador síncrono sobre rede de potência infinita $$(U_f=200\mathrm V, f=50\mathrm Hz)$$ com $$X_s=4\Omega$$ e $$R_s\thickapprox 0\Omega$$.
"""

# ╔═╡ 9b3e08e0-7207-4099-96e4-c6e1e9892a1f
md"""
## a) Análise vectorial 💻

**Traçar as rectas de potência activa e reactiva correspondentes a:**

$$0;\quad 5;\quad 10;\quad 15;\quad 20;\quad \mathrm {kW, kVAr}$$

"""

# ╔═╡ 159419d5-0555-43a0-8320-9cb51e0b05ba
md"""
Conforme se verificou anteriormente, no traçado do diagrama P-Q para um alternador síncrono (Exercício 2), no diagrama vectorial de tensões, o vector da queda de tensão na reactância síncrona, $$jX_s\overline I$$, pode ser transformado no vector de potência aparente, $$\overline S= P+ jQ$$, se multiplicarmos por um factor de escala constante: $$\frac{3U}{X_s}$$.

Desta forma, a posição dos afixos dos vectores, $$jX_s\overline I$$ ou $$\overline{E}_0$$, representam, adequando a escala para potências, o ponto de funcionamento da máquina, $$(Q, P)$$, num sistemas de eixos de potência activa e reactiva representados a partir do afixo do vector da tensão, $$\overline U$$:
"""

# ╔═╡ df708c4d-443b-4190-b72d-779c4e1e1bb1
begin
	H1=("P", @bind P PlutoUI.Slider(0:5.0e3:20e3, default=0,show_value=true))
	H2=("Q", @bind Q PlutoUI.Slider(-20e3:5.0e3:20e3, default=0, show_value=true))
	H4=("linhas de Q constante", @bind z2 CheckBox())
	H3=("linhas de P constante", @bind z1 CheckBox())
	H1, H2, H4, H3
end

# ╔═╡ 66de4e49-ede7-44d1-b7b4-49ecb3ec2e53

# ╔═╡ 3d8c7f7e-e765-41d9-8191-aef5e52984fc
md"""
## b) Curvas "V"  💻

**Traçar as curvas em V das potências requeridas.**
"""

# ╔═╡ db0fc7c2-9e8c-415f-95c1-686dbfc56347
md"""
O traçado das curvas em "V", ou curvas de Mordey, corresponde a uma representação do mapa de funcionamento da máquina síncrona, traduzido num conjunto de isolinhas para a potência activa, que relacionam diferentes pares de valores $$(I_{exc}, I)$$ ou $$(E_0, I)$$ representando diferentes factores de potência.

Assim, partindo do diagrama vectorial de tensões, para os pontos de funcionamento $$(Q, P)$$ sobre a mesma linha de potência activa, são registados consecutivamente os pares de valores relativos aos módulos dos vectores da fem e da corrente do estator, $$E_0$$ e $$I$$.

Repare-se que para $$P=0\mathrm W$$, $$(I\cos\varphi=0)$$, verifica-se que os vectores de tensão: $$\overline U, jX_s\overline I$$ e $$\overline E_0$$ são colineares (estão em fase), por conseguinte:
"""

# ╔═╡ 6a1ee842-a2f1-4810-83d7-5ce931c47891
md"""
Como alternador, de: $$\quad\overline{E}_0=\overline{U}+jX_s\overline{I}\quad$$ tém-se,

$$E_0=U+X_sI \quad\mathrm{se} \quad\varphi = -90° \Rightarrow E_0>U$$

$$E_0=U-X_sI \quad\mathrm{se} \quad\varphi = +90° \Rightarrow U>E_0$$

o que resulta nas duas rectas representadas no gráfico em $$P=0\mathrm W$$, representadas pelas equações:

$$I=\frac{1}{X_s}E_0-\frac{1}{X_s}U \quad\mathrm{para} \quad\varphi = -90°$$

$$I=-\frac{1}{X_s}E_0+\frac{1}{X_s}U \quad\mathrm{para} \quad\varphi = +90°$$

"""

# ╔═╡ 19822397-18c5-4a88-bac1-f3adbfd2b235
#begin
#	p2 = contour(c_cosφ)
#	plot(p2)
#end

# ╔═╡ 594360d4-9bb8-4756-8f40-a5f0f9555aba
md"""
Assinale-se também para $$Q=0\mathrm {VAr}$$, $$(I\sin\varphi=0)$$, que a corrente do estator terá o valor mais baixo em cada isolinha de potência activa. Esses pontos de funcionamento são designados por **pontos de excitação óptima**.
"""

# ╔═╡ 1b4d9fbd-be46-416a-a1fe-163f5a0b37a3
md"""
!!! nota
	O estudante deverá procurar perceber onde se encontram os modos sobreexcitado e subexcitado, nos regimes de funcionamento alternador e motor, bem como os casos particulares da máquina a funcionar em vazio como compensador síncrono.
"""

