#Citation (original paper) - Fountoukis, C., Nenes, A., 2007. ISORROPIA II: a computationally efficient thermodynamic equilibrium model for K+-Ca2+-Mg2+-NH4+-Na+-SO42--NO3--Cl--H2O aerosols. Atmospheric Chemistry and Physics 7, 4639–4659. https://doi.org/10.5194/acp-7-4639-2007

#The present code follows the algorithm devised by Fountoukis and Nenes, 2007 in julia language using various packages such as Catalyst.jl and ModellingToolkit.jl. The model utilizes input values for Temperature (T), Relative Humidity and aqueous concentrations (ug/m3) of Na, H2SO4, NH3, HNO3, HCL, Ca2+, K+ AND Mg2+ and predicts the concentrations of various other chemical species (38 species in total).

### A Pluto.jl notebook ###
# v0.17.3

using Markdown
using InteractiveUtils

# ╔═╡ 9014f3c0-5dec-11ec-1d46-efedaead02f9
using Catalyst, OrdinaryDiffEq, DiffEqBase,Plots,StochasticDiffEq, DifferentialEquations, ModelingToolkit, NonlinearSolve

# ╔═╡ e6cfd4c7-fe1f-4991-b5f7-3eaf157b6df9
@parameters p1 p2 p3 p4 p5 p6 p7 p8 p9 p10 p11 p12 p13 p14 p15 p16 p17 p18 p19 p20 p21 p22 p23 p24 p25 p26 p27 p28 p29 p30 p31 p32 p33 p34 p35 p36 p37 p38 p39 p40 p41 p42 p43 p44 p45 p46 p47 p48 p49 p50 p51 p52 p53 p54 t

# ╔═╡ 1bbc8b1b-6ecd-453a-a508-b561ca347ec7
@variables CANO32s(t) CA2aq(t) NO3aq(t) CACL2s(t) CLaq(t) CASO4s(t) SO42aq(t) H2Og(t) K2SO4s(t) Kaq(t) KHSO4s(t) HSO4aq(t) KNO3s(t) KCLs(t) MGSO4s(t) MG2aq(t) MGNO32s(t) MGCL2s(t) Haq(t) NH3g(t) NH3aq(t) NH4aq(t) OHaq(t) HNO3g(t) HNO3aq(t) HCLg(t) HCLaq(t) NA2SO4s(t) NAaq(t) NH42SO4s(t) NH4CLs(t) NANO3s(t) NO3aq(t) NACLs(t) NAHSO4s(t) NH4NO3s(t) NH4HSO4s(t) NH43HSO42s(t) H2Oaq(t)

# ╔═╡ 70c668e3-3b70-4f22-a9eb-415203032080
rxs = [Reaction(p1, [CANO32s], [CA2aq,NO3aq], [1], [1,2])
		#Ca(NO3)2 --> Ca2+ + 2NO3-
			Reaction(p2, [CA2aq,NO3aq], [CANO32s], [1,2], [1])
				#Ca2+ + 2NO3- --> Ca(NO3)2
			Reaction(p3, [CACL2s], [CA2aq,CLaq], [1], [1,2])
				#CaCl2 --> Ca2+ + 2Cl-
			Reaction(p4, [CA2aq,CLaq], [CACL2s], [1,2], [1])
				#Ca2+ + 2Cl- --> CaCl2
			Reaction(p5, [CASO4s], [CA2aq,SO42aq,H2Og], [1], [1,1,2])
				#CaSO4.2H2O --> Ca2+ + SO42- + 2H2O
			Reaction(p6, [CA2aq,SO42aq,H2Og], [CASO4s], [1,1,2], [1])
				#Ca2+ + SO42- + 2H2O --> CaSO4.2H2O
			Reaction(p7, [K2SO4s], [Kaq,SO42aq], [1], [1,2])
				#K2SO4 --> 2K+ + SO42-
			Reaction(p8, [Kaq,SO42aq], [K2SO4s], [1,2], [1])
				#2K+ + SO42- --> K2SO4
			Reaction(p9, [KHSO4s], [Kaq,HSO4aq], [1], [1,1])
				#KHSO4 --> K+ + HSO4-
			Reaction(p10, [Kaq,HSO4aq], [KHSO4s], [1,1], [1])
				#K+ + HSO4- --> KHSO4
			Reaction(p11, [KNO3s], [Kaq,NO3aq], [1], [1,1])
				#KNO3 --> K+ + NO3-
			Reaction(p12, [Kaq,NO3aq], [KNO3s], [1,1], [1])
				#K+ + NO3 --> KNO3
			Reaction(p13, [KCLs], [Kaq,CLaq], [1], [1,1])
				#KCl --> K+ + Cl-
			Reaction(p14, [Kaq,CLaq], [KCLs], [1,1], [1])
				#K+ + Cl- --> KCl
			Reaction(p15, [MGSO4s], [MG2aq,SO42aq], [1], [1,1])
				#MgSO4 --> Mg2+ + SO42-
			Reaction(p16, [MG2aq,SO42aq], [MGSO4s], [1,1], [1])
				#Mg2+ + SO42- --> MgSO4
			Reaction(p17, [MGNO32s], [MG2aq,NO3aq], [1], [1,2])
				#Mg(NO3)2 --> Mg2+ + 2NO3-
			Reaction(p18, [MG2aq,NO3aq], [MGNO32s], [1,2], [1])
				#Mg2+ + 2NO3- --> Mg(NO3)2
			Reaction(p19, [MGCL2s], [MG2aq,CLaq], [1], [1,2])
				#MgCL2 --> Mg2+ + 2Cl-
			Reaction(p20, [MG2aq,CLaq], [MGCL2s], [1,2], [1])
				#Mg2+ + 2Cl- --> MgCL2
			Reaction(p21, [HSO4aq], [Haq,SO42aq], [1], [1,1])
				#HSO4- --> H+ + SO42-
			Reaction(p22, [Haq,SO42aq], [HSO4aq], [1,1], [1])
				#H+ + SO42- --> HSO4-
			Reaction(p23, [NH3g], [NH3aq], [1], [1]) #NH3 --> NH3
			Reaction(p24, [NH3aq], [NH3g], [1], [1]) #NH3 --> NH3
			Reaction(p25, [NH3aq,H2Oaq], [NH4aq,OHaq], [1,1], [1,1])
				#NH3 + H2O --> NH4+ + OH-
			Reaction(p26, [NH4aq,OHaq], [NH3aq,H2Oaq], [1,1], [1,1])
				#NH4+ + OH- --> NH3 + H2O
			Reaction(p27, [HNO3g], [Haq,NO3aq], [1], [1,1])
				#HNO3 --> H+ + NO3-
			Reaction(p28, [Haq,NO3aq], [HNO3g], [1,1], [1])
				#H+ + NO3- --> HNO3
			Reaction(p29, [HNO3g], [HNO3aq], [1], [1])
				#HNO3 --> HNO3
			Reaction(p30, [HNO3aq], [HNO3g], [1], [1])
				#HNO3 --> HNO3
			Reaction(p31, [HCLg], [Haq,CLaq], [1], [1,1])
				#HCl --> H+ + Cl-
			Reaction(p32, [Haq,CLaq], [HCLg], [1,1], [1])
				#H+ + Cl- --> HCl
			Reaction(p33, [HCLaq], [HCLg], [1], [1])
				#HCl --> HCl
			Reaction(p34, [HCLg], [HCLaq], [1], [1])
				#HCl --> HCl
			Reaction(p35, [H2Oaq], [Haq,OHaq], [1], [1,1])
				#H20 --> H+ + OH-
			#Reaction(p36, [Haq,OHaq], [H2Oaq], [1,1], [1])
				#H+ + OH- --> H20
			Reaction(p37, [NA2SO4s], [NAaq,SO42aq], [1], [2,1])
				#Na2SO4 --> 2Na+ + SO42-
			Reaction(p38, [NAaq,SO42aq], [NA2SO4s], [2,1], [1])
				#2Na+ + SO42- --> Na2SO4
			Reaction(p39, [NH42SO4s], [NH4aq,SO42aq], [1], [2,1])
				#(NH4)2SO4 --> 2NH4+ + SO42-
			Reaction(p40, [NH4aq,SO42aq], [NH42SO4s], [2,1], [1])
				#2NH4+ + SO42- --> (NH4)2SO4
			Reaction(p41, [NH4CLs], [NH3g,SO42aq], [1], [1,1])
				#NH4Cl --> NH3 + HCl
			#Reaction(p42, [NH3g,SO42aq], [NH4CLs], [1,1], [1])
				#NH3 + HCl --> NH4Cl
			Reaction(p43, [NANO3s], [NAaq,NO3aq], [1], [1,1])
				#NaNO3 --> Na+ + NO3-
			Reaction(p44, [NAaq,NO3aq], [NANO3s], [1,1], [1])
				#Na+ + NO3- --> NaNO3
			Reaction(p45, [NACLs], [NAaq,CLaq], [1], [1,1])
				#NaCl --> Na+ + Cl-
			Reaction(p46, [NAaq,CLaq], [NACLs], [1,1], [1])
				#Na+ + Cl- --> NaCl
			Reaction(p47, [NAHSO4s], [NAaq,HSO4aq], [1], [1,1])
				#NaHSO4 --> Na+ + HSO4-
			Reaction(p48, [NAaq,HSO4aq], [NAHSO4s], [1,1], [1])
				#Na+ + HSO4- --> NaHSO4
			Reaction(p49, [NH4NO3s], [NH3g,HNO3g], [1], [1,1])
				#NH4NO3 --> NH3 + HNO3
			#Reaction(p50, [NH3g,HNO3g], [NH4NO3s], [1,1], [1])
				#NH3 + HNO3 --> NH4NO3
			Reaction(p51, [NH4HSO4s], [NH4aq,HSO4aq], [1], [1,1])
				#NH4HSO4 --> NH4+ + HSO4-
			Reaction(p52, [NH4aq,HSO4aq], [NH4HSO4s], [1,1], [1])
				#NH4+ + HSO4- --> NH4HSO4
			Reaction(p53, [NH43HSO42s], [NH4aq,HSO4aq,SO42aq], [1], [3,1,1])
				#(NH4)3H(SO4)2 --> 3NH4+ + HSO4- + SO42-
			Reaction(p54, [NH4aq,HSO4aq,SO42aq], [NH43HSO42s], [3,1,1], [1]) 						#3NH4+ + HSO4- + SO42- --> (NH4)3H(SO4)2

