### A Pluto.jl notebook ###
# v0.18.0

using Markdown
using InteractiveUtils

# ╔═╡ f851dfcb-bfb5-44e5-8d26-ec5143ded32c
begin
using Plots
using Printf
using Unitful
using DataFrames
using CSV
using Images
using Interpolations
using QuadGK
using UnitfulEquivalences
using Markdown
using InteractiveUtils
using PlutoUI
using LsqFit
using Distributions
end

# ╔═╡ 3a4c78f2-9cbf-11ec-0f38-9106893d8f37
md"# RuSL MLs"

# ╔═╡ 485b060c-c360-43f2-903f-3948fa4681d9
import Unitful:
    nm, μm, mm, cm, m, km,
    mg, g, kg,
    ps, ns, μs, ms, s, minute, hr, d, yr, Hz, kHz, MHz, GHz,
    eV,
    μJ, mJ, J,
	μW, mW, W,
    A, N, mol, mmol, μmol, V, L, mL, M

# ╔═╡ 41157231-1df3-4fb7-8922-877f391961a3
import PhysicalConstants.CODATA2018: N_A

# ╔═╡ 7e65685b-b3e6-49ac-80c2-2d71e28ef328
function ingredients(path::String)
	# this is from the Julia source code (evalfile in base/loading.jl)
	# but with the modification that it returns the module instead of the last object
	name = Symbol(basename(path))
	m = Module(name)
	Core.eval(m,
        Expr(:toplevel,
             :(eval(x) = $(Expr(:core, :eval))($name, x)),
             :(include(x) = $(Expr(:top, :include))($name, x)),
             :(include(mapexpr::Function, x) = $(Expr(:top, :include))(mapexpr, $name, x)),
             :(include($path))))
	m
end

# ╔═╡ 4c224e01-6427-4769-aa80-2738a7d208de
lfi = ingredients("../src/LaserLab.jl")

# ╔═╡ 2821e07c-330b-4432-9a79-8c8dd362e929
md"# Computing the density of RuSL MLs from absortion measurements"

# ╔═╡ 5d1bf64d-d0ec-4ced-881c-23e5350d4714
md" ## Method:

The relation between the coverage of a ML and the absorption measured for a given wavelength λ is:

$\Gamma = \frac{A(\lambda)}{10^3 \epsilon(\lambda)}$

where ϵ is the Molar extinction coefficient. When ϵ is expressed in $M^{-1}cm^{-1}$, Γ is expressed in mol/cm$^2$.

A way to compute the coverage when the UV-Vis of the ML is too weak is the following. The relation between abosorbance and extinction coefficient is:

$A = \epsilon \cdot c \cdot l$

Where c is the concentration of the sample and l is the thickness of the sample. Suppose now that one measures the absorbance of a sample before deep coating (the process in which one inserts the substrate in the sample to deposit the ML, aka, deep the biscuit). One gets:

$A_{bdc} = \epsilon \cdot c_{bdc} \cdot l$

If one measures now the absorbance ater deep coating:

$A_{adc} = \epsilon \cdot c_{adc} \cdot l$

The ratio between absorbances is known:

$r = \frac{A_{adc}}{A_{bdc}} = \frac{c_{adc}}{c_{bdc}}$

and thus the concentration after deep coating is simply:

$c_{adc} = r \cdot c_{bdc}$

The number of molecules deposited in the substarte is the difference of concentrations before and after deep coating multiplied by the volume of the solution.

$n = V (c_{bdc} - c_{adc}) = V \cdot c_{bdc}(1 -r)$
"

# ╔═╡ db6ba74f-d7d1-4499-8643-b664fb59d18d
md"
	function compute_coverage(absbdc::Vector{Float64}, absadc::Vector{Float64}, cbdc::typeof(1.0M), vol::typeof(1.0mL))
"

# ╔═╡ de411ad6-a134-44bd-abc3-0130278d17e5
function compute_coverage(absbdc::Vector{Float64}, absadc::Vector{Float64}, cbdc::typeof(1.0M), vol::typeof(1.0mL))
	r = sum(absadc) / sum(absbdc)
	dc = (1.0 - r) * cbdc
	r, uconvert(NoUnits, dc * N_A * vol)
end

# ╔═╡ 4fe2fc70-0cf8-48ee-a1b5-bb62d5dba989
begin
	spG = lfi.LaserLab.CsvG(';',',')  # spanish: decimals represented with ',' delimited with ';'
	enG = lfi.LaserLab.CsvG(',','.')  # english
	enG2 = lfi.LaserLab.CsvG('\t','.')  # english
	println("")
end