# ╔═╡ 5db1fd70-0bf9-462b-b6d3-bfc3ed8890cb

# ╔═╡ 89222965-d320-4a46-a11a-b66b2ed9c11d
md"""
# Setup
"""

# ╔═╡ 750b6ab7-0b11-4b91-be34-ab7426625204
md"""
## Notação polar $$\angle$$. $$\quad$$ Operador $$j$$ $$\quad$$
"""

# ╔═╡ 026c8f3e-8ecd-459f-b496-511c38065cc6
begin
	∠(x) = cis(deg2rad(x))
	j(x) = (x)*im
end;

# ╔═╡ fb03a3aa-f94b-4b73-a21b-f05bc548dd9d
begin
	Xₛ=4
	U=200.0
	U_=(U)∠(0)
	Icosφ=P/(3U)
	Isenφ=-Q/(3U)
	I_=(Icosφ)+j(Isenφ)
	S_=P+j(Q)
	E₀_=U_+j(Xₛ)*I_
	S_, I_, E₀_
end

# ╔═╡ 41eac123-fa10-42c3-a801-8fb5f7bce7ae
begin
# eixos: kW, kVAr
	plot([0+j(0), 400+j(0)],
		label="eixo de potência reactiva (VAr)", arrow=:head,
		linecolor=:black, linewidth=2)
	plot!([200-j(200), 200+j(200)],
		label="eixo de potência activa (W)", arrow=:head,
		linestyle=:dash, linecolor=:black, linewidth=2)

# diagrama vectorial de tensões
	K=3 # para tornar a corrente visível na escala de tensões
	plot!([0, U_], arrow=:closed,
		legend=:bottomright, label="U∠0°", linewidth=2, linecolor=:blue)
	plot!([0, K*I_], arrow=:closed,
		label="I∠φ", linewidth=2, linecolor=:red)
	plot!([U_, U_+j(Xₛ)*I_], arrow=:closed,
		label="XₛI∠(φ+90°)", linewidth=2, linecolor=:purple)
	plot!([0, E₀_], arrow=:closed,
		minorticks=5, label="E₀∠δ", linewidth=2,
		ylims=(-200,200), xlims=(0,400),size=(600,600) )

# lugar geométrico de Q constante
	φ_locus=-90:1:90
	φ_locus=deg2rad.(φ_locus)
	I=abs(I_)
	φ=atan(-Q/(P+0.001))
	Isinφ_Qlocus_=K*I*cos.(φ_locus).+j(K*I*sin(φ))
	plot!(z2*Isinφ_Qlocus_,
		linestyle=:dash, linecolor=:blue, label="linha Isinφ constante")
	δ_locus=0:1:90
	δ_locus=deg2rad.(δ_locus)
	E₀=abs(E₀_)
	δ=angle(E₀_)
	E₀Q_locus_=E₀*cos(δ).+j.(E₀*sin.(δ_locus))
	plot!(z2*E₀Q_locus_,
		linestyle=:dashdot, linecolor=:blue, label="linha de E₀cosδ constante")

# lugar geométrico de P constante
	Isinφ_Plocus_=K*I*cos(φ).+j(K*I*sin.(φ_locus))
	plot!(z1*Isinφ_Plocus_,
		linestyle=:dash, label="linha de Icosφ constante", linecolor=:red)
	E₀P_locus_=E₀.*cos.(δ_locus).+j(E₀*sin(δ))
	plot!(z1*E₀P_locus_,
		linestyle=:dashdot, linecolor=:red, label="linha de E₀sinδ constante")
end

# ╔═╡ d2ed65c3-24e3-42ee-ac6e-f743ef4b584d
begin
	#import GR
	Pᵥ=[0, 5, 10, 15, 20]
	Qᵥ=[-20, -15, -10, -5, 0, 5, 10, 15, 20]
	#Iᵥcosφ, Iᵥsinφ
	Iᵥcosφ=Pᵥ.*1e3./(3U)
	Iᵥsinφ=transpose(Qᵥ.*1e3./(3U))

	#Inicialização de matrizes:
	Iᵥ_=zeros(ComplexF64, 5, 9)
	E₀₁_=zeros(ComplexF64, 5, 9)
	Iᵥ=zeros(5,9)
	φᵥ=zeros(5,9)
	P₁=zeros(5,9)
	c_cosφ=zeros(5,9)
	E₀₁=zeros(5,9)
	#δᵥ=zeros(5,9)
	for l in 1:5
		for c in 1:9
			Iᵥ_[l,c]=Iᵥcosφ[l,1]+j(Iᵥsinφ[1,c])
			Iᵥ[l,c]=abs(Iᵥ_[l,c])
			φᵥ[l,c]=angle(Iᵥ_[l,c])
			P₁[l,c]=3*U*Iᵥ[l,c]*cos(φᵥ[l,c])
			#c_cosφ[l,c]=cos(φᵥ[l,c])
			E₀₁_[l,c]=(U)∠(0)+j(Xₛ*Iᵥ_[l,c])
			E₀₁[l,c]=abs(E₀₁_[l,c])
			#δᵥ[l,c]=angle(E₀₁_[l,c])
			#δᵥ[l,c]=rad2deg(δᵥ[l,c])
		end
	end
	plot(E₀₁[1,:],Iᵥ[1,:],
		legend=:bottomright, label="P=0kW", linewidth=2,
		xlabel = "E₀(V)", ylabel="I(A)",)
	plot!(E₀₁[2,:],Iᵥ[2,:], label="P=5kW", linewidth=2)
	plot!(E₀₁[3,:],Iᵥ[3,:], label="P=10kW", linewidth=2)
	plot!(E₀₁[4,:],Iᵥ[4,:], label="P=15kW", linewidth=2)
	plot!(E₀₁[5,:],Iᵥ[5,:], label="P=20kW", linewidth=2)
	plot!([E₀], [I], markershape=:circle,markersize=7, label="Ponto (P, Q)")
end