]

# ╔═╡ 2e687027-42ef-4370-b64a-dd083f37c7a5
@named ISORROPIA = ReactionSystem(rxs, t) #creating a reaction system

# ╔═╡ e1fafac6-3851-41ba-a4d6-2b78d7d40389
u₀map = [CANO32s => 0.0,  CA2aq => 0.4, NO3aq => 0.0,  CACL2s => 0.0, CLaq => 0.0, CASO4s => 0.0, SO42aq => 0.0, H2Og => 0.0, K2SO4s => 0.0, Kaq => 0.33, KHSO4s => 0.0, HSO4aq => 10.0, KNO3s => 0.0, KCLs => 0.0, MGSO4s => 0.0, MG2aq => 0.0, MGNO32s => 0.0, MGCL2s => 0.0, Haq => 10.0, NH3g => 0.0, NH3aq => 3.4, NH4aq => 0.0, OHaq => 0.0, HNO3g => 0.0, HNO3aq => 2.0, HCLg => 0.0, HCLaq => 0.0, NA2SO4s => 0.0, NAaq => 0.0, NH42SO4s => 0.0, NH4CLs => 0.0, NANO3s => 0.0, NO3aq => 0.0, NACLs => 0.0, NAHSO4s => 0.0, NH4NO3s => 0.0, NH4HSO4s => 0.0, NH43HSO42s => 0.0, H2Oaq => 0.0]

