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test_const.py

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    RDGW150914.ipynb 1.73 MiB
    In [76]: 
    import numpy as np
import corner
%matplotlib inline
import matplotlib.pyplot as plt
from matplotlib.ticker import MaxNLocator
import emcee
import math
import h5py
import inspect
import pandas as pd
import json
import qnm
import random
import ptemcee
from scipy.optimize import minimize
    In [77]: 
    rootpath="/Users/xisco"
npoints=20000
nmax=0
tshift=10
    In [78]: 
    def FindTmaximum(y):
    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
    In [79]: 
    gw = {}
gw["SXS:BBH:0305"] = h5py.File(rootpath+"/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"]
    In [80]: 
    metadata = {}
with open(rootpath+"/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 [82]: 
    times = gw_sxs_bbh_0305[:,0]
tmax=FindTmaximum(gw_sxs_bbh_0305)
t0=tmax +tshift
    In [83]: 
    position = np.argmax(times >= (t0))
gw_sxs_bbh_0305rd=gw_sxs_bbh_0305[position:-1]
timesrd=gw_sxs_bbh_0305[position:-1][:,0]
    In [84]: 
    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 [85]: 
    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)
    In [86]: 
    #deprecated
def model(theta):
    x0, y0, a0, b0 = theta
    #x0, y0= theta
    w = (np.real(omegas))[0]/mf
    tau=-1/(np.imag(omegas))[0]*mf
    

    # -1j to agree with SXS convention
    #return (x0+y0*1j)*(np.exp(-(timesrd-timesrd[0])/(tau*(1+b0))))*(np.cos((1+a0)*w*timesrd)-1j*np.sin((1+a0)*w*timesrd))

    return (x0+1j*y0)*np.exp(-(timesrd-timesrd[0])/tau)*(np.cos(w*timesrd)-1j*np.sin(w*timesrd))
    In [87]: 
    def model_dv(theta):
    #x0, y0= theta
    w = (np.real(omegas))/mf
    tau=-1/(np.imag(omegas))*mf
    dim =int(len(theta)/4)
    
    xvars = []
    yvars = []
    avars = []
    bvars = []
    for i in range (0,dim):
        xvar = theta[4*i]
        xvars.append(xvar)
        yvar = theta[4*i+1]
        yvars.append(yvar)
        avar = theta[4*i+2]
        avars.append(avar)
        bvar = theta[4*i+3]  
        bvars.append(bvar)
        
    
    ansatz = 0
    for i in range (0,dim):
        bvars[0]=0
        avars[0]=0
        ansatz = ansatz + (xvars[i]+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
    In [88]: 
    def model_dv_af(theta):
    #x0, y0= theta
    w = (np.real(omegas))/mf
    tau=-1/(np.imag(omegas))*mf
    dim =int(len(theta)/4)        
    tau=[1/0.0851903]
    w=[0.555733]
    
    xvars = []
    yvars = []
    avars = []
    bvars = []
    for i in range (0,dim):
        xvar = theta[4*i]
        xvars.append(xvar)
        yvar = theta[4*i+1]
        yvars.append(yvar)
        avar = theta[4*i+2]
        avars.append(avar)
        bvar = theta[4*i+3]  
        bvars.append(bvar)
        
    
    ansatz = 0
    for i in range (0,dim):
        bvars[0]=0
        avars[0]=0
        ansatz = 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
    In [89]: 
    def log_likelihood(theta):
    #modelev = model_dv(theta)
    #modelev = model(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)
    In [90]: 
    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
    In [91]: 
    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(-10 <= t <= 10 for t in x_s) and all(-10 <= t <= 10 for t in y_s) and all(-0.4 <= t <= 0.4 for t in a_s) and all(-0.4 <= t <= 0.4 for t in b_s):
        return 0.0
    return -np.inf
    In [92]: 
    def log_probability(theta):
    lp = log_prior(theta)
    if not np.isfinite(lp):
        return -np.inf
    return lp + log_likelihood(theta)
    In [93]: 
    def log_probability_match(theta):
    lp = log_prior(theta)
    if not np.isfinite(lp):
        return -np.inf
    return lp + log_likelihood_match(theta)

