""" Example usage :
@observation MyModel begin
    Categorical(epsilon_argmax(ucb(Q, U, c)))
end
or
@observation MyModel begin
    Categorical(epsilon_greedy(softmax(ucb(Q, U, c))))
end
"""

function epsilon_greedy!(P, ϵ)
    N = length(P)
    P .*= 1 - ϵ
    P .+= ϵ/(N)
    return P
end

function epsilon_argmax(Q::Vector{T}, ϵ) where T
    P = zero(Q)
    P[argmax(Q)] = one(T)
    return epsilon_greedy!(P, ϵ)
end

function ucb!(Q, U, c)
    Q .+= c * sqrt.(U)
end


######################################################
#
# Trading Time Plot
#
# Date:   2014-10-02
# Author: Hessel Tuinhof
#
# Plot trading time against physical time. Trading time
# is the cumulative sum of a multiplicative cascade.
# Here we use a canonical binomial cascade.
#
# Required packages: 	PyPlot
# Required functions:	BinomialCanonical.jl
#
######################################################

# load packages & functions
using PyPlot
require("../src/cascades/BinomialCanonical.jl")

# define colors
rouge = (0.79, 0.0, 0.1)
turquoise = (0, 0.41, 0.41)

# configure parameters
m0 = [0.5, 0.6, 0.65, 0.75]
num_cascades = 10

# set seed
srand(314159265358979323846)

# plot trading time
for i = 1:4
	figure()
	mu = BinomialCanonical(m0[i], num_cascades)
	x_coordinates = linspace(0, 1, 2^num_cascades)
	y_coordinates = cumsum(mu)/cumsum(mu)[end]
	plot(x_coordinates, y_coordinates, linewidth = 1, color = rouge)
	plot([0, 1], [0, 1], linewidth = 1, linestyle = "--", color = turquoise)
end


# 2D FWI gradient test with 4 sources
# The receiver positions and the source wavelets are the same for each of the four experiments.
# Author: Philipp Witte, pwitte@eos.ubc.ca
# Date: January 2017
#

using PyCall, PyPlot, JUDI.TimeModeling, Test, LinearAlgebra

## Set up model structure
n = (120,100)	# (x,y,z) or (x,z)
d = (10.,10.)
o = (0.,0.)

# Velocity [km/s]
v = ones(Float32,n) .* 2.0f0
v[:,Int(round(end/2)):end] .= 3.0f0
v0 = smooth10(v,n)
rho = ones(Float32, n)
rho[:, Int(round(end/2)):end] .= 1.5f0

# Slowness squared [s^2/km^2]
m = (1f0 ./ v).^2
m0 = (1f0 ./ v0).^2
dm = m0 - m

# Setup info and model structure
nsrc = 1	# number of sources
ntComp = 250
info = Info(prod(n), nsrc, ntComp)	# number of gridpoints, number of experiments, number of computational time steps
model = Model(n,d,o,m;rho=rho)
model0 = Model(n,d,o,m0;rho=rho)

## Set up receiver geometry
nxrec = 81
xrec = range(200f0,stop=1000f0,length=nxrec)
yrec = 0.
zrec = range(100f0,stop=100f0,length=nxrec)

# receiver sampling and recording time
timeR = 1000f0	# receiver recording time [ms]
dtR = 4f0	# receiver sampling interval

# Set up receiver structure
recGeometry = Geometry(xrec,yrec,zrec;dt=dtR,t=timeR,nsrc=nsrc)

## Set up source geometry (cell array with source locations for each shot)
xsrc = convertToCell([600f0])
ysrc = convertToCell([0f0])
zsrc = convertToCell([50f0])

# source sampling and number of time steps
timeS = 1000f0
dtS = 4f0	# receiver sampling interval

# Set up source structure
srcGeometry = Geometry(xsrc,ysrc,zsrc;dt=dtS,t=timeS)

# setup wavelet
f0 = 0.01f0
wavelet = ricker_wavelet(timeS,dtS,f0)

###################################################################################################

# Gradient test
h = 1f0
iter = 8
error1 = zeros(iter)
error2 = zeros(iter)
h_all = zeros(iter)
srcnum = 1:nsrc
modelH = deepcopy(model0)

