###############################################################################
 # This file is part of SWIFT.
 # Copyright (c) 2016 Stefan Arridge (stefan.arridge@durham.ac.uk)
 # 
 # This program is free software: you can redistribute it and/or modify
 # it under the terms of the GNU Lesser General Public License as published
 # by the Free Software Foundation, either version 3 of the License, or
 # (at your option) any later version.
 # 
 # This program is distributed in the hope that it will be useful,
 # but WITHOUT ANY WARRANTY; without even the implied warranty of
 # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 # GNU General Public License for more details.
 # 
 # You should have received a copy of the GNU Lesser General Public License
 # along with this program.  If not, see <http://www.gnu.org/licenses/>.
 # 
 ##############################################################################

import h5py
import sys
import numpy as np
import math
import random

# Generates N particles in a spherically symmetric distribution with density profile ~r^(-2)
# usage: python makeIC.py 1000: generate 1000 particles

# Some constants

OMEGA = 0.3 # Cosmological matter fraction at z = 0
PARSEC_IN_CGS = 3.0856776e18
KM_PER_SEC_IN_CGS = 1.0e5
CONST_G_CGS = 6.672e-8
h = 0.67777 # hubble parameter
gamma = 5./3.
eta = 1.2349
spin_lambda = 0.05 #spin parameter
f_b = 0.2 #baryon fraction

# First set unit velocity and then the circular velocity parameter for the isothermal potential
const_unit_velocity_in_cgs = 1.e5 #kms^-1

v_c = 200.
v_c_cgs = v_c * const_unit_velocity_in_cgs

# Now we use this to get the virial mass and virial radius, which we will set to be the unit mass and radius

# Find H_0, the inverse Hubble time, in cgs

H_0_cgs = 100. * h * KM_PER_SEC_IN_CGS / (1.0e6 * PARSEC_IN_CGS)

# From this we can find the virial radius, the radius within which the average density of the halo is
# 200. * the mean matter density

r_vir_cgs = v_c_cgs / (10. * H_0_cgs * np.sqrt(OMEGA))

# Now get the virial mass

M_vir_cgs = r_vir_cgs * v_c_cgs**2 / CONST_G_CGS

# Now set the unit length and mass

const_unit_mass_in_cgs = M_vir_cgs
const_unit_length_in_cgs = r_vir_cgs

print "UnitMass_in_cgs:     ", const_unit_mass_in_cgs 
print "UnitLength_in_cgs:   ", const_unit_length_in_cgs
print "UnitVelocity_in_cgs: ", const_unit_velocity_in_cgs

#derived quantities
const_unit_time_in_cgs = (const_unit_length_in_cgs / const_unit_velocity_in_cgs)
print "UnitTime_in_cgs:     ", const_unit_time_in_cgs
const_G                = ((CONST_G_CGS*const_unit_mass_in_cgs*const_unit_time_in_cgs*const_unit_time_in_cgs/(const_unit_length_in_cgs*const_unit_length_in_cgs*const_unit_length_in_cgs)))
print 'G=', const_G

# Parameters
periodic= 1            # 1 For periodic box
boxSize = 4.          
G       = const_G 
N       = int(sys.argv[1])  # Number of particles

# Create the file
filename = "CoolingHalo.hdf5"
file = h5py.File(filename, 'w')

#Units
grp = file.create_group("/Units")
grp.attrs["Unit length in cgs (U_L)"] = const_unit_length_in_cgs
grp.attrs["Unit mass in cgs (U_M)"] = const_unit_mass_in_cgs 
grp.attrs["Unit time in cgs (U_t)"] = const_unit_length_in_cgs / const_unit_velocity_in_cgs
grp.attrs["Unit current in cgs (U_I)"] = 1.
grp.attrs["Unit temperature in cgs (U_T)"] = 1.

# set seed for random number
np.random.seed(1234)

gas_mass = f_b * np.sqrt(3.) / 2. #virial mass of halo is 1, virial radius is 1, enclosed mass scales with r
gas_particle_mass = gas_mass / float(N)

# Positions
# r^(-2) distribution corresponds to uniform distribution in radius
radius = boxSize  * np.sqrt(3.) / 2.* np.random.rand(N) #the diagonal extent of the cube
ctheta = -1. + 2 * np.random.rand(N)
stheta = np.sqrt(1.-ctheta**2)
phi    =  2 * math.pi * np.random.rand(N)
coords      = np.zeros((N, 3))
coords[:,0] = radius * stheta * np.cos(phi)
coords[:,1] = radius * stheta * np.sin(phi)
coords[:,2] = radius * ctheta

