<jupyter_start><jupyter_text>Comparison between MC-SPAM LDCs and limiting LDCsAs described in other notebook, due to inherent difference between two methods to derive LDCs (the one from the stellar model atmospheres and those obtained from the exoplanet transit photometry), both sets of LDCs are not directly comparable. To deal with this issue, [Howarth (2011)](https://academic.oup.com/mnras/article/418/2/1165/1071889) proposed a new way to compute LDCs from synthetic transit lightcurves which were, in turn, calculated from a more realistic stellar intensity profile --- an algorithm which was dubbed as SPAM (Synthetica-Photometry/Atmosphere Model). However, this method doesn't take into account of uncertainties present in geometrical transit parameters. [Espinoza & Jordan (2015)](https://academic.oup.com/mnras/article/450/2/1879/985166) took care of this using Monte-Carlo methods, which came to know as MC-SPAM (Monte-Carlo SPAM).In other notebook, we described a way to compute MC-SPAM LDCs --- and we computed the same for ATLAS [Espinoza & Jordan (2015)](https://academic.oup.com/mnras/article/450/2/1879/985166) LDCs. We now want to compare these MC-SPAM LDCs to the limiting LDCs (see, [Espinoza & Jordan 2015](https://academic.oup.com/mnras/article/450/2/1879/985166)).<jupyter_code>import numpy as np
import matplotlib.pyplot as plt
import sys
import os
import seaborn as sns
from matplotlib import rcParams
from pylab import *

sys.path.append('/home/jayshil/Documents/Dissertation/ld-spam')
import utils as utl
path1 = '/home/jayshil/Documents/Dissertation/'

# MC-SPAM LDCs
u1_mcs, u1_mcs_err, u2_mcs, u2_mcs_err = np.loadtxt(path1 + '/ld-spam/Results/MCS_Atlas_code.dat', usecols=(1,2,3,4), unpack=True)

# Limiting LDCs
u1_lim, u2_lim = np.loadtxt(path1 + '/ld-project-updated/Atlas/code_limiting_LDC_ata.dat', usecols=(1,2), unpack=True)
u1_lim_err, u2_lim_err = np.zeros(len(u1_lim)), np.zeros(len(u1_lim))
sns.set_context("talk")
sns.set_style("ticks")

# Fonts:
rc('font', **{'family': 'serif', 'serif': ['Computer Modern']})
rc('text', usetex=True)
matplotlib.rcParams.update({'font.size':12})
plt.rc('legend', **{'fontsize':12})

# Ticks to the outside:
rcParams['axes.linewidth'] = 1.2 
rcParams['xtick.direction'] = 'out'
rcParams['ytick.direction'] = 'out'<jupyter_output><empty_output><jupyter_text>Let's plot 'em...<jupyter_code>utl.single_image(u1_lim, u1_lim_err, u1_mcs, u1_mcs_err, 'Limiting LDCs', 'MC-SPAM LDCs')
plt.ylim([-0.15, 0.05])
plt.show()
utl.single_image(u2_lim, u2_lim_err, u2_mcs, u2_mcs_err, 'Limiting LDCs', 'MC-SPAM LDCs')
plt.ylim([-0.05,0.15])
plt.show()<jupyter_output><empty_output><jupyter_text>So, it can be observed that the there is a strong correlation between the limiting LDCs and the MC-SPAM LDCs when ATLAS (Espinoza & Jordan 2015) LDCs are used. Furthermore, the bias between these two set is very low ($\sim 0.05-0.1$).  Comparing SPAM LDCsLet's, as a sanity check, compare one of the set of SPAM LDCs with the juliet LDCs. We choose ATLAS-C17 LDCs.<jupyter_code># <NAME> (2017) SPAM LDCs
u1a_c17, u2a_c17 = np.loadtxt(path1 + 'ld-spam/Results_New/SPAM_ATLAS-C17.dat', usecols=(1,2), unpack=True)
# juliet LDCs
u1_j, u1_jp, u1_jn, u2_j, u2_jp, u2_jn = np.loadtxt(path1 + 'ld-project-updated/Data/results.dat', usecols = (16,17,18,19,20,21), unpack = True)

# Plot 'em
utl.single_image(xdata=u1_j, xerr=u1_jp, ydata=u1a_c17, yerr=u1_lim_err, xlabel=r'$u_1$ (Empirical)', ylabel=r'$u_1$ (SPAM LDCs)')
plt.show()
utl.single_image(xdata=u2_j, xerr=u2_jp, ydata=u2a_c17, yerr=u1_lim_err, xlabel=r'$u_1$ (Empirical)', ylabel=r'$u_1$ (SPAM LDCs)')
plt.show()<jupyter_output><empty_output>
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