power.py 13.3 KB
 Daniel Johnson committed Aug 08, 2017 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 ``````#!/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 `````` Daniel Johnson committed Aug 08, 2017 242 ``````if(len(sys.argv) < 2): `````` Daniel Johnson committed Aug 08, 2017 243 `````` 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).") `````` Daniel Johnson committed Aug 08, 2017 244 `````` sys.exit() `````` Daniel Johnson committed Aug 08, 2017 245 ``````elif(os.path.isdir(sys.argv[1])): `````` Daniel Johnson committed Aug 08, 2017 246 247 `````` radiiUsedForExtrapolation = 7 #use the first n radii available paths = sys.argv[1:] `````` Daniel Johnson committed Aug 08, 2017 248 249 250 251 252 253 ``````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:] `````` Daniel Johnson committed Aug 08, 2017 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 `````` for sim_path in paths: 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))) `````` Daniel Johnson committed Aug 08, 2017 395 396 `````` np.savetxt("./Extrapolated_Strain/"+sim+"/"+sim+"_radially_extrapolated_amplitude.dat", np.column_stack((t, radially_extrapolated_amp))) np.savetxt("./Extrapolated_Strain/"+sim+"/"+sim+"_radially_extrapolated_phase.dat", np.column_stack((t, radially_extrapolated_phase)))``````