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Hubble_Diagrams.py
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Hubble_Diagrams.py
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## Create butterfly plots
from __future__ import division
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
from astropy.cosmology import WMAP9
from time import strftime
from matplotlib.ticker import MaxNLocator
import Data_Set_Generator as DSG ## for up to date relative normalization
def one_G(x, p):
mu, sig = p
p_A = np.sqrt(2*np.pi*sig**2)**(-1.0)*np.exp(-(x-mu)**2/(2*sig**2)) ##sig**2=variance
return p_A
def GMM(x, p):
mu_A, sig_A, mu_B, sig_B, w_A = p
p_A = np.sqrt(2*np.pi*sig_A**2)**(-1.0)*np.exp(-(x-mu_A)**2/(2*sig_A**2))
p_B = np.sqrt(2*np.pi*sig_B**2)**(-1.0)*np.exp(-(x-mu_B)**2/(2*sig_B**2))
return (w_A*p_A + (1-w_A) * p_B)
def data_GMM(mean_A, dM, n_A):
return n_A*mean_A + (1.0-n_A)*(mean_A -dM) #(2.0*mean_A - dM)/2.0
def std_err( p, Nbins, GMM = False):
if GMM:
sig_A, sig_B, n_A = p
return (n_A*sig_A**2/Nbins +(1.0-n_A)*sig_B**2/Nbins)**(0.5)
else:
return p/np.sqrt(Nbins)
def residual( M_data, M_model):
return M_data - M_model
# Create GMM model
def apparent_mag(z, p , GMM = False):
if GMM:
n_A, peak_A, peak_B = p
app_mag = WMAP9.distmod(z).value + n_A*peak_A + (1.0-n_A)*peak_B
else:
app_mag = WMAP9.distmod(z).value + p
return app_mag
#def distmod_residual():
# return
def bin_dat(data, bin_num, xmin, xmax):
bins = np.linspace(xmin, xmax, bin_num)
digitized = np.digitize(data, bins)
bin_means = [data[digitized == i].mean() for i in range(1, len(bins))]
return bin_means, digitized, bins
def bin_means(data, digitized, Nbins, bins):
digitized = np.repeat(digitized, Nbins)
bin_means = [data[digitized == i].mean() for i in range(1, len(bins))]
return bin_means
def residual_plot( One_G_data, sigma_1G, GMM_data, p_GMM, z, dM, Nbins, App_Mag = False, One_G = True, GMM = True, Model = True , save_fig = False, **kwargs):
"""
Residual plot testing
"""
figure_size = kwargs.pop('fig_size', (12.5,12.5))
title_size = kwargs.pop('suptitle_fontsize', 25)
y_label = kwargs.pop('y_label', 'Distance Modulus')
x_size = kwargs.pop('x_fontsize', 30)
y_size = kwargs.pop('y_fontsize', 30)
extra = kwargs.pop('save_fig_label', 'Normal')
line = kwargs.pop('linewidth', 3)
model_line = kwargs.pop('model_color', 'k-')
One_G_fmt = kwargs.pop('One_G_fmt', 'bo')
GMM_fmt = kwargs.pop('GMM_fmt', 'ro')
One_G_label = kwargs.pop('One_G_label', '1G')
GMM_label = kwargs.pop('GMM_label', 'GMM')
M_ave = kwargs.pop('M_ave', -19.5)
y_lim = kwargs.pop('y_lim', (38, 48))
xmin = kwargs.pop('x_min', 0.0)
xmax = kwargs.pop('x_max', 2.0)
z_model = np.linspace(0.001 , 2.5, 1000)
fig= plt.figure(figsize=figure_size)
fig.suptitle('Hubble Diagram with Two-Population Shift = %+6.2f mag' % (dM) , fontsize=title_size)
fig.subplots_adjust(hspace=0.001)
gs=gridspec.GridSpec(2, 1, height_ratios=[3,1])
ax1=plt.subplot(gs[0])
