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.
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# 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.
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# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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# Based off of SimulationTools Mathematica Package
# http://www.simulationtools.org/

import numpy as np
import glob
import os
import h5py
import re
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, "r")
        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.+math.sqrt(1.-4.*eta))/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/m1**2
    chi2 = S2/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))
    # TODO: rewrite as array operations (use numpy.argmax)
    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_)
                # TODO: rewrite as array notation using numpy.cumtrapz
        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))
    # TODO: rewrite as array operations (use numpy.argmax)
    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_) 
                # TODO: rewrite using array notation
        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_)
                # TODO: rewrite as array notation using numpy.cumtrapz. Move atoi call out of inner loop.
        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-----#

if __name__ == "__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 = os.path.split(sim_path)[-1]

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

            #Get simulation total mass
            ADMMass = None
            two_punctures_files = sorted(glob.glob(main_dir+"/output-????/%s/TwoPunctures.bbh" % (sim)))
            out_files = sorted(glob.glob(main_dir+"/output-????/%s.out" % (sim)))
            par_files = sorted(glob.glob(main_dir+"/output-????/%s.par" % (sim)))
            if(two_punctures_files):
                two_punctures_file = two_punctures_files[0]
                with open(two_punctures_file) 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])
            elif(out_files):
                  out_file = out_files[0]
                  with open(out_file) as file:
                        contents = file.readlines()
                        for line in contents:
                              m = re.match("INFO \(TwoPunctures\): The total ADM mass is (.*)", line)
                              if(m):
                                  ADMMass = float(m.group(1))
            elif(par_files):
                  par_file = par_files[0]
                  print("Not yet implemented")
                  raise ValueError
            else:
                print("Cannot determine ADM mass")
            raise ValueError

            #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)

            # TODO: fix this. It will fail if output-0000 does not contain any mp
            # output and also will open the output files multiple times
            fn = sorted(glob.glob(simdirs+"mp_psi4.h5"))[0]
            with h5py.File(fn, "r") as fh:
                    # get all radii
                    radii = set()
                    modes = set()
                    dsets = dict()
                    for dset in fh:
                            # TODO: extend Multipole to save the radii as attributes and/or
                            # use a group structure in the hdf5 file
                            m = re.match(r'l(\d*)_m(-?\d*)_r(\d*\.\d)', dset)
                            if m:
                                    radius = float(m.group(3))
                                    mode = (int(m.group(1)), int(m.group(2)))
                                    modes.add(mode)
                                    radii.add(radius)
                                    dsets[(radius, mode)] = dset
                    modes = sorted(modes)
                    radii = sorted(radii)

            #Get Psi4
            def Get_Psi4(modes, radii):
                for (l,m) in modes:
                    
                            
                        #Get Tortoise Coordinate
                        mp_psi4_vars = []
                        tortoise = []    
                        strain = []
                        phase = []
                        amp = []
                        for i in range(len(radii)):
                                #------------------------------------------------
                                # Read in HDF5 data
                                #------------------------------------------------                 
                                psi4dsetname = dsets[(radius, (l,m))]
                                mp_psi4 = loadHDF5Series(simdirs+"mp_psi4.h5", psi4dsetname)
                                mp_psi4_vars.append(mp_psi4)
                                #------------------------------------------------
                                # Coordinate conversion to Torus
                                #------------------------------------------------
                                tortoise.append(-RadialToTortoise(radius, ADMMass))
                                #-----------------------------------------
                                # Prepare for conversion to strain
                                #-----------------------------------------
                                #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 = np.sqrt(mp_psi4_vars[i][0, 1]**2 + mp_psi4_vars[i][0, 2]**2)
                                min_psi4_amp = cur_psi4_amp
                                # TODO: use array notatino for this since it finds the minimum amplitude
                                for j in range(0, len(mp_psi4_vars[i][:, 0])):
                                        cur_psi4_amp = np.sqrt(mp_psi4_vars[i][j, 1]**2 + mp_psi4_vars[i][j, 2]**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
                                #-----------------------------------------------------------------
                                # Strain Conversion
                                #-----------------------------------------------------------------
                                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.append(finalhTable)
                                
                                #-------------------------------------------------------------------
                                # Analysis of Strain
                                #-------------------------------------------------------------------
                                #Get phase and amplitude of strain
                                h_phase = np.unwrap(np.angle(h))
                                angleTable = np.column_stack((time, h_phase))
                                angleTable = angleTable.astype(float)
                                phase.append(angleTable)
                                h_amp = np.absolute(h)
                                ampTable = np.column_stack((time, h_amp))
                                ampTable = ampTable.astype(float)
                                amp.append(ampTable)
                        
                        #----------------------------------------------------------------------
                        # Extrapolation
                        #----------------------------------------------------------------------
                        #Interpolate phase and amplitude
                        t = phase[0][:, 0]
                        last_t = phase[radiiUsedForExtrapolation - 1][-1, 0]
                        last_index = 0;
                        # TODO: use array notation for this (this is a boolean
                        # plus a first_of or so)
                        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)
                                # try and keep all initial phases within 2pi of each other
                                if(i > 0):
                                    phase_shift = round((resampled_phase_vals[0] - phase[0][0,1])/(2.*math.pi))*2.*math.pi
                                    resampled_phase_vals -= phase_shift
                                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]
                        # TODO: replace by np.ones (which is all it does anyway)
                        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)