# Observed data
opt = Options(sum_padding=true)
F = judiModeling(info,model,srcGeometry,recGeometry;options=opt)
q = judiVector(srcGeometry,wavelet)
d = F*q

# FWI gradient and function value for m0
Jm0, grad = fwi_objective(model0,q,d;options=opt)

for j=1:iter
	# FWI gradient and function falue for m0 + h*dm
	modelH.m = model0.m + h*dm
	Jm, gradm = fwi_objective(modelH,q,d;options=opt)

	dJ = dot(grad,vec(dm))

	# Check convergence
	error1[j] = abs(Jm - Jm0)
	error2[j] = abs(Jm - (Jm0 + h*dJ))

	println(h, " ", error1[j], " ", error2[j])
	h_all[j] = h
	global h = h/2f0
end

# Check error decay
rate_0th_order = 2^(iter - 1)   # error decays w/ factor 2
rate_1st_order = 4^(iter - 1)   # error decays w/ factor 4

@test error1[end] <= error1[1] / rate_0th_order
@test error2[end] <= error2[1] / rate_1st_order

# Plot errors
if isinteractive()
    loglog(h_all, error1); loglog(h_all, 1e2*h_all)
    loglog(h_all, error2); loglog(h_all, 1e2*h_all.^2)
    legend([L"$\Phi(m) - \Phi(m0)$", "1st order", L"$\Phi(m) - \Phi(m0) - \nabla \Phi \delta m$", "2nd order"], loc="lower right")
    xlabel("h")
    ylabel(L"Error $||\cdot||^\infty$")
    title("FWI gradient test")
end


### A Pluto.jl notebook ###
# v0.19.2

using Markdown
using InteractiveUtils

# ╔═╡ 28329d08-9860-11ec-0a4d-a733da82b9cf
begin
	using PlutoUI
	using CSV
	using DataFrames
	using DataFramesMeta
	using StatsPlots
	using Statistics
	using Flux
end

# ╔═╡ 78e2c184-8085-46f6-a9a3-e317034761ae
begin
	using LinearAlgebra
	using ProgressMeter
end

# ╔═╡ 7e89944e-3be2-4db4-86c0-44bb1e8317e1
iris = CSV.File("./train.tsv") |> DataFrame

# ╔═╡ a8612317-fcf6-4271-a6bc-6007baf3aaff
LocalResource("./iris.JPG")

# ╔═╡ 08421c62-5c47-4c2d-91f0-935ba4cda0b6
rename!(iris, [:id, :SepalLength, :SepalWidth, :PetalLength, :PetalWidth, :Class])

# ╔═╡ 3589c515-8a20-471f-b1d1-ac197210d6d8
# 要約統計量
describe(iris)

# ╔═╡ ac0c53f6-eb54-4736-992f-5ad8abe7fcb8
# 各グループごとにそれぞれの長さの平均を見る
combine(groupby(iris, :Class), [:SepalLength, :SepalWidth, :PetalLength, :PetalWidth] .=> mean)

# ╔═╡ db754358-61ce-4233-83c9-72d541edba2d
ua = unique(iris[!, :Class])

# ╔═╡ 52cfe26c-f816-44c8-a05f-accb70479607
iris[!, :Class] = [findfirst(==(x), ua) - 1 for x in iris[!,:Class]]

# ╔═╡ 4e88a468-6852-4be6-89cf-807929f8b44d
iris

# ╔═╡ 49546d8f-177d-4330-bde3-3eaef617096b
setosa = @linq iris |> where(:Class .== 0)

# ╔═╡ 11b5f1ff-e3c7-4958-878c-4cc6bd82216a
versicolor = @linq iris |> where(:Class .== 1)

# ╔═╡ 9f452c48-90fc-47e9-bc0b-81af4236aae5
virginica = @linq iris |> where(:Class .== 2)

# ╔═╡ 9ffa10fb-b3b1-4d8c-b4fd-872ccc74b74d
let
	plot(xlim=(4.0, 7.5), ylim=(0.8, 5.8), framestyle=:box, legend=:topleft)
	plot!(xlabel="sepal length [cm]", ylabel="petal length [cm]")
	@df setosa scatter!(:SepalLength, :PetalLength; shape=:circle, c=:blue, label="setosa")
	@df versicolor scatter!(:SepalLength, :PetalLength; shape=:x, c=:red, label="versicolor")

