-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathprofilefit.py
127 lines (120 loc) · 4.73 KB
/
profilefit.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
import numpy as np
from scipy import integrate
from scipy.optimize import fmin_l_bfgs_b,curve_fit
def NFWprofile(r,rs,rhos):
x = r/rs
return rhos/(x*(1+x)**2)
def M99profile(r,rM,rhoM):
x = r/rM
return rhoM/(x**1.5 *(1+x)**1.5)
def EINprofile(r,r2,rho2,alpha):
x = r/r2
return rho2 * np.exp(-2/alpha * (x**alpha - 1))
def logNFWprofile(r,rs,logrhos):
x = r/rs
return logrhos-np.log10(x*(1+x)**2)
def logM99profile(r,rM,logrhoM):
x = r/rM
return logrhoM-np.log10(x**1.5 *(1+x)**1.5)
def logEINprofile(r,r2,logrho2,alpha):
x = r/r2
return logrho2+np.log10(np.e)*(-2/alpha * (x**alpha - 1))
def _ufunclike(f,x):
return np.array(map(f,np.ravel(x)))
def NFWmltr(r,rs,rhos):
def f(r):
return 4*np.pi*integrate.quad(lambda x: x*x*NFWprofile(x,rs,rhos),0,r)[0]
return _ufunclike(f,r)
def NFWmltr_analytic(r,rs,rhos):
def F(t):
return np.log(1+t)-t/(1.+t)
def f(r):
return 4*np.pi*rhos*rs**3*F(r/rs)
return _ufunclike(f,r)
def M99mltr(r,rM,rhoM):
return NotImplementedError
def EINmltr(r,r2,rho2,alpha):
def f(r):
return 4*np.pi*integrate.quad(lambda x: x*x*EINprofile(x,r2,rho2,alpha),0,r)[0]
return _ufunclike(f,r)
def calc_rhoarr(rbin,dr,mpart):
Varr = 4*np.pi/3 * (rbin[1:]**3-rbin[:-1]**3)
h,x = np.histogram(dr,bins=rbin)
Marr = h*mpart
return Marr/Varr
def _Q2(y1,y2):
assert len(y1)==len(y2)
return np.sum((y1-y2)**2)/len(y1)
def fitNFW(rarr,rhoarr,p0,verbose=False,retQ2=False,minr=None,maxr=None):
rmid = 10**((np.log10(rarr[1:])+np.log10(rarr[:-1]))/2.)
assert len(rmid) == len(rhoarr)
logrho = np.log10(rhoarr)
ii = np.isfinite(logrho); rmid = rmid[ii]; logrho = logrho[ii]
if minr != None:
ii = rmid >= minr; rmid = rmid[ii]; logrho = logrho[ii]
if maxr != None:
ii = rmid <= maxr; rmid = rmid[ii]; logrho = logrho[ii]
pNFW = curve_fit(logNFWprofile,rmid,logrho,p0=p0)[0]
Q2 = _Q2(logrho,logNFWprofile(rmid,pNFW[0],pNFW[1]))
if verbose: print "NFW Fit value:",pNFW,Q2
if retQ2: return pNFW[0],10**pNFW[1],Q2
return pNFW[0],10**pNFW[1]
def fitM99(rarr,rhoarr,p0,verbose=False,retQ2=False,minr=None,maxr=None):
rmid = 10**((np.log10(rarr[1:])+np.log10(rarr[:-1]))/2.)
assert len(rmid) == len(rhoarr)
logrho = np.log10(rhoarr)
ii = np.isfinite(logrho); rmid = rmid[ii]; logrho = logrho[ii]
if minr != None:
ii = rmid >= minr; rmid = rmid[ii]; logrho = logrho[ii]
if maxr != None:
ii = rmid <= maxr; rmid = rmid[ii]; logrho = logrho[ii]
pM99 = curve_fit(logM99profile,rmid,logrho,p0=p0)[0]
Q2 = _Q2(logrho,logM99profile(rmid,pM99[0],pM99[1]))
if verbose: print "M99 Fit value:",pM99,Q2
if retQ2: return pM99[0],10**pM99[1],Q2
return pM99[0],10**pM99[1]
def fitEIN(rarr,rhoarr,p0,verbose=False,retQ2=False,minr=None,maxr=None):
rmid = 10**((np.log10(rarr[1:])+np.log10(rarr[:-1]))/2.)
assert len(rmid) == len(rhoarr)
logrho = np.log10(rhoarr)
ii = np.isfinite(logrho); rmid = rmid[ii]; logrho = logrho[ii]
if minr != None:
ii = rmid >= minr; rmid = rmid[ii]; logrho = logrho[ii]
if maxr != None:
ii = rmid <= maxr; rmid = rmid[ii]; logrho = logrho[ii]
pEIN = curve_fit(logEINprofile,rmid,logrho,p0=p0,maxfev=1000000)
pEIN = pEIN[0]
Q2 = _Q2(logrho,logEINprofile(rmid,pEIN[0],pEIN[1],pEIN[2]))
if verbose: print "EIN Fit value:",pEIN,Q2
if retQ2: return pEIN[0],10**pEIN[1],pEIN[2],Q2
return pEIN[0],10**pEIN[1],pEIN[2]
#def fitNFW(rarr,rhoarr,x0=[.05,6.5],bounds=[(.001,3),(5,8)],verbose=False):
# nbins = len(rarr)
# logrho = np.log10(rhoarr)
# def Q2(x):
# rs,logrhos = x
# logrhomodel = logNFWprofile(rarr,rs,logrhos)
# return np.sum((logrho-logrhomodel)**2)/nbins
# x,f,d = fmin_l_bfgs_b(Q2,x0,approx_grad=True,bounds=bounds)
# if verbose: print "NFW Fit value:",x,Q2(x)
# return x[0],10**x[1]
#def fitM99(rarr,rhoarr,x0=[.05,6.5],bounds=[(.001,3),(5,8)],verbose=False):
# nbins = len(rarr)
# logrho = np.log10(rhoarr)
# def Q2(x):
# rs,logrhos = x
# logrhomodel = logM99profile(rarr,rs,logrhos)
# return np.sum((logrho-logrhomodel)**2)/nbins
# x,f,d = fmin_l_bfgs_b(Q2,x0,approx_grad=True,bounds=bounds)
# if verbose: print "M99 Fit value:",x,Q2(x)
# return x[0],10**x[1]
#def fitEinasto(rarr,rhoarr,x0=[.05,6.5,.17],bounds=[(.001,3),(5,8),(.01,.3)],verbose=False):
# nbins = len(rarr)
# logrho = np.log10(rhoarr)
# def Q2(x):
# r2,logrho2,alpha = x
# logrhomodel = logEINprofile(rarr,r2,logrho2,alpha)
# return np.sum((logrho-logrhomodel)**2)/nbins
# x,f,d = fmin_l_bfgs_b(Q2,x0,approx_grad=True,bounds=bounds)
# if verbose: print "EIN Fit value:",x,Q2(x)
# return x[0],10**x[1],x[2]