# cudnn wrapper

"""

`conv_f(x,w;kwargs...)` executes convolutions or cross-correlations
using filters specified with `w` over tensor `x`.
Here is a description of all available keyword arguments:
* padding: the number of extra zeros implicitly concatenated at the start and at the end of each dimension. Default=floor((filterSize-1)/2) which preserves the input size when filterSize is odd and stride=1.
* stride: the number of elements to slide to reach the next filtering window. Default=1.
* upscale: upscale factor for each dimension. Default=1.
* mode: 0 for convolution and 1 for cross-correlation.  Default=0.
* alpha: can be used to scale the result. Default=1.
* algo: specifies which convolution algorithm shoud be used to compute the results. Default=0. See the CUDNN User Guide for details.
* workSpace: data pointer to GPU memory to a workspace needed to able to execute the specified algorithm. Default=C_NULL.
* workSpaceSizeInBytes: the size in bytes of the provided workSpace. Default=0.
* handle: handle to a previously created cuDNN context. Default=Dex allocated context.

"""
function conv_f{T}(x::DexArray{T},w::DexArray{T};
                  handle=cudnnhandle, alpha=one(T), beta=zero(T),
                  algo=0, workSpace=C_NULL, workSpaceSizeInBytes=0, o...)
    y = similar(x, cdims(x,w;o...))
    @cuda(cudnn, cudnnConvolutionForward,
          (Cptr,Ptr{T},Cptr,Ptr{T},Cptr,Ptr{T},Cptr,UInt32,Cptr,Csize_t,Ptr{T},Cptr,Ptr{T}),
          handle,Ref(alpha),TD(x),x,FD(w),w,CD(x,w;o...),algo,workSpace,workSpaceSizeInBytes,Ref(beta),TD(y),y)
    return y
end

"""

`conv_bx(x,w,dy;kwargs...)` This function computes the convolution gradient with
respect to the output tensor, returning results in gradDesc.

"""
function conv_bx{T}(x::DexArray{T},w::DexArray{T},dy::DexArray{T};
                   handle=cudnnhandle, alpha=one(T), beta=zero(T),
                   algo=0, workSpace=C_NULL, workSpaceSizeInBytes=0, o...)
    dx = similar(x)
    @cuda(cudnn,cudnnConvolutionBackwardData,
          (Cptr,Ptr{T},Cptr,Ptr{T},Cptr,Ptr{T},Cptr,     UInt32,Cptr,     Csize_t,             Ptr{T},Cptr,Ptr{T}),
          handle,Ref(alpha),FD(w),w,TD(dy),dy,CD(x,w;o...),algo,workSpace,workSpaceSizeInBytes,Ref(beta),TD(dx),dx)
    return dx
end

"""

`conv_bw(x,w,dy;kwargs...)` This function computes the convolution gradient with
 respect to filter coefficients, returning results in gradDesc.

"""
function conv_bw{T}(x::DexArray{T},w::DexArray{T},dy::DexArray{T};
                   handle=cudnnhandle, alpha=one(T), beta=zero(T),
                   algo=0, workSpace=C_NULL, workSpaceSizeInBytes=0, o...)
    dw = similar(w)
    @cuda(cudnn,cudnnConvolutionBackwardFilter,
          (Cptr,Ptr{T},Cptr,Ptr{T},Cptr,Ptr{T},Cptr,     UInt32,Cptr,     Csize_t,             Ptr{T},Cptr,Ptr{T}),
          handle,Ref(alpha),TD(x),x,TD(dy),dy,CD(x,w;o...),algo,workSpace,workSpaceSizeInBytes,Ref(beta),FD(dw),dw)
    return dw
end

"""

`pool_f(x;kwargs...)` computes pooling of input values (i.e., the
maximum or average of several adjacent values) to produce an output
with smaller height and/or width.

Here is a description of all available keyword arguments:
* window: the pooling window size for each dimension. Default=2.
* padding: the number of extra zeros implicitly concatenated at the start and at the end of each dimension. Default=0.
* stride: the number of elements to slide to reach the next pooling window. Default=same as window.
* mode: 0 for max, 1 for average including padded values, 2 for average excluding padded values.  Default=0.
* maxpoolingNanOpt: Nan numbers are not propagated if 0, they are propagated if 1. Default=0.
* alpha: can be used to scale the result. Default=1.
* handle: Handle to a previously created cuDNN context. Default=Dex allocated context.

"""

function pool_f{T}(x::DexArray{T}; handle=cudnnhandle, alpha=one(T), beta=zero(T), o...)
    y = similar(x, pdims(x; o...))
    @cuda(cudnn, cudnnPoolingForward,
          (Cptr, Cptr,      Ptr{T},    Cptr,Ptr{T},Ptr{T},   Cptr,Ptr{T}),
          handle,PD(x;o...),Ref(alpha),TD(x),x,    Ref(beta),TD(y),y)
    return y
end

function pool_b{T}(x::DexArray{T},y::DexArray{T},dy::DexArray{T};
                  handle=cudnnhandle, alpha=one(T), beta=zero(T), o...)
    dx = similar(x)
    @cuda(cudnn,cudnnPoolingBackward,
          (Cptr,Cptr,Ptr{T},Cptr,Ptr{T},Cptr,Ptr{T},Cptr,Ptr{T},Ptr{T},Cptr,Ptr{T}),
          handle,PD(x;o...),Ref(alpha),TD(y),y,TD(dy),dy,TD(x),x,Ref(beta),TD(dx),dx)
    return dx
end

"""

`dropout_f(x;kwargs...)` computes the forward dropout operation over input values
to produce an output.

