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MCMC.py
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MCMC.py
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# -*- coding: utf-8 -*-
"""
Created on Thu Aug 17 15:02:38 2017
@author: Qijingzhao
"""
__package__ = 'qcosmc'
import numpy as np
import emcee
import os
import sys
import scipy.optimize as opt
from time import strftime,localtime
import matplotlib.pyplot as plt
from getdist import MCSamples,loadMCSamples,plots
from getdist.gaussian_mixtures import GaussianND
from .FigStyle import qstyle
from .Decorator import timer
os.environ["OMP_NUM_THREADS"] = "1"
class MCMC_class(object):
def __init__(self,params,chi2,Chains_name,data_num=0,nwalkers=32):
self.chi2=chi2
self.Chains_name= Chains_name
self.data_num = data_num
self.params_all={'name':[p[0] for p in params], 'fit':np.asarray([p[1] for p in params],dtype=object),
'lower':np.asarray([p[2] for p in params],dtype=object),'upper':np.asarray([p[3] for p in params],dtype=object)}
self.n=len(self.params_all['name'])
self.theta_fit=np.zeros(self.n)
self.theta_fact=np.zeros(self.n)
self.nwalkers = nwalkers
self.pos=self.optimize()
def _lnprior(self,x):
i=0
while i<self.n:
if self.params_all['lower'][i]<=x[i]<=self.params_all['upper'][i]:
s=0.0
else:
s=-np.inf
break
i=i+1
return s
def _lik(self,theta):
return np.exp(-self.chi2(theta)/2.)
def _lnprob(self,theta):
lp = self._lnprior(theta)
if not np.isfinite(lp):
return -np.inf
return lp-self.chi2(theta)/2.
def _ff(self,theta):
return -2.0*self._lnprob(theta)
def _check_err(self,gv,fv):
if gv==fv:
while(True):
print('你的程序可能有问题。')
print('%s=%s'%(self.chi2.__name__,self.chi2(self.params_all['fit'])))
print('中断，按\'b\'，\n继续，按\'c\'。')
print('如果想要一些帮助，按\'h\'。')
p1=input()
if p1=='b':
sys.exit(0)
elif p1=='c':
return
elif p1=='h':
print('出现这个问题的原因通常是X^2_min值太大或者太小')
print('所以检查你的参数输入范围和中心值是否合理')
print('如果没问题，检查X^2值，看是否和你用的数据点查了好几个数量级，就下面这个值')
print('%s=%s'%(self.chi2.__name__,self.chi2(self.params_all['fit'])))
print('如果差了好几个数量级，那就是你chi2程序有问题。')
print('中断程序按\'b\'，继续跑按\'c\'')
p2=input()
if p2=='b':
sys.exit()
elif p2=='c':
break
else:
return
else:
print('输入错误，重新输入')
# def Rc(self,chains,nwalkers):
# R_c = np.linspace(0, 1, chains.shape[-1])
# print('-'*40)
# for i in range(chains.shape[-1]):
# para = chains[:,i]
# para_reshape = para.reshape((-1,nwalkers))
# para_reshape = para_reshape[para_reshape.shape[0]//2:para_reshape.shape[0],:] # the second half of each chain is used to check the convergence state
# walker_mean = np.mean(para_reshape, axis=0, keepdims=True) # mean of each walker
# var_mean = np.var(walker_mean) # variance between each walker
# walker_var = np.var(para_reshape, axis=0, keepdims=True) # variance of each walker
# mean_var = np.mean(walker_var)
# # sample from one walker ==> one chain
# # For multiple (nwalkers) chains the code computes the Gelman and Rubin "R statistic"
# # Please See Page 38 of "eprint arXiv:0712.3028" for the definitions of "R statistic"
# R_c[i] = (mean_var*(1.0-2.0/para_reshape.shape[0])+var_mean*(1.0+1.0/nwalkers))/mean_var
# print('R[%s]-1='%i+'%s'%abs(R_c[i]-1))
# return R_c
def savefile(self,sampler):
chains_dir='./chains/'
if not os.path.exists(chains_dir):
os.makedirs(chains_dir)
savefile_name='./chains/'+self.Chains_name+'.npy'
burnin = 50
samples = sampler.chain[:, burnin:, :].reshape((-1, self.n))
vv=lambda v: (v[1], v[2]-v[1], v[1]-v[0])
