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FitOlivares.py
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FitOlivares.py
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#!/usr/bin/env python
# xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx #
# xxxxxxxxxxxxxxxx----------------FIT THE OLIVARES MODEL TO TYPE IIP SN LIGHT CURVES---------------xxxxxxxxxxxxxxxxxx #
# xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx #
# ------------------------------------------------------------------------------------------------------------------- #
# Import Required Libraries
# ------------------------------------------------------------------------------------------------------------------- #
import numpy as np
import pandas as pd
import uncertainties as unc
import matplotlib.pyplot as plt
import uncertainties.unumpy as unp
from scipy.optimize import curve_fit
from matplotlib.ticker import MultipleLocator
from mpl_toolkits.axes_grid1 import make_axes_locatable
# ------------------------------------------------------------------------------------------------------------------- #
# ------------------------------------------------------------------------------------------------------------------- #
# Global Variables
# ------------------------------------------------------------------------------------------------------------------- #
data_fmt = "{0:.3f}"
DIR_PHOT = "/home/avinash/Dropbox/SNData/IIP_Data/LC_Data/"
file_name = '2016gfy_HCT.dat'
date_explosion = 2457641.80
date_maximum = 2457650.0
fit_epoch = 250
# ------------------------------------------------------------------------------------------------------------------- #
# ------------------------------------------------------------------------------------------------------------------- #
# Useful Functions For Fitting And Conversions
# ------------------------------------------------------------------------------------------------------------------- #
def fermifunc(t, a0, tPT, w0):
return -a0 / (1 + np.exp((t - tPT) / w0))
def linefunc(t, p0, tPT, m0):
return p0 * (t - tPT) + m0
def gaussfunc(t, P, Q, R):
return -P * np.exp(-((t - Q) / R) ** 2)
def olifunc(t, a0, tPT, w0, p0, m0, P, Q, R):
return -a0 / (1 + np.exp((t - tPT) / w0)) + p0 * (t - tPT) + m0 - P * np.exp(-((t - Q) / R) ** 2)
def redchisq(ydata, ymod, sd, n=8):
"""
Args:
ydata : Observed data
ymod : Model data
sd : Uncertainties in ydata
n : Number of free parameters in the model
Returns:
RedChiSq : Reduced Chi-Square
"""
ydata = np.array(ydata)
ymod = np.array(ymod)
sd = np.array(sd)
if not sd.any():
chisq = np.sum((ydata - ymod) ** 2)
else:
chisq = np.sum(((ydata - ymod) / sd) ** 2)
nu = ydata.size - 1 - n
redchisq = chisq / nu
return redchisq
# ------------------------------------------------------------------------------------------------------------------- #
# ------------------------------------------------------------------------------------------------------------------- #
# Plot Confidence Intervals
# ------------------------------------------------------------------------------------------------------------------- #
def plot_confintervals(ax_obj, optpar, covpar, xarr, fcolor='grey'):
"""
Plots 3-Sigma Confidence Intervals in Fits of SN Parameters.