	#Input conditions for model

# ╔═╡ d65aa2b0-166f-467e-b25f-64326be2f22d
tspan = (0.0, 10.0)

# ╔═╡ 4a708fad-4be6-4e80-9aad-338b2bd746ad
T_ = 298.15

# ╔═╡ 9e9b70ee-3244-4688-af1c-0e9d96391c95
RH = 0.700

# ╔═╡ c188c227-32da-457a-bb29-2a7a95d31dce
	parammap = [p1 => ifelse(RH > 0.4906*exp(-509.4*((1/298.15)-(1/T_))), 6.067*10^(5)*exp((-11.299*((298.15/T_)-1))-(1+log((2.718),(298.15/T_))-(298.15/T_))), 0), #Ca(NO3)2
				p2 => 1.648*10^(-6)*exp((-11.299*((298.15/T_)-1))+(1+log((2.718),(298.15/T_))-(298.15/T_))),
				p3 => ifelse(RH > 0.2830*exp(-551.1*((1/298.15)-(1/T_))), 7.974*10^(11)*exp((-14.087*((298.15/T_)-1))-(1+log((2.718),(298.15/T_))-(298.15/T_))), 0), #CaCl2
				p4 => 1.254^(-12)*exp((-14.087*((298.15/T_)-1))+(1+log((2.718),(298.15/T_))-(298.15/T_))),
				p5 => ifelse(RH > 0.9700*exp(-((1/298.15)-(1/T_))), 4.319*10^(-5)*exp((((298.15/T_)-1))-(1+log((2.718),(298.15/T_))-(298.15/T_))), 0), #CaSO4
				p6 => 2.315*10^(4)*exp((((298.15/T_)-1))+(1+log((2.718),(298.15/T_))-(298.15/T_))),
				p7 => ifelse(RH > 0.9751*exp(-35.6*((1/298.15)-(1/T_))), 1.569*10^(-2)*exp((-9.589*((298.15/T_)-1))-(45.807(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0), #K2SO4
				p8 => 6.373*10^(-1)*exp((-9.589*((298.15/T_)-1))+(45.807(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p9 => ifelse(RH > 0.8600*exp(-((1/298.15)-(1/T_))), 24.016*exp((-8.423*((298.15/T_)-1))-(17.964(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0), #KHSO4
				p10 => 4.164*10^(-2)*exp((-8.423*((298.15/T_)-1))+(17.964(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p11 => ifelse(RH > 0.9248*exp(-((1/298.15)-(1/T_))), 0.872*exp((14.075*((298.15/T_)-1))-(19.388(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0), #KNO3
				p12 => 1.147*exp((14.075*((298.15/T_)-1))+(19.388(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p13 => ifelse(RH > 0.8426*exp(-158.9*((1/298.15)-(1/T_))), 8.680*exp((-6.167*((298.15/T_)-1))-(19.953(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0), #KCl
				p14 => 1.152*10^(-1)*exp((-6.167*((298.15/T_)-1))+(19.953(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p15 => ifelse(RH > 0.8613*exp(714.5*((1/298.15)-(1/T_))), 1.079*10^(5)*exp((36.798*((298.15/T_)-1))-((1+log((2.718),(298.15/T_))-(298.15/T_)))), 0), #MgSO4
				p16 => 9.268*10^(-6)*exp((36.798*((298.15/T_)-1))+((1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p17 => ifelse(RH > 0.5400*exp(-230.2*((1/298.15)-(1/T_))), 2.507*10^(15)*exp((-8.754*((298.15/T_)-1))-((1+log((2.718),(298.15/T_))-(298.15/T_)))), 0), #Mg(NO3)2
				p18 => 3.989*10^(-16)*exp((-8.754*((298.15/T_)-1))+((1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p19 => ifelse(RH > 0.3284*exp(-42.23*((1/298.15)-(1/T_))), 9.557*10^(21)*exp((-1.347*((298.15/T_)-1))-((1+log((2.718),(298.15/T_))-(298.15/T_)))), 0), #MgCl2
				p20 => 1.046*10^(-22)*exp((-1.347*((298.15/T_)-1))+((1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p21 => 1.015*10^(-2)*exp((8.85*((298.15/T_)-1))-(25.14(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p22 => 9.852*10^(1)*exp((8.85*((298.15/T_)-1))+(25.14(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p23 => 5.764*10^(1)*exp((13.79*((298.15/T_)-1))-(-5.39(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p24 => 1.735*10^(-2)*exp((13.79*((298.15/T_)-1))+(-5.39(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p25 => 1.805*10^(-5)*exp((-1.50*((298.15/T_)-1))-(26.92(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p26 => 5.540*10^(4)*exp((-1.50*((298.15/T_)-1))+(26.92(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p27 => 2.511*10^(6)*exp((29.17*((298.15/T_)-1))-(16.83(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p28 => 3.982*10^(-7)*exp((29.17*((298.15/T_)-1))+(16.83(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p29 => 2.1*10^(5)*exp((29.17*((298.15/T_)-1))-(16.83(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p30 => 4.762*10^(-6)*exp((29.17*((298.15/T_)-1))+(16.83(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p31 => 1.971*10^(6)*exp((30.20*((298.15/T_)-1))-(19.91(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p32 => 5.074*10^(-7)*exp((30.20*((298.15/T_)-1))+(19.91(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p33 => 2.5*10^(3)*exp((30.20*((298.15/T_)-1))-(19.91(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p34 => 4*10^(-4)*exp((30.20*((298.15/T_)-1))+(19.91(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p35 => 1.010*10^(-14)*exp((-22.52*((298.15/T_)-1))-(26.92(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				#p36 => 9.901*10^(13)*exp((-22.52*((298.15/T_)-1))+(26.92(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p37 => ifelse(RH > 0.9300exp(-80.0((1/298.15)-(1/T_))), 4.799*10^(-1)*exp((0.98*((298.15/T_)-1))-(39.75(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0), #Na2SO4
				p38 => 2.084*exp((0.98*((298.15/T_)-1))+(39.75(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p39 => ifelse(RH > 0.7997*exp(-80.0*((1/298.15)-(1/T_))), 1.817*exp((-2.65*((298.15/T_)-1))-(38.57(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0), #(NH4)2SO4
				p40 => 5.504*10^(-1)*exp((-2.65*((298.15/T_)-1))+(38.57(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p41 => ifelse(RH > 0.7710*exp(-239.0*((1/298.15)-(1/T_))), 1.086*10^(-16)*exp((-71*((298.15/T_)-1))-(2.4(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0),  #NH4Cl
				#p42 => 9.208*10^(15)*exp((-71*((298.15/T_)-1))+(2.4(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p43 => ifelse(RH > 0.7379*exp(-304.0*((1/298.15)-(1/T_))), 1.197*10^(1)*exp((-8.22*((298.15/T_)-1))-(16.01(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0), #NaNO3
				p44 => 8.354*10^(-2)*exp((-8.22*((298.15/T_)-1))+(16.01(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p45 => ifelse(RH > 0.7528*exp(-25.0*((1/298.15)-(1/T_))), 3.766*10^(1)*exp((-1.56*((298.15/T_)-1))-(16.90(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0), #NaCl
				p46 => 2.655*10^(-2)*exp((-1.56*((298.15/T_)-1))+(16.90(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p47 => ifelse(RH > 0.5200*exp(45*((1/298.15)-(1/T_))), 2.413*10^(4)*exp((0.79*((298.15/T_)-1))-(14.75(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0), #NaHSO4
				p48 => 4.144*10^(-5)*exp((0.79*((298.15/T_)-1))+(14.75(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p49 => ifelse(RH > 0.6183*exp(-852.0*((1/298.15)-(1/T_))), 4.199*10^(-17)*exp((-74.735*((298.15/T_)-1))-(6.025(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0), #NH4NO3
				#p50 => 2.382*10^(16)*exp((-74.735*((298.15/T_)-1))+(14.75(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p51 => ifelse(RH > 0.4000*exp(-384.0*((1/298.15)-(1/T_))), 1.383*exp((-2.87*((298.15/T_)-1))-(15.83(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0), #NH4HSO4
				p52 => 7.231*10^(-1)*exp((-2.87*((298.15/T_)-1))+(15.83(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p53 => ifelse(RH > 0.6900*exp(-186.0*((1/298.15)-(1/T_))), 2.972*10^(1)*exp((-5.19*((298.15/T_)-1))-(54.40(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0), #(NH4)3H(SO4)2
				p54 => 3.365*10^(-2)*exp((-5.19*((298.15/T_)-1))+(54.40(1+log((2.718),(298.15/T_))-(298.15/T_))))

	]

	#parammap calculates the equilibrium constant and also utlizes the Deliquescence Relative Humidity (DRH) of sleected salts (if DRH > RH, p[x] = 0)

# ╔═╡ 27b0f338-c071-45c6-9b9d-6f910a36748d
oprob = ODEProblem(ISORROPIA, u₀map, tspan, parammap)

# ╔═╡ 0f35870d-b175-4642-b1ce-13904395c7ff
sol = solve(oprob, Tsit5()) #testing the model for input conditions at RH = 0.70(70%)