Here is a description of all available keyword arguments:
* window: the pooling window size for each dimension. Default=2.
* padding: the number of extra zeros implicitly concatenated at the start and at the end of each dimension. Default=0.
* stride: the number of elements to slide to reach the next pooling window. Default=same as window.
* mode: 0 for max, 1 for average including padded values, 2 for average excluding padded values.  Default=0.
* maxpoolingNanOpt: Nan numbers are not propagated if 0, they are propagated if 1. Default=0.
* alpha: can be used to scale the result. Default=1.
* handle: Handle to a previously created cuDNN context. Default=Dex allocated context.

"""

function dropout_f{T}(x::DexArray, dropout;
                      handle=cudnnhandle)
    y = similar(x)
    @cuda(cudnn, cudnnDropoutForward,
          (Cptr,Cptr,        Cptr,Ptr{T}
          handle,DD(dropout),TD(x)),x,

end

# cudnn datatype
# an enumerated type indicating the data type to which a tensor descriptor
# or filter descriptor refers.
DT(::DexArray{Float32})=UInt32(0)
DT(::DexArray{Float64})=UInt32(1)
DT(::DexArray{Float16})=UInt32(2)

# accquire dimension
function cdims{T,N}(x::DexArray{T,N},w::DexArray{T,N}; padding=0, stride=1, o...)
    ntuple(N) do i
        if i < N-1
            pi = if isa(padding,Number); padding; else padding[i]; end
            si = if isa(stride,Number); stride; else stride[i]; end
            1 + div(size(x,i) - size(w,i) + 2*pi, si)
        elseif i == N-1
            size(w,N)
        else # i == N
            size(x,N)
        end
    end
end

function pdims{T,N}(x::DexArray{T,N}; window=2, padding=0, stride=window, o...)
    ntuple(N) do i
        if i < N-1
            wi = (if isa(window,Number); window; else window[i]; end)
            pi = (if isa(padding,Number); padding; else padding[i]; end)
            si = (if isa(stride,Number); stride; else stride[i]; end)
            1 + div(size(x,i) + 2*pi - wi, si)
        else
            size(x,i)
        end
    end
end

# cudnn descriptors

type TD; ptr
    function TD(a::DexArray)
        d = Cptr[0]
        @cuda(cudnn,cudnnCreateTensorDescriptor,(Ptr{Cptr},),d)
        n = ndims(a)
        sz = [Cint(size(a,n-i+1)) for i=1:n]    # why dim reversed?
        st = [Cint(stride(a,n-i+1)) for i=1:n]
        @cuda(cudnn,cudnnSetTensorNdDescriptor,
              (Cptr,UInt32,Cint,Ptr{Cint},Ptr{Cint}),
              d[1], DT(a), n, sz, st)
        td = new(d[1])
        finalizer(td, x->@cuda(cudnn,cudnnDestroyTensorDescriptor,(Cptr,),x.ptr))
        return td
    end
end

type FD; ptr
    function FD(a::DexArray)
        d = Cptr[0]
        @cuda(cudnn,cudnnCreateFilterDescriptor,(Ptr{Cptr},),d)
        n = ndims(a)
        sz = [Cint(size(a,n-i+1)) for i=1:n]
        @cuda(cudnn,cudnnSetFilterNdDescriptor,
              (Cptr,UInt32,UInt32,Cint,Ptr{Cint}),
              d[1], DT(a), 0,     n,   sz)
        fd = new(d[1])
        finalizer(fd, x->@cuda(cudnn,cudnnDestroyFilterDescriptor,(Cptr,),x.ptr))
        return fd
    end
end

type CD; ptr
    function CD(x::DexArray,w::DexArray; padding=0, stride=1, upscale=1, mode=0)
        d = Cptr[0]
        @cuda(cudnn,cudnnCreateConvolutionDescriptor,(Ptr{Cptr},),d)
        nd = ndims(x)-2
        @cuda(cudnn,cudnnSetConvolutionNdDescriptor,
              (Cptr,Cint,Ptr{Cint},Ptr{Cint},Ptr{Cint},UInt32,UInt32),
              d[1],nd,cdsize(padding,nd),cdsize(stride,nd),cdsize(upscale,nd),mode,DT(x))
        cd = new(d[1])
        finalizer(cd, x->@cuda(cudnn,cudnnDestroyConvolutionDescriptor,(Cptr,),x.ptr))
        return cd
    end
end

type PD; ptr
    function PD(x::DexArray; window=2, padding=0, stride=window, mode=0, maxpoolingNanOpt=0)
        d = Cptr[0]
        @cuda(cudnn,cudnnCreatePoolingDescriptor,(Ptr{Cptr},),d)
        nd = ndims(x)-2
        @cuda(cudnn,cudnnSetPoolingNdDescriptor,
              (Cptr,UInt32,UInt32,Cint,Ptr{Cint},Ptr{Cint},Ptr{Cint}),
              d[1],mode,maxpoolingNanOpt,nd,cdsize(window,nd),cdsize(padding,nd),cdsize(stride,nd))
        pd = new(d[1])
        finalizer(pd, x->@cuda(cudnn,cudnnDestroyPoolingDescriptor,(Cptr,),x.ptr))
        return pd
    end
end

