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#!/usr/bin/env python3

# Based off of SimulationTools Mathematica Package
# http://www.simulationtools.org/

import numpy as np
import glob
import os
import h5py
import string
import math
import sys
import warnings
import scipy.optimize
import scipy.interpolate

#-----Function Definitions-----#

#Function used in getting psi4 from simulation
def joinDsets(dsets):
	"""joints multiple datasets which each have a
	time like first column, eg iteration number of
	time. Removes overlapping segments, keeping the
	last segment.

	dsets = iterable of 2d array like objects with data"""
	# joins multiple datasets of which the first column is assumed to be "time"
	if(not dsets):
		return None
	length = 0
	for d in dsets:
		length += len(d)
	newshape = list(dsets[0].shape)
	newshape[0] = length
	dset = np.empty(shape=newshape, dtype=dsets[0].dtype)
	usedlength = 0
	for d in dsets:
		insertpointidx = np.where(dset[0:usedlength,0] >= d[0,0])
		if(insertpointidx[0].size):
			insertpoint = insertpointidx[0][0]
		else:
			insertpoint = usedlength
		newlength = insertpoint+len(d)
		dset[insertpoint:newlength] = d
		usedlength = newlength
	return dset[0:usedlength]

#Function used in getting psi4 from simulation
def loadHDF5Series(nameglob, series):
	"""load HDF5 timeseries data and concatenate the content of multiple files

	nameglob = a shell glob that matches all files to be loaded,
	files are sorted alphabetically
	series = HDF5 dataset name of dataset to load from files"""
	dsets = list()
	for fn in sorted(glob.glob(nameglob)):
		fh = h5py.File(fn)
		dsets.append(fh[series])
	return joinDsets(dsets)

#Convert radial to tortoise coordinates
def RadialToTortoise(r, M):
	"""
	Convert the radial coordinate to the tortoise coordinate

	r = radial coordinate
	M = ADMMass used to convert coordinate
	return = tortoise coordinate value
	"""
	return r + 2. * M * math.log( r / (2. * M) - 1.)

#Convert modified psi4 to strain
def psi4ToStrain(mp_psi4, f0):
	"""
	Convert the input mp_psi4 data to the strain of the gravitational wave
	
	mp_psi4 = Weyl scalar result from simulation
	f0 = cutoff frequency
	return = strain (h) of the gravitational wave
	"""
	#TODO: Check for uniform spacing in time
	t0 = mp_psi4[:, 0]
	list_len = len(t0)
	complexPsi = np.zeros(list_len, dtype=np.complex_)
	complexPsi = mp_psi4[:, 1]+1.j*mp_psi4[:, 2]

	freq, psif = myFourierTransform(t0, complexPsi)
	dhf = ffi(freq, psif, f0)
	hf = ffi(freq, dhf, f0)

	time, h = myFourierTransformInverse(freq, hf, t0[0])
	hTable = np.column_stack((time, h))
	return hTable

#Fixed frequency integration
# See https://arxiv.org/abs/1508.07250 for method
def ffi(freq, data, f0):
	"""
	Integrates the data according to the input frequency and cutoff frequency

	freq = fourier transform frequency
	data = input on which ffi is performed
	f0 = cutoff frequency
	"""
	f1 = f0/(2*math.pi)
	fs = freq
	gs = data
	mask1 = (np.sign((fs/f1) - 1) + 1)/2
	mask2 = (np.sign((-fs/f1) - 1) + 1)/2
	mask = 1 - (1 - mask1) * (1 - mask2)
	fs2 = mask * fs + (1-mask) * f1 * np.sign(fs - np.finfo(float).eps)
	new_gs = gs/(2*math.pi*1.j*fs2)
	return new_gs

#Fourier Transform
def myFourierTransform(t0, complexPsi):
	"""
	Transforms the complexPsi data to frequency space

	t0 = time data points
	complexPsi = data points of Psi to be transformed
	"""
	psif = np.fft.fft(complexPsi, norm="ortho")
	l = len(complexPsi)
	n = int(math.floor(l/2))
	newpsif = psif[l-n:]
	newpsif = np.append(newpsif, psif[:l-n])
	T = np.amin(np.diff(t0))*l
	freq = range(-n, l-n)/T
	return freq, newpsif