# ╔═╡ f559622d-8bb3-4068-a4a8-b4f561960da1
md"""
## Índice
"""

# ╔═╡ e4374691-885a-487e-bee5-dac9092dd567
TableOfContents(title="📚 Índice, Exercício sobre curvas V")

# ╔═╡ 995e0deb-8044-4cd8-b802-0bda0ce093e3
md"""
!!! info
	No índice deste *notebook*, os tópicos assinalados com "💻" permitem interacção com o utilizador.
"""

# ╔═╡ 773eb541-f02a-4d61-8d20-9c79a49f6d85
md"""
## _Julia packages_
*Links to package help*: [Plots](http://docs.juliaplots.org/latest/), [PlutoUI](https://juliahub.com/docs/PlutoUI/abXFp/0.7.6/)
"""

# ╔═╡ acb69a29-d406-4f43-ab59-37c4516a460a
md"""
!!! info
	## Programação _Julia_ e _notebooks Pluto_
	Saber mais sobre: [_Julia_/_Pluto_](https://github.com/Ricardo-Luis/notebooks/blob/main/ME2/README.md)
"""

# ╔═╡ c5058f6d-d489-4308-b010-472ae048a6a7
version=VERSION;

# ╔═╡ 50da3fc1-b450-4c56-b179-1e6c36af7265
md"""
## _Notebook_

*Notebook* realizado em linguagem de programação *Julia* versão $(version) para a unidade curricular de Máquinas Elétricas 2 (ISEL\LEE).

Tempo de cálculo do *notebook* (1ª execução): até cerca de 5 min.

**Ricardo Luís** (Professor Adjunto, ISEL\DEEEA\GDME) \
ISEL, 29/Nov/2021
"""

# ╔═╡ da4138d9-2723-4274-8bd1-a0c9a89c1163
md"""
Este conteúdo possui licença [![](https://img.shields.io/badge/License-CC%20BY--SA%204.0-lightgrey.svg)](http://creativecommons.org/licenses/by-sa/4.0/).
"""

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"

[compat]
Plots = "~1.24.2"
PlutoUI = "~0.7.20"
"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised

[[AbstractPlutoDingetjes]]
deps = ["Pkg"]
git-tree-sha1 = "0bc60e3006ad95b4bb7497698dd7c6d649b9bc06"
uuid = "6e696c72-6542-2067-7265-42206c756150"
version = "1.1.1"

[[Adapt]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7"
uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
version = "3.3.1"

[[ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"

[[Artifacts]]
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"

[[Base64]]
uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"

[[Bzip2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2"
uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
version = "1.0.8+0"

[[Cairo_jll]]
deps = ["Artifacts", "Bzip2_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "f2202b55d816427cd385a9a4f3ffb226bee80f99"
uuid = "83423d85-b0ee-5818-9007-b63ccbeb887a"
version = "1.16.1+0"

[[ChainRulesCore]]
deps = ["Compat", "LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "f885e7e7c124f8c92650d61b9477b9ac2ee607dd"
uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
version = "1.11.1"

[[ChangesOfVariables]]
deps = ["LinearAlgebra", "Test"]
git-tree-sha1 = "9a1d594397670492219635b35a3d830b04730d62"
uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
version = "0.1.1"

[[ColorSchemes]]
deps = ["ColorTypes", "Colors", "FixedPointNumbers", "Random"]
git-tree-sha1 = "a851fec56cb73cfdf43762999ec72eff5b86882a"
uuid = "35d6a980-a343-548e-a6ea-1d62b119f2f4"
version = "3.15.0"

[[ColorTypes]]
deps = ["FixedPointNumbers", "Random"]
git-tree-sha1 = "024fe24d83e4a5bf5fc80501a314ce0d1aa35597"
uuid = "3da002f7-5984-5a60-b8a6-cbb66c0b333f"
version = "0.11.0"

[[Colors]]
deps = ["ColorTypes", "FixedPointNumbers", "Reexport"]
git-tree-sha1 = "417b0ed7b8b838aa6ca0a87aadf1bb9eb111ce40"
uuid = "5ae59095-9a9b-59fe-a467-6f913c188581"
version = "0.12.8"