self.theta_fact= vv(np.percentile(samples, [16, 50, 84],axis=0))
self.minkaf=self.chi2(self.theta_fit)
self.samples=samples
ranges=list(zip(self.params_all['lower'],self.params_all['upper']))
np.save(savefile_name,(samples,self.params_all['name'],self.theta_fit,self.theta_fact,self.minkaf,self.data_num,ranges))
print('\nChains name is "%s".'%self.Chains_name+' data number:%s'%self.data_num)
def savefiles(self,sampler):
chains_dir='./chains/'
if not os.path.exists(chains_dir):
os.makedirs(chains_dir)
savefile_name='./chains/'+self.Chains_name
# tau = sampler.get_autocorr_time()
# burnin = int(2 * np.max(tau))
# thin = int(0.5 * np.min(tau))
# samples = sampler.get_chain(discard=burnin, flat=True, thin=thin)
burnin = 50
samples = sampler.chain[:, burnin:, :].reshape((-1, self.n))
# ranges=list(zip(self.params_all['lower'],self.params_all['upper']))
# minkaf=self.chi2(self.theta_fit)
# np.savez(savefile_name,sample=samples,names=self.params_all['name'],data_num=self.data_num,ranges=ranges,minkaf=minkaf,theta_fit=self.theta_fit)
# print('\nChains name is "%s".'%self.Chains_name+' data number:%s'%self.data_num)
vv=lambda v: (v[1], v[2]-v[1], v[1]-v[0])
self.theta_fact= vv(np.percentile(samples, [16, 50, 84],axis=0))
self.minkaf=self.chi2(self.theta_fit)
self.samples=samples
ranges=list(zip(self.params_all['lower'],self.params_all['upper']))
np.save(savefile_name,(samples,self.params_all['name'],self.theta_fit,self.theta_fact,self.minkaf,self.data_num,ranges))
print('\nChains name is "%s".'%self.Chains_name+' data number:%s'%self.data_num)
@timer
def MCMC(self,steps=10000,nc=1e-4,**kwargs):
print ('\n'+'='*50)
print (strftime("%Y-%m-%d %H:%M:%S",localtime())+'\n')
# Set up the sampler.
ndim= self.n
# print(pos)
sampler = emcee.EnsembleSampler(self.nwalkers, ndim, self._lnprob,**kwargs)
#print pos
# Clear and run the production chain.
print("Running MCMC...")
# try:
sampler.run_mcmc(self.pos, steps, progress=True)
# except ValueError:
# print(self.pos)
# raise ValueError("Probability function returned NaN")
print("Done.")
self.savefile(sampler)
return sampler
def optimize(self):
nc=1e-4
result = opt.minimize(self._ff,self.params_all['fit'],method='Nelder-Mead')
self.theta_fit= result['x']
# for i in range(self.n):
# print("""The best-fit value of {0}={1}""".format(self.params_all['name'][i],self.theta_fit[i]))
self._check_err(self.params_all['fit'][0],self.theta_fit[0])
pos = [result['x'] + nc*np.random.randn(self.n) for i in range(self.nwalkers)]
return pos
@timer
def runMC(self,max_n = 20000,**kwargs):
print ('\n'+'='*50)
print (strftime("%Y-%m-%d %H:%M:%S",localtime())+'\n')
# Set up the sampler.
sampler = emcee.EnsembleSampler(self.nwalkers, self.n, self._lnprob,**kwargs)
index = 0
autocorr = np.empty(max_n)
self.sampler=sampler
# This will be useful to testing convergence
old_tau = np.inf
# Now we'll sample for up to max_n steps
for sample in sampler.sample(self.pos, iterations=max_n, progress=True):
# Only check convergence every 100 steps
if sampler.iteration % 100:
continue
# Compute the autocorrelation time so far
# Using tol=0 means that we'll always get an estimate even
# if it isn't trustworthy
tau = sampler.get_autocorr_time(tol=0)
autocorr[index] = np.mean(tau)
index += 1
# Check convergence
converged = np.all(tau * 100 < sampler.iteration)
converged &= np.all(np.abs(old_tau - tau) / tau < 0.01)
if converged:
print('\n'+'='*50)
print("| The chains has converged.")
