#!/usr/bin/env python # coding: utf-8 # ### Let's try the NR_Interpolate for the 0.001 stepsize. # In[57]: #Import relevant modules, import data and all that import numpy as np from scipy import interpolate import corner import matplotlib.pyplot as plt from matplotlib.ticker import MaxNLocator from matplotlib import rc #plt.rcParams['font.family'] = 'DejaVu Sans' #rc('text', usetex=True) plt.rcParams.update({'font.size': 16.5}) import ptemcee from pycbc.pool import choose_pool import h5py import inspect import pandas as pd import json import qnm import random #Remember to change the following global variables #rootpath: root path to nr data #npoints: number of points you re using for your sampling #nmax: tone index --> nmax = 0 if fitting the fundamental tone #tshift: time shift after the strain peak #vary_fund: whether you vary the fundamental frequency. Works in the model_dv function. #rootpath= "/Users/RayneLiu"#"/work/rayne.liu" rootpath= "/work/francisco.jimenez/sio"#"/work/rayne.liu" project_path=rootpath+"/git/rdstackingproject" nmax=1 tshift=15 vary_fund = True tsampling_factor=100 #sampler parameters npoints = 2000 nwalkers = 1000 ntemps=16 #npoints = 100 #nwalkers = 32 #ntemps = 1 dim = nmax+1 ndim = 4*dim burnin = 600 #How many points do you burn before doing the corner plot. You need to watch the convergence of the chain plot a bit. #This is trivial but often forgotten: this cannot be more than npoints! Usually 1/5~1/4 npoints is what I observe. #burnin = 20 numbins = 42 #corner plot parameter - how many bins you want datacolor = '#105670' #'#4fa3a7' pkcolor = '#f2c977' #'#ffb45f' mediancolor = '#f7695c' #'#9b2814' #Import data and necessary functions #TimeOfMaximum def FindTmaximum(y): #Determines the maximum absolute value of the complex waveform absval = y[:,1]*y[:,1]+y[:,2]*y[:,2] vmax=np.max(absval) index = np.argmax(absval == vmax) timemax=gw_sxs_bbh_0305[index,0] return timemax #This loads the 22 mode data gw = {} gw["SXS:BBH:0305"] = h5py.File(rootpath+"/git/rdstackingproject/SXS/BBH_SKS_d14.3_q1.22_sA_0_0_0.330_sB_0_0_-0.440/Lev6/rhOverM_Asymptotic_GeometricUnits_CoM.h5", 'r') gw_sxs_bbh_0305 = gw["SXS:BBH:0305"]["Extrapolated_N2.dir"]["Y_l2_m2.dat"] # Remember to download metadata.json from the simulation with number: 0305. Download Lev6/metadata.json # This postprocesses the metadata file to find the final mass and final spin metadata = {} with open(rootpath+"/git/rdstackingproject/SXS/BBH_SKS_d14.3_q1.22_sA_0_0_0.330_sB_0_0_-0.440/Lev6/metadata.json") as file: metadata["SXS:BBH:0305"] = json.load(file) af = metadata["SXS:BBH:0305"]['remnant_dimensionless_spin'][-1] mf = metadata["SXS:BBH:0305"]['remnant_mass'] #times --> x axis of your data times = gw_sxs_bbh_0305[:,0] tmax=FindTmaximum(gw_sxs_bbh_0305) t0=tmax +tshift #Select the data from t0 onwards position = np.argmax(times >= (t0)) gw_sxs_bbh_0305rd=gw_sxs_bbh_0305[position:-1] timesrd=gw_sxs_bbh_0305[position:-1][:,0][:920] #print(timesrd[0]) #print(t0) (This checks that timesrd[0] is indeed t0) timespan = timesrd - t0 gwdata_re = gw_sxs_bbh_0305rd[:,1][:920] gwdata_im = gw_sxs_bbh_0305rd[:,2][:920] # Depending on nmax, you load nmax number of freqs. and damping times from the qnm package omegas = [qnm.modes_cache(s=-2,l=2,m=2,n=i)(a=af)[0] for i in range (0,dim)] w = (np.real(omegas))/mf tau=-1/(np.imag(omegas))*mf # In[58]: chain_file = project_path+'/plotsmc/NR_Int'+'nmax='+str(nmax)+'_tshift='+str(tshift)+'_tsampling='+str(tsampling_factor)+'_'+str(npoints)+'pt_chain.png' chain_file_dat=project_path+'/plotsmc/NR_Int'+'nmax='+str(nmax)+'_tshift='+str(tshift)+'_tsampling='+str(tsampling_factor)+'_'+str(npoints)+'pt_chain.csv' corner_file = project_path+'/plotsmc/NR_Int'+'nmax='+str(nmax)+'_tshift='+str(tshift)+'_tsampling='+str(tsampling_factor)+'_'+str(npoints)+'pt_corner.png' # In[59]: #Test plot (data was picked in the last cell) plt.figure(figsize = (12, 8)) plt.plot(timespan, gwdata_re, "r", alpha=0.3, lw=3, label=r'$NR\_re$') plt.plot(timespan, gwdata_im, "b", alpha=0.3, lw=3, label=r'$NR\_im$') plt.legend() # In[60]: gwdata_re.shape # In[61]: gwnew_re = interpolate.interp1d(timespan, gwdata_re, kind = 'cubic') gwnew_im = interpolate.interp1d(timespan, gwdata_im, kind = 'cubic') # In[62]: timespan; # In[63]: timespan_new = np.linspace(tshift, timespan[-1], len(timespan)*tsampling_factor) gwdatanew_re = gwnew_re(timespan_new) gwdatanew_im = gwnew_im(timespan_new) # # timespan_new[-1] # In[64]: timespan_new[0] # In[65]: timespan_new.shape # In[66]: #Test the new interpolated data plt.figure(figsize = (12, 8)) plt.plot(timespan, gwdata_re, "r", alpha=0.3, lw=2, label='Before_re') plt.plot(timespan_new, gwdatanew_re, "b", alpha=0.3, lw=2, label='After_re') plt.plot(timespan, gwdata_im, alpha=0.3, lw=2, label='Before_im') plt.plot(timespan_new, gwdatanew_im, alpha=0.3, lw=2, label='After_im') plt.legend() # ### Now the interpolation seems nice according to what we have above...let's start sampling! # In[67]: #Fitting #RD model for nmax tones. Amplitudes are in (xn*Exp[i yn]) version. Used here. def model_dv(theta): #x0, y0= theta #Your nmax might not align with the dim of theta. Better check it here. assert int(len(theta)/4) == dim, 'Please recheck your n and parameters' avars = theta[ : (dim)] bvars = theta[(dim) : 2*(dim)] xvars = theta[2*(dim) : 3*(dim)] yvars = theta[3*(dim) : ] if vary_fund == False: avars[0]=0 bvars[0]=0 ansatz = 0 for i in range (0,dim): #bvars[1]=0 #avars[1]=0 ansatz += (xvars[i]*np.exp(1j*yvars[i]))*np.exp(-timespan_new/(tau[i]*(1+bvars[i]))) * (np.cos((1+avars[i])*w[i]*timespan_new)-1j*np.sin((1+avars[i])*w[i]*timespan_new)) # -1j to agree with SXS convention return ansatz # Logprior distribution. It defines the allowed range my variables can vary over. #It works for the (xn*Exp[iyn]) version. def log_prior(theta): #Warning: we are specifically working with nmax=1 so here individual prior to the parameters are manually adjusted. This does not apply to all other nmax's. #avars = theta[ : (dim)] #bvars = theta[(dim) : 2*(dim)] #xvars = theta[2*(dim) : 3*(dim)] #yvars = theta[3*(dim) : ] alpha0, alpha1, beta0, beta1, xvar0, xvar1, yvar0, yvar1 = theta if all([-0.9 <= alpha0 <= 0.9, -0.9 <= alpha1 <= 0.9, -0.7 <= beta0 <= 2.0, -1.0 <= beta1 <= 2.2, 0 <= xvar0 <= 2.4, 0 <= xvar1 <= 3, -np.pi <= yvar0 <= np.pi, -np.pi <= yvar1 <= np.pi]): return 0.0 """ if nmax == 0: if all([0 <= tshift <= 5, vary_fund == True, -0.45 <= avars[0] <= 0.05, -0.95 <= bvars[0] <= 3.0, 0 <= xvars[0] <= 3.0, -np.pi <= yvars[0] <= np.pi]): return 0.0 elif all([tshift == 19, vary_fund == True, -3.0 <= avars[0] <= 3.0, -2.0 <= bvars[0] <= 5.0, 0 <= xvars[0] <= 1.0, 0 <= yvars[0] <= 2*np.pi]): return 0.0 if all([0 <= tshift <= 5, vary_fund == False, -1.0 <= avars[0] <= 1.0, -1.0 <= bvars[0] <= 1.0, 0 <= xvars[0] <= 3.0, -np.pi <= yvars[0] <= np.pi]): return 0.0 if all([tshift == 19, vary_fund == False, -1.0 <= avars[0] <= 1.0, -1.0 <= bvars[0] <= 1.0, 0 <= xvars[0] <= 3.0, 0 <= yvars[0] <= 2*np.pi]): return 0.0 elif nmax == 1: if all([0 <= tshift <= 5, vary_fund == True, -3.0 <= avars[0] <= 3.0, -3.0 <= avars[1] <= 3.0, -2.0 <= bvars[0] <= 12.0, -4.0 <= bvars[1] <= 30.0, 0 <= xvars[0] <= 1.6, 0 <= xvars[1] <= 1.4, -np.pi <= yvars[0] <= np.pi, -np.pi <= yvars[1] <= np.pi]): return 0.0 elif all([tshift == 19, vary_fund == True, -10.0 <= avars[0] <= 10.0, -10.0 <= avars[1] <= 10.0, -20.0 <= bvars[0] <= 30.0, -25.0 <= bvars[1] <= 30.0, 0 <= xvars[0] <= 0.6, 0 <= xvars[1] <= 0.9, 0 <= yvars[0] <= 2*np.pi, -np.pi <= yvars[1] <= np.pi]): return 0.0 elif all([0 <= tshift <= 5, vary_fund == False, -10.0 <= avars[0] <= 10.0, -1.5 <= avars[1] <= 1.5, -9.0 <= bvars[0] <= 9.0, -6.0 <= bvars[1] <= 20.0, 0 <= xvars[0] <= 2.4, 0 <= xvars[1] <= 2.5, -np.pi <= yvars[0] <= np.pi, -np.pi <= yvars[1] <= np.pi]): return 0.0 elif all([tshift == 19, vary_fund == False, -10.0 <= avars[0] <= 10.0, -8.0 <= avars[1] <= 8.0, -9.0 <= bvars[0] <= 9.0, -10.0 <= bvars[1] <= 12.0, 0 <= xvars[0] <= 0.6, 0 <= xvars[1] <= 0.7, 0 <= yvars[0] <= 2*np.pi, 0 <= yvars[1] <= 2* np.pi]): return 0.0 """ return -np.inf # LogLikelihood function. It is just a Gaussian loglikelihood based on computing the residuals^2 def log_likelihood(theta): modelev = model_dv(theta) result = -np.sum((gwdatanew_re - (modelev.real))**2+(gwdatanew_im - (modelev.imag))**2) if np.isnan(result): return -np.inf return result # Logposterior distribution for the residuals case. # The evidence is just a normalization factor def log_probability(theta): lp = log_prior(theta) if not np.isfinite(lp): return -np.inf return lp + log_likelihood(theta) # In[68]: #Check if my fit functions are correct using scipy.minimize from scipy.optimize import minimize np.random.seed(42) nll = lambda *args: -log_likelihood(*args) #This assigns the initial guess initial = np.array([0, 0, 0, 0, 1, 1, 1, 1]) soln = minimize(nll, initial) print("Maximum likelihood estimates:") #Maximum likelihood: minimum -log_likelihood. Log_likelihood is easier to calculate vars_ml=soln.x print(vars_ml) #Now plot the NR data against the ansatz data plt.plot(timespan_new, gwdatanew_re, "r", alpha=0.3, lw=3, label=r'$NR\_re$') modelfit = model_dv(vars_ml) plt.plot(timespan_new, modelfit.real,"b", alpha=0.3, lw=3, label=r'$Fit\_re$') #plt.plot(x0, np.dot(np.vander(x0, 2), w), "--k", label="LS") plt.legend(fontsize=14) plt.xlabel("t") plt.ylabel("h"); # In[13]: #Ok, nice. Now let's do ptemcee... np.random.seed(42) pos = np.array([random.uniform(-0.1,0.), random.uniform(-0.1,0.), random.uniform(-0.1,0.), random.uniform(-0.1,0.), random.uniform(0,1), random.uniform(0, 1), random.uniform(0.5, 0.6), random.uniform(0.5, 0.6)]) pos = list(pos) pos += 1e-5 * np.random.randn(ntemps, nwalkers, ndim) sampler = ptemcee.Sampler(nwalkers, ndim, log_likelihood, log_prior, ntemps=ntemps) sampler.run_mcmc(pos,npoints) dim = 2 paramlabels_a = [r'$\alpha_'+str(i)+'$' for i in range (dim)] paramlabels_b = [r'$\beta_'+str(i)+'$' for i in range (dim)] paramlabels_x = [r'$x_'+str(i)+'$' for i in range (dim)] paramlabels_y = [r'$y_'+str(i)+'$' for i in range (dim)] paramlabels = paramlabels_a + paramlabels_b + paramlabels_x + paramlabels_y print('The chain plot:') #Chain plot fig, axes = plt.subplots(ndim, 1, sharex=True, figsize=(12, 4*(4))) for i in range(ndim): axes[i].plot(sampler.chain[0,:, :, i].T, color="k", alpha=0.4, rasterized=True) axes[i].yaxis.set_major_locator(MaxNLocator(5)) axes[i].set_ylabel(paramlabels[i]) axes[-1].set_xlabel('Iterations') plt.show() print('We\'re using ptemcee. Our constraints:') #Burn samples, calculate peak likelihood value (not necessarily so in atlas) and make corner plot samples = sampler.chain[0,:, burnin:, :].reshape((-1, ndim)) #samples for corner plot samples_corn = samples #if vary_fund == True else np.delete(samples, np.s_[0,2], 1) #print('Values with peak likelihood:') lglk = np.array([log_likelihood(samples[i]) for i in range(len(samples))]) pk = samples[np.argmax(lglk)] #print('pk:') #print(pk) pk_corn = pk #if vary_fund == True else np.delete(pk, [0,2]) #y_0 range needs some messaging to make the plot. But in order to make the whole picture consistent, better change the range of y_1 too. #if vary_fund == False: # samples_corn.T[-dim:] -= np.pi #This indeed changes samples_corn itself # pk[-dim:] -= np.pi #print('pkFalse:') #print(pk) #print(pk) #Now calculate median (50-percentile) value median = np.median(samples_corn, axis=0) #print(samples) #print(samples_corn) figcorn = corner.corner(samples_corn, bins = numbins, hist_bin_factor = 5, color = datacolor, truths=pk_corn, truth_color = pkcolor, plot_contours = True, labels = paramlabels, quantiles=(0.05, 0.16, 0.5, 0.84, 0.95), levels=[1-np.exp(-0.5), 1-np.exp(-1.64 ** 2/2)], show_titles=True) #Extract the axes in order to add more important line plots naxes = len(pk_corn) axes = np.array(figcorn.axes).reshape((naxes, naxes)) # Loop over the diagonal for i in range(naxes): ax = axes[i, i] ax.axvline(median[i], color=mediancolor) # Loop over the histograms for yi in range(naxes): for xi in range(yi): ax = axes[yi, xi] ax.axvline(median[xi], color=mediancolor) ax.axhline(median[yi], color=mediancolor) ax.plot(median[xi], median[yi], color = mediancolor, marker = 's') fig.savefig(chain_file, format = 'png', dpi = 384, bbox_inches = 'tight') out = np.concatenate(sampler.chain[0,:]) np.savetxt(chain_file_dat,out, fmt='%d') figcorn.savefig(corner_file, format = 'png', dpi = 384, bbox_inches = 'tight') # In[ ]: