power.py

#!/usr/bin/env python

# Copyright (c) 2017 The Board of Trustees of the University of Illinois
# All rights reserved.
#
# Developed by: Daniel Johnson, E. A. Huerta, Roland Haas
#               NCSA Gravity Group
#               National Center for Supercomputing Applications
#               University of Illinois at Urbana-Champaign
#               http://gravity.ncsa.illinois.edu/
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to
# deal with the Software without restriction, including without limitation the
# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
# sell copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# Redistributions of source code must retain the above copyright notice, this
# list of conditions and the following disclaimers.
#
# Redistributions in binary form must reproduce the above copyright notice,
# this list of conditions and the following disclaimers in the documentation
# and/or other materials provided with the distribution.
#
# Neither the names of the National Center for Supercomputing Applications,
# University of Illinois at Urbana-Champaign, nor the names of its
# contributors may be used to endorse or promote products derived from this
# Software without specific prior written permission.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
# WITH THE SOFTWARE.

# 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

#Get Energy
def get_energy(sim):
	"""
	Save the energy radiated energy
	sim = string of simulation
	"""
	python_strain = np.loadtxt("./Extrapolated_Strain/"+sim+"/"+sim+"_radially_extrapolated_strain_l2_m2.dat")
	val = np.zeros(len(python_strain))
	val = val.astype(np.complex_)
	cur_max_time = python_strain[0][0]
	cur_max_amp = abs(pow(python_strain[0][1], 2))
	for i in python_strain[:]:
		cur_time = i[0]
		cur_amp = abs(pow(i[1], 2))
		if(cur_amp>cur_max_amp):
			cur_max_amp = cur_amp
			cur_max_time = cur_time

	max_idx = 0
	for i in range(0, len(python_strain[:])):
		if(python_strain[i][1] > python_strain[max_idx][1]):
			max_idx = i

	paths = glob.glob("./Extrapolated_Strain/"+sim+"/"+sim+"_radially_extrapolated_strain_l[2-4]_m*.dat")
	for path in paths:
		python_strain = np.loadtxt(path)

		t = python_strain[:, 0]
		t = t.astype(np.complex_)
		h = python_strain[:, 1] + 1j * python_strain[:, 2]
		dh = np.zeros(len(t), dtype=np.complex_) 
		for i in range(0, len(t)-1):
			dh[i] = ((h[i+1] - h[i])/(t[i+1] - t[i]))
		dh[len(t)-1] = dh[len(t)-2]

		dh_conj = np.conj(dh)
		prod = np.multiply(dh, dh_conj)
		local_val = np.zeros(len(t))
		local_val = local_val.astype(np.complex_)
		for i in range(0, len(t)):
			local_val[i] = np.trapz(prod[:i], x=(t[:i]))
		val += local_val
		
	val *= 1/(16 * math.pi)
	np.savetxt("./Extrapolated_Strain/"+sim+"/"+sim+"_radially_extrapolated_energy.dat", val)

#Get angular momentum
def get_angular_momentum(python_strain):
	"""
	Save the energy radiated angular momentum
	sim = string of simulation
	"""
	python_strain = np.loadtxt("./Extrapolated_Strain/"+sim+"/"+sim+"_radially_extrapolated_strain_l2_m2.dat")
	val = np.zeros(len(python_strain))
	val = val.astype(np.complex_)
	cur_max_time = python_strain[0][0]
	cur_max_amp = abs(pow(python_strain[0][1], 2))
	for i in python_strain[:]:
		cur_time = i[0]
		cur_amp = abs(pow(i[1], 2))
		if(cur_amp>cur_max_amp):
			cur_max_amp = cur_amp
			cur_max_time = cur_time

	max_idx = 0
	for i in range(0, len(python_strain[:])):
		if(python_strain[i][1] > python_strain[max_idx][1]):
			max_idx = i

	paths = glob.glob("./Extrapolated_Strain/"+sim+"/"+sim+"_radially_extrapolated_strain_l[2-4]_m*.dat")
	for path in paths:
		python_strain = np.loadtxt(path)

		t = python_strain[:, 0]
		t = t.astype(np.complex_)
		h = python_strain[:, 1] + 1j * python_strain[:, 2]
		dh = np.zeros(len(t), dtype=np.complex_) 
		for i in range(0, len(t)-1):
			dh[i] = ((h[i+1] - h[i])/(t[i+1] - t[i]))
		dh[len(t)-1] = dh[len(t)-2]

		dh_conj = np.conj(dh)
		prod = np.multiply(h, dh_conj)
		local_val = np.zeros(len(t))
		local_val = local_val.astype(np.complex_)
		for i in range(0, len(t)):
			local_val[i] = np.trapz(prod[:i], x=(t[:i])) * int(((path.split("_")[-1]).split("m")[-1]).split(".")[0])
		val += local_val
		
	val *= 1/(16 * math.pi)
	np.savetxt("./Extrapolated_Strain/"+sim+"/"+sim+"_radially_extrapolated_angular_momentum.dat", val)