[[Compat]]
deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
git-tree-sha1 = "dce3e3fea680869eaa0b774b2e8343e9ff442313"
uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
version = "3.40.0"

[[CompilerSupportLibraries_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"

[[Contour]]
deps = ["StaticArrays"]
git-tree-sha1 = "9f02045d934dc030edad45944ea80dbd1f0ebea7"
uuid = "d38c429a-6771-53c6-b99e-75d170b6e991"
version = "0.5.7"

[[DataAPI]]
git-tree-sha1 = "cc70b17275652eb47bc9e5f81635981f13cea5c8"
uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
version = "1.9.0"

[[DataStructures]]
deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
git-tree-sha1 = "7d9d316f04214f7efdbb6398d545446e246eff02"
uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
version = "0.18.10"

[[DataValueInterfaces]]
git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
version = "1.0.0"

[[Dates]]
deps = ["Printf"]
uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"

[[DelimitedFiles]]
deps = ["Mmap"]
uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"

[[Distributed]]
deps = ["Random", "Serialization", "Sockets"]
uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"

[[DocStringExtensions]]
deps = ["LibGit2"]
git-tree-sha1 = "b19534d1895d702889b219c382a6e18010797f0b"
uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
version = "0.8.6"

[[Downloads]]
deps = ["ArgTools", "LibCURL", "NetworkOptions"]
uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"

[[EarCut_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3f3a2501fa7236e9b911e0f7a588c657e822bb6d"
uuid = "5ae413db-bbd1-5e63-b57d-d24a61df00f5"
version = "2.2.3+0"

[[Expat_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b3bfd02e98aedfa5cf885665493c5598c350cd2f"
uuid = "2e619515-83b5-522b-bb60-26c02a35a201"
version = "2.2.10+0"

[[FFMPEG]]
deps = ["FFMPEG_jll"]
git-tree-sha1 = "b57e3acbe22f8484b4b5ff66a7499717fe1a9cc8"
uuid = "c87230d0-a227-11e9-1b43-d7ebe4e7570a"
version = "0.4.1"

[[FFMPEG_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "JLLWrappers", "LAME_jll", "Libdl", "Ogg_jll", "OpenSSL_jll", "Opus_jll", "Pkg", "Zlib_jll", "libass_jll", "libfdk_aac_jll", "libvorbis_jll", "x264_jll", "x265_jll"]
git-tree-sha1 = "d8a578692e3077ac998b50c0217dfd67f21d1e5f"
uuid = "b22a6f82-2f65-5046-a5b2-351ab43fb4e5"
version = "4.4.0+0"

[[FixedPointNumbers]]
deps = ["Statistics"]
git-tree-sha1 = "335bfdceacc84c5cdf16aadc768aa5ddfc5383cc"
uuid = "53c48c17-4a7d-5ca2-90c5-79b7896eea93"
version = "0.8.4"

[[Fontconfig_jll]]
deps = ["Artifacts", "Bzip2_jll", "Expat_jll", "FreeType2_jll", "JLLWrappers", "Libdl", "Libuuid_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "21efd19106a55620a188615da6d3d06cd7f6ee03"
uuid = "a3f928ae-7b40-5064-980b-68af3947d34b"
version = "2.13.93+0"

[[Formatting]]
deps = ["Printf"]
git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8"
uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
version = "0.4.2"

[[FreeType2_jll]]
deps = ["Artifacts", "Bzip2_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "87eb71354d8ec1a96d4a7636bd57a7347dde3ef9"
uuid = "d7e528f0-a631-5988-bf34-fe36492bcfd7"
version = "2.10.4+0"

[[FriBidi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "aa31987c2ba8704e23c6c8ba8a4f769d5d7e4f91"
uuid = "559328eb-81f9-559d-9380-de523a88c83c"
version = "1.0.10+0"

[[GLFW_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libglvnd_jll", "Pkg", "Xorg_libXcursor_jll", "Xorg_libXi_jll", "Xorg_libXinerama_jll", "Xorg_libXrandr_jll"]
git-tree-sha1 = "0c603255764a1fa0b61752d2bec14cfbd18f7fe8"
uuid = "0656b61e-2033-5cc2-a64a-77c0f6c09b89"
version = "3.3.5+1"

[[GR]]
deps = ["Base64", "DelimitedFiles", "GR_jll", "HTTP", "JSON", "Libdl", "LinearAlgebra", "Pkg", "Printf", "Random", "Serialization", "Sockets", "Test", "UUIDs"]
git-tree-sha1 = "30f2b340c2fff8410d89bfcdc9c0a6dd661ac5f7"
uuid = "28b8d3ca-fb5f-59d9-8090-bfdbd6d07a71"
version = "0.62.1"

[[GR_jll]]
deps = ["Artifacts", "Bzip2_jll", "Cairo_jll", "FFMPEG_jll", "Fontconfig_jll", "GLFW_jll", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Libtiff_jll", "Pixman_jll", "Pkg", "Qt5Base_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "fd75fa3a2080109a2c0ec9864a6e14c60cca3866"
uuid = "d2c73de3-f751-5644-a686-071e5b155ba9"
version = "0.62.0+0"