# ╔═╡ 0845980e-031a-4fa1-95d6-104fe862f6ae
md"## Calculations"

# ╔═╡ 353f8531-3b42-4c84-bc9e-8a976c371a55
begin
	dfrusl = lfi.LaserLab.load_df_from_csv("/Users/jj/JuliaProjects/LaserLab/data/fluorimeter", "RuSL062_before_after_dip_coating.csv", spG)
	dfrusl[!, :λ] = convert.(Float64, dfrusl[:, :λ])
	#sort!(dfrusl, rev = true)
	sort!(dfrusl, [order(:λ, rev=false)])
	first(dfrusl,10)
	println("")
end

# ╔═╡ a4d8258c-9623-44d8-a28d-c88893d90354
begin
	pbdc = plot(dfrusl.λ, dfrusl.Rus0_46muM_bdc, lw=2, label="RuSL 0.46 μM bdc")
	padc = plot(pbdc, dfrusl.λ, dfrusl.Rus0_46muM_adc, lw=2, label="RuSL 0.46 μM adc")
	xlabel!("λ (nm)")
	ylabel!("A")
	println("")
end

# ╔═╡ f98c6d82-469d-4723-a951-279bda55bd15
begin
	pbdc2 = plot(dfrusl.λ, dfrusl.Rus4_6muM_bdc, lw=2, label="RuSL 4.6 μM bdc")
	padc2 =plot(pbdc2, dfrusl.λ, dfrusl.Rus4_6muM_adc, lw=2, label="RuSL 4.6 μM adc")
	xlabel!("λ (nm)")
	ylabel!("A")
	println("")
end

# ╔═╡ 3120d6a0-07c9-499b-8fd7-53bc3d6bb4f4
begin
	pbdc3 = plot(dfrusl.λ, dfrusl.Rus46muM_bdc, lw=2, label="RuSL 46 μM bdc")
	padc3 = plot(pbdc3, dfrusl.λ, dfrusl.Rus46muM_adc, lw=2, label="RuSL 46 μM adc")
	xlabel!("λ (nm)")
	ylabel!("A")
	println("")
end

# ╔═╡ 30c1e4c7-832e-49f2-b4e3-330439a7fca7
begin
	pbdc4 = plot(dfrusl.λ, dfrusl.Rus460muM_bdc, lw=2, label="RuSL 460 μM bdc")
	padc4 = plot(pbdc4, dfrusl.λ, dfrusl.Rus460muM_adc, lw=2, label="RuSL 460 μM adc")
	xlabel!("λ (nm)")
	ylabel!("A")
	println("")
end

# ╔═╡ bd45b1ed-d43a-4b24-a362-0a5c32f95d27
plot(padc, padc2, padc3, padc4, layout = (2, 2), legend = :topright, fmt = :png)

# ╔═╡ 2c878765-524c-4e2e-8beb-b7b29fd732aa
begin
	cb     = 0.46e-6*M
	cb10   = 4.6e-6*M
	cb100  = 46.0e-6*M
	cb1000 = 460.0e-6*M
	vl = 2.0mL
	println("")
end

# ╔═╡ 88295e05-1367-4aa5-8099-d70ba5002b54
uconvert(NoUnits, cb * N_A * vl)

# ╔═╡ 27a672d3-e0f4-47b6-8ed9-666e1258790c
uconvert(NoUnits, 35.0e-9mol * N_A)

# ╔═╡ 304d53ac-c748-4f9a-80fd-05eb88073eb8
uconvert(NoUnits, 30.0e-6*M * N_A * 1.0mL)

# ╔═╡ ef090bec-5334-4d45-b6ce-1c9cc54cda1e
begin
	r0d46x, c0d46x = compute_coverage(dfrusl.Rus0_46muM_bdc, dfrusl.Rus0_46muM_adc,
	cb,vl)
	r4d6x, c4d6x   = compute_coverage(dfrusl.Rus4_6muM_bdc, dfrusl.Rus4_6muM_adc, cb10, vl)
	r46x, c46x     = compute_coverage(dfrusl.Rus46muM_bdc, dfrusl.Rus46muM_adc, cb100, vl)
	r460x, c460x   = compute_coverage(dfrusl.Rus460muM_bdc, dfrusl.Rus460muM_adc, cb1000, vl)
	println("")
end

# ╔═╡ c1855839-8b96-4077-afd7-bd290c4d0ce6
begin
	r0d46 = round(r0d46x, sigdigits=2)
	c0d46 = round(c0d46x, sigdigits=2)
	r4d6 = round(r4d6x, sigdigits=2)
	c4d6 = round(c4d6x, sigdigits=2)
	r46 = round(r46x, sigdigits=2)
	c46 = round(c46x, sigdigits=2)
	r460 = round(r460x, sigdigits=2)
	c460 = round(c460x, sigdigits=2)
	println("")
end

# ╔═╡ 6e6902c2-e61b-4101-a4ac-369d8317e26c
md"## Results (nmolec/cm$^2$)

| | 0.46 μM   | 4.6 μM      | 46 μM  | 460 μM
|:--|:-------| ---------- |:-----:|:-----:|
|n/cm2| $c0d46  | $c4d6| $c46 | $c460
|r| $r0d46  | $r4d6| $r46 | $r460

"

# ╔═╡ 00000000-0000-0000-0000-000000000001
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deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"

[[deps.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"

[[deps.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"

[[deps.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"

[[deps.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"

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

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

[[deps.Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e45044cd873ded54b6a5bac0eb5c971392cf1927"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.2+0"

[[deps.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"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"

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

[[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.libsixel_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "78736dab31ae7a53540a6b752efc61f77b304c5b"
uuid = "075b6546-f08a-558a-be8f-8157d0f608a5"
version = "1.8.6+1"

[[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"
"""

# ╔═╡ Cell order:
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# ╟─f851dfcb-bfb5-44e5-8d26-ec5143ded32c
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# ╟─7e65685b-b3e6-49ac-80c2-2d71e28ef328
# ╟─4c224e01-6427-4769-aa80-2738a7d208de
# ╠═2821e07c-330b-4432-9a79-8c8dd362e929
# ╟─5d1bf64d-d0ec-4ced-881c-23e5350d4714
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# ╟─6e6902c2-e61b-4101-a4ac-369d8317e26c
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# ╟─a4d8258c-9623-44d8-a28d-c88893d90354
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# ╟─3120d6a0-07c9-499b-8fd7-53bc3d6bb4f4
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# ╠═2c878765-524c-4e2e-8beb-b7b29fd732aa
# ╠═88295e05-1367-4aa5-8099-d70ba5002b54
# ╠═27a672d3-e0f4-47b6-8ed9-666e1258790c
# ╠═304d53ac-c748-4f9a-80fd-05eb88073eb8
# ╠═ef090bec-5334-4d45-b6ce-1c9cc54cda1e
# ╟─c1855839-8b96-4077-afd7-bd290c4d0ce6
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002


using MultivariateFunctions
using Random
using DataFrames
using Distributions
using DataStructures

Random.seed!(1992)
nObs = 1000
dd = DataFrame()
dd[:x] = rand( Normal(),nObs) + 0.1 .* rand( Normal(),nObs)
dd[:z] = rand( Normal(),nObs) + 0.1 .* rand( Normal(),nObs)
dd[:w] = (0.5 .* rand( Normal(),nObs)) .+ 0.7.*(dd[:z] .- dd[:x]) + 0.1 .* rand( Normal(),nObs)
dd[:y] = (dd[:x] .*dd[:w] ) .* (dd[:z] .- dd[:w]) .+ dd[:x] + rand( Normal(),nObs)
dd[7,:y] = 1.0
y = :y
x_variables = Set{Symbol}([:w, :x, :z])

dd2 = deepcopy(dd)
dd2[dd2[:x] .< 0.0, :y] = 2.7
dd2[(dd2[:x] .> 0.0) .& (dd2[:w] .> 0.0), :y] = 1.3
dd2[(dd2[:x] .> 0.0) .& (dd2[:w] .< 0.0), :y] = 1.1