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

#Initialize simulation data
if(len(sys.argv) < 2):
	print("Pass in the number n of the n innermost detector radii to be used in the extrapolation (optional, default=all) and the simulation folders (e.g., ./power.py 6 ./simulations/J0040_N40 /path/to/my_simulation_folder).")
	sys.exit()
elif(os.path.isdir(sys.argv[1])):
	radiiUsedForExtrapolation = 7	#use the first n radii available  
	paths = sys.argv[1:]
elif(not os.path.isdir(sys.argv[1])):
	radiiUsedForExtrapolation = int(sys.argv[1])	#use the first n radii available  
	if(radiiUsedForExtrapolation < 1 or radiiUsedForExtrapolation > 7):
		print("Invalid specified radii number")
		sys.exit()
	paths = sys.argv[2:]

for sim_path in paths:
	main_dir = sim_path
	sim = sim_path.split("/")[-1]

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

	#Check if necessary files exist
	par_file = main_dir+"/output-0000/%s.par" % (sim)
	two_punctures_file = main_dir+"/output-0000/%s/TwoPunctures.bbh" % (sim)
	if(not os.path.isfile(par_file) or not os.path.isfile(two_punctures_file)):
		continue

	#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])

	for l in [0, 1, 2, 3, 4]:
		ms_l0 = [0]
		ms_l1 = [-1, 0, 1]
		ms_l2 = [-2, -1, 0, 1, 2]
		ms_l3 = [-3, -2, -1, 0, 1, 2, 3]
		ms_l4 = [-4, -3, -2, -1, 0, 1, 2, 3, 4]
		ms = []
		if(l == 0):
			ms = ms_l0
		if(l == 1):
			ms = ms_l1
		if(l == 2):
			ms = ms_l2
		elif(l == 3):
			ms = ms_l3
		elif(l == 4):
			ms = ms_l4
		for m in ms:
			#Get Psi4
			radii = [100, 115, 136, 167, 214, 300, 500]
			psi4dsetname_100 = 'l'+str(l)+'_m'+str(m)+'_r'+str(radii[0])+'.00'
			psi4dsetname_115 = 'l'+str(l)+'_m'+str(m)+'_r'+str(radii[1])+'.00'
			psi4dsetname_136 = 'l'+str(l)+'_m'+str(m)+'_r'+str(radii[2])+'.00'
			psi4dsetname_167 = 'l'+str(l)+'_m'+str(m)+'_r'+str(radii[3])+'.00'
			psi4dsetname_214 = 'l'+str(l)+'_m'+str(m)+'_r'+str(radii[4])+'.00'
			psi4dsetname_300 = 'l'+str(l)+'_m'+str(m)+'_r'+str(radii[5])+'.00'
			psi4dsetname_500 = 'l'+str(l)+'_m'+str(m)+'_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]

				#Check for psi4 amplitude going to zero
				cur_psi4_amp = (mp_psi4_vars[i][0, 1]**2 + mp_psi4_vars[i][0, 2]**2)**(1/2)
				min_psi4_amp = cur_psi4_amp 
				for j in range(0, len(mp_psi4_vars[i][:, 0])):
					cur_psi4_amp = (mp_psi4_vars[i][j, 1]**2 + mp_psi4_vars[i][j, 2]**2)**(1/2)
					if(cur_psi4_amp < min_psi4_amp):
						min_psi4_amp = cur_psi4_amp
				if(min_psi4_amp < np.finfo(float).eps and l >= 2):
					print("The psi4 amplitude is near zero. The phase is ill-defined.")

				#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])+"_l"+str(l)+"_m"+str(m)+".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_l"+str(l)+"_m"+str(m)+".dat", np.column_stack((t, radially_extrapolated_h_plus, radially_extrapolated_h_cross)))
			np.savetxt("./Extrapolated_Strain/"+sim+"/"+sim+"_radially_extrapolated_amplitude_l"+str(l)+"_m"+str(m)+".dat", np.column_stack((t, radially_extrapolated_amp)))
			np.savetxt("./Extrapolated_Strain/"+sim+"/"+sim+"_radially_extrapolated_phase_l"+str(l)+"_m"+str(m)+".dat", np.column_stack((t, radially_extrapolated_phase[:])))

	get_energy(sim)
	get_angular_momentum(sim)