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Copy pathFrench_Flag_All_Types.jl
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French_Flag_All_Types.jl
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using DifferentialEquations
using Random
using NPZ
#============================================================#
function int_to_trinary(a)
s = "" ;
quotient = a ;
while quotient > 2
rem = quotient % 3 ;
quotient = div(quotient,3) ;
s = string(rem) * s ;
end
s = string(quotient) * s ;
if length(s) < 6
for i = 1:(6-length(s))
s = '0'*s ;
end
end
return(s) ;
end
#=============================================================#
function get_omegas(ctstring,theta4,theta5,theta6)
if ctstring[4] == '0'
omegaA = 0 ;
omegaD = 0 ;
elseif ctstring[4] == '1'
omegaA = theta4 ;
omegaD = 1 ;
elseif ctstring[4] == '2'
omegaA = 0 ;
omegaD = theta4 ;
end
#-----------------------#
if ctstring[5] == '0'
omegaB = 0 ;
omegaE = 0 ;
elseif ctstring[5] == '1'
omegaB = theta5 ;
omegaE = 1 ;
elseif ctstring[5] == '2'
omegaB = 0 ;
omegaE = theta5 ;
end
#-----------------------#
if ctstring[6] == '0'
omegaC = 0 ;
omegaF = 0 ;
elseif ctstring[6] == '1'
omegaC = theta6 ;
omegaF = 1 ;
elseif ctstring[6] == '2'
omegaC = 0 ;
omegaF = theta6 ;
end
#-------------------------#
return(omegaA,omegaB,omegaC,omegaD,omegaE,omegaF) ;
end
#=============================================================#
function get_final_state(sol,NCells)
A = sol[(1*NCells+1):2*NCells,end] ;
B = sol[(2*NCells+1):3*NCells,end] ;
C = sol[(3*NCells+1):4*NCells,end] ;
States = zeros(Int8,NCells) ;
for i = 1:NCells
if (A[i] > B[i]) & (A[i] > C[i])
States[i] = 0 ;
elseif (B[i] > A[i]) & (B[i] > C[i])
States[i] = 1 ;
else
States[i] = 2 ;
end
end
return(States)
end
#=====================================================#
function coupled_frenchflag_ultimate!(du,u,p,t)
Kappa,h1,h2,h3,h4,h5,k1,k2,k3,alpha,beta,gamma,tauD,tauNb,betaD,betaNb,K_N,NCells,Smax,Slambda,theta1,theta2,theta3,theta4,theta5,theta6,ctstring = p ;
S = u[1:NCells]
A = u[(1*NCells+1):2*NCells]
B = u[(2*NCells+1):3*NCells]
C = u[(3*NCells+1):4*NCells]
D = u[(4*NCells+1):5*NCells]
Nb = u[(5*NCells+1):6*NCells]
for i in 1:NCells
if i == 1
D_N = D[2] ;
elseif i == NCells
D_N = D[NCells-1] ;
else
D_N = 0.5 * (D[i-1] + D[i+1]) ;
end
#------------------------------------#
du[i] = (Smax* exp(-Slambda*(i-1))) - S[i] ;
du[(5*NCells)+i] = betaNb * (D_N/(1 + D_N)) - Nb[i]/tauNb ;
#-------------------------------------#
if ctstring[1] == '0'
du[(1*NCells)+i] = (alpha)/(1 + (C[i]/Kappa)^h1 + (B[i]/Kappa)^h2) - k1*A[i] ;
elseif ctstring[1] == '1'
du[(1*NCells)+i] = (alpha + theta1*Nb[i])/(1 + (C[i]/Kappa)^h1 + (B[i]/Kappa)^h2 + Nb[i]) - k1*A[i] ;
elseif ctstring[1] == '2'
du[(1*NCells)+i] = (alpha)/(1 + (C[i]/Kappa)^h1 + (B[i]/Kappa)^h2 + theta1*Nb[i]) - k1*A[i] ;