[[GeometryBasics]]
deps = ["EarCut_jll", "IterTools", "LinearAlgebra", "StaticArrays", "StructArrays", "Tables"]
git-tree-sha1 = "58bcdf5ebc057b085e58d95c138725628dd7453c"
uuid = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
version = "0.4.1"

[[Gettext_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "9b02998aba7bf074d14de89f9d37ca24a1a0b046"
uuid = "78b55507-aeef-58d4-861c-77aaff3498b1"
version = "0.21.0+0"

[[Glib_jll]]
deps = ["Artifacts", "Gettext_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Libiconv_jll", "Libmount_jll", "PCRE_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "7bf67e9a481712b3dbe9cb3dac852dc4b1162e02"
uuid = "7746bdde-850d-59dc-9ae8-88ece973131d"
version = "2.68.3+0"

[[Graphite2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "344bf40dcab1073aca04aa0df4fb092f920e4011"
uuid = "3b182d85-2403-5c21-9c21-1e1f0cc25472"
version = "1.3.14+0"

[[Grisu]]
git-tree-sha1 = "53bb909d1151e57e2484c3d1b53e19552b887fb2"
uuid = "42e2da0e-8278-4e71-bc24-59509adca0fe"
version = "1.0.2"

[[HTTP]]
deps = ["Base64", "Dates", "IniFile", "Logging", "MbedTLS", "NetworkOptions", "Sockets", "URIs"]
git-tree-sha1 = "0fa77022fe4b511826b39c894c90daf5fce3334a"
uuid = "cd3eb016-35fb-5094-929b-558a96fad6f3"
version = "0.9.17"

[[HarfBuzz_jll]]
deps = ["Artifacts", "Cairo_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "Graphite2_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg"]
git-tree-sha1 = "8a954fed8ac097d5be04921d595f741115c1b2ad"
uuid = "2e76f6c2-a576-52d4-95c1-20adfe4de566"
version = "2.8.1+0"

[[Hyperscript]]
deps = ["Test"]
git-tree-sha1 = "8d511d5b81240fc8e6802386302675bdf47737b9"
uuid = "47d2ed2b-36de-50cf-bf87-49c2cf4b8b91"
version = "0.0.4"

[[HypertextLiteral]]
git-tree-sha1 = "2b078b5a615c6c0396c77810d92ee8c6f470d238"
uuid = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2"
version = "0.9.3"

[[IOCapture]]
deps = ["Logging", "Random"]
git-tree-sha1 = "f7be53659ab06ddc986428d3a9dcc95f6fa6705a"
uuid = "b5f81e59-6552-4d32-b1f0-c071b021bf89"
version = "0.2.2"

[[IniFile]]
deps = ["Test"]
git-tree-sha1 = "098e4d2c533924c921f9f9847274f2ad89e018b8"
uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f"
version = "0.5.0"

[[InteractiveUtils]]
deps = ["Markdown"]
uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"

[[InverseFunctions]]
deps = ["Test"]
git-tree-sha1 = "a7254c0acd8e62f1ac75ad24d5db43f5f19f3c65"
uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
version = "0.1.2"

[[IrrationalConstants]]
git-tree-sha1 = "7fd44fd4ff43fc60815f8e764c0f352b83c49151"
uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
version = "0.1.1"

[[IterTools]]
git-tree-sha1 = "05110a2ab1fc5f932622ffea2a003221f4782c18"
uuid = "c8e1da08-722c-5040-9ed9-7db0dc04731e"
version = "1.3.0"

[[IteratorInterfaceExtensions]]
git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
uuid = "82899510-4779-5014-852e-03e436cf321d"
version = "1.0.0"

[[JLLWrappers]]
deps = ["Preferences"]
git-tree-sha1 = "642a199af8b68253517b80bd3bfd17eb4e84df6e"
uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
version = "1.3.0"

[[JSON]]
deps = ["Dates", "Mmap", "Parsers", "Unicode"]
git-tree-sha1 = "8076680b162ada2a031f707ac7b4953e30667a37"
uuid = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
version = "0.21.2"

[[JpegTurbo_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "d735490ac75c5cb9f1b00d8b5509c11984dc6943"
uuid = "aacddb02-875f-59d6-b918-886e6ef4fbf8"
version = "2.1.0+0"

[[LAME_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "f6250b16881adf048549549fba48b1161acdac8c"
uuid = "c1c5ebd0-6772-5130-a774-d5fcae4a789d"
version = "3.100.1+0"

[[LZO_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e5b909bcf985c5e2605737d2ce278ed791b89be6"
uuid = "dd4b983a-f0e5-5f8d-a1b7-129d4a5fb1ac"
version = "2.10.1+0"

[[LaTeXStrings]]
git-tree-sha1 = "f2355693d6778a178ade15952b7ac47a4ff97996"
uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
version = "1.3.0"