print('='*50)
break
old_tau = tau
self.savefiles(sampler)
print('| Done ')
def check(self,*arg):
if arg:
print('%s=%s'%(self.chi2.__name__,self.chi2(arg)))
else:
print('%s=%s'%(self.chi2.__name__,self.chi2(self.params_all['fit'])))
qstyle(0)
colors=['#348ABD', '#A60628', '#467821', '#7A68A6', '#E24A33' ,'#ffb3a6', '#188487']
lss=['-','--','-.',':']
outdir='./results/'
class MCplot(object):
def __init__(self,Chains,new_name=None,ignore_rows=0.0,ccolor=None):
self.root=[i[0] for i in Chains]
self.lengend=[i[1] for i in Chains]
self.aic_g=True
self.Samp=[]
self._n = len(Chains)
self.minkaf=np.zeros(self._n)
self.data_num=np.zeros(self._n)
self.ccolor=ccolor
# self.theta_fit=np.zeros(self._n)
# self.theta_fact=np.zeros(self._n)
for i in range(self._n):
savefile_name='./chains/'+self.root[i]+'.npy'
self.samples,self.theta_name,self.theta_fit,self.theta_fact,self.minkaf[i],self.data_num[i],ranges=np.load(savefile_name, allow_pickle=True)
if new_name:
self.theta_name=new_name
self.label_name=[x.replace('H_0','H_0 ~[\mathrm{km~s^{-1}~Mpc^{-1}}]') for x in self.theta_name]
self.Samp.append(MCSamples(samples=self.samples,names = self.theta_name, labels = self.label_name,ranges=ranges,settings={'ignore_rows':ignore_rows}))
self.param_names=[]
for na in self.Samp[0].getParamNames().names:
self.param_names.append(na.name)
def rename(self,new_name):
for i in range(self._n):
savefile_name='./chains/'+self.root[i]+'.npy'
samples,self.theta_name,self.theta_fit,self.theta_fact,self.minkaf[i],self.data_num[i],ranges=np.load(savefile_name, allow_pickle=True)
np.save(savefile_name,(samples,new_name,self.theta_fit,self.theta_fact,self.minkaf[i],self.data_num[i],ranges))
self.param_names=[]
for na in self.Samp[0].getParamNames().names:
self.param_names.append(na.name)
def plot1D(self,n,colorn=0,width_inch=8,**kwargs):
# if colorn:
# colors=cmap.colors
g = plots.getSinglePlotter(width_inch=width_inch)
g.plot_1d(self.Samp,self.param_names[n-1],ls=lss,colors=colors[colorn:colorn+self._n],lws=[1.5]*self._n,**kwargs)
# g.settings.figure_legend_frame = False
ax=plt.gca()
if all(self.lengend):
leg = ax.legend(self.lengend,loc=1,fontsize=16,frameon=False)
for line,text in zip(leg.get_lines(), leg.get_texts()):
text.set_color(line.get_color())
if 'x_marker' in kwargs:
g.add_x_marker(kwargs['x_marker'],lw=1.5)
# if 'x_bands' in kwargs:
# g.add_x_bands(0,0.01)
if 'xaxis' in kwargs:
ax.xaxis.set_major_locator(plt.MultipleLocator(kwargs['xaxis']))
if 'title' in kwargs:
ax.set_title(kwargs['title'])
# plt.tight_layout()
if 'name' in kwargs:
g.export(os.path.join(outdir,'%s.pdf'%kwargs['name']))
else:
g.export(os.path.join(outdir+''.join(self.root)+self.param_names[n-1].replace('\\','')+'_1D.pdf'))
return g
def plot2D(self,pp,colorn=0,contour_num=2,width_inch=8,**kwargs):
g = plots.getSinglePlotter(width_inch=width_inch,ratio=1)
if self.ccolor:
g.settings.solid_colors=self.ccolor
g.settings.num_plot_contours = contour_num
g.settings.axes_fontsize = 14
g.settings.lab_fontsize = 18
g.settings.legend_frame = False
g.plot_2d(self.Samp,self.param_names[pp[0]-1],self.param_names[pp[1]-1],filled=True,**kwargs)
if 'x_locator' in kwargs:
ax=g.get_axes()
ax.xaxis.set_major_locator(plt.MultipleLocator(kwargs['x_locator']))
del kwargs['x_locator']
if 'y_locator' in kwargs:
ax=g.get_axes()
ax.yaxis.set_major_locator(plt.MultipleLocator(kwargs['y_locator']))