type DD; ptr
    function DD(dropout;handle=cudnnhandle)
        d = Cptr[0]
        @cuda(cudnn, cudnnCreateDropoutDescriptor, (Ptr{Cptr},),d)
        statessize_p = Csize_t[0]
        @cuda(cudnn, cudnnDropoutGetStatesSize, (Cptr,Ptr{Csize_t}), handle,statessize_p)
        statessize = statessize_p[1]
        states = DexArray(Int8, Int(statessize))
        @cude(cudnn, cudnnSetDropoutDescriptor,
              (Cptr,Cptr, Cfloat,Cptr,  Cint,Culonglong),
              d[1],handle,Cfloat(dropout),state,statessize, 0)
        dd = new(d[1])
        finalizer(dd, x->@cuda(cudnn, cudnnDestroyDropoutDescriptor, (Cptr,),x.ptr)
        return dd
    end
end

import Base: unsafe_convert
unsafe_convert(::Type{Cptr}, td::TD)=td.ptr
unsafe_convert(::Type{Cptr}, fd::FD)=fd.ptr
unsafe_convert(::Type{Cptr}, cd::CD)=cd.ptr
unsafe_convert(::Type{Cptr}, pd::PD)=pd.ptr

function cdsize(w, nd)
    if isa(w,Integer)
        fill(Cint(w),nd)
    elseif length(w)==nd
        [ Cint(w[nd-i+1]) for i=1:nd ]
    else
        throw(DimensionMismatch())
    end
end

# convolution padding size that preserves the input size when filter size is odd and stride=1
padsize(w)=ntuple(i->div(size(w,i)-1,2), ndims(w)-2)


const ED_DEFAULT_SCALE  = 0.2
const ED_DEFAULT_SIGMA  = 2
const ED_DEFAULT_ITER   = 1
const ED_DEFAULT_BORDER = false
const ED_DEFAULT_NORM   = true

@doc """
    ElasticDistortion <: Augmentor.ImageOperation

Description
--------------

Distorts the given image using a randomly (uniform) generated
vector field of the given grid size. This field will be stretched
over the given image when applied, which in turn will morph the
original image into a new image using a linear interpolation of
both the image and the vector field.

In contrast to [`RandomDistortion`], the resulting vector
field is also smoothed using a Gaussian filter with of parameter
`sigma`. This will result in a less chaotic vector field and thus
resemble a more natural distortion.

Usage
--------------

    ElasticDistortion(gridheight, gridwidth, scale, sigma, [iter=$ED_DEFAULT_ITER], [border=$ED_DEFAULT_BORDER], [norm=$ED_DEFAULT_NORM])

    ElasticDistortion(gridheight, gridwidth, scale; [sigma=$ED_DEFAULT_SIGMA], [iter=$ED_DEFAULT_ITER], [border=$ED_DEFAULT_BORDER], [norm=$ED_DEFAULT_NORM])

    ElasticDistortion(gridheight, [gridwidth]; [scale=$ED_DEFAULT_SCALE], [sigma=$ED_DEFAULT_SIGMA], [iter=$ED_DEFAULT_ITER], [border=$ED_DEFAULT_BORDER], [norm=$ED_DEFAULT_NORM])

Arguments
--------------

- **`gridheight`** : The grid height of the displacement vector
    field. This effectively specifies the number of vertices
    along the Y dimension used as landmarks, where all the
    positions between the grid points are interpolated.

- **`gridwidth`** : The grid width of the displacement vector
    field. This effectively specifies the number of vertices
    along the Y dimension used as landmarks, where all the
    positions between the grid points are interpolated.

- **`scale`** : Optional. The scaling factor applied to all
    displacement vectors in the field. This effectively defines
    the "strength" of the deformation. There is no theoretical
    upper limit to this factor, but a value somewhere between
    `0.01` and `1.0` seem to be the most reasonable choices.
    Default to `$ED_DEFAULT_SCALE`.

- **`sigma`** : Optional. Sigma parameter of the Gaussian filter.
    This parameter effectively controls the strength of the
    smoothing. Defaults to `$ED_DEFAULT_SIGMA`.

- **`iter`** : Optional. The number of times the smoothing
    operation is applied to the displacement vector field. This
    is especially useful if `border = false` because the border
    will be reset to zero after each pass. Thus the displacement
    is a little less aggressive towards the borders of the image
    than it is towards its center. Defaults to
    `$ED_DEFAULT_ITER`.

- **`border`** : Optional. Specifies if the borders should be
    distorted as well. If `false`, the borders of the image will
    be preserved. This effectively pins the outermost vertices on
    their original position and the operation thus only distorts
    the inner content of the image. Defaults to
    `$ED_DEFAULT_BORDER`.

- **`norm`** : Optional. If `true`, the displacement vectors of
    the field will be normalized by the norm of the field. This
    will have the effect that the `scale` factor should be more
    or less independent of the grid size. Defaults to
    `$ED_DEFAULT_NORM`.

