/
mcmc_pal5.py
277 lines (270 loc) · 13 KB
/
mcmc_pal5.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
###############################################################################
# mcmc_pal5.py: module to run MCMC analysis of the Pal 5 stream
###############################################################################
import sys
import os, os.path
import copy
import time
import pickle
import csv
from optparse import OptionParser
import subprocess
import warnings
import numpy
from scipy.misc import logsumexp
import emcee
import pal5_util
_DATADIR= os.getenv('DATADIR')
def get_options():
usage = "usage: %prog [options]"
parser = OptionParser(usage=usage)
# Potential parameters
parser.add_option("--bf_b15",action="store_true",
dest="bf_b15",default=False,
help="If set, use the best-fit to the MWPotential2014 data")
parser.add_option("--seed",dest='seed',default=1,type='int',
help="seed for everything except for potential")
parser.add_option("--fitsigma",action="store_true",
dest="fitsigma",default=False,
help="If set, fit for the velocity-dispersion parameter")
parser.add_option("--dt",dest='dt',default=10.,type='float',
help="Run MCMC for this many minutes")
parser.add_option("-i",dest='pindx',default=None,type='int',
help="Index into the potential samples to consider")
parser.add_option("--ro",dest='ro',default=pal5_util._REFR0,type='float',
help="Distance to the Galactic center in kpc")
parser.add_option("--td",dest='td',default=5.,type='float',
help="Age of the stream")
parser.add_option("--samples_savefilename",
dest='samples_savefilename',
default='mwpot14varyc-samples.pkl',
help="Name of the file that contains the potential samples")
# Output file
parser.add_option("-o",dest='outfilename',
default=None,
help="Name of the file that will hold the output")
# Multi-processing
parser.add_option("-m",dest='multi',default=1,type='int',
help="Number of CPUs to use for streamdf setup")
return parser
def filelen(filename):
p= subprocess.Popen(['wc','-l',filename],stdout=subprocess.PIPE,
stderr=subprocess.PIPE)
result,err = p.communicate()
if p.returncode != 0:
raise IOError(err)
return int(result.strip().split()[0])
def load_samples(options):
if os.path.exists(options.samples_savefilename):
with open(options.samples_savefilename,'rb') as savefile:
s= pickle.load(savefile)
else:
raise IOError("File %s that is supposed to hold the potential samples does not exist" % options.samples_savefilename)
return s
def find_starting_point(options,pot_params,dist,pmra,pmdec,sigv):
# Find a decent starting point, useTM to speed this up, bc it doesn't matter much
interpcs=[0.65,0.75,0.875,1.,1.125,1.25,1.5,1.65]
cs= numpy.arange(0.7,1.61,0.01)
pal5varyc_like= pal5_util.predict_pal5obs(pot_params,cs,
dist=dist,pmra=pmra,pmdec=pmdec,
sigv=sigv,td=options.td,
ro=options.ro,vo=220.,
interpk=1,
interpcs=interpcs,useTM=True,
trailing_only=True,verbose=False)
pos_radec, rvel_ra= pal5_util.pal5_data()
if options.fitsigma:
lnlike= numpy.sum(\
pal5_util.pal5_lnlike(pos_radec,rvel_ra,
pal5varyc_like[0],
pal5varyc_like[1],
pal5varyc_like[2],
pal5varyc_like[3],
pal5varyc_like[4],
pal5varyc_like[5],
pal5varyc_like[6])[:,:3:2],axis=1)
else:
# For each one, move the track up and down a little to simulate sig changes
deco= numpy.linspace(-0.5,0.5,101)
lnlikes= numpy.zeros((len(cs),len(deco)))-100000000000000000.
