test 4 parameters

code/RDGW150914_ptemceeX.py

+#!/usr/bin/env python
+# coding: utf-8
+
+# In[191]:
+
+
+import numpy as np
+import corner
+#get_ipython().run_line_magic('matplotlib', 'inline')
+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': 19})
+import ptemcee
+import h5py
+import inspect
+import pandas as pd
+import json
+import qnm
+import random
+#import hope
+
+
+# ### <font text color = 'Goldenrod'>Import data and necessary functions</font>
+
+# In[192]:
+
+
+#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
+
+# You do not need that. This is a fit to the energy radiated = 1 - final_mass
+def EradUIB2017(eta,chi1,chi2):
+    
+    m1=0.5*(1+(1-4*eta)**0.5)
+    m2=0.5*(1-(1-4*eta)**0.5)
+    S= (m1**2*chi1 + m2**2*chi2)/(m1*m1 + m2*m2)
+    
+    erad=(((1-(2*(2)**0.5)/3)*eta+0.5609904135313374*eta**2-0.84667563764404*eta**3+3.145145224278187*eta**4)*(1+S**3 *(-0.6320191645391563+ 4.952698546796005*eta-10.023747993978121*eta**2)+S**2*(-0.17762802148331427+ 2.176667900182948*eta**2)+S*(-0.13084389181783257- 1.1387311580238488*eta+5.49074464410971*eta**2)))/(1+S*(-0.9919475346968611+ 0.367620218664352*eta+4.274567337924067*eta**2))-0.01978238971523653*S*(1-4.91667749015812*eta)*(1-4*eta)**0.5 *eta *(chi1-chi2)-0.09803730445895877*(1-4*eta)**0.5*(1-3.2283713377939134*eta)*eta**2 *(chi1-chi2)+0.01118530335431078*eta**3 *(chi1-chi2)**2
+    return  erad
+
+
+# In[193]:
+
+
+#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
+rootpath="/Users/xisco"
+#npoints=5000 (This is more conveniently defined in the MCMC section)
+nmax=0
+tshift=0
+
+
+# In[194]:
+
+print('hello')
+#This loads the 22 mode data
+gw = {}
+gw["SXS:BBH:0305"] = h5py.File(rootpath+"/sio/git/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+"/sio/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']
+
+
+# In[195]:
+
+
+#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]
+
+# Depending on nmax, you load nmax number of freqs. and damping times from the qnm package
+omegas = []
+for i in range (0,nmax+1):
+    grav_220 = qnm.modes_cache(s=-2,l=2,m=2,n=i)
+    omega = grav_220(a=af)[0]
+    omegas.append(omega)
+
+
+# ### <font text color = 'Goldenrod'>Fitting</font>
+
+# In[196]:
+
+
+#Functions
+
+#RD model for nmax tones. Amplitudes are in (xn*Exp[i yn]) version. Used here.
+def model_dv_af(theta):
+    #x0, y0= theta
+    #Your nmax might not align with the dim of theta. Better check it here.
+    assert int(len(theta)/4) == nmax + 1, 'Please recheck your n and parameters'
+    w = (np.real(omegas))/mf
+    tau=-1/(np.imag(omegas))*mf
+    dim =int(len(theta)/4)        
+    
+    xvars = [theta[4*i] for i in range (0, dim)]
+    yvars = [theta[4*i+1] for i in range (0, dim)]
+    avars = [theta[4*i+2] for i in range (0, dim)]
+    bvars = [theta[4*i+3] for i in range (0, dim)]        
+
+    ansatz = 0
+    for i in range (0,dim):
+       # bvars[0]=0
+       # avars[0]=0
+       # bvars[1]=0
+       # avars[1]=0
+        ansatz += (xvars[i]*np.exp(1j*yvars[i]))*np.exp(-(timesrd-timesrd[0])/(tau[i]*(1+bvars[i])))        *(np.cos((1+avars[i])*w[i]*timesrd)-1j*np.sin((1+avars[i])*w[i]*timesrd))
+    # -1j to agree with SXS convention
+    return ansatz
+
+
+# LogLikelihood function. It is just a Gaussian loglikelihood based on computing the residuals^2
+def log_likelihood(theta):
+    #modelev = model_dv(theta)
+    modelev = model_dv_af(theta)
+    
+    #return  -np.sum((gw_sxs_bbh_0305rd[:,1] - (modelev.real))**2+(gw_sxs_bbh_0305rd[:,2] - (modelev.imag))**2)
+    return  -np.sum((gw_sxs_bbh_0305rd[:,1] - modelev.real)**2+(gw_sxs_bbh_0305rd[:,2] - modelev.imag)**2)
+
+
+# LogLikelihood match function. Not used at the moment. It is just a Gaussian match loglikelihood based on computing the match
+'''def log_likelihood_match(theta):
+    
+    #model and data
+    modelev = model_dv(theta)
+    data = gw_sxs_bbh_0305rd[:,1] - 1j*gw_sxs_bbh_0305rd[:,2]
+    
+    #norms
+    norm1=np.sum(modelev*np.conj(modelev))
+    norm2=np.sum(data*np.conj(data))
+
+    #mismatch
+    myTable = data*np.conj(modelev);    
+    return -(1-(np.sum(myTable)).real/np.sqrt(norm1*norm2)).real'''
+
+
+# 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)
+
+
+# Logposterior distribution for the mismatch case. Not used yet.