    Maximum estimator Fitting

    In [94]: 
    np.random.seed(42)
nll = lambda *args: -log_likelihood(*args)
initial = np.array([4,1,0,0])
soln = minimize(nll, initial)
x0_ml, y0_ml, a0_ml, b0_ml = soln.x
print("Maximum likelihood estimates:")
print("x0 = {0:.3f}".format(x0_ml))
print("y0 = {0:.3f}".format(y0_ml))
print("a0 = {0:.3f}".format(a0_ml))
print("b0 = {0:.3f}".format(b0_ml))
    Out [94]: 
    Maximum likelihood estimates:
x0 = 0.357
y0 = -1.245
a0 = 0.000
b0 = 0.000
    In [98]: 
    plt.plot(timesrd, gw_sxs_bbh_0305rd[:,1], "r", alpha=0.3, lw=3, label="NR_re")
modelfit = model_dv_af([x0_ml,y0_ml,a0_ml,b0_ml])
plt.plot(timesrd, modelfit.real,"b", alpha=0.3, lw=3, label="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");
    out [98]:
    In [99]: 
    plt.plot(timesrd, gw_sxs_bbh_0305rd[:,2], "r", alpha=0.3, lw=3, label="NR_im")
modelfit = model_dv_af([x0_ml,y0_ml,a0_ml,b0_ml])
plt.plot(timesrd, modelfit.imag,"b", alpha=0.3, lw=3, label="Fit_im")
#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");
    out [99]:

    mcmc Fitting

    In [113]: 
    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(-0.4 <= t <= 0.4 for t in a_s) and all(-0.4 <= t <= 0.4 for t in b_s):
        return 0.0
    return -np.inf
    In [114]: 
    nwalkers = 32
ndim = int(4*(nmax+1))

pos = [random.uniform(0.01,10) ,random.uniform(0,2*np.pi) ,random.uniform(-0.1,0.1) ,random.uniform(-0.1,0.1)]
for i in range (1,nmax+1):
       pos_aux = [random.uniform(0.01,10) ,random.uniform(0,2*np.pi) ,random.uniform(-0.1,0.1) ,random.uniform(-0.1,0.1)]
       pos = pos + pos_aux

pos = pos + 1e-3 * np.random.randn(nwalkers, ndim)
    In [115]: 
    sampler = emcee.EnsembleSampler(nwalkers, ndim, log_probability)
sampler.run_mcmc(pos,npoints,progress=True);
    Out [115]: 
    100%|██████████| 20000/20000 [01:06<00:00, 298.64it/s]
    In [118]: 
    plt.clf()
fig, axes = plt.subplots(4, 1, sharex=True, figsize=(8, 9))
axes[0].plot(sampler.chain[:, :, 0].T, color="k", alpha=0.4)
axes[0].yaxis.set_major_locator(MaxNLocator(5))
axes[0].set_ylabel("$x0$")
axes[1].plot(sampler.chain[:, :, 1].T, color="k", alpha=0.4)
axes[1].yaxis.set_major_locator(MaxNLocator(5))
axes[1].set_ylabel("$y0$")
axes[2].plot(sampler.chain[:, :, 2].T, color="k", alpha=0.4)
axes[2].yaxis.set_major_locator(MaxNLocator(5))
axes[2].set_ylabel("$a0$")
axes[3].plot(sampler.chain[:, :, 3].T, color="k", alpha=0.4)
axes[3].yaxis.set_major_locator(MaxNLocator(5))
axes[3].set_ylabel("$b0$")
plt.show()
    Out [118]: 
    <Figure size 432x288 with 0 Axes>
    In [119]: 
    label = ['x0','y0','a0','b0']
for i in range (1,nmax+1):
    label2 = ['x' + str(i),'y' + str(i),'a' + str(i),'b' + str(i)]
    label = label + label2
    In [122]: 
    burnin = 500
flat_samples = sampler.get_chain(discard=burnin, thin=15, flat=True)
median=np.median(sampler.flatchain, axis=0)
print(median)