# ╔═╡ b31ecee6-8bb1-46ae-9360-76fdcf5dfc27
plot(sol)

# ╔═╡ fa5a4623-3bc1-4776-8233-249bdc4bf73f
function model(T_,RH,a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,u,v,w,x,y,z,aa,ab,ac,ad,ae,af,ag,ah,ai,aj,ak,al,am,an)

	u₀map_ = [CANO32s => a,  CA2aq => b, NO3aq => c,  CACL2s => d, CLaq => e, CASO4s => f, SO42aq => g, H2Og => h, K2SO4s => i, Kaq => j, KHSO4s => k, HSO4aq => l, KNO3s => m, KCLs => n, MGSO4s => o, MG2aq => p, MGNO32s => q, MGCL2s => r, Haq => s, NH3g => u, NH3aq => v, NH4aq => w, OHaq => x, HNO3g => y, HNO3aq => z, HCLg => aa, HCLaq => ab, NA2SO4s => ac, NAaq => ad, NH42SO4s => ae, NH4CLs => af, NANO3s => ag, NO3aq => ah, NACLs => ai, NAHSO4s => aj, NH4NO3s => ak, NH4HSO4s => al, NH43HSO42s => am, H2Oaq => an]

	parammap_ = [p1 => ifelse(RH > 0.4906*exp(-509.4*((1/298.15)-(1/T_))), 6.067*10^(5)*exp((-11.299*((298.15/T_)-1))-(1+log((2.718),(298.15/T_))-(298.15/T_))), 0),
				p2 => 1.648*10^(-6)*exp((-11.299*((298.15/T_)-1))+(1+log((2.718),(298.15/T_))-(298.15/T_))),
				p3 => ifelse(RH > 0.2830*exp(-551.1*((1/298.15)-(1/T_))), 7.974*10^(11)*exp((-14.087*((298.15/T_)-1))-(1+log((2.718),(298.15/T_))-(298.15/T_))), 0),
				p4 => 1.254^(-12)*exp((-14.087*((298.15/T_)-1))+(1+log((2.718),(298.15/T_))-(298.15/T_))),
				p5 => ifelse(RH > 0.9700*exp(-((1/298.15)-(1/T_))), 4.319*10^(-5)*exp((((298.15/T_)-1))-(1+log((2.718),(298.15/T_))-(298.15/T_))), 0),
				p6 => 2.315*10^(4)*exp((((298.15/T_)-1))+(1+log((2.718),(298.15/T_))-(298.15/T_))),
				p7 => ifelse(RH > 0.9751*exp(-35.6*((1/298.15)-(1/T_))), 1.569*10^(-2)*exp((-9.589*((298.15/T_)-1))-(45.807(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0),
				p8 => 6.373*10^(-1)*exp((-9.589*((298.15/T_)-1))+(45.807(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p9 => ifelse(RH > 0.8600*exp(-((1/298.15)-(1/T_))), 24.016*exp((-8.423*((298.15/T_)-1))-(17.964(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0),
				p10 => 4.164*10^(-2)*exp((-8.423*((298.15/T_)-1))+(17.964(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p11 => ifelse(RH > 0.9248*exp(-((1/298.15)-(1/T_))), 0.872*exp((14.075*((298.15/T_)-1))-(19.388(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0),
				p12 => 1.147*exp((14.075*((298.15/T_)-1))+(19.388(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p13 => ifelse(RH > 0.8426*exp(-158.9*((1/298.15)-(1/T_))), 8.680*exp((-6.167*((298.15/T_)-1))-(19.953(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0),
				p14 => 1.152*10^(-1)*exp((-6.167*((298.15/T_)-1))+(19.953(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p15 => ifelse(RH > 0.8613*exp(714.5*((1/298.15)-(1/T_))), 1.079*10^(5)*exp((36.798*((298.15/T_)-1))-((1+log((2.718),(298.15/T_))-(298.15/T_)))), 0),
				p16 => 9.268*10^(-6)*exp((36.798*((298.15/T_)-1))+((1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p17 => ifelse(RH > 0.5400*exp(-230.2*((1/298.15)-(1/T_))), 2.507*10^(15)*exp((-8.754*((298.15/T_)-1))-((1+log((2.718),(298.15/T_))-(298.15/T_)))), 0),
				p18 => 3.989*10^(-16)*exp((-8.754*((298.15/T_)-1))+((1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p19 => ifelse(RH > 0.3284*exp(-42.23*((1/298.15)-(1/T_))), 9.557*10^(21)*exp((-1.347*((298.15/T_)-1))-((1+log((2.718),(298.15/T_))-(298.15/T_)))), 0),
				p20 => 1.046*10^(-22)*exp((-1.347*((298.15/T_)-1))+((1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p21 => 1.015*10^(-2)*exp((8.85*((298.15/T_)-1))-(25.14(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p22 => 9.852*10^(1)*exp((8.85*((298.15/T_)-1))+(25.14(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p23 => 5.764*10^(1)*exp((13.79*((298.15/T_)-1))-(-5.39(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p24 => 1.735*10^(-2)*exp((13.79*((298.15/T_)-1))+(-5.39(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p25 => 1.805*10^(-5)*exp((-1.50*((298.15/T_)-1))-(26.92(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p26 => 5.540*10^(4)*exp((-1.50*((298.15/T_)-1))+(26.92(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p27 => 2.511*10^(6)*exp((29.17*((298.15/T_)-1))-(16.83(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p28 => 3.982*10^(-7)*exp((29.17*((298.15/T_)-1))+(16.83(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p29 => 2.1*10^(5)*exp((29.17*((298.15/T_)-1))-(16.83(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p30 => 4.762*10^(-6)*exp((29.17*((298.15/T_)-1))+(16.83(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p31 => 1.971*10^(6)*exp((30.20*((298.15/T_)-1))-(19.91(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p32 => 5.074*10^(-7)*exp((30.20*((298.15/T_)-1))+(19.91(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p33 => 2.5*10^(3)*exp((30.20*((298.15/T_)-1))-(19.91(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p34 => 4*10^(-4)*exp((30.20*((298.15/T_)-1))+(19.91(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p35 => 1.010*10^(-14)*exp((-22.52*((298.15/T_)-1))-(26.92(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				#p36 => 9.901*10^(13)*exp((-22.52*((298.15/T_)-1))+(26.92(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p37 => ifelse(RH > 0.9300exp(-80.0((1/298.15)-(1/T_))), 4.799*10^(-1)*exp((0.98*((298.15/T_)-1))-(39.75(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0),
				p38 => 2.084*exp((0.98*((298.15/T_)-1))+(39.75(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p39 => ifelse(RH > 0.7997*exp(-80.0*((1/298.15)-(1/T_))), 1.817*exp((-2.65*((298.15/T_)-1))-(38.57(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0),
				p40 => 5.504*10^(-1)*exp((-2.65*((298.15/T_)-1))+(38.57(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p41 => ifelse(RH > 0.7710*exp(-239.0*((1/298.15)-(1/T_))), 1.086*10^(-16)*exp((-71*((298.15/T_)-1))-(2.4(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0),
				#p42 => 9.208*10^(15)*exp((-71*((298.15/T_)-1))+(2.4(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p43 => ifelse(RH > 0.7379*exp(-304.0*((1/298.15)-(1/T_))), 1.197*10^(1)*exp((-8.22*((298.15/T_)-1))-(16.01(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0),
				p44 => 8.354*10^(-2)*exp((-8.22*((298.15/T_)-1))+(16.01(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p45 => ifelse(RH > 0.7528*exp(-25.0*((1/298.15)-(1/T_))), 3.766*10^(1)*exp((-1.56*((298.15/T_)-1))-(16.90(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0),
				p46 => 2.655*10^(-2)*exp((-1.56*((298.15/T_)-1))+(16.90(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p47 => ifelse(RH > 0.5200*exp(45*((1/298.15)-(1/T_))), 2.413*10^(4)*exp((0.79*((298.15/T_)-1))-(14.75(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0),
				p48 => 4.144*10^(-5)*exp((0.79*((298.15/T_)-1))+(14.75(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p49 => ifelse(RH > 0.6183*exp(-852.0*((1/298.15)-(1/T_))), 4.199*10^(-17)*exp((-74.735*((298.15/T_)-1))-(6.025(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0),
				#p50 => 2.382*10^(16)*exp((-74.735*((298.15/T_)-1))+(14.75(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p51 => ifelse(RH > 0.4000*exp(-384.0*((1/298.15)-(1/T_))), 1.383*exp((-2.87*((298.15/T_)-1))-(15.83(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0),
				p52 => 7.231*10^(-1)*exp((-2.87*((298.15/T_)-1))+(15.83(1+log((2.718),(298.15/T_))-(298.15/T_)))),
				p53 => ifelse(RH > 0.6900*exp(-186.0*((1/298.15)-(1/T_))), 2.972*10^(1)*exp((-5.19*((298.15/T_)-1))-(54.40(1+log((2.718),(298.15/T_))-(298.15/T_)))), 0),
				p54 => 3.365*10^(-2)*exp((-5.19*((298.15/T_)-1))+(54.40(1+log((2.718),(298.15/T_))-(298.15/T_))))

	]

	oprob_ = ODEProblem(ISORROPIA, u₀map_, tspan, parammap_)
	sol_ = solve(oprob_, Tsit5())
end

#Examples

# ╔═╡ 5bbdc0e8-97ce-4706-a266-4e9df3fbe058
model(298.15,0.75,0.0,0.4,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.33,0.0,10.0,0.0,0.0,0.0,0.0,0.0,0.0,10.0,0.0,3.4,0.0,0.0,2.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0)
#testing model for input conditions at RH = 0.75(75%)

# ╔═╡ 9c67e2ba-1d50-4e63-95bc-dd769bfce93e
model(298.15,0.80,0.0,0.4,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.33,0.0,10.0,0.0,0.0,0.0,0.0,0.0,0.0,10.0,0.0,3.4,0.0,0.0,2.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0)
#testing model for input conditions at RH = 0.80(80%)

# ╔═╡ cd76be8b-4267-4996-8fc1-0facfa149f97
model(298.15,0.85,0.0,0.4,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.33,0.0,10.0,0.0,0.0,0.0,0.0,0.0,0.0,10.0,0.0,3.4,0.0,0.0,2.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0)
#testing model for input conditions at RH = 0.85(85%)

# ╔═╡ 5c74962a-4b28-4fab-8fc2-e86c6f533cd7
model(298.15,0.90,0.0,0.4,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.33,0.0,10.0,0.0,0.0,0.0,0.0,0.0,0.0,10.0,0.0,3.4,0.0,0.0,2.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0)
#testing model for input conditions at RH = 0.90(90%)

# ╔═╡ dba4af4a-85ac-457e-ad5c-8d7820a6e942
model(298.15,0.98,0.0,0.4,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.33,0.0,10.0,0.0,0.0,0.0,0.0,0.0,0.0,10.0,0.0,3.4,0.0,0.0,2.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0)
#testing model for input conditions at RH = 0.98(98%)

# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
Catalyst = "479239e8-5488-4da2-87a7-35f2df7eef83"
DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa"
ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
NonlinearSolve = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
StochasticDiffEq = "789caeaf-c7a9-5a7d-9973-96adeb23e2a0"

[compat]
Catalyst = "~10.2.0"
DiffEqBase = "~6.77.1"
DifferentialEquations = "~6.20.0"
ModelingToolkit = "~7.1.3"
NonlinearSolve = "~0.3.12"
OrdinaryDiffEq = "~5.71.0"
Plots = "~1.25.2"
StochasticDiffEq = "~6.41.0"
"""

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

[[AbstractAlgebra]]
deps = ["GroupsCore", "InteractiveUtils", "LinearAlgebra", "Markdown", "Random", "RandomExtensions", "SparseArrays", "Test"]
git-tree-sha1 = "b5c1a469f9afd3a9d79930d2cead20c562458aae"
uuid = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
version = "0.22.3"

[[AbstractTrees]]
git-tree-sha1 = "03e0550477d86222521d254b741d470ba17ea0b5"
uuid = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
version = "0.3.4"

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

[[ArgCheck]]
git-tree-sha1 = "dedbbb2ddb876f899585c4ec4433265e3017215a"
uuid = "dce04be8-c92d-5529-be00-80e4d2c0e197"
version = "2.1.0"

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

[[ArnoldiMethod]]
deps = ["LinearAlgebra", "Random", "StaticArrays"]
git-tree-sha1 = "62e51b39331de8911e4a7ff6f5aaf38a5f4cc0ae"
uuid = "ec485272-7323-5ecc-a04f-4719b315124d"
version = "0.2.0"

[[ArrayInterface]]
deps = ["Compat", "IfElse", "LinearAlgebra", "Requires", "SparseArrays", "Static"]
git-tree-sha1 = "265b06e2b1f6a216e0e8f183d28e4d354eab3220"
uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
version = "3.2.1"

[[ArrayLayouts]]
deps = ["FillArrays", "LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "e1ba79094cae97b688fb42d31cbbfd63a69706e4"
uuid = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"
version = "0.7.8"

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

[[AutoHashEquals]]
git-tree-sha1 = "45bb6705d93be619b81451bb2006b7ee5d4e4453"
uuid = "15f4f7f2-30c1-5605-9d31-71845cf9641f"
version = "0.2.0"

[[BandedMatrices]]
deps = ["ArrayLayouts", "FillArrays", "LinearAlgebra", "Random", "SparseArrays"]
git-tree-sha1 = "ce68f8c2162062733f9b4c9e3700d5efc4a8ec47"
uuid = "aae01518-5342-5314-be14-df237901396f"
version = "0.16.11"

[[BangBang]]
deps = ["Compat", "ConstructionBase", "Future", "InitialValues", "LinearAlgebra", "Requires", "Setfield", "Tables", "ZygoteRules"]
git-tree-sha1 = "0ad226aa72d8671f20d0316e03028f0ba1624307"
uuid = "198e06fe-97b7-11e9-32a5-e1d131e6ad66"
version = "0.3.32"

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

[[Baselet]]
git-tree-sha1 = "aebf55e6d7795e02ca500a689d326ac979aaf89e"
uuid = "9718e550-a3fa-408a-8086-8db961cd8217"
version = "0.1.1"