ax2=plt.subplot(gs[1], sharex=ax1)
if Model:
mu_model = WMAP9.distmod(z_model).value
if not App_Mag:
ax1.plot(z_model, mu_model, model_line, linewidth = line)
if App_Mag:
ax1.plot(z_model, mu_model + M_ave, model_line, linewidth = line)
if not App_Mag:
Model_data = WMAP9.distmod(z).value
if App_Mag:
Model_data = WMAP9.distmod(z).value + M_ave
if One_G:
yerr_1G = std_err(sigma_1G, Nbins, GMM = False)
ax1.errorbar(z, One_G_data, yerr=yerr_1G, fmt=One_G_fmt, label=One_G_label, lw = line)
ax2.errorbar(z, residual(One_G_data, Model_data),yerr=yerr_1G, fmt= One_G_fmt, lw = line)
if GMM:
yerr_GMM = std_err(p_GMM, Nbins, GMM = True)
ax1.errorbar(z, GMM_data, yerr=yerr_GMM, fmt=GMM_fmt, label=GMM_label, lw = line)
ax2.errorbar(z,residual(GMM_data, Model_data), yerr=yerr_GMM, fmt=GMM_fmt, lw = line)
ax1.set_ylim(y_lim)
plt.setp(ax1.get_xticklabels(), visible=False)
if App_Mag:
ax1.set_ylabel('Apparent Magnitude', fontsize=y_size)
else:
ax1.set_ylabel('%s'%(y_label), fontsize=y_size)
ax2.plot(np.linspace(xmin, xmax, len(z_model)), np.zeros(len(z_model)), model_line, lw=line)
ax2.set_xlim(xmin, xmax)
plt.gca().yaxis.set_major_locator(MaxNLocator(prune='lower'))
#fig.add_subplot(ax1)
#fig.add_subplot(ax2)
ax2.set_xlabel('Redshift', fontsize = x_size)
if save_fig:
plt.savefig('/Users/karaponder/Spring14/Figures/%s_Hubble_Diagram_wResdiual_%s.pdf'%(strftime('%Y%m%d'), extra))
#plt.show()
return #fig
#def hubble_diagram( dM ,residual = False, save_fig = False, **kwargs):
# if residual:
# return
def butterfly( One_G_data, sigma_1G, GMM_data, p_GMM, z , Nbins, hist_Nbins = 11, save_fig = False, residual_label = False, legend = True, **kwargs):
figure_size = kwargs.pop('fig_size', (12.5,12.5))
x_size = kwargs.pop('x_fontsize', 30)
One_G_fmt = kwargs.pop('One_G_fmt', 'bo')
GMM_fmt = kwargs.pop('GMM_fmt', 'ro')
One_G_label = kwargs.pop('One_G_label', '1G')
GMM_label = kwargs.pop('GMM_label', 'GMM')
marker = kwargs.pop('markersize', 9)
M_ave = kwargs.pop('M_ave', -19.5)
x_size = kwargs.pop('x_fontsize', 30)
legend_size = kwargs.pop('legend_fontsize', 30)
model_line = kwargs.pop('model_color', 'k-')
line = kwargs.pop('linewidth', 3)
extra = kwargs.pop('save_fig_label', 'Normal')
xmin = kwargs.pop('x_min', 0.0)
xmax = kwargs.pop('x_max', 2.0)
y_lim = kwargs.pop('y_lim', (18, 28))
fig=plt.figure(figsize=figure_size)
fig.subplots_adjust(hspace=0.001)
gs=gridspec.GridSpec(2, 1, height_ratios=[3,1])
ax1=plt.subplot(gs[0])
ax2=plt.subplot(gs[1], sharex=ax1)
GMM_A_peak, dM = GMM_data
dM = np.mean(dM, dtype=np.float64)
plt.suptitle('Hubble Diagram with Two-Population Shift = %+6.2f mag' % (dM) , fontsize=30)
z_model = np.linspace(0.001 , 2.5, 1000)
Model_data = WMAP9.distmod(z).value + M_ave
mu_model = WMAP9.distmod(z_model).value
ax1.plot(z_model, mu_model+M_ave, 'k', linewidth = 3)
# Set x values for subplots
zero=np.zeros(100)
m = np.linspace(-1.5, +1.5, 100) + M_ave
r = np.linspace(-1.5, +1.5, 100)
