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plot_mcmc.py
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plot_mcmc.py
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import numpy as np
import scipy.stats
import scipy.integrate
import scipy.interpolate
import matplotlib.pyplot as plt
import corner
from LF_refs import M16_LF_pars
def get_binsize(data):
# Freedman-Diaconis Rule
return 2*(np.percentile(data,75)-np.percentile(data,25)) / len(data)**(1./3.)
class MCMC_Output():
def __init__(self,drop_filt,sample_type,fname=None,best_pars=None,
nwalkers=10,ndim=3,burnin=200,
labels=['$\\alpha$','M$^\\star$','$\\phi^\\star$'],
verbose=False):
self.drop_filt = drop_filt
self.sample_type = sample_type
self.fname = fname if fname else "output/mcmc_%s_%s.dat" % (drop_filt,sample_type[:4])
self.verbose = verbose
self.best_pars = np.array(best_pars) if best_pars else np.array(M16_LF_pars["%s_%s"%(drop_filt,sample_type[:4])]['coeff'])
self.nwalkers = 10
self.ndim = 3
self.burnin = burnin
self.labels = labels
self.chain = np.genfromtxt(self.fname)
self.setup()
def setup(self):
self.chain2d_full = self.chain
self.chain3d_full = self.chain.reshape((-1,self.nwalkers,3))
self.chain2d = self.chain3d_full[self.burnin:,:,:].reshape((-1,3))
self.chain3d = self.chain3d_full[self.burnin:,:,:]
self.steps = self.chain3d_full.shape[0]
self.mode3D,self.conf_ints3D,self.errors3D = self.get_3D_confidence_intervals()
self.mode1D,self.conf_ints1D,self.errors1D = self.get_1D_confidence_intervals()
def get_3D_confidence_intervals(self):
xdata, ydata, zdata = self.chain2d.T
limx = [min(xdata), max(xdata)]
limy = [min(ydata), max(ydata)]
limz = [min(zdata), max(zdata)]
dbinx = get_binsize(xdata)
dbiny = get_binsize(ydata)
dbinz = get_binsize(zdata)
binsx = np.arange(limx[0],limx[1],dbinx)
binsy = np.arange(limy[0],limy[1],dbiny)
binsz = np.arange(limz[0],limz[1],dbinz)
bincx = 0.5*(binsx[1:]+binsx[:-1])
bincy = 0.5*(binsy[1:]+binsy[:-1])
bincz = 0.5*(binsz[1:]+binsz[:-1])
hist = np.histogramdd(self.chain2d,bins=[binsx,binsy,binsz])[0]
hist = hist / dbinx / dbiny / dbinz / self.chain2d.shape[0]
def find_crit(x,c):
_hist = hist.copy()
_hist[hist < x] = 0
res = scipy.integrate.simps(
scipy.integrate.simps(
scipy.integrate.simps(_hist,dx=dbinz,axis=2),
dx=dbiny,axis=1),
dx=dbinx,axis=0)
return res - c
crit68 = scipy.optimize.brentq(find_crit, 0, np.max(hist), args=(0.68,))
crit95 = scipy.optimize.brentq(find_crit, 0, np.max(hist), args=(0.95,))
ypos,xpos,zpos = np.meshgrid(bincy,bincx,bincz)
cix = np.array([np.min(xpos[hist>=crit68]), np.max(xpos[hist>=crit68])])
ciy = np.array([np.min(ypos[hist>=crit68]), np.max(ypos[hist>=crit68])])
ciz = np.array([np.min(zpos[hist>=crit68]), np.max(zpos[hist>=crit68])])
imax = np.argmax(hist.ravel())
mode = np.array([xpos.ravel()[imax],ypos.ravel()[imax],zpos.ravel()[imax]])
conf_ints = np.array([cix,ciy,ciz])
errors = conf_ints - self.best_pars[:,np.newaxis]
if self.verbose:
print
print "==== %s %s LF ====" % (self.drop_filt.upper(),self.sample_type.capitalize())
print "-- 3D Confidence Intervals --"
print "alpha: Fit=%8.3f Mode=%8.3f Err=[%8.3f,%8.3f] CI=[%8.3f,%8.3f]" % (self.best_pars[0],mode[0],errors[0][0],errors[0][1],conf_ints[0][0],conf_ints[0][1])
print "Mst: Fit=%8.3f Mode=%8.3f Err=[%8.3f,%8.3f] CI=[%8.3f,%8.3f]" % (self.best_pars[1],mode[1],errors[1][0],errors[1][1],conf_ints[1][0],conf_ints[1][1])
