from numpy import sqrt, abs, cos, sin, arcsin, searchsorted, loadtxt, log, array, select, exp

from numpy import pi, sqrt

from scipy.integrate import quad
from read import ReadProfile,resultdir

from constants import *

# Value for analytic expression
Ee_default=1e3 #GeV

Egamma_default=1 #GeV

B_default=1e-15 #Gauss

lambda_B_default=0.3 #Mpc

def Analytic_flux(E_ic,fileId):
   zs=ReadProfile(fileId,[3]) #Gauss #GeV #Mpc 
   return  me*1e3/4*sqrt(3e9/Ecmb)*1e-9*E_ic**(-3/2.) / (1+zs) #GeV

def Analytic_dNdtheta(theta,fileId):
   B,Eg0,Ds,zs=ReadProfile(fileId,[0,1,2,3]) #Gauss #GeV #Mpc 

   lgg = 1.32#lambda_gg(Eg0*1e3,zs)[1]

   tau_gg = Ds/lgg
   dNdtheta = m*c**2 *sqrt((3*sigmaT*nCMB)/(2*e*Ecmb*1e-9/erg_to_GeV) * tau_gg/(theta/degre*B)) # rad^-1
   return dNdtheta

def Analytic_dNdt(t,fileId):
   B,Eg0,zs=ReadProfile(fileId,[0,1,3]) #Gauss #GeV 

   lgg = 1.32#lambda_gg(Eg0*1e3,zs)[1]

   dNdt = (m*c**2/4) *sqrt((3*sigmaT*nCMB)/(e*Ecmb*1e-9/erg_to_GeV*B))*(8*c*t*yr/(lgg*Mpc))**(0.25)
   return dNdt

def Analytic_delay_vs_theta(theta,fileId):

   Esource,distSource=ReadProfile(fileId,[1,2]) #GeV #Mpc 

   E0_source = Esource*1e-3 #TeV

   Dic0=Dic(E0_source/2)

   lgg = 1.32#lambda_gg(Esource*1e3)[0]

   delta_ic = arcsin(distSource/lgg*sin(theta))

   c_delta_t = (lgg*(1-cos(delta_ic)) - distSource*(1-cos(theta)))

   lgg = 117#lambda_gg(8e3)[0]

   delta_ic = arcsin(distSource/lgg*sin(theta))
   c_delta_t2 = (lgg*(1-cos(delta_ic)) - distSource*(1-cos(theta)))
   return c_delta_t *Mpc/c, c_delta_t2 *Mpc/c  # sec.

def Analytic_observables_vs_energy(Egamma, fileId):
   B,Eg0,Ds,zs=ReadProfile(fileId,[0,1,2,3]) #Gauss #GeV #Mpc 
   Ee0=Eg0*1e3/2 #GeV

   RL0=RL(Ee0,B,zs)
   Dic0=Dic(Ee0,zs)
   E_e = Ee(Egamma,zs)
   delta = Dic0/(2*RL0)*((Ee0/E_e)**2 -1)

   lgg = lambda_gg(Eg0*1e3,zs)[1]

   theta = arcsin(lgg/Ds*sin(delta))

   c_delta_t = lgg*(1-cos(delta)) - Ds*(1-cos(theta)) #+Dic(E_e,zs)

   lgg = lambda_gg(8e3,zs)[1]
   theta2 = arcsin(lgg/Ds*sin(delta))
   c_delta_t2 = lgg*(1-cos(delta)) - Ds*(1-cos(theta)) #+Dic(E_e,zs)
   return abs(theta)/degre, c_delta_t *Mpc/c, abs(theta2)/degre, c_delta_t2 *Mpc/c # sec.

def arrival_approx(B=B_default,z=0.13,Egamma0=1e5): # Pour Egamma = 1GeV

   delta = Dic(Ee=Ee(1),z=z)/(2*RL(B=B,z=z))  
   lgg =  1.32# lambda_gg(Egamma0,z)[0]
   print distance(z)[0], lgg, distance(z)[0]/lgg
   theta = lgg/distance(z)[0] * delta
   cdt = lgg/2 * delta**2

   return theta/degre, cdt*Mpc/c /yr

# Compton accumulation

def ECompton_threshold(Compton_threshold = 0.005,z=0):
   return Compton_threshold/(4/3*Ecmb*(1+z)/me*1e-3) *me*1e-6 #GeV

# Compton scattering

def Dic(Ee=Ee_default,z=0): # Ee (GeV)
   return 3*(me*1e3)**2/(4*sigmaT*Ee*1e9*rhoCMB*(1+z)**4) /Mpc #Mpc

def lambdaIC(z=0):
   return 1/(sigmaT*Mpc*nCMB*(1+z)**3) #Mpc

def Eic(Ee=Ee_default,z=0):
   return 4*Ecmb*(1+z) *Ee**2/(3*me**2)*1e3 #GeV 

def Ee(Egamma=Egamma_default,z=0):
   return me*sqrt((3*Egamma*1e-3 )/(4*Ecmb*(1+z))) #GeV 