fig = corner.corner(
    flat_samples, labels=label, truths=median,quantiles=(0.1, 0.9)
);
    Out [122]: 
    [ 0.33810786  5.02060618 -0.00915384 -0.01628947]
    In [123]: 
    sampler.
    Out [123]: 
    array([0.469  , 0.47145, 0.45355, 0.4765 , 0.46735, 0.46935, 0.4647 ,
       0.4694 , 0.48365, 0.47425, 0.4823 , 0.48   , 0.472  , 0.4814 ,
       0.47185, 0.47435, 0.45325, 0.4705 , 0.0864 , 0.47365, 0.48135,
       0.45385, 0.47545, 0.2995 , 0.476  , 0.473  , 0.47965, 0.47605,
       0.46365, 0.47625, 0.4936 , 0.478  ])
    In [112]: 
    plt.clf()
fig, axes = plt.subplots(4, 1, sharex=True, figsize=(8, 9))
axes[0].plot(sampler.chain[:, :, 0].T, color="k", alpha=0.4)
axes[0].yaxis.set_major_locator(MaxNLocator(5))
axes[0].set_ylabel("$x0$")
axes[1].plot(sampler.chain[:, :, 1].T, color="k", alpha=0.4)
axes[1].yaxis.set_major_locator(MaxNLocator(5))
axes[1].set_ylabel("$y0$")
axes[2].plot(sampler.chain[:, :, 2].T, color="k", alpha=0.4)
axes[2].yaxis.set_major_locator(MaxNLocator(5))
axes[2].set_ylabel("$a0$")
axes[3].plot(sampler.chain[:, :, 3].T, color="k", alpha=0.4)
axes[3].yaxis.set_major_locator(MaxNLocator(5))
axes[3].set_ylabel("$b0$")
plt.show()
    Out [112]: 
    <Figure size 432x288 with 0 Axes>
    In [140]: 
    fig.savefig(rootpath+'/git/rdstackingproject/plots/fit_chi2_'+str(nmax)+'.pdf')
    In [138]: 
    burnin = 500
samples = sampler.chain[0,:, burnin:, :].reshape((-1, ndim))
sampler.chain.shape
    Out [138]: 
    ---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
<ipython-input-138-0f683973fc4f> in <module>
      1 burnin = 500
----> 2 samples = sampler.chain[0,:, burnin:, :].reshape((-1, ndim))
      3 sampler.chain.shape

IndexError: too many indices for array

    sampler.flatchain?
    fig = corner.corner(samples, labels=["$x0$", "$y0$",  "$a0$", "$b0$"],truths=median,quantiles=(0.1, 0.9))
    In [716]: 
    #sampler = emcee.EnsembleSampler(nwalkers, ndim, log_probability_match, args=(timesrd, gw_sxs_bbh_0305rd))
#sampler.run_mcmc(pos,npoints, progress=True);
    Out [716]: 
    100%|██████████| 100000/100000 [14:00<00:00, 118.99it/s]
    In [205]: 
    plt.clf()
fig, axes = plt.subplots(4, 1, sharex=True, figsize=(8, 9))
axes[0].plot(sampler.chain[0,:, :, 0].T, color="k", alpha=0.4)
axes[0].yaxis.set_major_locator(MaxNLocator(5))
axes[0].set_ylabel("$x0$")
axes[1].plot(sampler.chain[0,:, :, 1].T, color="k", alpha=0.4)
axes[1].yaxis.set_major_locator(MaxNLocator(5))
axes[1].set_ylabel("$y0$")
axes[2].plot(sampler.chain[0,:, :, 2].T, color="k", alpha=0.4)
axes[2].yaxis.set_major_locator(MaxNLocator(5))
axes[2].set_ylabel("$a0$")
axes[3].plot(sampler.chain[0,:, :, 3].T, color="k", alpha=0.4)
axes[3].yaxis.set_major_locator(MaxNLocator(5))
axes[3].set_ylabel("$b0$")
plt.show()
    Out [205]: 
    <Figure size 432x288 with 0 Axes>
    In [170]: 
    nwalkers = 32
ntemps=10
ndim = int(4*(nmax+1))

pos = [random.uniform(-10,10) ,random.uniform(-10,10) ,random.uniform(-1,1) ,random.uniform(-1,1)]
for i in range (1,nmax+1):
       pos_aux = [random.uniform(-4,4) ,random.uniform(-4,4) ,random.uniform(-.1,.1) ,random.uniform(-.1,.1)]
       pos = pos + pos_aux

pos = pos + 1e-5 * np.random.randn(ntemps,nwalkers,ndim)
    In [171]: 
    sampler = ptemcee.Sampler(nwalkers, 4,log_likelihood,log_prior, ntemps=10)
sampler.run_mcmc(pos,10000);
    Out [171]: 
    ---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-171-e3f877d33c5c> in <module>
      1 sampler = ptemcee.Sampler(nwalkers, 4,log_likelihood,log_prior, ntemps=10)
----> 2 sampler.run_mcmc(pos,10000);

~/Library/Python/3.7/lib/python/site-packages/ptemcee/sampler.py in run_mcmc(self, *args, **kwargs)
    275 
    276         """
--> 277         for x in self.sample(*args, **kwargs):
    278             pass
    279         return x

~/Library/Python/3.7/lib/python/site-packages/ptemcee/sampler.py in sample(self, p0, iterations, thin, storechain, adapt, swap_ratios)
    353 
    354         if (logpost == -np.inf).any():
--> 355             raise ValueError('Attempting to start with samples outside posterior support.')
    356 
    357         # Expand the chain in advance of the iterations