Args:
ax_obj : Axes object on which the confidence interval is to be plotted
optpar : Optimised Parameters of the Fit
covpar : Covariance Parameters of the Fit
xarr : Array of X-Values over which confidence intervals are to be plotted
fcolor : Fill color for the confidence intervals
Returns:
None
"""
a0, tPT, w0, p0, m0, P, Q, R = unc.correlated_values(optpar, covpar)
func = -a0 / (1 + unp.exp((xarr - tPT) / w0)) + p0 * (xarr - tPT) + m0 - P * unp.exp(-((xarr - Q) / R) ** 2)
fit = unp.nominal_values(func)
sigma = unp.std_devs(func)
fitlow = fit - 3 * sigma
fithigh = fit + 3 * sigma
ax_obj.plot(xarr, fitlow, ls='-.', c='k', lw=0.7, alpha=0.3, label='_nolegend_')
ax_obj.plot(xarr, fithigh, ls='-.', c='k', lw=0.7, alpha=0.3, label='_nolegend_')
ax_obj.fill_between(xarr, fitlow, fithigh, facecolor=fcolor, alpha=0.3)
# ------------------------------------------------------------------------------------------------------------------- #
# ------------------------------------------------------------------------------------------------------------------- #
# Read The Apparent Magnitude LC & Lay Out The Guess Parameters For The Fit
# ------------------------------------------------------------------------------------------------------------------- #
data_df = pd.read_csv(DIR_PHOT + file_name, sep='\s+', comment='#').drop('Date', axis=1)
data_df = data_df.replace('INDEF', np.nan).astype('float64')[data_df['Phase'] < fit_epoch]
list_bands = ['B', 'V', 'R', 'I']
dict_guess = {'B': [1.970, 99.247, 7.575, 0.0078, 19.7122, 0.8606, -5.0377, 28.1691],
'V': [1.2449, 110.2644, 2.8179, 0.00989, 18.2976, 0.4402, 78, 29.1894],
'R': [1.392, 104.2053, 3.590, 0.0087, 17.3458, -0.2, 10, 30],
'I': [1.220, 105.5630, 3.598, 0.0110, 16.8611, -0.9668, 0.2952, 51.6011]}
# dict_guess = {'B': [1.970, 99.247, 7.575, 0.0078, 19.7122, 0.8606, -5.0377, 28.1691],
# 'V': [1.2449, 110.2644, 2.8179, 0.00989, 18.2976, 0.4402, 78.5989, 29.1894],
# 'R': [1.392, 104.2053, 3.590, 0.0087, 17.3458, -0.2, 10, 20],
# 'I': [1.220, 105.5630, 3.598, 0.0110, 16.8611, -0.9668, 0.2952, 51.6011]}
# ------------------------------------------------------------------------------------------------------------------- #
# ------------------------------------------------------------------------------------------------------------------- #
# Fit Olivares Model & Determine Light Curve Parameters For SN In Study (Technique - 1)
# ------------------------------------------------------------------------------------------------------------------- #
fig, axes = plt.subplots(nrows=2, ncols=4, gridspec_kw={'height_ratios': [4, 1]}, figsize=(30, 10), sharex=True)
for j in range(axes.shape[1]):
band = list_bands[j]
band_df = data_df[['JD', 'Phase', band, band + 'Err']].copy().dropna()
band_df = band_df[band_df['JD'] >= date_maximum]
opt, cov = curve_fit(olifunc, band_df['Phase'], band_df[band], sigma=band_df[band + 'Err'], p0=dict_guess[band])
print np.round(np.array(opt).astype('float64'), 4)
print np.round(np.sqrt(np.diagonal(cov).astype('float64')), 4)
print np.round(redchisq(band_df[band], olifunc(band_df['Phase'], *opt), sd=band_df[band + 'Err']), 2)
jdarr = np.round(np.arange(band_df['Phase'].min(), band_df['Phase'].max(), 0.1), 1)