#Inverse Fourier Transform
def myFourierTransformInverse(freq, hf, t0):
	l = len(hf)
	n = int(math.floor(l/2))
	newhf = hf[n:]
	newhf = np.append(newhf, hf[:n])
	amp = np.fft.ifft(newhf, norm="ortho")
	df = np.amin(np.diff(freq))
	time = t0 + range(0, l)/(df*l)
	return time, amp

def angular_momentum(x, q, m, chi1, chi2, LInitNR):
	eta = q/(1.+q)**2.
	m1 = (1.+(1.-4.*eta)**0.5)/2.
	m2 = m - m1
	S1 = m1**2. * chi1
	S2 = m2**2. * chi2
	Sl = S1+S2
	Sigmal = S2/m2 - S1/m1
	DeltaM = m1 - m2
	mu = eta
	nu = eta
	GammaE = 0.5772156649;
	e4 = -(123671./5760.)+(9037.* math.pi**2.)/1536.+(896.*GammaE)/15.+(-(498449./3456.)+(3157.*math.pi**2.)/576.)*nu+(301. * nu**2.)/1728.+(77.*nu**3.)/31104.+(1792. *math.log(2.))/15.
	e5 = -55.13
	j4 = -(5./7.)*e4+64./35.
	j5 = -(2./3.)*e5-4988./945.-656./135. * eta;
	a1 = -2.18522;
	a2 = 1.05185;
	a3 = -2.43395;
	a4 = 0.400665;
	a5 = -5.9991;
	CapitalDelta = (1.-4.*eta)**0.5

	l = (eta/x**(1./2.)*(
		1. +
		x*(3./2. + 1./6.*eta) + 
        x**2. *(27./8. - 19./8.*eta + 1./24.*eta**2.) + 
        x**3. *(135./16. + (-6889./144. + 41./24. * math.pi**2.)*eta + 31./24.*eta**2. + 7./1296.*eta**3.) + 
        x**4. *((2835./128.) + eta*j4 - (64.*eta*math.log(x)/3.))+ 
        x**5. *((15309./256.) + eta*j5 + ((9976./105.) + (1312.*eta/15.))*eta*math.log(x))+
        x**(3./2.)*(-(35./6.)*Sl - 5./2.*DeltaM* Sigmal) + 
        x**(5./2.)*((-(77./8.) + 427./72.*eta)*Sl + DeltaM* (-(21./8.) + 35./12.*eta)*Sigmal) + 
        x**(7./2.)*((-(405./16.) + 1101./16.*eta - 29./16.*eta**2.)*Sl + DeltaM*(-(81./16.) + 117./4.*eta - 15./16.*eta**2.)*Sigmal) + 
        (1./2. + (m1 - m2)/2. - eta)* chi1**2. * x**2. +
        (1./2. + (m2 - m1)/2. - eta)* chi2**2. * x**2. + 
        2.*eta*chi1*chi2*x**2. +
        ((13.*chi1**2.)/9. +
        (13.*CapitalDelta*chi1**2.)/9. -
        (55.*nu*chi1**2.)/9. - 
        29./9.*CapitalDelta*nu*chi1**2. + 
        (14.*nu**2. *chi1**2.)/9. +
        (7.*nu*chi1*chi2)/3. +
        17./18.* nu**2. * chi1 * chi2 + 
        (13.* chi2**2.)/9. -
        (13.*CapitalDelta*chi2**2.)/9. -
        (55.*nu*chi2**2.)/9. +
        29./9.*CapitalDelta*nu*chi2**2. +
        (14.*nu**2. * chi2**2.)/9.)
        * x**3.))
	return l - LInitNR

#Get cutoff frequency
def getCutoffFrequency(sim_name):
	"""
	Determine cutoff frequency of simulation

	sim_name = string of simulation
	return = cutoff frequency
	"""
	filename = main_dir+"/output-0000/%s.par" % (sim_name)
	with open(filename) as file:
		contents = file.readlines()
		for line in contents:
			line_elems = line.split(" ")
			if(line_elems[0] == "TwoPunctures::par_b"):
				par_b = float(line_elems[-1])
			if(line_elems[0] == "TwoPunctures::center_offset[0]"):
				center_offset = float(line_elems[-1])
			if(line_elems[0] == "TwoPunctures::par_P_plus[1]"):
				pyp = float(line_elems[-1])
			if(line_elems[0] == "TwoPunctures::par_P_minus[1]"):
				pym = float(line_elems[-1])
			if(line_elems[0] == "TwoPunctures::target_M_plus"):
				m1 = float(line_elems[-1])
			if(line_elems[0] == "TwoPunctures::target_M_minus"):
				m2 = float(line_elems[-1])
			if(line_elems[0] == "TwoPunctures::par_S_plus[2]"):
				S1 = float(line_elems[-1])
			if(line_elems[0] == "TwoPunctures::par_S_minus[2]"):
				S2 = float(line_elems[-1])