del kwargs['y_locator']
if 'lims' in kwargs:
[xmin, xmax, ymin, ymax]=kwargs['lims']
plt.xlim(xmin, xmax)
plt.ylim(ymin, ymax)
del kwargs['lims']
if 'x_marker' in kwargs:
g.add_x_marker(kwargs['x_marker'],lw=1.5)
if all(self.lengend):
kwarg=kwargs.copy()
if 'name' in kwarg: del kwarg['name']
g.add_legend(self.lengend,colored_text=True, fontsize=16,**kwarg)
# plt.tight_layout()
if 'name' in kwargs:
g.export(os.path.join(outdir,'%s.pdf'%kwargs['name']))
else:
g.export(os.path.join(outdir,''.join(self.root)+'_2D.pdf'))
return g
def plot3D(self,pp,colorn=None,contour_num=2,**kwargs):
if colorn:
cmap=plt.get_cmap(self.ccolor)
colors=cmap.colors
colorss=colors[colorn-1:colorn-1+self._n]
else:
colorss=None
if pp==0:
t_name=self.param_names
else:
t_name=[]
for i in pp:
t_name.append(self.param_names[i-1])
g = plots.get_subplot_plotter(width_inch=9)
if self.ccolor:
g.settings.solid_colors=self.ccolor
g.settings.num_plot_contours = contour_num
g.settings.legend_fontsize = 20
g.settings.axes_fontsize = 14
g.settings.lab_fontsize = 18
g.settings.figure_legend_frame = False
g.settings.alpha_filled_add=0.8
if all(self.lengend):
print(t_name)
g.triangle_plot(self.Samp,t_name,filled_compare=True,contour_lws=2,legend_labels=self.lengend,contour_colors=colorss,legend_loc='upper right',**kwargs)
else:
g.triangle_plot(self.Samp,t_name,filled_compare=True,contour_lws=2,contour_colors=colorss,**kwargs)
if 'xlim' in kwargs:
for xi in kwargs['xlim']:
for ax in g.subplots[:,xi[0]-1]:
if ax is not None:
ax.set_xlim(xi[1][0],xi[1][1])
if 'tline' in kwargs:
for ax in g.subplots[:,0]:
ax.axvline(kwargs['tline'], color='k', ls='--',alpha=0.5)
# plt.tight_layout()
if 'ax_range' in kwargs:
for axi in kwargs['ax_range']:
g.subplots[-1,axi[0]-1].xaxis.set_major_locator(plt.MultipleLocator(axi[1]))
if axi[0]-1>0:
g.subplots[axi[0]-1,0].yaxis.set_major_locator(plt.MultipleLocator(axi[1]))
if 'name' in kwargs:
g.export(os.path.join(outdir,'%s.pdf'%kwargs['name']))
else:
g.export(os.path.join(outdir,''.join(self.root)+'_tri.pdf'))
return g
@property
def results(self):
re=[]
for k in range(self._n):
n=len(self.Samp[k].getParamNames().names)
pnames=self.Samp[k].getParamNames().names
plt.figure(figsize=(10,6+(n-1)), dpi=90)
plt.axes([0.025,0.025,0.95,0.95])
plt.xticks([]), plt.yticks([])
plt.text(0.1,0.9,'The results of "{0}":'.format(self.root[k].replace('_',' ')), fontsize=18)
plt.text(0.2,0.83,'$1\sigma$',fontsize=14)
plt.text(0.7,0.83,'$2\sigma$',fontsize=14)
size = 20
for i in range(n):
# eqs="${{{0}}}^{{+{1}}}_{{-{2}}}$".format(round(theta_fact[i][0],5),round(theta_fact[i][1],5),round(theta_fact[i][2],5))
# tt="${0}$ = {1}".format(pnames[i].label,eqs)
tt='$%s$'%(self.Samp[k].getInlineLatex(pnames[i].name,limit=1))
re.append(tt)
tt2='$%s$'%(self.Samp[k].getInlineLatex(pnames[i].name,limit=2))
x,y = (0.1,0.75-i*0.12)
xx,yy=(0.6,0.75-i*0.12)
plt.text(x,y,tt, fontsize=size)
plt.text(xx,yy,tt2, fontsize=size)
if self.aic_g:
aic="$\mathrm{{AIC}}$=${0}$".format(round(self.minkaf[k]+2.0*n,3))
bic="$\mathrm{{BIC}}$=${0}$".format(round(self.minkaf[k]+n*np.log(self.data_num[k]),3))
kafm="$\chi^2_{{min}}$=${0}$".format(round(self.minkaf[k],3))
dof="$\chi^2_{{min}}/d.o.f.$=${0}$".format(round(self.minkaf[k]/(n+self.data_num[k]),3))
plt.text(0.1,0.8-(n+1)*0.11,kafm,fontsize=size)
plt.text(0.6,0.8-(n+1)*0.11,dof,fontsize=size)
plt.text(0.1,0.8-(n+2)*0.11,aic,fontsize=size)