print "phi: Fit=%8.3f Mode=%8.3f Err=[%8.3f,%8.3f] CI=[%8.3f,%8.3f]" % (self.best_pars[2],mode[2],errors[2][0],errors[2][1],conf_ints[2][0],conf_ints[2][1])
return mode, conf_ints, errors
def get_1D_confidence_intervals(self):
xdata, ydata, zdata = self.chain2d.T
limx = [min(xdata), max(xdata)]
limy = [min(ydata), max(ydata)]
limz = [min(zdata), max(zdata)]
dbinx = get_binsize(xdata)
dbiny = get_binsize(ydata)
dbinz = get_binsize(zdata)
binsx = np.arange(limx[0],limx[1],dbinx)
binsy = np.arange(limy[0],limy[1],dbiny)
binsz = np.arange(limz[0],limz[1],dbinz)
bincx = 0.5*(binsx[1:]+binsx[:-1])
bincy = 0.5*(binsy[1:]+binsy[:-1])
bincz = 0.5*(binsz[1:]+binsz[:-1])
histx = np.histogram(xdata,bins=binsx)[0] / dbinx / len(xdata)
histy = np.histogram(ydata,bins=binsy)[0] / dbiny / len(ydata)
histz = np.histogram(zdata,bins=binsz)[0] / dbinz / len(zdata)
cix = np.percentile(xdata,[16,84])
ciy = np.percentile(ydata,[16,84])
ciz = np.percentile(zdata,[16,84])
mode = np.array([bincx[np.argmax(histx)],bincy[np.argmax(histy)],bincz[np.argmax(histz)]])
conf_ints = np.array([cix,ciy,ciz])
errors = conf_ints - self.best_pars[:,np.newaxis]
if self.verbose:
print "-- 1D Confidence Intervals --"
print "alpha: Fit=%8.3f Mode=%8.3f Err=[%8.3f,%8.3f] CI=[%8.3f,%8.3f]" % (self.best_pars[0],mode[0],errors[0][0],errors[0][1],conf_ints[0][0],conf_ints[0][1])
print "Mst: Fit=%8.3f Mode=%8.3f Err=[%8.3f,%8.3f] CI=[%8.3f,%8.3f]" % (self.best_pars[1],mode[1],errors[1][0],errors[1][1],conf_ints[1][0],conf_ints[1][1])
print "phi: Fit=%8.3f Mode=%8.3f Err=[%8.3f,%8.3f] CI=[%8.3f,%8.3f]" % (self.best_pars[2],mode[2],errors[2][0],errors[2][1],conf_ints[2][0],conf_ints[2][1])
print
return mode, conf_ints, errors
def plot_walkers(self,savename=None):
fig,axes = plt.subplots(3,1,figsize=(12,6),dpi=75,sharex=True)
fig.subplots_adjust(left=0.08,right=0.96,bottom=0.12,top=0.92,hspace=0,wspace=0)
for j in range(self.ndim):
for i in range(self.nwalkers):
axes[j].plot(np.arange(self.steps)+1,self.chain3d_full[:,i,j],lw=0.5,alpha=0.8)
axes[j].axhline(self.best_pars[j],c='k',lw=1.5,ls='--')
axes[j].set_ylabel(self.labels[j])
axes[2].set_xlabel('Step #')
fig.suptitle("%s %s Sample" % (self.drop_filt.upper(),self.sample_type.capitalize()),fontsize=20)
if savename: fig.savefig(savename)
plt.show(block=False)
def plot_corner(self,quantiles=[0.16,0.84],savename=None):
fig = corner.corner(self.chain2d,
truths=self.best_pars,
labels=self.labels,
quantiles=quantiles,
show_titles=True,
title_kwargs={"fontsize":16},
label_kwargs={"fontsize":16})
for ax in fig.get_axes():
_ = [i.set_fontsize(14) for i in ax.get_xticklabels()]
_ = [i.set_fontsize(14) for i in ax.get_yticklabels()]
fig.text(0.9,0.9,"%s %s Sample" % (self.drop_filt.upper(),self.sample_type.capitalize()),
fontsize=20,va='top',ha='right',transform=fig.transFigure)
fig.set_size_inches(10,8)
if savename: fig.savefig(savename)
plt.show(block=False)
def plot_2D_contours(self,xdata,ydata,axis,c='k'):
limx = min(xdata)-np.std(xdata),max(xdata)+np.std(xdata)
limy = min(ydata)-np.std(ydata),max(ydata)+np.std(ydata)
dbinx= get_binsize(xdata)*1.5
dbiny= get_binsize(ydata)*1.5
binsx = np.arange(limx[0],limx[1],dbinx)
binsy = np.arange(limy[0],limy[1],dbiny)
bincx = 0.5*(binsx[1:]+binsx[:-1])
bincy = 0.5*(binsy[1:]+binsy[:-1])
hist2d = np.histogram2d(xdata,ydata,bins=[binsx,binsy])[0]