end

# ╔═╡ 8f5656bc-0757-4f5c-b6fc-ea43a456a0e6
sort!(iris, [:Class])

# ╔═╡ de1a2edd-785c-49df-9ab1-902e2050f01a
features_raw = Matrix(iris[!, 2:5])

# ╔═╡ a0e28ba3-6bf1-44ff-aad6-105b70c25e42
labels_raw = iris[!, :Class]

# ╔═╡ 8d3599e2-d4e0-4dce-806b-efad129c0e3f
length(labels_raw)

# ╔═╡ 49909aef-843b-4d32-9909-8fc8fe84416f
begin
	X1 = features_raw[1:25, 1]
	Y1 = features_raw[1:25, 2]
	Z1 = features_raw[1:25, 3]
	W1 = features_raw[1:25, 4]

	X2 = features_raw[26:50, 1]
	Y2 = features_raw[26:50, 2]
	Z2 = features_raw[26:50, 3]
	W2 = features_raw[26:50, 4]

	X3 = features_raw[51:75, 1]
	Y3 = features_raw[51:75, 2]
	Z3 = features_raw[51:75, 3]
	W3 = features_raw[51:75, 4]
end

# ╔═╡ 201212f2-68b3-4e58-b01d-20679cf3a46a
let
	default( markersize = 4 )
	plot(xaxis=("sepal length (cm)"), yaxis=("sepal width (cm)"), zaxis=("petal length (cm)"))
	scatter!( X1, Y1, Z1, label = "Iris setosa")
	scatter!( X2, Y2, Z2, label = "Iris versicolor")
	scatter!( X3, Y3, Z3, label = "Iris virginica")
end

# ╔═╡ e298a8ca-d239-4162-a242-4990322eb558

# ╔═╡ bc719327-d7d7-4f9a-a96d-603fa3019ae5
# ラベルをもらって、どの分類化に書き換える関数
function LabelToNum(labels)
	if labels == 0
		return [ 1.0, 0, 0 ]
	elseif labels == 1
		return [ 0, 1.0, 0 ]
	else
		return [ 0, 0, 1.0 ]
	end
end

# ╔═╡ a1daf9f7-1406-407f-9ab9-7b15d9a1c04c
labels = LabelToNum.(labels_raw)

# ╔═╡ 10c86974-250c-4bbc-8098-8154bf4e6364
begin
	toCheckIDs = vcat( 21:25, 46:50, 71:75)
	features_raw_toCheck = features_raw[toCheckIDs, :]
	labels_toCheck = labels[toCheckIDs]
end

# ╔═╡ 76205f2c-990e-4927-b819-e3a4efb2d4ea
begin
	SampleIDs = setdiff( 1:75, toCheckIDs)
	features_raw_sample = features_raw[SampleIDs, :]
	labels_sample = labels[SampleIDs]
end

# ╔═╡ dedb846e-584b-4a58-8c45-a19c1cf161c4
begin
	Std = [ std( features_raw_sample[:,i] ) for i in 1:4]
	Mean = [ mean( features_raw_sample[:,i] ) for i in 1:4]
end

# ╔═╡ 7b9d1531-3fd8-438f-9c98-31721fbf050f
begin
	features_toCheck = (features_raw_toCheck' .- Mean) ./ Std
	features_sample  = (features_raw_sample'  .- Mean) ./ Std
end

# ╔═╡ fdbe39d0-ac58-4a28-8ae4-af650968a797
features_toCheck

# ╔═╡ 309fb568-f7ef-4fe9-b50d-c4cb04e86f65
function nn(M, input; n=20)

    Ci = view( M, :, 1:4)
    bi = view( M, :, 5 )

    C1 = view( M, :, 6:n+5)
    b1 = view( M, :, n+6)

    C2 = view( M, :, n+7:2n+6)
    b2 = view( M, :, 2n+7)

    C3 = view( M, :, 2n+8:3n+7)
    b3 = view( M, :, 3n+8)

    C4 = view( M, :, 3n+9:4n+8)
    b4 = view( M, :, 4n+9)

    C5 = view( M, :, 4n+10:5n+9)
    b5 = view( M, :, 5n+10)