for jj,do in enumerate(deco):
tra= pal5varyc_like[0]
tra[:,:,1]+= do
lnlikes[:,jj]= pal5_util.pal5_lnlike(pos_radec,rvel_ra,
tra,pal5varyc_like[1],
pal5varyc_like[2],
pal5varyc_like[3],
pal5varyc_like[4],
pal5varyc_like[5],
pal5varyc_like[6])[:,0]
lnlike= numpy.amax(lnlikes,axis=1)
return cs[numpy.argmax(lnlike)]
def lnp(p,pot_params,options):
warnings.filterwarnings("ignore",
message="Using C implementation to integrate orbits")
#p=[c,vo/220,dist/22.,pmo_parallel,pmo_perp] and ln(sigv) if fitsigma
c= p[0]
vo= p[1]*pal5_util._REFV0
dist= p[2]*22.
pmra= -2.296+p[3]+p[4]
pmdecpar= 2.257/2.296
pmdecperp= -2.296/2.257
pmdec= -2.257+p[3]*pmdecpar+p[4]*pmdecperp
if options.fitsigma:
sigv= 0.4*numpy.exp(p[5])
else:
sigv= 0.4
# Priors
if c < 0.5: return -100000000000000000.
elif c > 2.: return -10000000000000000.
elif vo < 200: return -10000000000000000.
elif vo > 250: return -10000000000000000.
elif dist < 19.: return -10000000000000000.
elif dist > 24.: return -10000000000000000.
elif options.fitsigma and sigv < 0.1: return -10000000000000000.
elif options.fitsigma and sigv > 1.: return -10000000000000000.
# Setup the model
pal5varyc_like= pal5_util.predict_pal5obs(pot_params,c,singlec=True,
dist=dist,pmra=pmra,pmdec=pmdec,
ro=options.ro,vo=vo,
trailing_only=True,verbose=False,
sigv=sigv,td=options.td,
useTM=False,
nTrackChunks=8)
pos_radec, rvel_ra= pal5_util.pal5_data()
if options.fitsigma:
lnlike= pal5_util.pal5_lnlike(pos_radec,rvel_ra,
pal5varyc_like[0],
pal5varyc_like[1],
pal5varyc_like[2],
pal5varyc_like[3],
pal5varyc_like[4],
pal5varyc_like[5],
pal5varyc_like[6])
if not pal5varyc_like[7]: addllnlike= -15. # penalize
else: addllnlike= 0.
#print addllnlike, pal5varyc_like[7]
#sys.stdout.flush()
return lnlike[0,0]+lnlike[0,2]+addllnlike+\
-0.5*(pmra+2.296)**2./0.186**2.-0.5*(pmdec+2.257)**2./0.181**2.
# If not fitsigma, move the track up and down a little to simulate sig changes
deco= numpy.linspace(-0.5,0.5,101)
lnlikes= numpy.zeros(len(deco))-100000000000000000.
for jj,do in enumerate(deco):
tra= copy.deepcopy(pal5varyc_like[0])
tra[:,:,1]+= do
lnlikes[jj]= pal5_util.pal5_lnlike(pos_radec,rvel_ra,
tra,pal5varyc_like[1],
pal5varyc_like[2],
pal5varyc_like[3],
pal5varyc_like[4],
pal5varyc_like[5],
pal5varyc_like[6])[0,0]
return logsumexp(lnlikes)\
+pal5_util.pal5_lnlike(pos_radec,rvel_ra,
pal5varyc_like[0],pal5varyc_like[1],
pal5varyc_like[2],pal5varyc_like[3],
pal5varyc_like[4],pal5varyc_like[5],
pal5varyc_like[6])[0,2]\
-0.5*(pmra+2.296)**2./0.186**2.-0.5*(pmdec+2.257)**2./0.181**2.
if __name__ == '__main__':
parser= get_options()
options,args= parser.parse_args()
# Set random seed for potential selection
numpy.random.seed(1)
# Load potential parameters
if options.bf_b15:
pot_params= [0.60122692,0.36273147,-0.97591502,-3.34169377,
0.71877924,-0.01519337,-0.01928001]
else:
pot_samples= load_samples(options)
rndindx= numpy.random.permutation(pot_samples.shape[1])[options.pindx]
pot_params= pot_samples[:,rndindx]
print pot_params
# Now set the seed for the MCMC
numpy.random.seed(options.seed)
nwalkers= 10+2*options.fitsigma
# For a fiducial set of parameters, find a good fit to use as the starting
# point
all_start_params= numpy.zeros((nwalkers,5+options.fitsigma))
start_lnprob0= numpy.zeros(nwalkers)
if not os.path.exists(options.outfilename):
pmra= -2.296
pmdec= -2.257
dist= 23.2
#cstart= find_starting_point(options,pot_params,dist,pmra,pmdec,0.4)
cstart= 1.
