from Constants import *
from numpy import sqrt, abs, cos, sin, arcsin
from Read import ReadE_source, ReadD_source, ReadEGMF

# Value for analytic expression
Ee_default=1e3 #GeV
Egamma_default=1 #GeV
B_default=1e-17 #Gauss
lambda_B_default=0.3 #Mpc

def Analytic_flux(E_ic):
   return  me*1e3/4*sqrt(3e9/Ecmb)*1e-9*E_ic**(1/2.) #GeV

def Analytic_theta(E_ic,fileId):
   Esource=ReadE_source(fileId) #GeV
   Dsource=ReadD_source(fileId) #Mpc
   B=ReadEGMF(fileId) #Gauss
   delta_to_theta=lambda_gg(Esource)/Dsource
   RL0=RL(Esource/2,B)
   Dic0=Dic(Esource/2)
   Ee2= E_ic /Eic(1) #GeV^2 
   delta=Dic0/(2*RL0)*((Esource/2)**2 /Ee2 -1)
   return abs(arcsin(delta_to_theta*sin(delta))*degre)

def Analytic_delay_vs_theta(theta,fileId):
   E0_source = ReadE_source(fileId)*1e-3 #TeV
   distSource = ReadD_source(fileId)
   delta_ic = arcsin(distSource/lambda_gg(E0_source)*sin(theta/degre))
   c_delta_t = lambda_gg(E0_source)*(1-cos(delta_ic)) - distSource*(1-cos(theta/degre))
   return c_delta_t *Mpc/c # sec.

def Analytic_delay_vs_Egamma(Egamma, fileId):
   Esource=ReadE_source(fileId) #GeV
   Dsource=ReadD_source(fileId) #Mpc
   B=ReadEGMF(fileId) #Gauss
   RL0=RL(Esource/2,B)
   Dic0=Dic(Esource/2)
   Ee2 = Ee(Egamma)**2
   delta_ic = Dic0/(2*RL0)*((Esource/2)**2 /Ee2 -1)
   theta = arcsin(lambda_gg(Esource)/Dsource*sin(delta_ic/degre))
   c_delta_t = lambda_gg(Esource)*(1-cos(delta_ic)) - Dsource*(1-cos(theta/degre))
   return c_delta_t *Mpc/c # sec.

# Compton accumulation
def ECompton_threshold(Compton_threshold = 0.005):
   return Compton_threshold/(4/3*Ecmb/me*1e-3) *me*1e-6 #GeV

# Compton scattering
def Dic(Ee=Ee_default): # Ee (GeV)
   return 3*(me*1e-6)**2/(4*sigmaT*rhoCMB*1e-9*Ee) /Mpc #Mpc

def lambdaIC():
   return 1/(nCMB*sigmaT*Mpc) #Mpc

def Eic(Ee=Ee_default):
   return 4*Ecmb*Ee**2/(3*me**2)*1e3 #GeV 

def Ee(Egamma=Egamma_default):
   return sqrt((3*me**2)/(4*Ecmb)*1e-3 *Egamma) #GeV 

def tIC():
   return lambdaIC()/(c*yr/Mpc) #yr

# Larmor radius
def RL(Ee=Ee_default,B=B_default):
   return (Ee/erg_to_GeV)/(e*B) /Mpc #Mpc

# Magnetic deflection
def delta(Ee=Ee_default,B=B_default):
   return lambdaIC()/RL(Ee,B)*degre

def Delta(Ee=Ee_default,B=B_default,lambda_B=lambda_B_default):
   Delta1=Dic(Ee)/RL(Ee,B)*degre                #degre if Dic >> lambda_B 
   Delta2=sqrt(Dic(Ee)*lambda_B)/RL(Ee,B)*degre #degre if Dic << lambda_B
   return Delta1, Delta2

# Threshold energy when Dic = RL
def Ethreshold_ic(Ee=Ee_default,B=B_default):
   return Eic(Ee)*Dic(Ee)/RL(Ee,B) # GeV
# Pair production

def Ethreshold_gg():
   return (me)**2/Eebl *1e-3 #GeV

def lambda_gg(Egamma=1): # Egamma (GeV)
   return 800. /(Egamma)#Mpc (from Durrer and Neronov 2013)