# Define my parameters for the PDFs. ONLY WANT A FEW FOR THE DATA.
binned_z, digitized, bins = bin_dat( z, hist_Nbins, xmin, xmax)
binned_One_G_data = bin_means( One_G_data, digitized, Nbins, bins)
if len(One_G_data) == len(sigma_1G):
binned_sigma_1G = bin_means( sigma_1G, digitized, Nbins, bins)
p_1G = np.column_stack((binned_One_G_data, binned_sigma_1G))
else:
mult_sigma_1G = [sigma_1G]*len(One_G_data)
binned_sigma_1G = bin_means( mult_sigma_1G, digitized, Nbins, bins)
p_1G = np.column_stack((binned_One_G_data, binned_sigma_1G))
binned_GMM_A_peak = bin_means( GMM_A_peak, digitized, Nbins, bins)
binned_GMM_B_peak = bin_means( GMM_A_peak - dM,digitized, Nbins, bins)
sigma_A_GMM, sigma_B_GMM, n_A = p_GMM
if len(GMM_A_peak) == len(sigma_A_GMM):
binned_sigma_A = bin_means( sigma_A_GMM, digitized, Nbins, bins)
binned_sigma_B = bin_means( sigma_B_GMM,digitized, Nbins, bins)
binned_n_A = bin_means( n_A, digitized, Nbins, bins)
p_2G = np.column_stack((binned_GMM_A_peak, binned_sigma_A , binned_GMM_B_peak, binned_sigma_B , binned_n_A)) # mu_A, sig_A, mu_B, sig_B = p
else:
sigma_A_GMM, sigma_B_GMM, n_A = [sigma_A_GMM]*len(GMM_A_peak) , [sigma_B_GMM]*len(GMM_A_peak), [n_A]*len(GMM_A_peak)
binned_sigma_A = bin_means( sigma_A_GMM,digitized, Nbins, bins)
binned_sigma_B = bin_means( sigma_B_GMM, digitized, Nbins, bins)
binned_n_A = bin_means( n_A, digitized, Nbins, bins)
p_2G = np.column_stack((binned_GMM_A_peak, binned_sigma_A , binned_GMM_B_peak, binned_sigma_B , binned_n_A))
dz = np.mean(binned_z[1:] - binned_z[0:-1])
# MWV: I just chose a factor of 3 because it looked good with the given PDFs. You could have much more sharply peaked PDFs that would extend too far.
pdf_scale = dz / 3
## Plot the PDFs on top of my data points
distmod_table = WMAP9.distmod(binned_z).value
for i in range ( 0 , len(binned_z)):
ax1.plot(-one_G(m, p_1G[i])*pdf_scale +binned_z[i], m+distmod_table[i], 'b', lw=3) #what to plot
ax1.plot( GMM(m, p_2G[i]) *pdf_scale +binned_z[i], m+distmod_table[i], 'r', lw=3) #what to plot
ax2.plot(-one_G(m, p_1G[i])*pdf_scale +binned_z[i], r, 'b', lw=3) #what to plot r+residual_mag_10z[i]
ax2.plot( GMM(m, p_2G[i]) *pdf_scale +binned_z[i], r, 'r', lw=3) #what to plot
if legend:
ax1.legend(numpoints=1, loc = 4, fontsize=legend_size)
ax1.set_ylim(y_lim)
ax1.set_xlim(xmin, xmax)
ax2.plot(np.linspace(xmin, xmax, len(z_model)), np.zeros(len(z_model)), model_line, lw=line)
GMM_data_1 = data_GMM(GMM_A_peak, dM, n_A)
yerr_1G = std_err(sigma_1G, Nbins, GMM = False)
ax1.errorbar(z, One_G_data + distmod_table, yerr=yerr_1G, fmt=One_G_fmt, label=One_G_label, lw = line, markersize=marker)
ax2.errorbar(z, residual(One_G_data + distmod_table, Model_data),yerr=yerr_1G, fmt= One_G_fmt, lw = line, markersize=marker)
yerr_GMM = std_err(p_GMM, Nbins, GMM = True)
ax1.errorbar(z, GMM_data_1 + distmod_table, yerr=yerr_GMM, fmt=GMM_fmt, label=GMM_label, lw = line, markersize=marker)
ax2.errorbar(z,residual(GMM_data_1 + distmod_table, Model_data), yerr=yerr_GMM, fmt=GMM_fmt, lw = line, markersize=marker)
if residual_label:
ax2.set_ylabel(r'$m - m_{\Lambda CDM}$',fontsize = y_size)
ax2.set_ylim((-2.0, 2.0))
plt.setp(ax1.get_xticklabels(), visible=False)
yticks = ax2.yaxis.get_major_ticks()
yticks[-1].label1.set_visible(False)
ax1.tick_params(axis='y', labelsize=30)
ax2.tick_params(axis='x', labelsize=30)
ax2.tick_params(axis='y', labelsize=30)
ax1.set_ylabel('Apparent Magnitude [mag]', fontsize=x_size)
ax2.set_xlabel('Redshift', fontsize = x_size)
ax2.set_yticks([ -1.5, 0.0, 1.5])
if save_fig:
plt.savefig('/Users/karaponder/Spring14/Figures/%s_Butterfly_wResdiual_%s.pdf'%(strftime('%Y%m%d'), extra))
plt.show()
print m
print p_2G[0]
p_test = 15.66462843, 0.1,14.66462843,0.1, 0.5
plt.plot(m, GMM(m,p_test))
plt.show()
return