[[Latexify]]
deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "Printf", "Requires"]
git-tree-sha1 = "a8f4f279b6fa3c3c4f1adadd78a621b13a506bce"
uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
version = "0.15.9"

[[LibCURL]]
deps = ["LibCURL_jll", "MozillaCACerts_jll"]
uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"

[[LibCURL_jll]]
deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"

[[LibGit2]]
deps = ["Base64", "NetworkOptions", "Printf", "SHA"]
uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"

[[LibSSH2_jll]]
deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"

[[Libdl]]
uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"

[[Libffi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "0b4a5d71f3e5200a7dff793393e09dfc2d874290"
uuid = "e9f186c6-92d2-5b65-8a66-fee21dc1b490"
version = "3.2.2+1"

[[Libgcrypt_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgpg_error_jll", "Pkg"]
git-tree-sha1 = "64613c82a59c120435c067c2b809fc61cf5166ae"
uuid = "d4300ac3-e22c-5743-9152-c294e39db1e4"
version = "1.8.7+0"

[[Libglvnd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll", "Xorg_libXext_jll"]
git-tree-sha1 = "7739f837d6447403596a75d19ed01fd08d6f56bf"
uuid = "7e76a0d4-f3c7-5321-8279-8d96eeed0f29"
version = "1.3.0+3"

[[Libgpg_error_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "c333716e46366857753e273ce6a69ee0945a6db9"
uuid = "7add5ba3-2f88-524e-9cd5-f83b8a55f7b8"
version = "1.42.0+0"

[[Libiconv_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "42b62845d70a619f063a7da093d995ec8e15e778"
uuid = "94ce4f54-9a6c-5748-9c1c-f9c7231a4531"
version = "1.16.1+1"

[[Libmount_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "9c30530bf0effd46e15e0fdcf2b8636e78cbbd73"
uuid = "4b2f31a3-9ecc-558c-b454-b3730dcb73e9"
version = "2.35.0+0"

[[Libtiff_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "Zlib_jll", "Zstd_jll"]
git-tree-sha1 = "340e257aada13f95f98ee352d316c3bed37c8ab9"
uuid = "89763e89-9b03-5906-acba-b20f662cd828"
version = "4.3.0+0"

[[Libuuid_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7f3efec06033682db852f8b3bc3c1d2b0a0ab066"
uuid = "38a345b3-de98-5d2b-a5d3-14cd9215e700"
version = "2.36.0+0"

[[LinearAlgebra]]
deps = ["Libdl"]
uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

[[LogExpFunctions]]
deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
git-tree-sha1 = "be9eef9f9d78cecb6f262f3c10da151a6c5ab827"
uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
version = "0.3.5"

[[Logging]]
uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"

[[MacroTools]]
deps = ["Markdown", "Random"]
git-tree-sha1 = "3d3e902b31198a27340d0bf00d6ac452866021cf"
uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
version = "0.5.9"

[[Markdown]]
deps = ["Base64"]
uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"

[[MbedTLS]]
deps = ["Dates", "MbedTLS_jll", "Random", "Sockets"]
git-tree-sha1 = "1c38e51c3d08ef2278062ebceade0e46cefc96fe"
uuid = "739be429-bea8-5141-9913-cc70e7f3736d"
version = "1.0.3"

[[MbedTLS_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"

[[Measures]]
git-tree-sha1 = "e498ddeee6f9fdb4551ce855a46f54dbd900245f"
uuid = "442fdcdd-2543-5da2-b0f3-8c86c306513e"
version = "0.3.1"

[[Missings]]
deps = ["DataAPI"]
git-tree-sha1 = "bf210ce90b6c9eed32d25dbcae1ebc565df2687f"
uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
version = "1.0.2"

[[Mmap]]
uuid = "a63ad114-7e13-5084-954f-fe012c677804"

[[MozillaCACerts_jll]]
uuid = "14a3606d-f60d-562e-9121-12d972cd8159"

[[NaNMath]]
git-tree-sha1 = "bfe47e760d60b82b66b61d2d44128b62e3a369fb"
uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
version = "0.3.5"

[[NetworkOptions]]
uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"

[[Ogg_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "7937eda4681660b4d6aeeecc2f7e1c81c8ee4e2f"
uuid = "e7412a2a-1a6e-54c0-be00-318e2571c051"
version = "1.3.5+0"

[[OpenSSL_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "15003dcb7d8db3c6c857fda14891a539a8f2705a"
uuid = "458c3c95-2e84-50aa-8efc-19380b2a3a95"
version = "1.1.10+0"

[[Opus_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "51a08fb14ec28da2ec7a927c4337e4332c2a4720"
uuid = "91d4177d-7536-5919-b921-800302f37372"
version = "1.3.2+0"

[[OrderedCollections]]
git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c"
uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
version = "1.4.1"

[[PCRE_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b2a7af664e098055a7529ad1a900ded962bca488"
uuid = "2f80f16e-611a-54ab-bc61-aa92de5b98fc"
version = "8.44.0+0"