[[Bijections]]
git-tree-sha1 = "705e7822597b432ebe152baa844b49f8026df090"
uuid = "e2ed5e7c-b2de-5872-ae92-c73ca462fb04"
version = "0.1.3"

[[BitTwiddlingConvenienceFunctions]]
deps = ["Static"]
git-tree-sha1 = "bc1317f71de8dce26ea67fcdf7eccc0d0693b75b"
uuid = "62783981-4cbd-42fc-bca8-16325de8dc4b"
version = "0.1.1"

[[BoundaryValueDiffEq]]
deps = ["BandedMatrices", "DiffEqBase", "FiniteDiff", "ForwardDiff", "LinearAlgebra", "NLsolve", "Reexport", "SparseArrays"]
git-tree-sha1 = "fe34902ac0c3a35d016617ab7032742865756d7d"
uuid = "764a87c0-6b3e-53db-9096-fe964310641d"
version = "2.7.1"

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

[[CEnum]]
git-tree-sha1 = "215a9aa4a1f23fbd05b92769fdd62559488d70e9"
uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82"
version = "0.4.1"

[[CPUSummary]]
deps = ["Hwloc", "IfElse", "Static"]
git-tree-sha1 = "87b0c9c6ee0124d6c1f4ce8cb035dcaf9f90b803"
uuid = "2a0fbf3d-bb9c-48f3-b0a9-814d99fd7ab9"
version = "0.1.6"

[[CSTParser]]
deps = ["Tokenize"]
git-tree-sha1 = "f9a6389348207faf5e5c62cbc7e89d19688d338a"
uuid = "00ebfdb7-1f24-5e51-bd34-a7502290713f"
version = "3.3.0"

[[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"

[[Catalyst]]
deps = ["AbstractAlgebra", "DataStructures", "DiffEqBase", "DiffEqJump", "DocStringExtensions", "Graphs", "Latexify", "MacroTools", "ModelingToolkit", "Parameters", "Reexport", "Requires", "SparseArrays", "Symbolics"]
git-tree-sha1 = "f1734a45a0799abc58b08bc1e9bbee75d68a61a2"
uuid = "479239e8-5488-4da2-87a7-35f2df7eef83"
version = "10.2.0"

[[ChainRulesCore]]
deps = ["Compat", "LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "4c26b4e9e91ca528ea212927326ece5918a04b47"
uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
version = "1.11.2"

[[ChangesOfVariables]]
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git-tree-sha1 = "8351f8d73d7e880bfc042a8b6922684ebeafb35c"
uuid = "19fa3120-7c27-5ec5-8db8-b0b0aa330d6f"
version = "0.2.0"

[[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"

[[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:
# ╠═9014f3c0-5dec-11ec-1d46-efedaead02f9
# ╠═e6cfd4c7-fe1f-4991-b5f7-3eaf157b6df9
# ╠═1bbc8b1b-6ecd-453a-a508-b561ca347ec7
# ╠═70c668e3-3b70-4f22-a9eb-415203032080
# ╠═2e687027-42ef-4370-b64a-dd083f37c7a5
# ╠═e1fafac6-3851-41ba-a4d6-2b78d7d40389
# ╠═d65aa2b0-166f-467e-b25f-64326be2f22d
# ╠═4a708fad-4be6-4e80-9aad-338b2bd746ad
# ╠═9e9b70ee-3244-4688-af1c-0e9d96391c95
# ╠═c188c227-32da-457a-bb29-2a7a95d31dce
# ╠═27b0f338-c071-45c6-9b9d-6f910a36748d
# ╠═0f35870d-b175-4642-b1ce-13904395c7ff
# ╠═b31ecee6-8bb1-46ae-9360-76fdcf5dfc27
# ╠═fa5a4623-3bc1-4776-8233-249bdc4bf73f
# ╠═5bbdc0e8-97ce-4706-a266-4e9df3fbe058
# ╠═9c67e2ba-1d50-4e63-95bc-dd769bfce93e
# ╠═cd76be8b-4267-4996-8fc1-0facfa149f97
# ╠═5c74962a-4b28-4fab-8fc2-e86c6f533cd7
# ╠═dba4af4a-85ac-457e-ad5c-8d7820a6e942
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002


"""
        mcdm(df, w, fns, method)

    Perform selected method for a given decision matrix, weight vector, and function list.

# Arguments:
 - `df::DataFrame`: n × m matrix of decision matrix in type of DataFrame.
 - `weights::Array{Float64, 1}`: m-vector of weights for criteria.
 - `fs::Array{Function, 1}`: m-vector of functions that are either maximize or minimize for each single criterion.
 - `method::MCDMMethod`: Preferred MCDMMethod.

# Description
The method is one of the subtypes of MCDMMethod type. See examples.

# Output
- `::MCDMResult`: An object derived from subtypes of MCDMResult type.

# Examples

```julia-repl

julia> subtypes(MCDMMethod)
18-element Vector{Any}:
 ArasMethod
 CocosoMethod
 CodasMethod
 CoprasMethod
 CriticMethod
 EdasMethod
 ElectreMethod
 GreyMethod
 MabacMethod
 MaircaMethod
 MarcosMethod
 MooraMethod
 PrometheeMethod
 SawMethod
 TopsisMethod
 VikorMethod
 WPMMethod
 WaspasMethod

julia> # mcdm() for Topsis:
julia> # mcdm(df, w, fns, TopsisMethod())

julia> # mcdm() for Saw:
julia> # mcdm(df, w, fns, SawMethod())

julia> # mcdm() with optional parameters:
julia> # mcdm(df, w, fns, GreyMethod(0.6))
```

"""
function mcdm(df::DataFrame,
    w::Array{Float64, 1},
    fns::Array{Function, 1},
    method::T1)::MCDMResult where {T1 <: MCDMMethod}

    if method isa TopsisMethod
        topsis(df, w, fns)
    elseif method isa ElectreMethod
        electre(df, w, fns)
    elseif method isa ArasMethod
        aras(df, w, fns)
    elseif method isa CocosoMethod
        cocoso(df, w, fns, lambda = method.lambda)
    elseif method isa CodasMethod
        codas(df, w, fns, tau = method.tau)
    elseif method isa CoprasMethod
        copras(df, w, fns)
    elseif method isa CriticMethod
        critic(df, fns)
    elseif method isa EdasMethod
        edas(df, w, fns)
    elseif method isa GreyMethod
        grey(df, w, fns, zeta = method.zeta)
    elseif method isa MabacMethod
        mabac(df, w, fns)
    elseif method isa MaircaMethod
        mairca(df, w, fns)
    elseif method isa MooraMethod
        moora(df, w, fns)
    elseif method isa PrometheeMethod
        promethee(df, w, fns, method.pref, method.qs, method.ps)
    elseif method isa SawMethod
        saw(df, w, fns)
    elseif method isa VikorMethod
        vikor(df, w, fns, v = method.v)
    elseif method isa WaspasMethod
        waspas(df, w, fns, lambda = method.lambda)
    elseif method isa WPMMethod
        wpm(df, w, fns)
    elseif method isa MarcosMethod
        marcos(df, w, fns)
    else
        error("Method is not defined")
    end
end

"""
    mcdm(setting, method)

    Perform selected method for a given decision matrix, weight vector, and function list.