axes[0, j].scatter(band_df['Phase'], band_df[band], marker='*', s=40, c='k', label='Observed Data')
axes[0, j].plot(jdarr, olifunc(jdarr, *opt), c='r', lw=1.2, label='Best Fit')
axes[0, j].plot(jdarr, fermifunc(jdarr, *opt[0:3]) + opt[4], c='orange', lw=1.2, ls='--', label='Fermi Dirac')
axes[0, j].plot(jdarr, linefunc(jdarr, *[opt[i] for i in [3, 1, 4]]), c='b', lw=1.2, ls='-.', label='Linear Decay')
axes[0, j].plot(jdarr, gaussfunc(jdarr, *opt[5:]) + opt[4], c='g', lw=1.2, ls=':', label='Gaussian Peak')
axes[0, j].axvline(opt[1], ls='--', lw=0.8, c='k')
axes[0, j].set_ylim(20.5, 15)
axes[0, j].set_xlim(-2, 242)
axes[0, j].yaxis.set_ticks_position('both')
axes[0, j].xaxis.set_ticks_position('both')
axes[0, j].yaxis.set_major_locator(MultipleLocator(1))
axes[0, j].yaxis.set_minor_locator(MultipleLocator(0.1))
axes[0, j].xaxis.set_major_locator(MultipleLocator(50))
axes[0, j].xaxis.set_minor_locator(MultipleLocator(5))
axes[0, j].tick_params(which='major', direction='in', length=8, width=1.4, labelsize=16)
axes[0, j].tick_params(which='minor', direction='in', length=4, width=0.7, labelsize=16)
axes[0, j].text(190, 15.5, '${0}$-Band'.format(band), fontsize=18)
axes[1, j].scatter(band_df['Phase'], band_df[band] - olifunc(band_df['Phase'], *opt), marker='^', c='k', s=30)
axes[1, j].axvline(opt[1], ls='--', lw=0.8, c='k')
axes[1, j].set_ylim(-0.25, 0.25)
axes[1, j].yaxis.set_ticks_position('both')
axes[1, j].xaxis.set_ticks_position('both')
axes[1, j].yaxis.set_major_locator(MultipleLocator(0.2))
axes[1, j].yaxis.set_minor_locator(MultipleLocator(0.04))
axes[1, j].xaxis.set_major_locator(MultipleLocator(50))
axes[1, j].xaxis.set_minor_locator(MultipleLocator(5))
axes[1, j].tick_params(which='major', direction='in', length=8, width=1.4, labelsize=16)
axes[1, j].tick_params(which='minor', direction='in', length=4, width=0.7, labelsize=16)
axes[1, j].set_xlabel('Time Since Explosion [Days]', fontsize=16)
if j != 0:
axes[0, j].set_yticklabels([])
axes[1, j].set_yticklabels([])
plot_confintervals(axes[0, j], opt, cov, jdarr, fcolor='dimgrey')
axes[0, j].text(opt[1] + 1.5, axes[0, j].get_ylim()[-1] + 0.3, r'Transition Phase', rotation=90, fontsize=12)
axes[0, 3].legend(markerscale=3, fontsize=14, loc='lower right')
axes[0, 0].set_ylabel('Apparent Magnitude', fontsize=18)
axes[1, 0].set_ylabel(r'Residuals', fontsize=18)
fig.subplots_adjust(hspace=0.01, wspace=0.01)
fig.savefig('PLOT_FitOlivares.pdf', format='pdf', dpi=2000, bbox_inches='tight')
plt.show()
plt.close(fig)
# ------------------------------------------------------------------------------------------------------------------- #
# ------------------------------------------------------------------------------------------------------------------- #
# Fit Olivares Model & Determine Light Curve Parameters For SN In Study (Technique - 2)
# ------------------------------------------------------------------------------------------------------------------- #
def create_plot(ax1, band_df, opt):
divider = make_axes_locatable(ax1)
ax2 = divider.append_axes('bottom', size='20%', pad=0)
ax1.figure.add_axes(ax2)
ax1.set_xlim(-2, 242)
ax2.set_xlim(-2, 242)
ax1.set_xticklabels([])
jdarr = np.round(np.arange(band_df['Phase'].min(), band_df['Phase'].max(), 0.1), 1)