hist2d = hist2d / dbinx / dbiny / len(xdata)
def find_crit(x,c):
_hist2d = hist2d.copy()
_hist2d[hist2d < x] = 0
res = scipy.integrate.simps(
scipy.integrate.simps(_hist2d,x=bincy,axis=1),
x=bincx,axis=0)
return res - c
crit68 = scipy.optimize.brentq(find_crit, 0, np.max(hist2d), args=(0.68,))
crit95 = scipy.optimize.brentq(find_crit, 0, np.max(hist2d), args=(0.95,))
ypos, xpos = np.meshgrid(bincy,bincx)
cix = np.array([np.min(xpos[hist2d>=crit68]), np.max(xpos[hist2d>=crit68])])
ciy = np.array([np.min(ypos[hist2d>=crit68]), np.max(ypos[hist2d>=crit68])])
axis.contour(bincx, bincy, hist2d.T,
levels=[crit95,crit68],
colors=[c,c],
linewidths=[0.5,1.5])
def plot_corner2(self):
fig,axes = plt.subplots(self.ndim,self.ndim,figsize=(10,8),dpi=75)
fig.subplots_adjust(left=0.1,right=0.9,bottom=0.1,top=0.9,hspace=0,wspace=0)
fig.text(0.9,0.9,"%s %s Sample" % (self.drop_filt.upper(),self.sample_type.capitalize()),
fontsize=20,va='top',ha='right',transform=fig.transFigure)
for j in range(self.ndim):
for i in range(self.ndim):
if j<i: axes[j,i].set_visible(False)
if j>0: axes[j,0].set_ylabel(self.labels[j])
if j!=self.ndim-1: axes[j,i].set_xticklabels([])
if i!=0: axes[j,i].set_yticklabels([])
if i==j: axes[j,i].set_yticklabels([])
axes[-1,i].set_xlabel(self.labels[i])
axes[j,i].set_xlim(min(self.chain2d[:,i]),max(self.chain2d[:,i]))
if i!=j: axes[j,i].set_ylim(min(self.chain2d[:,j]),max(self.chain2d[:,j]))
_ = [i.set_fontsize(12) for i in axes[j,i].get_xticklabels()+axes[j,i].get_yticklabels()]
for i,c in zip(range(self.ndim),['r','g','b']):
hist,bins = axes[i,i].hist(self.chain2d[:,i],
bins=np.arange(min(self.chain2d[:,i]),max(self.chain2d[:,i]),get_binsize(self.chain2d[:,i])),
color=c,lw=0,histtype='stepfilled',alpha=0.5)[:2]
binc = 0.5*(bins[1:]+bins[:-1])
axes[i,i].vlines(self.conf_ints1D[i],0,1e4,linestyle=':',color=c,alpha=0.8)
axes[i,i].axvline(self.best_pars[i],c=c,lw=1.5,alpha=0.8)
axes[i,i].set_title("%s: $%.2f_{%.2f}^{+%.2f}$" % (self.labels[i],self.best_pars[i],self.errors1D[i][0],self.errors1D[i][1]))
axes[i,i].set_ylim(0,1.2*np.max(hist))
axes[1,0].scatter(self.chain2d[:,0],self.chain2d[:,1],c='r',s=3,lw=0,alpha=0.05)
axes[2,0].scatter(self.chain2d[:,0],self.chain2d[:,2],c='b',s=3,lw=0,alpha=0.05)
axes[2,1].scatter(self.chain2d[:,1],self.chain2d[:,2],c='g',s=3,lw=0,alpha=0.05)
axes[1,0].scatter(self.best_pars[0],self.best_pars[1],c='r',marker='x',s=50,lw=2,alpha=1)
axes[2,0].scatter(self.best_pars[0],self.best_pars[2],c='b',marker='x',s=50,lw=2,alpha=1)
axes[2,1].scatter(self.best_pars[1],self.best_pars[2],c='g',marker='x',s=50,lw=2,alpha=1)
self.plot_2D_contours(xdata=self.chain2d[:,0],ydata=self.chain2d[:,1],axis=axes[1,0],c='r')
self.plot_2D_contours(xdata=self.chain2d[:,0],ydata=self.chain2d[:,2],axis=axes[2,0],c='b')
self.plot_2D_contours(xdata=self.chain2d[:,1],ydata=self.chain2d[:,2],axis=axes[2,1],c='g')
plt.show(block=False)
if __name__ == '__main__':
# m = MCMC_Output(drop_filt='f275w',sample_type='dropout',verbose=True)
# m = MCMC_Output(drop_filt='f336w',sample_type='dropout',verbose=True)
# m = MCMC_Output(drop_filt='f225w',sample_type='photoz',verbose=True)
m = MCMC_Output(drop_filt='f275w',sample_type='photoz',verbose=True)
# m = MCMC_Output(drop_filt='f336w',sample_type='photoz',verbose=True)
# m.plot_walkers()
# m.plot_corner()
m.plot_corner2()
plt.show()