# Arguments:
 - `setting::MCDMSetting`: MCDMSetting object that holds the decision matrix, weight vector, and functions.
 - `method::MCDMMethod`: Preferred MCDMMethod.

# Description
The method is one of the subtypes of MCDMMethod type. See examples.

# Output
- `::MCDMResult`: An object derived from subtypes of MCDMResult type.

# Examples

```julia-repl
julia> # mcdm() for Topsis:
julia> # mcdm(setting, TopsisMethod())

julia> # mcdm() for Saw:
julia> # mcdm(setting, SawMethod())

julia> # mcdm() with optional parameters:
julia> # mcdm(setting, GreyMethod(0.6))
```

"""
function mcdm(setting::MCDMSetting,
    method::T1)::MCDMResult where {T1 <: MCDMMethod}

    mcdm(
        setting.df,
        setting.weights,
        setting.fns,
        method
    )
end


export get_Jacobian

"""
$(SIGNATURES)

Obtain the symbolic Jacobian matrix of `eom` (either a `HarmonicEquation` or a `DifferentialEquation`).

"""
function get_Jacobian(eom::HarmonicEquation)

    lhs = Num.(getfield.(HarmonicBalance.rearrange_standard(eom).equations, :lhs))

    old_vars = get_variables(eom)
    bracket_rules = [var => HarmonicBalance.declare_variable(var_name(var)) for var in old_vars]

    lhs = substitute_all(lhs,bracket_rules)
    vars = getindex.(bracket_rules, 2)
    J = Matrix{Num}(undef, length(vars), length(vars))
    for idx in CartesianIndices(J)
        J[idx] = expand_derivatives(d(lhs[idx[1]], vars[idx[2]]))
    end
    J

end

#   Obtain a Jacobian from a `DifferentialEquation` by first converting it into a `HarmonicEquation`.
function get_Jacobian(diff_eom::DifferentialEquation)
    @variables T
    harmonic_eq = get_harmonic_equations(diff_eom, slow_time=T, fast_time=first(get_independent_variables(diff_eom)))
    get_Jacobian(harmonic_eq)
end

"""Convert a set of equations in variables `vars` into matrix form.
If the equations are linear, this matrix does not depends on the variables."""
function equations_to_matrix(eqs::Vector{Num}, vars::Vector{Num})
    length(eqs) != length(vars) ? error("System under- or over-constrained!") : nothing
    M = Matrix{Num}(undef, length(eqs), length(eqs))
    for idx in CartesianIndices(M)
        M[idx] = expand_derivatives(d(eqs[idx[1]], vars[idx[2]]))
    end
    M
end

# get the Jacobian of a set of equations `eqs` with respect to the variables `vars`
function get_Jacobian(eqs::Vector{Num}, vars::Vector{Num})
    length(eqs) == length(vars) || error("Jacobians are only defined for square matrices!")
    M = Matrix{Num}(undef, length(vars), length(vars))

    for idx in CartesianIndices(M)
        M[idx] = expand_derivatives(d(eqs[idx[1]], vars[idx[2]]))
    end
    M
end

get_Jacobian(eqs::Vector{Equation}, vars::Vector{Num}) = get_Jacobian(Num.(getfield.(eqs, :lhs) .- getfield.(eqs, :rhs)), vars)

function get_Jacobian_steady(eom::HarmonicEquation; differential_order=0)
    vars_simp = Dict([var => HarmonicBalance.declare_variable(var_name(var)) for var in get_variables(eom)])
    T = get_independent_variables(eom)[1]
    J = get_Jacobian(eom.equations, d(get_variables(eom), T, differential_order))
    expand_derivatives.(HarmonicBalance.substitute_all(J, vars_simp))
end

# COMPILE THIS!
function get_implicit_Jacobian(eom::HarmonicEquation)
    M = get_Jacobian_steady(eom, differential_order=0)
    Mp = get_Jacobian_steady(eom, differential_order=1)
    function J(soln::Dict)
        -inv(ComplexF64.(substitute_all(Mp, soln))) * ComplexF64.(substitute_all(M, soln))
    end
    J
end

###
# STUFF BELOW IS FOR THE CORRECTED JACOBIAN METHOD
###

"""
    get_response_matrix(diff_eq::DifferentialEquation, freq::Num; order=2)

Obtain the symbolic linear response matrix of a `diff_eq` corresponding to a perturbation frequency `freq`.
This routine cannot accept a `HarmonicEquation` since there, some time-derivatives are already dropped.
`order` denotes the highest differential order to be considered.

"""
function get_response_matrix(diff_eq::DifferentialEquation, freq::Num; order=2)::Matrix
    @variables T, i
    time = get_independent_variables(diff_eq)[1]

    eom = HarmonicBalance.harmonic_ansatz(diff_eq, time)

    # replace the time-dependence of harmonic variables by slow time BUT do not drop any derivatives
    eom = HarmonicBalance.slow_flow(eom, fast_time=time, slow_time=T, degree=order+1)

    eom = HarmonicBalance.fourier_transform(eom, time)

    M = get_Jacobian(eom.equations, get_variables(eom))
    for n in 1:order
        M += (i * freq)^n * get_Jacobian(eom.equations, d(get_variables(eom), T, n))
    end
    M = substitute_all(M, [var => HarmonicBalance.declare_variable(var_name(var)) for var in get_variables(eom)])
    substitute_all(expand_derivatives.(M), i => im)
end


#const CIS_LUT = SVector{32}(complex.(floor.(Int8, cos.(2π .* (0:31) ./ 32) .* (1 << 4)), floor.(Int8, sin.(2π .* (0:31) ./ 32) .* (1 << 4))))
#cis_fast(x) = @inbounds CIS_LUT[x & 31 + 1]
"""
$(SIGNATURES)

Get sine approximation very fast. It is valid between -π and π.
```julia-repl
julia> sin_vfast(π / 4)
```
"""
@inline function sin_vfast(x::T) where T <: Real
    B = T(4 / π)
    C = T(-4 / (π * π))
    B * x + C * x * abs(x)
end

"""
$(SIGNATURES)

Get cosine approximation very fast. It is valid between -π and π.
```julia-repl
julia> cos_vfast(π / 4)
```
"""
@inline function cos_vfast(x::T) where T <: Real
    x += T(π / 2)
    x -= (x > T(π)) * T(2π)
    sin_vfast(x)
end

"""
$(SIGNATURES)

Get sine approximation fast. It is valid between -π and π.
```julia-repl
julia> sin_fast(π / 4)
```
"""
@inline function sin_fast(x::T) where T <: Real
    P = T(0.225)
    y = sin_vfast(x)
    P * (y * abs(y) - y) + y
end

"""
$(SIGNATURES)

Get cosine approximation fast. It is valid between -π and π.
```julia-repl
julia> cos_fast(π / 4)
```
"""
@inline function cos_fast(x::T) where T <: Real
    x += T(π / 2)
    x -= (x > T(π)) * T(2π)
    sin_fast(x)
end