+'''def log_probability_match(theta):
+    lp = log_prior(theta)
+    if not np.isfinite(lp):
+        return -np.inf
+    return lp + log_likelihood_match(theta)'''
+
+
+# Logprior distribution. It defines the allowed range my variables can vary over. 
+#It works for the (xn*Exp[iyn]) version!!! 
+def log_prior(theta):
+    x_s = theta[0::4]
+    y_s = theta[1::4]
+    a_s = theta[2::4]
+    b_s = theta[3::4]
+    if all(0 <= t <= 10 for t in x_s) and all(0 <= t <= 2*np.pi for t in y_s) and all(-1 <= t <= 1 for t in a_s) and all(-1 <= t <= 5 for t in b_s):
+        return 0.0
+    return -np.inf
+
+
+# Maximum estimator Fitting. Same use as in mathematica
+
+# Interesting. This "overflow encountered in square" error message doesn't happen again when I'm not doing the fitting of parameters..
+
+# In[197]:
+
+
+nwalkers = 10
+ntemps=10
+#Why can't I change the number of temperatures here?
+ndim = int(4*(nmax+1))
+npoints=100
+
+#Does the difference in pos and pos_aux matter? Why the range is different here?
+pos = [random.uniform(0.,10) ,random.uniform(0.01,2*np.pi) ,random.uniform(-1,1) ,random.uniform(-0.99,1)]
+for i in range (1,nmax+1):
+    pos_aux = [random.uniform(1,8) ,random.uniform(0.01,0.9*2*np.pi) ,random.uniform(-.1,.1) ,random.uniform(-.1,.1)]
+    pos = pos + pos_aux
+
+pos = pos + 1e-4 * np.random.randn(ntemps,nwalkers,ndim)
+sampler = ptemcee.Sampler(nwalkers, ndim,log_likelihood,log_prior, ntemps=ntemps)
+sampler.run_mcmc(pos,npoints);
+
+
+# In[202]:
+
+
+paramlabels = []
+for i in range (nmax+1):
+    sublabel = [r'$x_' + str(i) + '$', r'$y_' + str(i) + '$', r'$\alpha_' + str(i) + '$',r'$\beta_' + str(i) + '$']
+    paramlabels += sublabel
+
+
+# In[203]:
+
+
+plt.clf()
+fig, axes = plt.subplots(4*(nmax+1), 1, sharex=True, figsize=(12, 13.5*(nmax+1)))
+for i in range(4*(nmax+1)):
+    axes[i].plot(sampler.chain[0,:, :, i].T, color="k", alpha=0.4)
+    axes[i].yaxis.set_major_locator(MaxNLocator(5))
+    axes[i].set_ylabel(paramlabels[i])
+fig.savefig(rootpath+'/sio/git/rdstackingproject/plotsmc/Test'+'nmax='+str(nmax)+'_tshift='+str(tshift)+'_'+str(npoints)+'pt_chain.png', format = 'png', dpi = 384, bbox_inches = 'tight')
+#plt.show()
+
+
+# In[204]:
+
+
+atcrr = sampler.get_autocorr_time()[0]
+
+atcrr
+
+
+# In[206]:
+
+
+burnin = 200
+samples = sampler.chain[0,:, burnin:, :].reshape((-1, ndim))
+median=np.median(samples, axis=0)
+print(median)
+figcorn = corner.corner(samples, bins = 50, labels=paramlabels,truths=median,quantiles=(0.1, 0.9))
+figcorn.savefig(rootpath+'/sio/git/rdstackingproject/plotsmc/Test'+'nmax='+str(nmax)+'_tshift='+str(tshift)+'_'+str(npoints)+'pt_corner.pdf', format = 'pdf')
+
+
+# In[143]:
+
+
+#Now plot the NR data against the ansatz data
+plt.plot(timesrd, gw_sxs_bbh_0305rd[:,1], "r", alpha=0.3, lw=3, label=r'$NR\_re$')
+modelfit = model_dv_af(median)
+plt.plot(timesrd, 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.xlim(timesrd[0], timesrd[0]+80)
+plt.xlabel("t")
+plt.ylabel("h");
+
+
+# In[ ]:
+
+
+
+