	xp = par_b + center_offset
	xm = -1*par_b + center_offset
	LInitNR = xp*pyp + xm*pym
	M = m1+m2
	q = m1/m2
	chi1 = S1/math.pow(m1, 2.)
	chi2 = S2/math.pow(m2, 2.)
	# .014 is the initial guess for cutoff frequency
	omOrbPN = scipy.optimize.fsolve(angular_momentum, .014, (q, M, chi1, chi2, LInitNR))[0]
	omOrbPN = omOrbPN**(3./2.)
	omGWPN = 2. * omOrbPN
	omCutoff = 0.75 * omGWPN
	return omCutoff


#-----Main-----#

#Initialize simulation data
if(len(sys.argv) == 2):
	radiiUsedForExtrapolation = 7	#use the first n radii available  
elif(len(sys.argv) == 3):
	radiiUsedForExtrapolation = int(sys.argv[2])	#use the first n radii available  
else:
	print("Pass in simulation folder and the number of radii to be used in the extrapolation (optional, default=all) (e.g., ./power.py ./simulations/J0040_N40 6).")
	sys.exit()
sim_path = sys.argv[1]
main_dir = sim_path
sim = sim_path.split("/")[-1]

simdirs = main_dir+"/output-????/%s/" % (sim)
f0 = getCutoffFrequency(sim)

#Create data directories
main_directory = "Extrapolated_Strain"
sim_dir = main_directory+"/"+sim
if not os.path.exists(main_directory):
    os.makedirs(main_directory)
if not os.path.exists(sim_dir):
    os.makedirs(sim_dir)

#Get ADMMass
ADMMass = -1
filename = main_dir+"/output-0000/%s/TwoPunctures.bbh" % (sim)
with open(filename) as file:
	contents = file.readlines()
	for line in contents:
		line_elems = line.split(" ")
		if(line_elems[0] == "initial-ADM-energy"):
			ADMMass = float(line_elems[-1])

#Get Psi4
radii = [100, 115, 136, 167, 214, 300, 500]
psi4dsetname_100 = 'l2_m2_r'+str(radii[0])+'.00'
psi4dsetname_115 = 'l2_m2_r'+str(radii[1])+'.00'
psi4dsetname_136 = 'l2_m2_r'+str(radii[2])+'.00'
psi4dsetname_167 = 'l2_m2_r'+str(radii[3])+'.00'
psi4dsetname_214 = 'l2_m2_r'+str(radii[4])+'.00'
psi4dsetname_300 = 'l2_m2_r'+str(radii[5])+'.00'
psi4dsetname_500 = 'l2_m2_r'+str(radii[6])+'.00'
mp_psi4_100 = loadHDF5Series(simdirs+"mp_psi4.h5", psi4dsetname_100)
mp_psi4_115 = loadHDF5Series(simdirs+"mp_psi4.h5", psi4dsetname_115)
mp_psi4_136 = loadHDF5Series(simdirs+"mp_psi4.h5", psi4dsetname_136)
mp_psi4_167 = loadHDF5Series(simdirs+"mp_psi4.h5", psi4dsetname_167)
mp_psi4_214 = loadHDF5Series(simdirs+"mp_psi4.h5", psi4dsetname_214)
mp_psi4_300 = loadHDF5Series(simdirs+"mp_psi4.h5", psi4dsetname_300)
mp_psi4_500 = loadHDF5Series(simdirs+"mp_psi4.h5", psi4dsetname_500)
mp_psi4_vars = [mp_psi4_100, mp_psi4_115, mp_psi4_136, mp_psi4_167, mp_psi4_214, mp_psi4_300, mp_psi4_500]

#Get Tortoise Coordinate
tortoise = [None] * 7
for i in range(0, 7):
	tortoise[i] = -RadialToTortoise(radii[i], ADMMass)

strain = [None]*7
phase = [None]*7
amp = [None]*7
for i in range(0, 7):
	#Get modified Psi4 (Multiply real and imaginary psi4 columns by radii and add the tortoise coordinate to the time colum)
	mp_psi4_vars[i][:, 0] += tortoise[i]
	mp_psi4_vars[i][:, 1] *= radii[i]
	mp_psi4_vars[i][:, 2] *= radii[i]