"""
$(SIGNATURES)

Get \exp(iz) approximation fast. It is valid between -π and π.
```julia-repl
julia> cos_fast(π / 4)
```
"""
function cis_fast(x)
    complex(cos_fast(x), sin_fast(x))
end

"""
$(SIGNATURES)

Get \exp(iz) approximation very fast. It is valid between -π and π.
```julia-repl
julia> cis_vfast(π / 4)
```
"""
function cis_vfast(x)
    complex(cos_vfast(x), sin_vfast(x))
end

"""
$(SIGNATURES)

Get \exp(iz) approximation fast. It is valid between -π and π.
```julia-repl
julia> get_carrier_fast_unsafe(π / 4)
```
"""
@inline function get_carrier_fast_unsafe(x)
    cis_fast(x)
end

"""
$(SIGNATURES)

Get \exp(iz) approximation very fast. It is valid between -π and π.
```julia-repl
julia> get_carrier_vfast_unsafe(π / 4)
```
"""
@inline function get_carrier_vfast_unsafe(x)
    cis_vfast(x)
end

"""
$(SIGNATURES)

Fixed point carrier phases
"""
function fpcarrier_phases!(
    phases::Vector{T},
    carrier_frequency,
    sample_frequency,
    start_phase::AbstractFloat;
    start_sample::Integer = 1,
    num_samples::Integer = length(phases),
    bits::Val{N} = Val(5)
) where {T <: Integer, N}
    n = N + 2
    fixed_point = 32 - n - 2
    delta = floor(Int32, carrier_frequency * 1 << (fixed_point + n) / sample_frequency)
    fixed_point_start_phase = floor(Int32, start_phase * 1 << (fixed_point + n))
    fixed_point_phase = fixed_point_start_phase - delta
    @inbounds for i = start_sample:num_samples + start_sample - 1
        fixed_point_phase = fixed_point_phase + delta
        phases[i] = T(fixed_point_phase >> fixed_point)
    end
    phases
end

"""
$(SIGNATURES)

Fixed point carrier
"""
function fpcarrier!(
    carrier_sin::VT,
    carrier_cos::VT,
    phases::VT;
    start_sample::Integer = 1,
    num_samples::Integer = length(phases),
    bits::Val{N} = Val(5)
) where {VT <: Vector{Int16}, N}
    @avx unroll = 6 for i = start_sample:num_samples + start_sample - 1
        carrier_sin[i] = fpsin(phases[i], bits)
        carrier_cos[i] = fpcos(phases[i], bits)
    end
end

"""
$(SIGNATURES)

Fixed point carrier
"""
function fpcarrier!(
    carrier::StructArray{Complex{Int16}},
    carrier_frequency,
    sample_frequency,
    start_phase::AbstractFloat;
    start_sample::Integer = 1,
    num_samples::Integer = length(carrier),
    bits::Val{N} = Val(5)
) where N
    fpcarrier_phases!(
        carrier.re,
        carrier_frequency,
        sample_frequency,
        start_phase,
        start_sample = start_sample,
        num_samples = num_samples,
        bits = bits
    )
    fpcarrier!(
        carrier.im,
        carrier.re,
        carrier.re,
        start_sample = start_sample,
        num_samples = num_samples,
        bits = bits
    )
    carrier
end


# ESCB-2, "efficient sampling for combinatorial bandits".
# Based on https://arxiv.org/abs/1502.03475.

abstract type ESCB2OptimisationAlgorithm end
function optimise_linear_sqrtlinear(instance::CombinatorialInstance{T}, ::ESCB2OptimisationAlgorithm,
                                    linear::Dict{T, Float64}, sqrtlinear::Dict{T, Float64}) where T end

mutable struct ESCB2 <: Policy
  algo::ESCB2OptimisationAlgorithm
end

mutable struct ESCB2Details <: PolicyDetails
  n_iterations::Int
  best_objective::Float64
  solver_time::Float64

  function ESCB2Details()
    return new(0, 0.0, 0.0)
  end
end

function _escb2_confidence_values(state::State{T}) where T
  t = state.arm_counts
  w = state.arm_average_reward
  n = state.round

  d = length(t) # n_arms
  fn = log(n) + 4 * d * log(log(n))
  fn = max(0, fn) # f is negative for some values of d and small values of n (sometimes as small as 2 or 3).

  return Dict(k => (fn / 2) / v for (k, v) in t)
end

# TODO: shouldn't it go to a more generic function? Many algorithm work with indices, so maybe there is something to do... but only for black-box algorithms?
function escb2_index(state::State{T}, solution::Vector{T}) where T
  w = state.arm_average_reward
  s2 = _escb2_confidence_values(state)
  return escb2_index(w, s2, solution)
end
function escb2_index(linear::Dict{T, Float64}, sqrtlinear::Dict{T, Float64}, solution::Vector{T}) where T
  if length(solution) == 0
    return 0.0
  end

  avg_reward = sum(linear[arm] for arm in keys(linear) if arm in solution)
  confidence = sum(sqrtlinear[arm] for arm in keys(sqrtlinear) if arm in solution)
  return avg_reward + sqrt(confidence)
end

function choose_action(instance::CombinatorialInstance{T}, policy::ESCB2, state::State{T}; with_trace::Bool=false) where T
  # For initialisation, if some arms have never been tried, force them to be tried.
  # Without this, the standard deviation term cannot exist.
  if any(v == 0 for v in values(state.arm_counts))
    weights = Dict(arm => iszero(state.arm_counts[arm]) ? 1.0 : 0.0 for arm in keys(state.arm_counts))

    t0 = time_ns()
    sol = solve_linear(instance, weights)
    t1 = time_ns()

    if with_trace
      run_details = ESCB2Details()
      run_details.n_iterations = 1
      run_details.solver_time = (t1 - t0) / 1_000_000_000
      return sol, run_details
    else
      return sol
    end
  end

  # If all arms have been tried, can compute the two parts of the objective function: the average reward and a standard deviation.
  w = state.arm_average_reward
  s2 = _escb2_confidence_values(state)

  # Solve the maximisation w^T x + \sqrt{s2^T x} with the required algorithm.
  return optimise_linear_sqrtlinear(instance, policy.algo, w, s2, with_trace=with_trace)
end


include("../oracles/portfolio_oracle.jl")

using Test, Random, LinearAlgebra

@testset "Portfolio Oracle" begin
    Random.seed!(342)

    d = 10
    factors = 4
    F = 0.05*rand(d, factors)

    mu = rand(d)
    r = mu + F*randn(factors) + 0.2*randn(d)

    println("R is : $r")

    Sigma = F*F' + Matrix(0.2I, d, d)

    (z1, w1) = portfolio_simplex_oracle_jump_basic(-r, Sigma, 0.1)

    oracle = portfolio_simplex_jump_setup(Sigma, 0.1)
    (z2, w2) = oracle(-r)

    @test isapprox(z1, z2; atol = 0.0001)
    @test isapprox(w1, w2; atol = 0.0001)
end