[[Parsers]]
deps = ["Dates"]
git-tree-sha1 = "ae4bbcadb2906ccc085cf52ac286dc1377dceccc"
uuid = "69de0a69-1ddd-5017-9359-2bf0b02dc9f0"
version = "2.1.2"

[[Pixman_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "b4f5d02549a10e20780a24fce72bea96b6329e29"
uuid = "30392449-352a-5448-841d-b1acce4e97dc"
version = "0.40.1+0"

[[Pkg]]
deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"

[[PlotThemes]]
deps = ["PlotUtils", "Requires", "Statistics"]
git-tree-sha1 = "a3a964ce9dc7898193536002a6dd892b1b5a6f1d"
uuid = "ccf2f8ad-2431-5c83-bf29-c5338b663b6a"
version = "2.0.1"

[[PlotUtils]]
deps = ["ColorSchemes", "Colors", "Dates", "Printf", "Random", "Reexport", "Statistics"]
git-tree-sha1 = "b084324b4af5a438cd63619fd006614b3b20b87b"
uuid = "995b91a9-d308-5afd-9ec6-746e21dbc043"
version = "1.0.15"

[[Plots]]
deps = ["Base64", "Contour", "Dates", "Downloads", "FFMPEG", "FixedPointNumbers", "GR", "GeometryBasics", "JSON", "Latexify", "LinearAlgebra", "Measures", "NaNMath", "PlotThemes", "PlotUtils", "Printf", "REPL", "Random", "RecipesBase", "RecipesPipeline", "Reexport", "Requires", "Scratch", "Showoff", "SparseArrays", "Statistics", "StatsBase", "UUIDs", "UnicodeFun"]
git-tree-sha1 = "93f484f18848234ac2c1387c7e5263f840cdafe3"
uuid = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
version = "1.24.2"

[[PlutoUI]]
deps = ["AbstractPlutoDingetjes", "Base64", "Dates", "Hyperscript", "HypertextLiteral", "IOCapture", "InteractiveUtils", "JSON", "Logging", "Markdown", "Random", "Reexport", "UUIDs"]
git-tree-sha1 = "1e0cb51e0ccef0afc01aab41dc51a3e7f781e8cb"
uuid = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
version = "0.7.20"

[[Preferences]]
deps = ["TOML"]
git-tree-sha1 = "00cfd92944ca9c760982747e9a1d0d5d86ab1e5a"
uuid = "21216c6a-2e73-6563-6e65-726566657250"
version = "1.2.2"

[[Printf]]
deps = ["Unicode"]
uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"

[[Qt5Base_jll]]
deps = ["Artifacts", "CompilerSupportLibraries_jll", "Fontconfig_jll", "Glib_jll", "JLLWrappers", "Libdl", "Libglvnd_jll", "OpenSSL_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libxcb_jll", "Xorg_xcb_util_image_jll", "Xorg_xcb_util_keysyms_jll", "Xorg_xcb_util_renderutil_jll", "Xorg_xcb_util_wm_jll", "Zlib_jll", "xkbcommon_jll"]
git-tree-sha1 = "ad368663a5e20dbb8d6dc2fddeefe4dae0781ae8"
uuid = "ea2cea3b-5b76-57ae-a6ef-0a8af62496e1"
version = "5.15.3+0"

[[REPL]]
deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"

[[Random]]
deps = ["Serialization"]
uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"

[[RecipesBase]]
git-tree-sha1 = "6bf3f380ff52ce0832ddd3a2a7b9538ed1bcca7d"
uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
version = "1.2.1"

[[RecipesPipeline]]
deps = ["Dates", "NaNMath", "PlotUtils", "RecipesBase"]
git-tree-sha1 = "7ad0dfa8d03b7bcf8c597f59f5292801730c55b8"
uuid = "01d81517-befc-4cb6-b9ec-a95719d0359c"
version = "0.4.1"

[[Reexport]]
git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
uuid = "189a3867-3050-52da-a836-e630ba90ab69"
version = "1.2.2"

[[Requires]]
deps = ["UUIDs"]
git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621"
uuid = "ae029012-a4dd-5104-9daa-d747884805df"
version = "1.1.3"

[[SHA]]
uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"

[[Scratch]]
deps = ["Dates"]
git-tree-sha1 = "0b4b7f1393cff97c33891da2a0bf69c6ed241fda"
uuid = "6c6a2e73-6563-6170-7368-637461726353"
version = "1.1.0"

[[Serialization]]
uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"

[[SharedArrays]]
deps = ["Distributed", "Mmap", "Random", "Serialization"]
uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"

[[Showoff]]
deps = ["Dates", "Grisu"]
git-tree-sha1 = "91eddf657aca81df9ae6ceb20b959ae5653ad1de"
uuid = "992d4aef-0814-514b-bc4d-f2e9a6c4116f"
version = "1.0.3"

[[Sockets]]
uuid = "6462fe0b-24de-5631-8697-dd941f90decc"

[[SortingAlgorithms]]
deps = ["DataStructures"]
git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508"
uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
version = "1.0.1"

[[SparseArrays]]
deps = ["LinearAlgebra", "Random"]
uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"