See also
--------------

[`augment`](@ref)

Examples
--------------

```julia
using Augmentor
img = testpattern()

# distort with pinned borders
augment(img, ElasticDistortion(15, 15; scale = 0.1))

# distort everything more smoothly.
augment(img, ElasticDistortion(10, 10; sigma = 4, iter=3, border=true))
```
""" ->
struct ElasticDistortion <: ImageOperation
    gridheight::Int
    gridwidth::Int
    scale::Float64
    sigma::Float64
    iterations::Int
    border::Bool
    normalize::Bool

    function ElasticDistortion(
            gridheight::Integer, gridwidth::Integer,
            scale, sigma, iterations = ED_DEFAULT_ITER,
            border::Bool = ED_DEFAULT_BORDER, normalize::Bool = ED_DEFAULT_NORM)
        (gridwidth > 2 && gridheight > 2) || throw(ArgumentError("gridwidth and gridheight need to be greater than 2"))
        sigma > 0 || throw(ArgumentError("sigma needs to be greater than 0"))
        iterations > 0 || throw(ArgumentError("iterations needs to be greater than 0"))
        new(Int(gridheight), Int(gridwidth), Float64(scale), Float64(sigma), Int(iterations), border, normalize)
    end
end

function ElasticDistortion(
        gridheight::Integer, gridwidth::Integer, scale;
        sigma = ED_DEFAULT_SIGMA, iter = ED_DEFAULT_ITER,
        border::Bool = ED_DEFAULT_BORDER, norm::Bool = ED_DEFAULT_NORM)
    ElasticDistortion(gridheight, gridwidth, scale, sigma, iter, border, norm)::ElasticDistortion
end

function ElasticDistortion(
        gridheight::Integer, gridwidth::Integer = gridheight;
        scale = ED_DEFAULT_SCALE,
        sigma = ED_DEFAULT_SIGMA, iter = ED_DEFAULT_ITER,
        border::Bool = ED_DEFAULT_BORDER, norm::Bool = ED_DEFAULT_NORM)
    ElasticDistortion(gridheight, gridwidth, scale, sigma, iter, border, norm)::ElasticDistortion
end

@inline supports_eager(::Type{<:ElasticDistortion}) = false
@inline supports_lazy(::Type{<:ElasticDistortion})  = true

function randparam(op::ElasticDistortion, img)
    gaussian_field(op.gridheight, op.gridwidth, op.scale, op.sigma, op.iterations, op.border, op.normalize)
end

function applylazy(op::ElasticDistortion, img::AbstractArray, field)
    DistortedView(img, field)
end

function showconstruction(io::IO, op::ElasticDistortion)
    str_size   = join(map(string,(op.gridheight,op.gridwidth)), ", ")
    str_scale  = op.scale      == ED_DEFAULT_SCALE  ? "" : "scale=$(op.scale)"
    str_sigma  = op.sigma      == ED_DEFAULT_SIGMA  ? "" : "sigma=$(op.sigma)"
    str_iter   = op.iterations == ED_DEFAULT_ITER   ? "" : "iter=$(op.iterations)"
    str_border = op.border     == ED_DEFAULT_BORDER ? "" : "border=$(op.border)"
    str_norm   = op.normalize  == ED_DEFAULT_NORM   ? "" : "norm=$(op.normalize)"
    str_all = filter(str->str!="", [str_size, str_scale, str_sigma, str_iter, str_border, str_norm])
    print(io, typeof(op).name.name, '(', join(str_all, ", "), ')')
end

function Base.show(io::IO, op::ElasticDistortion)
    if get(io, :compact, false)
        str_size   = join(map(string,(op.gridheight,op.gridwidth)), "×")
        str_sigma  = op.sigma      == ED_DEFAULT_SIGMA ? "" : "(σ=$(op.sigma)) "
        str_iter   = op.iterations == 1     ? "" : "$(op.iterations)-times "
        str_norm   = op.normalize  == true  ? "and normalized " : ""
        str_border = op.border     == false ? " with pinned border" : ""
        print(io, "Distort using a $(str_iter)smoothed $(str_norm)$(str_size) grid$(str_border)")
    else
        print(io, "Augmentor.")
        showconstruction(io, op)
    end
end


struct FDGZProblem{TBCL, TBCR}
    a # (a,b) define the domain
    b
    Δx # mesh spacing
    n # number of points in the interior, excluding a and b
    x # interior mesh
    ϵ # scalar parameter
    F # holds the residual values
    left_bc::TBCL
    right_bc::TBCR
end

struct DirichletBC
    u_bc
end

struct NeumannBC
    v_bc
end

struct PeriodicBC
end


using Dolo

# # model = Model("examples/models/rbc.yaml")
# model = Model("examples/models/consumption_savings_iid.yaml")

model = Model("experiments/rbc.yaml")

F = Dolo.Euler(model, ignore_constraints=false);

sol = improved_time_iteration(model)

z0 = SVector(model.calibration[:exogenous][1:2]...)
x0 = F.x0

F(x0,x0,z0,z0) - F(x0,x0)

r = F(F.x0, F.x0; set_future=false)

##### Compare with dolo.py
import Dolo: norm

import Dolo: MSM
import Dolo: df_A

f = u->F(u, F.x0; set_future=false, ignore_constraints=false)
df = u->df_A(F, u, F.x0; set_future=false)
v1 , j_num = Dolo.DiffFun(f, F.x0)

f0 = u->F(u, F.x0; set_future=false, ignore_constraints=true)
v1 , j_0 = Dolo.DiffFun(f0, F.x0)

j = Dolo.df_A(F, F.x0, F.x0)

println(v1.data[1])

println("j_0")
println(j_0.data[1])

println("j num")
println(j_num.data[1])

println("j phi")
println(j.data[1])

function PhiTest(u,v)
    sq = sqrt(u^2+v^2)
    p = u+v-sq
    return p
end

function PhiPhiTest(x, a, b)
    f = x
    y = PhiTest(f,x-a)
    z = PhiTest(-y, b-x)
    return z
end

fun(u) = PhiPhiTest(u,0, 1)
dfun(u) = (fun(u+0.000001) - fun(u))/0.000001

zvec = range(-1,1;length=100)
fvec = fun.(zvec)
dfvec = dfun.(zvec)