ValueError: Attempting to start with samples outside posterior support.
    In [157]: 
    sampler.chain.shape
    Out [157]: 
    (10, 32, 10000, 4)
    In [161]: 
    burnin = 1000
samples = sampler.chain[0,:, burnin:, :].reshape((-1, ndim))
fig = corner.corner(samples, labels=["$x0$", "$y0$",  "$a0$", "$b0$"],truths=median,quantiles=(0.1, 0.9))
    out [161]:
    In [156]: 
    plt.clf()
fig, axes = plt.subplots(4, 1, sharex=True, figsize=(8, 9))
axes[0].plot(sampler.chain[0,:, :, 0].T, color="k", alpha=0.4)
axes[0].yaxis.set_major_locator(MaxNLocator(5))
axes[0].set_ylabel("$x0$")
axes[1].plot(sampler.chain[0,:, :, 1].T, color="k", alpha=0.4)
axes[1].yaxis.set_major_locator(MaxNLocator(5))
axes[1].set_ylabel("$y0$")
axes[2].plot(sampler.chain[0,:, :, 2].T, color="k", alpha=0.4)
axes[2].yaxis.set_major_locator(MaxNLocator(5))
axes[2].set_ylabel("$a0$")
axes[3].plot(sampler.chain[0,:, :, 3].T, color="k", alpha=0.4)
axes[3].yaxis.set_major_locator(MaxNLocator(5))
axes[3].set_ylabel("$b0$")
plt.show()
    Out [156]: 
    <Figure size 432x288 with 0 Axes>
    In [183]: 
    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(0.1 <= 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 <= 1 for t in b_s):
        return 0.0
    return -np.inf
    In [195]: 
    def log_likelihood(theta):
    #modelev = model_dv(theta)
    #modelev = model(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)
    In [196]: 
    def model_dv_af(theta):
    #x0, y0= theta
    w = (np.real(omegas))/mf
    tau=-1/(np.imag(omegas))*mf
    dim =int(len(theta)/4)
    
    xvars = []
    yvars = []
    avars = []
    bvars = []
    for i in range (0,dim):
        xvar = theta[4*i]
        xvars.append(xvar)
        yvar = theta[4*i+1]
        yvars.append(yvar)
        avar = theta[4*i+2]
        avars.append(avar)
        bvar = theta[4*i+3]  
        bvars.append(bvar)
        
    
    ansatz = 0
    for i in range (0,dim):
        ansatz = 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
    In [199]: 
    np.random.seed(42)
nll = lambda *args: -log_likelihood(*args)
initial = np.array([0.4,-0.1,0.0,0.0])
soln = minimize(nll, initial)
x0_ml, y0_ml, a0_ml, b0_ml = soln.x
print("Maximum likelihood estimates:")
print("x0 = {0:.3f}".format(x0_ml))
print("y0 = {0:.3f}".format(y0_ml))
print("a0 = {0:.3f}".format(a0_ml))
print("b0 = {0:.3f}".format(b0_ml))
    Out [199]: 
    Maximum likelihood estimates:
x0 = 0.342
y0 = -374.430
a0 = -0.044
b0 = 0.113
    In [203]: 
    modelfit = model_dv_af([x0_ml,y0_ml,a0_ml,b0_ml])
plt.plot(timesrd, gw_sxs_bbh_0305rd[:,1], "r", alpha=0.3, lw=3, label="NR_re")
plt.plot(timesrd, modelfit.real,"b", alpha=0.3, lw=3, label="Fit_re")
plt.plot(timesrd, gw_sxs_bbh_0305rd[:,2], "o", alpha=0.3, lw=3, label="NR_im")
plt.plot(timesrd, modelfit.imag,"g", alpha=0.3, lw=3, label="Fit_im")
#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");
    out [203]:
    In [208]: 
    nwalkers = 32
ntemps=10
ndim = int(4*(nmax+1))
npoints=5000

pos = [random.uniform(0.1,4) ,random.uniform(0.01,2*np.pi) ,random.uniform(-1,1) ,random.uniform(-1,1)]
for i in range (1,nmax+1):
       pos_aux = [random.uniform(0.1,3) ,random.uniform(0.01,0.02) ,random.uniform(-.1,.1) ,random.uniform(-.1,.1)]
       pos = pos + pos_aux