#shift to centre of box
coords += np.full((N,3),boxSize/2.)
print "x range = (%f,%f)" %(np.min(coords[:,0]),np.max(coords[:,0]))
print "y range = (%f,%f)" %(np.min(coords[:,1]),np.max(coords[:,1]))
print "z range = (%f,%f)" %(np.min(coords[:,2]),np.max(coords[:,2]))

print np.mean(coords[:,0])
print np.mean(coords[:,1])
print np.mean(coords[:,2])

#now find the particles which are within the box

x_coords = coords[:,0]
y_coords = coords[:,1]
z_coords = coords[:,2]

ind = np.where(x_coords < boxSize)[0]
x_coords = x_coords[ind]
y_coords = y_coords[ind]
z_coords = z_coords[ind]

ind = np.where(x_coords > 0.)[0]
x_coords = x_coords[ind]
y_coords = y_coords[ind]
z_coords = z_coords[ind]

ind = np.where(y_coords < boxSize)[0]
x_coords = x_coords[ind]
y_coords = y_coords[ind]
z_coords = z_coords[ind]

ind = np.where(y_coords > 0.)[0]
x_coords = x_coords[ind]
y_coords = y_coords[ind]
z_coords = z_coords[ind]

ind = np.where(z_coords < boxSize)[0]
x_coords = x_coords[ind]
y_coords = y_coords[ind]
z_coords = z_coords[ind]

ind = np.where(z_coords > 0.)[0]
x_coords = x_coords[ind]
y_coords = y_coords[ind]
z_coords = z_coords[ind]

#count number of particles

N = x_coords.size

print "Number of particles in the box = " , N

#make the coords and radius arrays again
coords= np.zeros((N,3))
coords[:,0] = x_coords
coords[:,1] = y_coords
coords[:,2] = z_coords

radius = np.sqrt((coords[:,0]-boxSize/2.)**2 + (coords[:,1]-boxSize/2.)**2 + (coords[:,2]-boxSize/2.)**2)

#now give particle's velocities
v = np.zeros((N,3))

#first work out total angular momentum of the halo within the virial radius
#we work in units where r_vir = 1 and M_vir = 1
Total_E = v_c**2 / 2.0
J = spin_lambda * const_G / np.sqrt(Total_E)
print "J =", J
#all particles within the virial radius have omega parallel to the z-axis, magnitude 
#is proportional to 1 over the radius
omega = np.zeros((N,3))
for i in range(N):
    omega[i,2] = 3.*J / radius[i]
    v[i,:] = np.cross(omega[i,:],(coords[i,:]-boxSize/2.))
        
# Header
grp = file.create_group("/Header")
grp.attrs["BoxSize"] = boxSize
grp.attrs["NumPart_Total"] =  [N ,0, 0, 0, 0, 0]
grp.attrs["NumPart_Total_HighWord"] = [0, 0, 0, 0, 0, 0]
grp.attrs["NumPart_ThisFile"] = [N, 0, 0, 0, 0, 0]
grp.attrs["Time"] = 0.0
grp.attrs["NumFilesPerSnapshot"] = 1
grp.attrs["MassTable"] = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
grp.attrs["Flag_Entropy_ICs"] = [0, 0, 0, 0, 0, 0]
grp.attrs["Dimension"] = 3

# Particle group
grp = file.create_group("/PartType0")

ds = grp.create_dataset('Coordinates', (N, 3), 'd')
ds[()] = coords
coords = np.zeros(1)

ds = grp.create_dataset('Velocities', (N, 3), 'f')
ds[()] = v
v = np.zeros(1)

# All particles of equal mass
m = np.full((N,),gas_particle_mass)
ds = grp.create_dataset('Masses', (N, ), 'f')
ds[()] = m
m = np.zeros(1)

# Smoothing lengths
l = (4. * np.pi * radius**2 / N)**(1./3.) #local mean inter-particle separation
h = np.full((N, ), eta * l)
ds = grp.create_dataset('SmoothingLength', (N,), 'f')
ds[()] = h
h = np.zeros(1)

# Internal energies
u = v_c**2 / (2. * (gamma - 1.)) 
u = np.full((N, ), u)
ds = grp.create_dataset('InternalEnergy', (N,), 'f')
ds[()] = u
u = np.zeros(1)

# Particle IDs
ids = 1 + np.linspace(0, N, N, endpoint=False)
ds = grp.create_dataset('ParticleIDs', (N, ), 'L')
ds[()] = ids

file.close()