	#Fixed-frequency integration twice to get strain
	hTable = psi4ToStrain(mp_psi4_vars[i], f0)
	time = hTable[:, 0]
	h = hTable[:, 1]
	hplus = h.real
	hcross = h.imag
	newhTable = np.column_stack((time, hplus, hcross))
	warnings.filterwarnings('ignore')
	finalhTable = newhTable.astype(float)
	np.savetxt("./Extrapolated_Strain/"+sim+"/"+sim+"_strain_at_"+str(radii[i])+".dat", finalhTable)
	strain[i] = finalhTable

	#Get phase and amplitude of strain
	h_phase = np.unwrap(np.angle(h))
	while(h_phase[0] < 0):
		h_phase[:] += 2*math.pi
	angleTable = np.column_stack((time, h_phase))
	angleTable = angleTable.astype(float)
	phase[i] = angleTable
	h_amp = np.absolute(h)
	ampTable = np.column_stack((time, h_amp))
	ampTable = ampTable.astype(float)
	amp[i] = ampTable

#Interpolate phase and amplitude
t = phase[0][:, 0]
last_t = phase[radiiUsedForExtrapolation - 1][-1, 0]
last_index = 0;
for i in range(0, len(phase[0][:, 0])):
	if(t[i] > last_t):
		last_index = i
		break
last_index = last_index-1
t = phase[0][0:last_index, 0]
dts = t[1:] - t[:-1]
dt = float(np.amin(dts))
t = np.arange(phase[0][0, 0], phase[0][last_index, 0], dt)
interpolation_order = 9
for i in range(0, radiiUsedForExtrapolation):
	interp_function = scipy.interpolate.interp1d(phase[i][:, 0], phase[i][:, 1], kind=interpolation_order)
	resampled_phase_vals = interp_function(t)
	while(resampled_phase_vals[0] < 0):
		resampled_phase_vals[:] += 2*math.pi
	phase[i] = np.column_stack((t, resampled_phase_vals))
	interp_function = scipy.interpolate.interp1d(amp[i][:, 0], amp[i][:, 1], kind=interpolation_order)
	resampled_amp_vals = interp_function(t)
	amp[i] = np.column_stack((t, resampled_amp_vals))

#Extrapolate
phase_extrapolation_order = 1
amp_extrapolation_order = 2
radii = np.asarray(radii, dtype=float)
radii = radii[0:radiiUsedForExtrapolation]
A_phase = np.power(radii, 0)
A_amp = np.power(radii, 0)
for i in range(1, phase_extrapolation_order+1):
	A_phase = np.column_stack((A_phase, np.power(radii, -1*i)))

for i in range(1, amp_extrapolation_order+1):
	A_amp = np.column_stack((A_amp, np.power(radii, -1*i)))

radially_extrapolated_phase = np.empty(0)
radially_extrapolated_amp = np.empty(0)
for i in range(0, len(t)):
	b_phase = np.empty(0)
	for j in range(0, radiiUsedForExtrapolation):
		b_phase = np.append(b_phase, phase[j][i, 1])
	x_phase = np.linalg.lstsq(A_phase, b_phase)[0]
	radially_extrapolated_phase = np.append(radially_extrapolated_phase, x_phase[0])

	b_amp = np.empty(0)
	for j in range(0, radiiUsedForExtrapolation):
		b_amp = np.append(b_amp, amp[j][i, 1])
	x_amp = np.linalg.lstsq(A_amp, b_amp)[0]
	radially_extrapolated_amp = np.append(radially_extrapolated_amp, x_amp[0])

radially_extrapolated_h_plus = np.empty(0)
radially_extrapolated_h_cross = np.empty(0)
for i in range(0, len(radially_extrapolated_amp)):
	radially_extrapolated_h_plus = np.append(radially_extrapolated_h_plus, radially_extrapolated_amp[i] * math.cos(radially_extrapolated_phase[i]))
	radially_extrapolated_h_cross = np.append(radially_extrapolated_h_cross, radially_extrapolated_amp[i] * math.sin(radially_extrapolated_phase[i]))

np.savetxt("./Extrapolated_Strain/"+sim+"/"+sim+"_radially_extrapolated_strain.dat", np.column_stack((t, radially_extrapolated_h_plus, radially_extrapolated_h_cross)))