# Recursive Partitioning
rp_1, rp_reg_1 = create_recursive_partitioning(dd, y, x_variables, 3; rel_tol = 1e-3)
rp_2, rp_reg_2 = create_recursive_partitioning(dd, y, x_variables, 3; rel_tol = 1e-10)
SSR_1 = sum((rp_reg_1.rr.mu .- rp_reg_1.rr.y) .^ 2)
rp_3, rp_reg_3 = create_recursive_partitioning(dd, y, x_variables, 4; rel_tol = 1e-3)
SSR_3 = sum((rp_reg_3.rr.mu .- rp_reg_3.rr.y) .^ 2)
SSR_3 <= SSR_1
rp_4, rp_reg_4 = create_recursive_partitioning(dd, y, x_variables, 7; rel_tol = 1e-3)
SSR_4 = sum((rp_reg_4.rr.mu .- rp_reg_4.rr.y) .^ 2)
SSR_4 <= SSR_3
# Where we have piecewise constant data.
rp_21, rp_reg_21 = create_recursive_partitioning(dd2, y, x_variables, 3; rel_tol = 1e-3)
sum(abs.(evaluate(rp_21, dd2) .- dd2[:y])) < 1e-10

# MARS Spline
rp_1, rp_reg_1 = create_mars_spline(dd, y, x_variables, 3; rel_tol = 1e-3)
dd3 = deepcopy(dd)
dd3[:y] = 8.0 .* max.(0.0, dd3[:x] .+ 3.2) .+ 2.0 .* max.(0.0, dd3[:z] .+ 2.4) .+ 2.7 .* max.(0.0, dd3[:w] .- 1.2)
rp_32, rp_reg_32 = create_mars_spline(dd3, y, x_variables, 7; rel_tol = 1e-3)
sum(abs.(evaluate(rp_32, dd3) .- dd3[:y])) < 1e-08
dd4 = deepcopy(dd)
dd4[:y] = 1.0 .* max.(0.0, dd4[:x] .+ 3.2) .+ 2.0 .* max.(0.0, dd4[:z] .+ 2.4) .* max.(0.0, dd4[:w] .- 1.2)
rp_41, rp_reg_41 = create_mars_spline(dd4, y, x_variables, 7; rel_tol = 1e-3)
rp_41_RSS = sum(abs.(evaluate(rp_41, dd4) .- dd4[:y]))
rp_41_RSS < 0.05 # Here we dont get a great result. Because first it splits but w and then z so both are out of whack.
rp_41_5, rp_reg_41_5 = create_mars_spline(dd4, y, x_variables, 3; rel_tol = 1e-3)
reg_41_5_RSS = sum(abs.(evaluate(rp_41_5, dd4) .- dd4[:y]))

# Trim number of functions
trimmed_rp_41_fin, trimmed_rp_reg_41_fin = trim_mars_spline(dd4, y, rp_41; final_number_of_functions = 5)
reg_41_RSS_trimmed_to_five = sum(abs.(evaluate(trimmed_rp_41_fin, dd4) .- dd4[:y]))
reg_41_RSS_trimmed_to_five < reg_41_5_RSS # Because building a bigger model and then trimming should probably lead to lower RSS
reg_41_RSS_trimmed_to_five > rp_41_RSS # Because trimmed model should have higher RSS
# Maximum increase in RSS
trimmed_rp_41_maxinc, trimmed_rp_reg_41_maxinc = trim_mars_spline(dd4, y, rp_41; maximum_increase_in_RSS = 5.0)
trimmed_rp_41_maxrss, trimmed_rp_reg_41_maxrss = trim_mars_spline(dd4, y, rp_41; maximum_RSS = 100.0)
trimmed_rp_41_maxrss_trimmed = sum(abs.(evaluate(trimmed_rp_41_maxrss, dd4) .- dd4[:y]))
trimmed_rp_41_maxrss_trimmed < 100.0


__precompile__(true)

module Sorting

	function is_sorted(data::Array)
		sorted = true
		for i in 1 : length(data) - 1
			sorted &= data[i + 1] >= data[i]
		end

		return sorted
	end

	function is_sorted(data::Array, length::Int)
		sorted = true
		for i in 1 : length - 1
			sorted &= data[i + 1] >= data[i]
		end

		return sorted
	end

	function median!(a::Array)
		p, r = 1, length(a) + 1
		mid = fld(r + p, 2)
		if (r - p) % 2 == 0
			return (select_element!(a, mid) + select_element!(a, mid - 1)) / 2
		else
			return select_element!(a, mid)
		end
	end

	function median(a::Array)
		return median!(copy(a))
	end

	include("insertionsort.jl")
	include("bubblesort.jl")
	include("quicksort.jl")
	include("mergesort.jl")
	include("bisect.jl")
	include("select.jl")
	include("radix.jl")
	include("heapsort.jl")
	include("filesort.jl")
end