    Co = ( view( M, :, 5n+11:5n+13) )'  # 転置
    bo = view( M, 1:3, 5n+14 )

    r1 = sigmoid.( Ci * input + bi)

    r2 = sigmoid.( C1 * r1 + b1 )
    r3 = sigmoid.( C2 * r2 + b2 )
    r4 = sigmoid.( C3 * r3 + b3 )
    r5 = sigmoid.( C4 * r4 + b4 )
    r6 = sigmoid.( C5 * r5 + b5 )

    output = softmax( Co * r6 + bo)

    return output
end

# ╔═╡ 219fc7e5-6c91-44a8-b989-de494ec713d5
loss( output, v_true ) = Flux.crossentropy( output, v_true )

# ╔═╡ 90bb8c35-8094-4019-a0b1-f80c5b05f653
begin
	n = 20
	H = 10.0 * (rand(n, 5n+14) .- 0.5)

	g(H, i) = loss( nn(H, features_sample[:, i]), labels_sample[i])

	itr = 500
	datasize = size(labels_sample)[1]

	@showprogress for i in 1:(itr * datasize)
		global H
		num = rand(1:datasize)
		grad_f = Flux.gradient(M -> g(M, num), H)[1]
		grad_size = norm(grad_f)^2

		if grad_size < 0.01
			γ = 0.1
		else
			γ = g(H, num) / grad_size
		end

		H += -γ * grad_f
	end
end

# ╔═╡ 21a1013e-2ca2-4910-87af-7ed6b9138e3a
begin
	nn_sample(i) = nn( H, features_sample[:, i])
	nn_sample(1)
end

# ╔═╡ e3f61d75-d2ea-4702-8971-4f81b30430f6
labels_sample[1]

# ╔═╡ dd18e4ee-5b77-4302-9d81-7c384193b19c
nn_sample(30)

# ╔═╡ 1e51cf50-410f-4a50-8b70-8684af0fa497
function decision(x)
	v = similar(x)
	max_i = argmax(x)

	for i in 1:size(x)[1]
		if i == max_i
			v[i] = 1.0
		else
			v[i] = 0.0
		end
	end
	return v
end

# ╔═╡ 84bf9edf-fb54-44de-ad8a-eea9b93a4616
error_sample = labels_sample - decision.(nn_sample.(1:60))

# ╔═╡ 8a85bf9b-8314-48a8-842c-f3c53e155459
nn_toCheck(i) = nn( H, features_toCheck[:, i])

# ╔═╡ 3ae1d144-ce7b-4729-b5a4-d3748088ae41
features_toCheck[:, 1]

# ╔═╡ cab39868-cd2e-4641-85ee-4912c4aafe07
nn_toCheck(1)

# ╔═╡ 724392ba-6973-4db9-8c21-fa7ddd76ca66
test_iris = CSV.File("./test.tsv") |> DataFrame

# ╔═╡ e89b3ec1-cacf-4501-9a1e-bc2a7a29c76d
features_raw_toTest = Matrix(test_iris)[:,2:end]

# ╔═╡ 2308910f-7091-4779-97de-30d9f080eeb8
id_Test =  Matrix(test_iris)[:,1]

# ╔═╡ bfb95b52-d0b7-4a56-9642-ea96200ebeef
features_toTest = (features_raw_toTest' .- Mean) ./ Std

# ╔═╡ 02e78399-1ade-40fd-ad72-1dd7320c0e4d
nn_toTest(i) = nn( H, features_toTest[:,i])

# ╔═╡ 568105a2-a9fa-4250-99a5-37ffa81b7d4d
function get_answers()
	answers = []
	for i in 1:75
		ans = nn_toTest(i) |> argmax
		push!(answers, ans)
	end
	return answers
end

# ╔═╡ 90d6d48a-04cc-44a2-8b00-20188484d472
ans = get_answers()

# ╔═╡ 81018fb1-496c-4985-804a-f189d60f6e65
test_iris[:,1]

# ╔═╡ 08479be2-3e69-4f33-a04b-bdbd14620e14
out = hcat( test_iris[:,1], ans) |> x -> DataFrame(x, :auto)

# ╔═╡ 8d394251-e703-46e1-982c-8b427ada625f
begin
	out.x3 = similar(out.x2)
	for i in 1:75
		if out.x2[i] == 1
			out.x3[i] = "Iris-setosa"
		elseif out.x2[i] == 2
			out.x3[i] = "Iris-versicolor"
		else
			out.x3[i] = "Iris-virginica"
		end
	end
end