ax1.plot(band_df['Phase'], band_df[band], marker='*', ls='', ms=12, c='k', markerfacecolor='grey',
label='Observed Data')
ax1.plot(jdarr, olifunc(jdarr, *opt), c='r', lw=1.2, label='Best Fit')
ax1.plot(jdarr, fermifunc(jdarr, *opt[0:3]) + opt[4], c='darkgoldenrod', lw=1.4, ls='--', label='Fermi Dirac')
ax1.plot(jdarr, linefunc(jdarr, *[opt[i] for i in [3, 1, 4]]), c='b', lw=1.4, ls='-.', label='Linear Decay')
ax1.plot(jdarr, gaussfunc(jdarr, *opt[5:]) + opt[4], c='g', lw=1.4, ls=':', label='Gaussian Peak')
ax1.axvline(opt[1], ls='--', lw=0.8, c='k')
# ax1.yaxis.tick_right()
ax1.yaxis.set_ticks_position('both')
ax1.xaxis.set_ticks_position('both')
ax1.yaxis.set_label_position('right')
ax1.yaxis.set_major_locator(MultipleLocator(1))
ax1.yaxis.set_minor_locator(MultipleLocator(0.1))
ax1.xaxis.set_major_locator(MultipleLocator(50))
ax1.xaxis.set_minor_locator(MultipleLocator(5))
ax1.tick_params(which='major', direction='in', length=8, width=1.4, labelsize=18, pad=8)
ax1.tick_params(which='minor', direction='in', length=4, width=0.7, labelsize=18)
ax2.scatter(band_df['Phase'], band_df[band] - olifunc(band_df['Phase'], *opt), marker='^', c='r', s=30)
ax2.axvline(opt[1], ls='--', lw=0.8, c='k')
ax2.set_ylim(-0.25, 0.25)
ax2.yaxis.set_ticks_position('both')
ax2.xaxis.set_ticks_position('both')
ax2.yaxis.set_label_position('right')
ax2.yaxis.set_major_locator(MultipleLocator(0.2))
ax2.yaxis.set_minor_locator(MultipleLocator(0.04))
ax2.xaxis.set_major_locator(MultipleLocator(50))
ax2.xaxis.set_minor_locator(MultipleLocator(5))
ax2.tick_params(axis='y', which='major', direction='in', length=8, width=1.4, labelsize=16)
ax2.tick_params(axis='x', which='major', direction='in', length=8, width=1.4, labelsize=18)
ax2.tick_params(which='minor', direction='in', length=4, width=0.7, labelsize=18)
if ax1 == axes[0, 0] or ax1 == axes[1, 0]:
ax1.set_ylabel('Apparent Magnitude', fontsize=18)
ax2.set_ylabel('Residuals', color='r', fontsize=18)
else:
ax1.set_yticklabels([])
ax2.set_yticklabels([])
if ax1 == axes[0, 0] or ax1 == axes[0, 1]:
ax2.set_xticklabels([])
ax1.set_ylim(20.5, 15.8)
ax1.text(200, 16.2, '${0}$-Band'.format(band), color='orangered', fontsize=18)
else:
ax1.set_ylim(18.7, 15.2)
ax1.text(200, 15.5, '${0}$-Band'.format(band), color='orangered', fontsize=18)
ax2.set_xlabel('Time Since Explosion [Days]', fontsize=18)
plot_confintervals(ax1, opt, cov, jdarr, fcolor='grey')
ax1.text(opt[1] + 1.5, ax1.get_ylim()[-1] + 0.2, r'Transition Phase', rotation=90, fontsize=13)
fig, axes = plt.subplots(nrows=len(list_bands) / 2, ncols=2, figsize=(18, 18))
for i in range(axes.shape[0]):
for j in range(axes.shape[1]):
band = list_bands[i * axes.shape[0] + j]
band_df = data_df[['JD', 'Phase', band, band + 'Err']].copy().dropna()
band_df = band_df[band_df['JD'] >= date_maximum]
opt, cov = curve_fit(olifunc, band_df['Phase'], band_df[band], sigma=band_df[band + 'Err'],
p0=dict_guess[band])
create_plot(axes[i, j], band_df, opt)
axes[0, 1].legend(markerscale=2.5, fontsize=18, frameon=False, loc='lower left')
fig.subplots_adjust(hspace=0.01, wspace=0.05)
fig.savefig('PLOT_FitOlivares2.pdf', format='pdf', dpi=2000, bbox_inches='tight')
plt.show()
plt.close(fig)
# ------------------------------------------------------------------------------------------------------------------- #