plot(zvec, fvec)

plot(zvec, dfvec)

l = [Dolo.PhiPhi(SVector(x), SMatrix{1,1}(1.0), SVector(x), SVector(0.0), SVector(1.0)) for x in zvec]
fvec2= [e[1][1] for e in l]
dfvec2= [e[2][1,1] for e in l]

plot(zvec, fvec)
plot!(zvec, fvec2)

plot(zvec, dfvec)
plot!(zvec, dfvec2)

using SimplePlots

(ddf - j).data[1]

function newton(fun, dfun, x0::MSM; maxit=50, dampen=1.0, verbose=false, bcksteps = 5)

    r0 = fun(x0)

    err = norm(r0)

    local x1

    x1data = deepcopy(x0.data)
    x1 = MSM(x1data, x0.sizes)

    for n=1:maxit

        r0 = fun(x0)
        err_0 = norm(r0)

        j = dfun(x0)
        δ = (j\r0)
        for i=0:(bcksteps-1)
            u = 0.5^i
            x1.data[:] .= x0.data - δ.data*u
            r1 = fun(x1)
            err_1 = norm(r1)
            if verbose
                println( "-    $i: ", err_1)
            end
            if err_1<err_0
                break
            end
        end

        if verbose
            println(n, " | ", norm(r0), " | ",  norm(δ))
        end

        x0 = x1

    end

    return x0

end

sol = newton(f, df, F.x0; maxit=15, verbose=true, bcksteps = 20)

norm(F(sol, F.x0))

F(sol, sol; set_future=true);

function loop(F, K)

    x0 = F.x0
    x1 = x0

    for k=1:K

        res = F(x0, x0; set_future=true)
        ε = norm(res)

        f = u->F(u, x0; set_future=false)
        df = u->df_A(F, u, x0; set_future=false)

        x1 = newton(f, df, x0; verbose=false)

        δ = x1 - x0
        η = norm(δ)

        println(ε, " : ", η)

        x0 = x1
    end

    return x1

end

loop(F, 100);

# tab = Dolo.tabulate(model, F.dr.dr, :k)
# plot(tab[:k], tab[:k])
# plot!(tab[:j], tab[:c])

using SimplePlots

tab = Dolo.tabulate(model, F.dr.dr, :w)
plot(tab[:w], tab[:w])
plot!(tab[:w], tab[:c])

# l = Dolo.df_B(F, F.x0, F.x0)

# Dolo.newton(u->F(u,F.x0), F.x0)

sol = Dolo.time_iteration(model, maxit=1000);
tab = tabulate(model, sol.dr, :m)
pl = plot(tab[:m], tab[:m])
plot!(pl, tab[:m], tab[:c])

Dolo.time_iteration(model; ignore_constraints=true);

Dolo.improved_time_iteration(model);

# grid, exo = Dolo.discretize(model)

println("Endo Grid size: $(Dolo.n_nodes(grid.endo))")
println("Exo Grid size: $(Dolo.n_nodes(grid.exo))")
println("Exo Grid I size: $(Dolo.n_inodes(exo, 1))")

grid, exo = Dolo.discretize(model;)

println("Endo Grid size: $(Dolo.n_nodes(grid.endo))")
println("Exo Grid size: $(Dolo.n_nodes(grid.exo))")
println("Exo Grid I size: $(Dolo.n_inodes(exo, 1))")

sol0 = time_iteration(model)

F = Dolo.Euler(model)

@time Dolo.loop_iti(F, F.x0)

@time Dolo.loop_ti(F, F.x0)

# μ = Dolo.ergodic_distribution(model, sol)

# using Plots


### A Pluto.jl notebook ###
# v0.17.2

using Markdown
using InteractiveUtils

# ╔═╡ d9015225-b635-42ad-ae96-fe7772a031b7
using Pkg, DrWatson

# ╔═╡ 727e041b-fe08-4f7d-ad19-e3c57772c967
begin
	using GLM
	using CSV
	using Random
	using StatsBase
	using DataFrames
	using Dagitty
	using Turing
	using StatsPlots
	using StatisticalRethinking
	using StatisticalRethinkingPlots
	using Logging
end

# ╔═╡ 5a128323-2c19-4efa-989f-ff345e6a9cb3
# Pkg.update()

# ╔═╡ 078fdb65-5bd6-4b0d-b672-617f5912480d
begin
	default(labels=false)
	Logging.disable_logging(Logging.Warn);
end;

# ╔═╡ 5141dfdf-490d-479e-ac58-63c929ae8fd1
md"## 7.1 The problem with parameters."

# ╔═╡ 611c3828-f01f-4721-830b-736b28620e7e
md"### Code 7.1"

# ╔═╡ ad511be2-fd88-4aba-a830-21e242d994f1
begin
	sppnames = ["afarensis", "africanus", "habilis", "boisei",
		"rudolfensis", "ergaster", "sapiens"]
	brainvolcc = [438, 452, 612, 521, 752, 871, 1350]
	masskg = [37.0, 35.5, 34.5, 41.5, 55.5, 61.0, 53.5]
	d = DataFrame(:species => sppnames, :brain => brainvolcc, :mass => masskg)
end;

# ╔═╡ 4ee38b80-aded-40af-93ac-11a4ac2b9378
md"### Code 7.2"

# ╔═╡ 5c7f1f26-02ac-4325-a06c-8c26c75e6cf4
begin
	d[!,:mass_std] = (d.mass .- mean(d.mass))./std(d.mass)
	d[!,:brain_std] = d.brain ./ maximum(d.brain)
	d
end