# ╔═╡ dc23ed0d-55b7-4ac2-9532-b38765aa0b6e
out

# ╔═╡ e2f6378c-869e-4307-8858-78ddbb063139
out2 = hcat( out.x1, out.x3) |> x -> DataFrame(x, :auto)

# ╔═╡ 0032fc94-b4b5-40fd-af95-11f678d4450d
CSV.write("./output.csv", out2)

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
DataFramesMeta = "1313f7d8-7da2-5740-9ea0-a2ca25f37964"
Flux = "587475ba-b771-5e3f-ad9e-33799f191a9c"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
ProgressMeter = "92933f4c-e287-5a05-a399-4b506db050ca"
Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"

[compat]
CSV = "~0.10.2"
DataFrames = "~1.3.2"
DataFramesMeta = "~0.10.0"
Flux = "~0.12.9"
PlutoUI = "~0.7.35"
ProgressMeter = "~1.7.1"
StatsPlots = "~0.14.33"
"""

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

julia_version = "1.7.2"
manifest_format = "2.0"

[[deps.AbstractFFTs]]
deps = ["ChainRulesCore", "LinearAlgebra"]
git-tree-sha1 = "6f1d9bc1c08f9f4a8fa92e3ea3cb50153a1b40d4"
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[[deps.AbstractPlutoDingetjes]]
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[[deps.libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"

[[deps.libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"

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

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

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

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

[[deps.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"
"""

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using Test, Random, LinearAlgebra, SparseArrays
using BitBasis

using QuAlgorithmZoo
import QuAlgorithmZoo: _num_grover_step
using Yao

function GroverSearch(oracle, num_bit::Int; psi::DefaultRegister = uniform_state(num_bit))
    it = groveriter(psi, oracle)
    for l_psi in it psi = l_psi end
    return (it.niter, psi)
end

function inference(psi::DefaultRegister, evidense::Vector{Int}, num_iter::Int)
    oracle = inference_oracle(evidense)(nqubits(psi))
    it = groveriter(psi, oracle)
    for l_psi in it psi = l_psi end
    it.niter, psi
end

@testset "oracle" begin
    oracle = inference_oracle([2,-1,3])(3)
    # ≈ method for Identity/PermuteMultiply/Sparse
    # add and mimus between sparse matrices.
    # alway use sorted CSC format.
    v = ones(1<<3)
    v[Int(0b110)+1] *= -1
    @test mat(oracle) ≈ Diagonal(v)
    @test mat(chain(phase(π), Z)) ≈ -mat(Z)
end

@testset "Grover Search" begin
    ####### Construct Grover Search Using Reflection Block
    num_bit = 12
    oracle = inference_oracle(push!(collect(Int, 1:num_bit-1), num_bit))(num_bit)

    niter, psi = GroverSearch(oracle, 12)
    target_state = zeros(1<<num_bit); target_state[end] = 1
    @test isapprox(abs(statevec(psi)'*target_state), 1, atol=1e-3)
end

@testset "groverblock" begin
    psi = uniform_state(5)
    or = inference_oracle(5, [-1,2,5,4,3])
    func_or = or
    gb = groverblock(or, psi)
    gb2 = groverblock(func_or, psi)
    @test apply!(copy(psi), gb) == (for l_psi in groveriter(copy(psi), func_or) psi = l_psi end; psi)
    @test apply!(copy(psi), gb) == apply!(copy(psi), gb2)
end

@testset "test inference" begin
    num_bit = 12
    psi0 = rand_state(num_bit)
    #psi0 = uniform_state(num_bit)
    evidense = [1, 2, 3, 4, 5, 6, 7, 8, 9]
    #evidense = collect(1:num_bit)

    # the desired subspace
    basis = collect(UInt, 0:1<<num_bit-1)
    subinds = [itercontrol(num_bit, abs.(evidense), Int.(evidense.>0))...]

    v_desired = statevec(psi0)[subinds .+ 1]
    p = norm(v_desired)^2
    v_desired[:] ./= sqrt(p)

    # search the subspace
    num_iter = _num_grover_step(p)
    niter, psi = inference(psi0, evidense, num_iter)
    @test isapprox((psi.state[subinds .+ 1]'*v_desired) |> abs2, 1, atol=3e-2)
end