if cstart > 1.15: cstart= 1.15 # Higher c doesn't typically really work
if options.fitsigma:
start_params= numpy.array([cstart,1.,dist/22.,0.,0.,0.])
step= numpy.array([0.05,0.05,0.05,0.05,0.01,0.05])
else:
start_params= numpy.array([cstart,1.,dist/22.,0.,0.])
step= numpy.array([0.05,0.05,0.05,0.05,0.01])
nn= 0
while nn < nwalkers:
all_start_params[nn]= start_params\
+numpy.random.normal(size=len(start_params))*step
start_lnprob0[nn]= lnp(all_start_params[nn],pot_params,options)
if start_lnprob0[nn] > -1000000.:
print all_start_params[nn], start_lnprob0[nn]
if start_lnprob0[nn] > -1000000.: nn+= 1
else:
# Get the starting point from the output file
with open(options.outfilename,'rb') as savefile:
all_lines= savefile.readlines()
for nn in range(nwalkers):
lastline= all_lines[-1-nn]
tstart_params= numpy.array([float(s) for s in lastline.split(',')])
start_lnprob0[nn]= tstart_params[-1]
all_start_params[nn]= tstart_params[:-1]
# Output
if os.path.exists(options.outfilename):
outfile= open(options.outfilename,'a',0)
else:
# Setup the file
outfile= open(options.outfilename,'w',0)
outfile.write('# potparams:%.8f,%.8f,%.8f,%.8f,%.8f\n' % \
(pot_params[0],pot_params[1],pot_params[2],
pot_params[3],pot_params[4]))
for nn in range(nwalkers):
if options.fitsigma:
outfile.write('%.8f,%.8f,%.8f,%.8f,%.8f,%.8f,%.8f\n' % \
(all_start_params[nn,0],all_start_params[nn,1],
all_start_params[nn,2],all_start_params[nn,3],
all_start_params[nn,4],all_start_params[nn,5],
start_lnprob0[nn]))
else:
outfile.write('%.8f,%.8f,%.8f,%.8f,%.8f,%.8f\n' % \
(all_start_params[nn,0],all_start_params[nn,1],
all_start_params[nn,2],all_start_params[nn,3],
all_start_params[nn,4],start_lnprob0[nn]))
outfile.flush()
outwriter= csv.writer(outfile,delimiter=',')
# Run MCMC
sampler= emcee.EnsembleSampler(nwalkers,all_start_params.shape[1],
lnp,args=(pot_params,options),
threads=options.multi)
rstate0= numpy.random.mtrand.RandomState().get_state()
start= time.time()
while time.time() < start+options.dt*60.:
new_params, new_lnp, new_rstate0=\
sampler.run_mcmc(all_start_params,1,lnprob0=start_lnprob0,
rstate0=rstate0,storechain=False)
all_start_params= new_params
start_lnprob0= new_lnp
rstate0= new_rstate0
for nn in range(nwalkers):
if options.fitsigma:
outfile.write('%.8f,%.8f,%.8f,%.8f,%.8f,%.8f,%.8f\n' % \
(all_start_params[nn,0],all_start_params[nn,1],
all_start_params[nn,2],all_start_params[nn,3],
all_start_params[nn,4],all_start_params[nn,5],
start_lnprob0[nn]))
else:
outfile.write('%.8f,%.8f,%.8f,%.8f,%.8f,%.8f\n' % \
(all_start_params[nn,0],all_start_params[nn,1],
all_start_params[nn,2],all_start_params[nn,3],
all_start_params[nn,4],start_lnprob0[nn]))
outfile.flush()
outfile.close()