# ╔═╡ 5a2f79ca-2d3e-4cd4-9de9-7c7e283a5052
md"### Code 7.3"

# ╔═╡ 94b5539b-4374-40b8-9501-8d3df49f20c3
@model function model_m7_1(mass_std, brain_std)
    a ~ Normal(0.5, 1)
    b ~ Normal(0, 10)
    μ = @. a + b*mass_std
    log_σ ~ Normal()
    brain_std ~ MvNormal(μ, exp(log_σ))
end

# ╔═╡ 2aafe78c-b1b1-4963-ad89-dbe09b546d96
begin
	m7_1_ch = sample(model_m7_1(d.mass_std, d.brain_std), NUTS(), 1000)
	m7_1 = DataFrame(m7_1_ch)
	PRECIS(m7_1)
end

# ╔═╡ 45122674-c5d2-4f61-af03-c74482618e90
md"### Code 7.4"

# ╔═╡ 3b7ca48f-078f-4eef-9d0c-fa8724e711d3
X = hcat(ones(length(d.mass_std)), d.mass_std)

# ╔═╡ 40c173f3-3dbb-4907-9188-632d34b3d7cf
m = lm(X, d.brain_std)

# ╔═╡ 39dc811c-2742-4977-a203-c9fdcb5b218d
md"### Code 7.5"

# ╔═╡ 85bb82da-efe7-4b34-8af5-cf60ae6e4757
Random.seed!(12);

# ╔═╡ 53806285-ea68-4f5c-b3fb-a382a894ec56
md"## Do explicit simulation due to log_σ."

# ╔═╡ 59b9a24b-6967-418b-a4f8-e67ceb0a5474
begin
	s = [
		rand(MvNormal((@. r.a + r.b * d.mass_std), exp(r.log_σ)))
		for r ∈ eachrow(m7_1)
	]
	s = vcat(s'...);

	r = mean.(eachcol(s)) .- d.brain_std;
	resid_var = var(r, corrected=false)
	outcome_var = var(d.brain_std, corrected=false)
	1 - resid_var/outcome_var
end

# ╔═╡ ed541621-2245-49f9-9672-31e20b9b7765
md"### Code 7.6"

# ╔═╡ 47d9566c-93ec-4f70-b7b6-5586193bcdef
md"#### Function is implemented in a generic way to support any amount of b[x] coefficients."

# ╔═╡ 1e5a39c0-6b5b-4d29-826e-e68c31c8f34e
function R2_is_bad(df; sigma=missing)
    degree = ncol(df[!,r"b"])
    # build mass_std*degree matrix, with each col exponentiated to col's index
    t = repeat(d.mass_std, 1, degree)
    t = hcat(map(.^, eachcol(t), 1:degree)...)
    s = [
        begin
            # calculate product on coefficient's vector
            b = collect(r[r"b"])
            μ = r.a .+ t * b
            s = ismissing(sigma) ? exp(r.log_σ) : sigma
            rand(MvNormal(μ, s))
        end
        for r ∈ eachrow(df)
    ]
    s = vcat(s'...);

    r = mean.(eachcol(s)) .- d.brain_std;
    v1 = var(r, corrected=false)
    v2 = var(d.brain_std, corrected=false)
    1 - v1 / v2
end

# ╔═╡ e8f6166f-20e5-40a2-a8fc-692ea8704b6d
md"### Code 7.7"

# ╔═╡ f74d5bc3-747b-4b12-9fb2-7e4a19cfe2c1
@model function model_m7_2(mass_std, brain_std)
    a ~ Normal(0.5, 1)
    b ~ MvNormal([0, 0], 10)
    μ = @. a + b[1]*mass_std + b[2]*mass_std^2
    log_σ ~ Normal()
    brain_std ~ MvNormal(μ, exp(log_σ))
end

# ╔═╡ fa9522ce-d91d-4cbd-9a1a-fe63fd2b7d15
begin
	m7_2_ch = sample(model_m7_2(d.mass_std, d.brain_std), NUTS(), 10000)
	m7_2 = DataFrame(m7_2_ch)
	PRECIS(m7_2)
end

# ╔═╡ 41fc983a-9209-4ff5-b9fa-5798c7d387af
md"### Code 7.8"

# ╔═╡ 0f8d2476-7379-4bec-8a6f-e6ef81066ebb
md"#### Implemented the sample in a general way."

# ╔═╡ 4632e385-2417-4683-9e31-72825cf5501c
@model function model_m7_n(mass_std, brain_std; degree::Int)
    a ~ Normal(0.5, 1)
    b ~ MvNormal(zeros(degree), 10)
    # build matrix n*degree
    t = repeat(mass_std, 1, degree)
    # exponent its columns
    t = hcat(map(.^, eachcol(t), 1:degree)...)
    # calculate product on coefficient's vector
    μ = a .+ t * b

    log_σ ~ Normal()
    brain_std ~ MvNormal(μ, exp(log_σ))
end

# ╔═╡ bf763ccd-2c72-4529-b6ac-747f39f1b9cf
begin
	m7_3_ch = sample(model_m7_n(d.mass_std, d.brain_std, degree=3), NUTS(), 1000)
	m7_3 = DataFrame(m7_3_ch)
	PRECIS(m7_3)
end