end
#--------------------------------------#
if ctstring[2] == '0'
du[(2*NCells)+i] = ((beta*S[i])/(1 + S[i]))*(1/(1 + (C[i]/Kappa)^h3)) - k2*B[i] ;
elseif ctstring[2] == '1'
du[(2*NCells)+i] = ((beta*S[i] + theta2*Nb[i])/(1 + S[i] + Nb[i]))*(1/(1 + (C[i]/Kappa)^h3)) - k2*B[i] ;
elseif ctstring[2] == '2'
du[(2*NCells)+i] = ((beta*S[i])/(1 + S[i] + theta2*Nb[i]))*(1/(1 + (C[i]/Kappa)^h3)) - k2*B[i] ;
end
#--------------------------------------#
if ctstring[3] == '0'
du[(3*NCells)+i] = ((gamma*S[i])/(1 + S[i]))*(1/(1 + (B[i]/Kappa)^h4 + (A[i]/Kappa)^h5)) - k3*C[i] ;
elseif ctstring[3] == '1'
du[(3*NCells)+i] = ((gamma*S[i] + theta3*Nb[i])/(1 + S[i] + Nb[i]))*(1/(1 + (B[i]/Kappa)^h4 + (A[i]/Kappa)^h5)) - k3*C[i] ;
elseif ctstring[3] == '2'
du[(3*NCells)+i] = ((gamma*S[i])/(1 + S[i] + theta3*Nb[i]))*(1/(1 + (B[i]/Kappa)^h4 + (A[i]/Kappa)^h5)) - k3*C[i] ;
end
#---------- remaining three strings to be considered together giving raise to 8 possibilities ----------------------------#
omegaA,omegaB,omegaC,omegaD,omegaE,omegaF = get_omegas(ctstring,theta4,theta5,theta6) ;
du[(4*NCells)+i] = (betaD + omegaA*A[i] + omegaB*B[i] + omegaC*C[i] )/(1 + omegaD*A[i] + omegaE*B[i] + omegaF*C[i] ) - D[i]/tauD ;
end
end#function
#==================================================================================================#
#CID = 1 : 728
function Explore_All_Thetas(CID,niters)
PATH = "Data/" ;
n_vals = 100 ;
ctstring = int_to_trinary(CID) ;
println(ctstring) ;
NCells = 30 ;
Smax,Slambda = 100, 0.3 ;
Kappa = 1.0 ;
h1,h2,h3,h4,h5 = 6,2,5,1,1 ;
k1,k2,k3 = 1.0,1.0,1.0 ;
alpha,beta,gamma = 4.0,6.3,5.0 ;
tauD,tauNb = 1.0,1.0 ;
betaD,betaNb = 5.0,5.0 ;
K_N = 1.0 ;
OD = zeros(Int16,niters,NCells) ;
Thetas = zeros(6) ;
ThetaUP = LinRange(1.0,10.0,n_vals);
ThetaDN = LinRange(0.1,1.0,n_vals);
for i = 1:niters
println(i) ;
for j = 1:6
if ctstring[j] == '0'
Thetas[j] = 0.0 ;
elseif ctstring[j] == '1'
Thetas[j] = ThetaUP[rand(1:n_vals)] ;
elseif ctstring[j] == '2'
Thetas[j] = ThetaDN[rand(1:n_vals)] ;
end
end
theta1,theta2,theta3,theta4,theta5,theta6 = Thetas ;
#--------------------------------------------------#
p = Kappa,h1,h2,h3,h4,h5,k1,k2,k3,alpha,beta,gamma,tauD,tauNb,betaD,betaNb,K_N,NCells,Smax,Slambda,theta1,theta2,theta3,theta4,theta5,theta6,ctstring ;
u0 = zeros(6*NCells) ;
for k = 1 : NCells
u0[k] = (Smax* exp(-Slambda*(k-1))) ;
end
tmax = 100 ;
tspan = (0.0,tmax) ;
prob = ODEProblem(coupled_frenchflag_ultimate!,u0,tspan,p) ;
sol = solve(prob) ;
FS = get_final_state(sol,NCells) ;
OD[i,:] = FS ;
end
ofilename = PATH * "Ensemble_Ultimate_NCells_"*string(NCells)*"_CID_"*string(CID)*".npy" ;
npzwrite(ofilename,OD) ;
end#function
#===================================================================================#
CID = 345 ;
niters = 100 ;
Explore_All_Thetas(CID,niters) ;