plt.text(0.6,0.8-(n+2)*0.11,bic,fontsize=size)
plt.savefig(outdir+self.root[k]+'_results.png',dpi=300)
for i in range(self._n):
print(', '.join(re[i:i+n])+'\n')
return re
@property
def results2(self):
re=[]
for k in range(self._n):
n=len(self.Samp[k].getParamNames().names)
pnames=self.label_name
plt.figure(figsize=(10,6+(n-1)), dpi=90)
plt.axes([0.025,0.025,0.95,0.95])
plt.xticks([]), plt.yticks([])
plt.text(0.1,0.9,'The results of "{0}":'.format(self.root[k].replace('_',' ')), fontsize=18)
plt.text(0.5,0.83,'$1\sigma$',fontsize=14)
# plt.text(0.7,0.83,'$2\sigma$',fontsize=14)
size = 20
for i in range(n):
mcmc = np.percentile(self.Samp[k].samples[:, i], [16, 50, 84])
q = np.diff(mcmc)
txt = "$\mathrm{{{3}}} = {0:.3f}_{{-{1:.3f}}}^{{+{2:.3f}}}$"
tt = txt.format(mcmc[1], q[0], q[1], pnames[i])
# tt='$%s$'%(self.Samp[k].getInlineLatex(pnames[i].name,limit=1))
re.append(tt)
x,y = (0.2,0.75-i*0.12)
plt.text(x,y,tt, fontsize=size)
if self.aic_g:
aic="$\mathrm{{AIC}}$=${0}$".format(round(self.minkaf[k]+2.0*n,3))
bic="$\mathrm{{BIC}}$=${0}$".format(round(self.minkaf[k]+n*np.log(self.data_num[k]),3))
kafm="$\chi^2_{{min}}$=${0}$".format(round(self.minkaf[k],3))
dof="$\chi^2_{{min}}/d.o.f.$=${0}$".format(round(self.minkaf[k]/(n+self.data_num[k]),3))
plt.text(0.1,0.8-(n+1)*0.11,kafm,fontsize=size)
plt.text(0.6,0.8-(n+1)*0.11,dof,fontsize=size)
plt.text(0.1,0.8-(n+2)*0.11,aic,fontsize=size)
plt.text(0.6,0.8-(n+2)*0.11,bic,fontsize=size)
plt.savefig(outdir+self.root[k]+'_results2.png',dpi=300)
for i in range(self._n):
print(', '.join(re[i:i+n])+'\n')
return re
class Fisherplot(MCplot):
def __init__(self,mean,Cov,labels,lengend='',nsample=1000000):
self.mean = mean
self.Cov = Cov
self.param_names = labels
self.lengend = [lengend]
self.nsample = nsample
self._n = 1
self.root = [lengend]
self.init()
self.aic_g=False
def init(self):
# self.param_names=[x.replace('H_0','H_0 ~[\mathrm{km~s^{-1}~Mpc^{-1}}]') for x in self.param_names]
gauss=GaussianND(self.mean, self.Cov ,names = self.param_names, labels =self.param_names)
self.Samp = [gauss.MCSamples(self.nsample)]
def addCov(self,mean,Cov,lengend):
gauss=GaussianND(mean, Cov ,names = self.param_names, labels =self.param_names)
self.Samp.append(gauss.MCSamples(self.nsample))
self.lengend.append(lengend)
self._n = len(self.Samp)
self.root.append(lengend)
def addChains(self,Chains,ignore_rows=0.3):
root=[i[0] for i in Chains]
lengend=[i[1] for i in Chains]
n = len(Chains)
for i in range(n):
savefile_name='./chains/'+root[i]+'.npy'
samples,theta_name,theta_fit,theta_fact,minkaf,data_num,ranges=np.load(savefile_name, allow_pickle=True)
self.Samp.append(MCSamples(samples=samples,names = theta_name, labels = theta_name,ranges=ranges,settings={'ignore_rows':ignore_rows}))
self.param_names=[]
for na in self.Samp[-1].getParamNames().names:
self.param_names.append(na.name)
self.lengend+=lengend
self._n = len(self.Samp)
self.root+=root
class CMCplot(MCplot):
def __init__(self,Chains,ignore_rows=0.3):
self.root=[i[0] for i in Chains]
self.lengend=[i[1] for i in Chains]
self.aic_g=False
self.Samp=[]
self._n = len(Chains)
self.minkaf=np.zeros(self._n)
self.data_num=np.zeros(self._n)
for i in list(range(self._n)):
self.Samp.append(loadMCSamples('./chains/'+self.root[i], settings={'ignore_rows':ignore_rows}))
self.param_names=[]
for na in self.Samp[0].getParamNames().names:
self.param_names.append(na.name)