# ╔═╡ ef2e821a-d947-40e1-9855-79819aec5dbb
begin
	m7_4_ch = sample(model_m7_n(d.mass_std, d.brain_std, degree=4), NUTS(), 1000)
	m7_4 = DataFrame(m7_4_ch)
	PRECIS(m7_4)
end

# ╔═╡ e1e48fb9-bb0f-4fe6-a34e-46ea2ced2510
begin
	m7_5_ch = sample(model_m7_n(d.mass_std, d.brain_std, degree=5), NUTS(), 1000)
	m7_5 = DataFrame(m7_5_ch)
	PRECIS(m7_5)
end

# ╔═╡ bff2a56e-e799-4d50-b97b-79983df86565
@model function model_m7_6(mass_std, brain_std)
    a ~ Normal(0.5, 1)
    b ~ MvNormal(zeros(6), 10)
    μ = @. a + b[1]*mass_std + b[2]*mass_std^2 + b[3]*mass_std^3 +
               b[4]*mass_std^4 + b[5]*mass_std^5 + b[6]*mass_std^6
    brain_std ~ MvNormal(μ, 0.001)
end

# ╔═╡ 5c26fd02-6695-4f3d-8f17-37c9b2ada2e6
begin
	m7_6_ch = sample(model_m7_6(d.mass_std, d.brain_std), NUTS(), 1000)
	m7_6 = DataFrame(m7_6_ch)
	PRECIS(m7_6)
end

# ╔═╡ 941248e9-c1ec-4d6a-8a2a-dbdd9aee17d8
md"### Code 7.10"

# ╔═╡ 97a58b2a-a200-4249-acf3-c52d28ca6aea
mass_seq = range(extrema(d.mass_std)...; length=100)

# ╔═╡ 7174161a-6536-4ec7-a89e-2c385de7052c
begin
	l = [
    	@. r.a + r.b * mass_seq
    	for r ∈ eachrow(m7_1)
	]
	l = vcat(l'...)
	μ = mean.(eachcol(l))
end

# ╔═╡ f4955154-ea66-4523-aacd-1a4beef6d41b
begin
	ci = PI.(eachcol(l))
	ci = vcat(ci'...)
end

# ╔═╡ caa5e742-7606-43fa-8ae3-a1287ff24951
scatter(d.mass_std, d.brain_std; title="1: R² = $(round(R2_is_bad(m7_1); digits=3))")

# ╔═╡ 2f524064-abcc-40a1-a21e-99a0a4636545
plot!(mass_seq, [μ μ]; fillrange=ci, c=:black, fillalpha=0.3)

# ╔═╡ 0f92b3fa-1b99-45f4-8a8e-5b7ea33a464d
md"### Reimplemented the brain_plot function to check my results."

# ╔═╡ cb2d9bdf-3cf3-48f2-a984-5440dba08ad9
function brain_plot(df; sigma=missing)
    degree = ncol(df[!,r"b"])
    # build mass_seq*degree matrix, with each col exponentiated to col's index
    t = repeat(mass_seq, 1, degree)
    t = hcat(map(.^, eachcol(t), 1:degree)...)
    l = [
        r.a .+ t * collect(r[r"b"])
        for r ∈ eachrow(df)
    ]
    l = vcat(l'...)
    μ = mean.(eachcol(l))
    ci = PI.(eachcol(l))
    ci = vcat(ci'...)

    r2 = round(R2_is_bad(df, sigma=sigma); digits=3)
    scatter(d.mass_std, d.brain_std; title="$degree: R² = $r2")
    plot!(mass_seq, [μ μ]; fillrange=ci, c=:black, fillalpha=0.3)
end;

# ╔═╡ 29f7fc44-1d5c-4912-a0b0-07a7e97cfe26
plot(
    brain_plot(m7_1),
    brain_plot(m7_2),
    brain_plot(m7_3),
    brain_plot(m7_4),
    brain_plot(m7_5),
    brain_plot(m7_6, sigma=0.001);
    size=(1000, 600)
)

# ╔═╡ bb21db38-31cf-4e88-86d2-922d62533769
md"### Code 7.11"

# ╔═╡ 4f7bfda2-297d-432d-83c9-c931f5f62868
i = 3;

# ╔═╡ 90d5c3e8-a045-4d96-aebc-2ec99609e10b
d_minus_i = d[setdiff(1:end,i),:];

# ╔═╡ 3babf620-dd01-45ae-b21c-e46e136057f6
function brain_loo_plot(model, data; title::String)
    (a, b) = extrema(data.brain_std)
    p = scatter(data.mass_std, data.brain_std; title=title, ylim=(a-0.1, b+0.1))
    mass_seq = range(extrema(data.mass_std)...; length=100)

    for i ∈ 1:nrow(data)
        d_minus_i = data[setdiff(1:end,i),:]
        df = DataFrame(sample(
				model(d_minus_i.mass_std, d_minus_i.brain_std),
				NUTS(),
				1000))

        degree = ncol(df[!,r"b"])

        # build mass_seq*degree matrix, with each col exponentiated to col's index

        t = repeat(mass_seq, 1, degree)
        t = hcat(map(.^, eachcol(t), 1:degree)...)
        l = [
            r.a .+ t * collect(r[r"b"])
            for r ∈ eachrow(df)
        ]
        l = vcat(l'...)
        μ = mean.(eachcol(l))
        plot!(mass_seq, μ; c=:black)
    end
    p
end

# ╔═╡ 9a5d927d-e816-4f5f-a460-c89a507ce1ae
model_m7_4 = (mass, brain) -> model_m7_n(mass, brain, degree=4)

# ╔═╡ b3778ab5-03b7-4ba5-9501-3e6bb643e4d5
plot(
    brain_loo_plot(model_m7_1, d, title="m7.1"),
    brain_loo_plot(model_m7_4, d, title="m7.4");
    size=(800, 400)
)

# ╔═╡ b55cffd3-d5ce-41db-968d-0b54b1b872a7
md"## 7.2 Entropy and accuracy."

# ╔═╡ e8765238-eec6-41c0-9c8c-148c9e51aad9
md"### Code 7.12"

# ╔═╡ fd1f8ae2-6839-4f7e-9141-66824490df72
p = [0.3, 0.7];

# ╔═╡ 3a3537ec-039a-434d-a7d4-15ab41eb97d8
-sum(p .* log.(p))

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
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DrWatson = "634d3b9d-ee7a-5ddf-bec9-22491ea816e1"
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StatisticalRethinking = "2d09df54-9d0f-5258-8220-54c2a3d4fbee"
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Turing = "fce5fe82-541a-59a6-adf8-730c64b5f9a0"

[compat]
CSV = "~0.8.5"
Dagitty = "~0.0.1"
DataFrames = "~1.2.2"
DrWatson = "~2.4.1"
GLM = "~1.5.1"
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StatisticalRethinkingPlots = "~0.3.0"
StatsBase = "~0.33.10"
StatsPlots = "~0.14.26"
Turing = "~0.18.0"
"""

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

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deps = ["ArrayInterface", "CPUSummary", "HostCPUFeatures", "Hwloc", "IfElse", "LayoutPointers", "Libdl", "LinearAlgebra", "SIMDTypes", "Static"]
git-tree-sha1 = "5239606cf3552aff43d79ecc75b1af1ce4625109"
uuid = "3d5dd08c-fd9d-11e8-17fa-ed2836048c2f"
version = "0.21.21"

[[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"

[[Widgets]]
deps = ["Colors", "Dates", "Observables", "OrderedCollections"]
git-tree-sha1 = "80661f59d28714632132c73779f8becc19a113f2"
uuid = "cc8bc4a8-27d6-5769-a93b-9d913e69aa62"
version = "0.6.4"

[[WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "de67fa59e33ad156a590055375a30b23c40299d3"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.5.5"

[[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"

[[ZygoteRules]]
deps = ["MacroTools"]
git-tree-sha1 = "8c1a8e4dfacb1fd631745552c8db35d0deb09ea0"
uuid = "700de1a5-db45-46bc-99cf-38207098b444"
version = "0.2.2"

[[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:
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### A Pluto.jl notebook ###
# v0.12.17

using Markdown
using InteractiveUtils

# ╔═╡ f38a5752-3e3e-11eb-256c-eb1f8de56937
begin
	import Pda
	using Plots
	using PlutoUI
	using HDF5
	using Statistics
end

# ╔═╡ 09068b50-3e3f-11eb-330c-ab8cf9ce1600
file = "/media/HDD1/singlewall/U2.154singlewall.h5"

# ╔═╡ 14f7b2da-3e40-11eb-1aca-593125a5c40c
frame =99

# ╔═╡ a7c0b072-3e3f-11eb-1498-4343ce3bfccc
begin
	t = Pda.get_h5data(file, "config/$(frame)/t")
	x = Pda.get_h5data(file, "config/$(frame)/x")
end

# ╔═╡ be7aa564-3e41-11eb-343a-6f8d2a3367e9
function average_density()
	bins=100
	n = zeros(bins)
	loc = zeros(bins)
	for i in 0:99
		loc, n_ = Pda.density1d(Pda.get_h5data(file, "config/$(i)/x"),
			bins=bins,
			normalize=false)
		n += n_
	end
	return loc, n
end

# ╔═╡ 2bed370c-3e41-11eb-1fb8-c7f187b21521
loc,n = average_density()

# ╔═╡ 7e1e3a7a-3e42-11eb-06c8-679cebbbc9ec
function density_Qclosure(x, Pel::Real)
	laml = sqrt(Pel+0.5*Pel^2)
	n = 1 + 0.5*Pel*exp(-laml*x)
	return n
end

# ╔═╡ abfa5be6-3e41-11eb-0c1a-4d5d565887d3
begin
	scatter(loc[2:end-1],n[2:end-1]/(n[end-10:end-1] |>mean),
		framestyle=:box,
		label="BD")
	U0 = Pda.get_h5attr(file, "U0")
	tauR = Pda.get_h5attr(file, "tauR")
	DT = Pda.get_h5attr(file,"DT")
	Pel = (U0*tauR/sqrt(DT*tauR))^2
	plot!(loc, density_Qclosure.(loc, Pel),
		lw=2,
		label="Q closure")
end

# ╔═╡ Cell order:
# ╠═f38a5752-3e3e-11eb-256c-eb1f8de56937
# ╠═09068b50-3e3f-11eb-330c-ab8cf9ce1600
# ╠═14f7b2da-3e40-11eb-1aca-593125a5c40c
# ╠═a7c0b072-3e3f-11eb-1498-4343ce3bfccc
# ╠═be7aa564-3e41-11eb-343a-6f8d2a3367e9
# ╠═2bed370c-3e41-11eb-1fb8-c7f187b21521
# ╠═7e1e3a7a-3e42-11eb-06c8-679cebbbc9ec
# ╠═abfa5be6-3e41-11eb-0c1a-4d5d565887d3