[[StaticArrays]]
deps = ["LinearAlgebra", "Random", "Statistics"]
git-tree-sha1 = "3c76dde64d03699e074ac02eb2e8ba8254d428da"
uuid = "90137ffa-7385-5640-81b9-e52037218182"
version = "1.2.13"

[[Statistics]]
deps = ["LinearAlgebra", "SparseArrays"]
uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"

[[StatsAPI]]
git-tree-sha1 = "0f2aa8e32d511f758a2ce49208181f7733a0936a"
uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
version = "1.1.0"

[[StatsBase]]
deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
git-tree-sha1 = "2bb0cb32026a66037360606510fca5984ccc6b75"
uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
version = "0.33.13"

[[StructArrays]]
deps = ["Adapt", "DataAPI", "StaticArrays", "Tables"]
git-tree-sha1 = "2ce41e0d042c60ecd131e9fb7154a3bfadbf50d3"
uuid = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
version = "0.6.3"

[[TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"

[[TableTraits]]
deps = ["IteratorInterfaceExtensions"]
git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
version = "1.0.1"

[[Tables]]
deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
git-tree-sha1 = "fed34d0e71b91734bf0a7e10eb1bb05296ddbcd0"
uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
version = "1.6.0"

[[Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"

[[Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

[[URIs]]
git-tree-sha1 = "97bbe755a53fe859669cd907f2d96aee8d2c1355"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.3.0"

[[UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"

[[Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

[[UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"

[[Wayland_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.19.0+0"

[[Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "66d72dc6fcc86352f01676e8f0f698562e60510f"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.23.0+0"

[[XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "1acf5bdf07aa0907e0a37d3718bb88d4b687b74a"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.9.12+0"

[[XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"

[[Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"

[[Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"

[[Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"

[[Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"

[[Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"

[[Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"

[[Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"

[[Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"

[[Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"

[[Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"

[[Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"

[[Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"

[[Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"

[[Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"

[[Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"

[[Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"

[[Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"

[[Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"

[[Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"

[[Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"

[[Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"

[[Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "cc4bf3fdde8b7e3e9fa0351bdeedba1cf3b7f6e6"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.0+0"

[[libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"

[[libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"

[[libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "c45f4e40e7aafe9d086379e5578947ec8b95a8fb"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+0"

[[nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"

[[p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"

[[x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"

[[x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"

[[xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "ece2350174195bb31de1a63bea3a41ae1aa593b6"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "0.9.1+5"
"""

# ╔═╡ Cell order:
# ╟─c0e4d750-b9a4-11eb-2e0c-edaeaaf3f36a
# ╟─606ac8d7-7cd6-4da3-b83f-9889f6883190
# ╟─4c9ce872-1164-4c7f-9a26-3af89b345c41
# ╟─9b3e08e0-7207-4099-96e4-c6e1e9892a1f
# ╟─159419d5-0555-43a0-8320-9cb51e0b05ba
# ╠═fb03a3aa-f94b-4b73-a21b-f05bc548dd9d
# ╟─df708c4d-443b-4190-b72d-779c4e1e1bb1
# ╟─41eac123-fa10-42c3-a801-8fb5f7bce7ae
# ╟─66de4e49-ede7-44d1-b7b4-49ecb3ec2e53
# ╟─3d8c7f7e-e765-41d9-8191-aef5e52984fc
# ╟─db0fc7c2-9e8c-415f-95c1-686dbfc56347
# ╟─6a1ee842-a2f1-4810-83d7-5ce931c47891
# ╟─d2ed65c3-24e3-42ee-ac6e-f743ef4b584d
# ╟─19822397-18c5-4a88-bac1-f3adbfd2b235
# ╟─594360d4-9bb8-4756-8f40-a5f0f9555aba
# ╟─1b4d9fbd-be46-416a-a1fe-163f5a0b37a3
# ╟─5db1fd70-0bf9-462b-b6d3-bfc3ed8890cb
# ╟─89222965-d320-4a46-a11a-b66b2ed9c11d
# ╟─750b6ab7-0b11-4b91-be34-ab7426625204
# ╠═026c8f3e-8ecd-459f-b496-511c38065cc6
# ╟─f559622d-8bb3-4068-a4a8-b4f561960da1
# ╠═e4374691-885a-487e-bee5-dac9092dd567
# ╟─995e0deb-8044-4cd8-b802-0bda0ce093e3
# ╟─773eb541-f02a-4d61-8d20-9c79a49f6d85
# ╠═c29521d1-6563-4c9f-9d06-656eb8b98a6f
# ╟─acb69a29-d406-4f43-ab59-37c4516a460a
# ╟─50da3fc1-b450-4c56-b179-1e6c36af7265
# ╟─c5058f6d-d489-4308-b010-472ae048a6a7
# ╟─da4138d9-2723-4274-8bd1-a0c9a89c1163
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002

max_stars_repo_name: Ricardo-Luis/notebooks

max_issues_repo_name: Ricardo-Luis/notebooks

max_forks_repo_name: Ricardo-Luis/notebooks