RDGW150914_ptemcee.py

#!/usr/bin/env python
# coding: utf-8
'''
This script calculates the RDGW150914 constraints with ptemcee - specifically, the n=1 case both varying or not varying the fundamental frequencies. It produces the chain plot, corner plot, parameter constraints, and data plotted with the 1-sigma band. Since we are working specifically for the n=1 case, we also add in the corner plot the combined chain of alpha_0 and alpha_1, in order to demonstrate that the two are indistinguishable with each other.

--- R^a_{yne} L^i_u, 08/09/2020
'''

import numpy as np
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
#from multiprocessing import Pool
import math
import h5py
import inspect
import pandas as pd
import json
import qnm
import random
from scipy.optimize import minimize

#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" 
nmax=1
tshift=19
vary_fund = True

#sampler parameters
npoints=101 
nwalkers = 42
ntemps=12
ndim = int(4*(nmax+1))
burnin = 10 #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.

numbins = 21 #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]

# 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,nmax+1)]




#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) == nmax + 1, 'Please recheck your n and parameters'
    w = (np.real(omegas))/mf
    tau=-1/(np.imag(omegas))*mf
    dim =int(len(theta)/4)        
    
    avars = theta[ : (nmax+1)]
    bvars = theta[(nmax+1) : 2*(nmax+1)]
    xvars = theta[2*(nmax+1) : 3*(nmax+1)]
    yvars = theta[3*(nmax+1) : ]
    
    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(-(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


# 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.
    a_0 = theta[0]
    a_1 = theta[1]
    b_0 = theta[2]
    b_1 = theta[3]
    x_0 = theta[4]
    x_1 = theta[5]
    y_0 = theta[6]
    y_1 = theta[7]

    if all([nmax == 1, 0 <= tshift <= 5, vary_fund == True, 0 <= x_0 <= 2.0, 0 <= y_0 <= 2*np.pi, -0.4 <= a_0 <= 0.4, -1.0 <= b_0 <= 1.6, 0 <= x_1 <= 1.8, 0 <= y_1 <= 2*np.pi, -1.0 <= a_1 <= 1.6, -1.0 <= b_1 <= 2.0]):        
        return 0.0
    elif all([nmax == 1, tshift == 19, vary_fund == True, 0 <= x_0 <= 1.5, 0 <= y_0 <= 2*np.pi, -1.0 <= a_0 <= 3.0, -1.0 <= b_0 <= 2.0, 0 <= x_1 <= 1.8, 0 <= y_1 <= 2*np.pi, -1.0 <= a_1 <= 3.0, -1.0 <= b_1 <= 2.0]):
        return 0.0
    
#PAY EXTRA ATTENTION TO THESE TWO CASES, SINCE WE SHIFTED y_0. THE CORNER PLOTS LABELS NEED TO BE TREATED WITH CARE.
    elif all([nmax == 1, 0 <= tshift <= 5, vary_fund == False, 0 <= x_0 <= 2.0, 0 <= y_0-np.pi <= 2*np.pi, -1.0 <= a_0 <= 1.0, -1.0 <= b_0 <= 1.0, 0 <= x_1 <= 1.6, 0 <= y_1 <= 2*np.pi, -1.0 <= a_1 <= 1.2, -1.0 <= b_1 <= 2.8]):
        return 0.0
    elif all([nmax == 1, tshift == 19, vary_fund == False, 0 <= x_0 <= 0.6, 0 <= y_0-np.pi <= 2*np.pi, -1.0 <= a_0 <= 1.0, -1.0 <= b_0 <= 1.0, 0 <= x_1 <= 1.2, 0 <= y_1 <= 2*np.pi, -1.0 <= a_1 <= 3.0, -1.0 <= b_1 <= 2.0]):
        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)
    return  -np.sum((gw_sxs_bbh_0305rd[:,1] - (modelev.real))**2+(gw_sxs_bbh_0305rd[:,2] - (modelev.imag))**2)


# Logposterior distribution for the residuals case.
# The evidence is just a normalization factor
def log_probability(theta):
    lp = log_prior(theta)
    #print('lp:')
    #print(lp)
    if not np.isfinite(lp):
        return -np.inf
    return lp + log_likelihood(theta)




#Fit with ptemcee
#Set the number of cores of your processors
pool = choose_pool(4)
pool.size = 4
vary_param = float(vary_fund)
pos = np.array([[random.uniform(-0.1,0.1), random.uniform(-0.1,0.1), 4.28313743e-01, random.uniform(2.5, 2.6) + (1-vary_param) * np.pi]])
for i in range (1,nmax+1):
    pos_aux = np.array([[random.uniform(-0.1,0.1), random.uniform(-0.1,0.1), random.uniform(0.3,0.4), random.uniform(2.01, 2.02) + (1-vary_param) * np.pi]])
    pos = np.concatenate((pos, pos_aux), axis = 0)
    
pos = pos.T.flatten()
pos = list(pos)
pos += 1e-5 * np.random.randn(ntemps, nwalkers, ndim)
#print(pos)

sampler = ptemcee.Sampler(nwalkers, ndim, log_likelihood, log_prior, ntemps=ntemps, pool=pool)
sampler.run_mcmc(pos,npoints)




#Define labels and start plotting
paramlabels_a = [r'$\alpha_'+str(i)+'$' for i in range (nmax+1)]
paramlabels_b = [r'$\beta_'+str(i)+'$' for i in range (nmax+1)]
paramlabels_x = [r'$x_'+str(i)+'$' for i in range (nmax+1)]
paramlabels_y = [r'$y_'+str(i)+'$' for i in range (nmax+1)] if vary_fund == True else ['$y_'+str(i)+'-\pi$' for i in range (nmax+1)]
paramlabels = paramlabels_a + paramlabels_b + paramlabels_x + paramlabels_y
#Need to delete alpha_0 and alpha_1 for the corner plot
paramlabels_corner = paramlabels_a + paramlabels_b + paramlabels_x + paramlabels_y
if vary_fund == False:
    del paramlabels_corner[0]
    del paramlabels_corner[1]



#Chain plot
fig, axes = plt.subplots(4*(nmax+1), 1, sharex=True, figsize=(12, 9*(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])
axes[-1].set_xlabel('Iterations')
#plt.show()
fig.savefig(rootpath+'/git/rdstackingproject/plotsmc/vary'+str(vary_fund)+'nmax='+str(nmax)+'_tshift='+str(tshift)+'_'+str(npoints)+'pt_chain.pdf', format = 'pdf')



#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])
#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_corner, 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')
figcorn.savefig(rootpath+'/git/rdstackingproject/plotsmc/vary'+str(vary_fund)+'nmax='+str(nmax)+'_tshift='+str(tshift)+'_'+str(npoints)+'pt_corner.pdf', format = 'pdf')



#Now plot alpha_0 on top of alpha_1 - only on top, not stacked, and only valid for vary_fund == True
if vary_fund == True:
    samplea0 = samples.T[0]
    samplea1 = samples.T[1]
    fighist1 = plt.figure(figsize = (8, 6))
    n0, bins0, patches0 = plt.hist(samplea0, bins = numbins * 6, alpha = 0.5, label = r'$\alpha_0$')
    n1, bins1, patches1 = plt.hist(samplea1, bins = numbins * 10, alpha = 0.5, label = r'$\alpha_1$')
    #n01, bins01, patches01 = plt.hist([samplea0, samplea1], numbins * 10, rwidth = 3, alpha = 0.5, label = [r'$\alpha_0$', r'$\alpha_1$'])
    plt.legend()
    fighist1.savefig(rootpath+'/git/rdstackingproject/plotsmc/vary'+str(vary_fund)+'nmax='+str(nmax)+'_tshift='+str(tshift)+'_'+str(npoints)+'pt_histtop.pdf', format = 'pdf')

    #This plot is stacked
    fighist1 = plt.figure(figsize = (8, 6))
    sn01, sbins01, spatches01 = plt.hist([samplea0, samplea1], numbins * 10, rwidth = 1, stacked = True, alpha = 0.5, label = [r'$\alpha_0$', r'$\alpha_1$'])
    plt.legend()
    fighist1.savefig(rootpath+'/git/rdstackingproject/plotsmc/vary'+str(vary_fund)+'nmax='+str(nmax)+'_tshift='+str(tshift)+'_'+str(npoints)+'pt_histstack.pdf', format = 'pdf')


    
#Now plot the NR data against the mcmc fit data, together with the 1-sigma varying error data
onesig_bounds = np.array([np.percentile(samples[:, i], [16, 84]) for i in range(len(samples[0]))]).T
modelfitpk = model_dv(pk)
figband = plt.figure(figsize = (12, 9))
#Plot the 1-sigma_percentile
for j in range(len(samples)):
    sample = samples[j]
    if np.all(onesig_bounds[0] <= sample) and np.all(sample <= onesig_bounds[1]):
        plt.plot(timesrd, model_dv(sample).real, "#79CAF2", alpha=0.3)
    
plt.plot(timesrd, gw_sxs_bbh_0305rd[:,1], "k", alpha=0.7, lw=2, label=r'NR_re')
plt.plot(timesrd, modelfitpk.real, "r", alpha=0.7, lw=2, label=r'FitMCmax_re')
plt.title(r'Comparison of the MC fit data and the $1-\sigma$ error band')
plt.legend()
plt.xlim(timesrd[0], timesrd[0]+80)
plt.xlabel("t")
plt.ylabel("h")

figband.savefig(rootpath+'/git/rdstackingproject/plotsmc/vary'+str(vary_fund)+'nmax='+str(nmax)+'_tshift='+str(tshift)+'_'+str(npoints)+'pt_band.pdf', format = 'pdf')