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test_waveform.dat
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A_test_with_n=1.py 5.11 KiB
"""
In this script I use a mock data generated from combining n=0 and n=1 overtones together, and sample it with the ptemcee sampler under the n=1 scenario. It seems that either there are some fundamental internal problems that prevent us from separating alpha_0 from alpha_1, or that ptemcee doesn't work as well for this problem. Either way, there should be something going on with our approach for this entire project...
--- R^a_{yne} L^i_u
"""
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': 19})
import pandas as pd
import ptemcee
import qnm
import random
ntemps = 20
nwalkers = 100
npoints = 150
ndim = 8
burnin = 75
numbins = 42
datacolor = '#105670' #'#4fa3a7'
pkcolor = '#f2c977' #'#ffb45f'
mediancolor = '#f7695c' #'#9b2814'
rootpath = "/Users/RayneLiu"
t = np.arange(0, 80, 0.1)
w0, tau0, x0, y0 = [0.55578191, 11.74090006, 0.978518, -2.11289]
#Can get the w and tau from example nb and amplitude and phase from the 1910 paper
w1, tau1, x1, y1 = [0.54351639, 3.88312743, 4.29435, 1.38519]
mockdata = x0*np.exp(1j*y0)*np.exp(-t/(tau0)) * (np.cos(w0*t)-1j*np.sin(w0*t)) + \
x1*np.exp(1j*y1)*np.exp(-t/(tau1)) * (np.cos(w1*t)-1j*np.sin(w1*t))
def modelmock(theta):
"""
theta: comprised of alpha0, alpha1, beta0, beta1, x0, x1, and y0, y1
"""
alpha0, alpha1, beta0, beta1, xvar0, xvar1, yvar0, yvar1 = theta
tauvar0 = tau0*(1+beta0)
wvar0 = w0*(1+alpha0)
tauvar1 = tau1*(1+beta1)
wvar1 = w1*(1+alpha1)
ansatz = (xvar0*np.exp(1j*yvar0))*np.exp(-t/tauvar0)*(np.cos(wvar0*t)-1j*np.sin(wvar0*t))+\
(xvar1*np.exp(1j*yvar1))*np.exp(-t/tauvar1)*(np.cos(wvar1*t)-1j*np.sin(wvar1*t))
# -1j to agree with SXS convention
return ansatz
def log_prior(theta):
alpha0, alpha1, beta0, beta1, xvar0, xvar1, yvar0, yvar1 = theta
if all([-0.4 <= alpha0 <= 0.4, -1.0 <= beta0 <= 2.0, 0 <= xvar0 <= 2.4, -2*np.pi <= yvar0 <= 0, \
-0.4 <= alpha1 <= 0.4, -1.0 <= beta1 <= 2.0, 0 <= xvar1 <= 6.0, -np.pi <= yvar1 <= 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):
model_mock = modelmock(theta)
return -np.sum((mockdata.real - model_mock.real)**2+(mockdata.imag - model_mock.imag)**2)
# 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)
#Define labels used in plotting
paramlabels_a = [r'$\alpha_0$', r'$\alpha_1$']
paramlabels_b = [r'$\beta_0$', r'$\beta_1$']
paramlabels_x = [r'$x_0$', r'$x_1$']
paramlabels_y = [r'$y_0$', r'$y_1$']
paramlabels = paramlabels_a + paramlabels_b + paramlabels_x + paramlabels_y
np.random.seed(42)
pos = [random.uniform(-0.1,0.1), random.uniform(-0.1,0.1), random.uniform(-0.1,0.1), random.uniform(-0.1,0.1), \
random.uniform(0.8, 1.0), random.uniform(4, 5), random.uniform(-3, -2), random.uniform(1, 2)]
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);
#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')
fig.savefig(rootpath+'/git/rdstackingproject/plotsmc/Test_with_mockdatan=1'+ str(npoints)+'pts_chainplot.png', format = 'png', bbox_inches = 'tight')
#Output chain
samples = sampler.chain[0,:, burnin:, :].reshape((-1, ndim))
df0 = pd.DataFrame(samples, columns=paramlabels)
df0.to_csv(rootpath+'/git/rdstackingproject/plotsmc/Test_with_mockdatan=1'+ str(npoints)+'pts_chain.csv', index = False)
#Corner plot
lglk = np.array([log_likelihood(samples[i]) for i in range(len(samples))])
pk = samples[np.argmax(lglk)]
median = np.median(samples, axis=0)
figcorn = corner.corner(samples, bins = numbins, hist_bin_factor = 5, color = datacolor, truths=pk, 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)
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/Test_with_mockdatan=1'+ str(npoints)+'pts_corner.pdf', format = 'pdf')