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

# Larmor radius

def RL(Ee=Ee_default,B=B_default,z=0):
   return (Ee/erg_to_GeV)/(e*B) /(1+z) /Mpc #Mpc

# Magnetic deflection

def delta(Ee=Ee_default,B=B_default,lambda_B=lambda_B_default,z=0):

   Ee=array(Ee)

   D_ic=Dic(Ee,z)
   condlist=[lambda_B>=D_ic,lambda_B<D_ic]
   delta=[D_ic/RL(Ee,B),sqrt(D_ic*lambda_B)/RL(Ee,B)]
   return select(condlist,delta)

def Delta(Ee=Ee_default,B=B_default,lambda_B=lambda_B_default,z=0,Esource=1e5):
   lgg=lambda_gg(Esource)[0]
   Dsource=distance(z)[1]

   return arcsin(lgg/Dsource*delta(Ee,B,lambda_B,z))/degre

def Dt(Ee=Ee_default,B=B_default,lambda_B=lambda_B_default,z=0,Esource=1e5):
   lgg=lambda_gg(Esource)[0]
   return lgg/2*delta(Ee,B,lambda_B,z)**2 /c *Mpc/yr

#synchrotron radiation
def Esc(Ee=Ee_default,B=B_default): # eV
   return (3*hb*e*c)/(2*m**3*c**6) * B*(Ee/erg_to_GeV)**2 *erg_to_GeV*1e9

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

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

def lambda_gg(Egamma=1e3,z=0): # Egamma (GeV)

   # Bilinear interpolation 

   z_tab = [0,0.03,0.1,0.5,1,2,3]

   E_tab = loadtxt("Results/lambda_e.dat",unpack=True,usecols=[0])*me*1e-6

   i2 = searchsorted(z_tab,z)
   if z<=0:
      fy=1
      i1=i2
   elif z>3:
      fy=1
      i2-=1
      i1=i2
   else:
      i1 = i2-1
      fy=(z-z_tab[i1])/(z_tab[i2]-z_tab[i1])
   j2 = searchsorted(E_tab,Egamma)
   j1 = j2-1
   fx=(Egamma-E_tab[j1])/(E_tab[j2]-E_tab[j1])

   lambda_e = loadtxt("Results/lambda_e.dat",unpack=True,usecols=[i1+1,i2+1,i1+7,i2+7])

   lambda11 = lambda_e[0,j1]*((1-fx)*(1-fy))
   lambda12 = lambda_e[1,j1]*((1-fx)*fy)
   lambda21 = lambda_e[0,j2]*(fx*(1-fy))
   lambda22 = lambda_e[1,j2]*(fx*fy)
   lambda_proper = lambda11 + lambda12 + lambda21 + lambda22
   lambda11 = lambda_e[2,j1]*((1-fx)*(1-fy))
   lambda12 = lambda_e[3,j1]*((1-fx)*fy)
   lambda21 = lambda_e[2,j2]*(fx*(1-fy))
   lambda22 = lambda_e[3,j2]*(fx*fy)
   lambda_comobile = lambda11 + lambda12 + lambda21 + lambda22
   return lambda_proper, lambda_comobile, 800.e3/Egamma #Mpc (from Durrer and Neronov 2013)

def comobileTime(z):
   return -1/(H0*(1+z)*sqrt(omegaM*(1+z)**3+omegaK*(1+z)**2+omegaL))

def distPhoton(z):
   return -c/(H0*a0*sqrt(omegaM*(1+z)**3+omegaK*(1+z)**2+omegaL))

def distLepton(z,E):
   beta = sqrt(1-m**2*c**4/E**2)
   return -beta*c/(H0*a0*sqrt(omegaM*(1+z)**3+omegaK*(1+z)**2+omegaL))

def properIntegrand(z):
   return -c/(H0*(1+z)*sqrt(omegaM*(1+z)**3+omegaK*(1+z)**2+omegaL))

def comobileIntegrand(z):
   return -c/(H0*sqrt(omegaM*(1+z)**3+omegaK*(1+z)**2+omegaL))

def distance(z=0):
   return quad(properIntegrand,z,0)[0]/Mpc, quad(comobileIntegrand,z,0)[0]/Mpc

def Ecut(z=0.1): # TeV
   z=array(z)
   z1= 0.045
   z2= 0.1
   condlist=[z<z1,(z>=z1)&(z<z2),z>=z2]
   Ecut=[54*(z/0.001)**(-0.5),3.4*(z/0.06)**(-3),0.35*(z/0.4)**(-0.5)]
   return select(condlist,Ecut)

def Etarget(Egamma=1): # Egamma en TeV, Etarget en eV

   return 6.9*(Egamma/0.2)**(-0.9)

def PSF_Taylor2011(E): # E in GeV -> PSF in degre

   return 1.7 * E**(-0.74) * (1+(E/15)**2)**0.37