pos = pos + 1e-5 * np.random.randn(ntemps,nwalkers,ndim)
sampler = ptemcee.Sampler(nwalkers, ndim,log_likelihood,log_prior, ntemps=10)
sampler.run_mcmc(pos,npoints);
    In [209]: 
    plt.clf()
fig, axes = plt.subplots(4, 1, sharex=True, figsize=(8, 9))
axes[0].plot(sampler.chain[0,:, :, 0].T, color="k", alpha=0.4)
axes[0].yaxis.set_major_locator(MaxNLocator(5))
axes[0].set_ylabel("$x0$")
axes[1].plot(sampler.chain[0,:, :, 1].T, color="k", alpha=0.4)
axes[1].yaxis.set_major_locator(MaxNLocator(5))
axes[1].set_ylabel("$y0$")
axes[2].plot(sampler.chain[0,:, :, 2].T, color="k", alpha=0.4)
axes[2].yaxis.set_major_locator(MaxNLocator(5))
axes[2].set_ylabel("$a0$")
axes[3].plot(sampler.chain[0,:, :, 3].T, color="k", alpha=0.4)
axes[3].yaxis.set_major_locator(MaxNLocator(5))
axes[3].set_ylabel("$b0$")
plt.show()
    Out [209]: 
    <Figure size 432x288 with 0 Axes>
    In [215]: 
    burnin = 2000
samples = sampler.chain[1,:, burnin:, :].reshape((-1, ndim))
fig = corner.corner(samples, labels=["$x0$", "$y0$",  "$a0$", "$b0$"],truths=median,quantiles=(0.1, 0.9))
    out [215]:
    In [212]: 
    median
    Out [212]: 
    array([ 0.0085003 , -0.01569561, -0.05168496, -0.06578066])
    In [284]: 
    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(0.1 <= t <= 2 for t in x_s) and all(0 <= t <= 2*np.pi for t in y_s) and all(-0.4 <= t <= 0.4 for t in a_s) and all(-0.4 <= t <= 0.4 for t in b_s):
        return 0.0
    return -np.inf
    In [296]: 
    nwalkers = 32
ntemps=10
ndim = int(4*(nmax+1))

pos = [random.uniform(0,10) ,random.uniform(0,2*np.pi) ,random.uniform(-0.1,0.1) ,random.uniform(-0.1,0.1)]
for i in range (1,nmax+1):
       pos_aux = [random.uniform(0,4) ,random.uniform(0,4) ,random.uniform(-.05,.05) ,random.uniform(-.05,.05)]
       pos = pos + pos_aux

pos = pos + 1e-5 * np.random.randn(ntemps,nwalkers,ndim)

sampler = ptemcee.Sampler(nwalkers, ndim,log_likelihood,log_prior, ntemps=10)
sampler.run_mcmc(pos,10000);
    In [301]: 
    plt.clf()
fig, axes = plt.subplots(4, 1, sharex=True, figsize=(8, 9))
axes[0].plot(sampler.chain[0,:, :, 0].T, color="k", alpha=0.4)
axes[0].yaxis.set_major_locator(MaxNLocator(5))
axes[0].set_ylabel("$x0$")
axes[1].plot(sampler.chain[0,:, :, 1].T, color="k", alpha=0.4)
axes[1].yaxis.set_major_locator(MaxNLocator(5))
axes[1].set_ylabel("$y0$")
axes[2].plot(sampler.chain[0,:, :, 2].T, color="k", alpha=0.4)
axes[2].yaxis.set_major_locator(MaxNLocator(5))
axes[2].set_ylabel("$a0$")
axes[3].plot(sampler.chain[0,:, :, 3].T, color="k", alpha=0.4)
axes[3].yaxis.set_major_locator(MaxNLocator(5))
axes[3].set_ylabel("$b0$")
plt.show()
    Out [301]: 
    <Figure size 432x288 with 0 Axes>
    In [312]: 
    burnin = 200
samples = sampler.chain[0,:, burnin:, :].reshape((-1, ndim))
median=np.median(samples, axis=0)
print(median)
fig = corner.corner(samples, labels=["$x0$", "$y0$",  "$a0$", "$b0$"],truths=median,quantiles=(0.1, 0.9))
    Out [312]: 
    [ 0.3364835   3.08117345 -0.05128693 -0.03812301]
    In [314]: 
    modelfit = model_dv_af(median)
plt.plot(timesrd, gw_sxs_bbh_0305rd[:,1], "r", alpha=0.3, lw=3, label="NR_re")
plt.plot(timesrd, modelfit.real,"b", alpha=0.3, lw=3, label="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");
    out [314]:

    AEI Privacy Policy Imprint