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JcodeOM.py
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JcodeOM.py
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import yaml
import numpy as np
from math import *
from sys import argv
from scipy import special
from scipy.integrate import quad
from scipy import optimize as sciopt
from scipy.interpolate import interp1d as interp
from functions import integral2, Jfactor, get_data
from multiprocessing import Pool
################################################################################################################
# dwarf surface brightness profile
def I(R,rh):
return 4./3. * rh/(1+(R/rh)**2)**2
###########################################################
dwarf = argv[1]
R,v,dv,D,rh,rt = get_data(dwarf)
u=v.mean()
theta=0.5
r0_i,r0_f,Nr0 = 4,4,200
ra_i,ra_f,Nra = 4,4,200
case = 'OM_%s_%i%i%i%i_%i'%(dwarf,r0_i,r0_f,ra_i,ra_f,theta*10)
r0_array = np.logspace(-r0_i,r0_f,Nr0)
ra_array = np.logspace(-ra_i,ra_f,Nra)
gamma_array = R/rh
alpha_array = rh/r0_array
delta_array = ra_array/rh
A_array = np.array([gamma_array[i]/I(Ri,rh) for i,Ri in enumerate(R)])
I_array = np.zeros(shape=(len(A_array),len(ra_array),len(r0_array)))
def array_builder(gamma_array, delta_array, alpha_array):
for k,gamma in enumerate(gamma_array):
for i,delta in enumerate(delta_array):
for j,alpha in enumerate(alpha_array):
yield (k, i, j), (gamma, delta, alpha)
def proxy(args):
return args[0], A_array[args[0][0]]*integral2(*args[1])
pool = Pool(processes=4)
results = pool.map(proxy, array_builder(gamma_array, delta_array, alpha_array))
pool.close()
pool.join()
for idx,value in results:
I_array[idx] = value
Jf = np.sqrt([Jfactor(D,np.inf,r0,1.,theta) for r0 in r0_array])
cst = 8.*np.pi*4.3e-6
# Likelihood definition (for free beta)
def logLike(J,i,j):
I = cst*sqrt(J)*r0_array[j]**3*I_array[:,i,j]/Jf[j]
S = dv**2.+I
res = (np.log(S) + (v-u)**2./S).sum()
return res/2.
##########################################################################################################################################################
# fitting scheme
J_array = np.linspace(14,22,200)
J_new = np.empty([0])
min_LikeJ = np.empty([0])
min_ra_arr = np.empty([0])
min_r0_arr = np.empty([0])
for J in J_array: # scan over an array of J values
r0_new = np.empty([0])
ra_new = np.empty([0])
LikeJr0 = np.empty([0])
for j,r0 in enumerate(r0_array): # for each J scan over an array of r0 values
LikeJra = np.zeros_like(ra_array)
for i in range(ra_array.size): LikeJra[i] = logLike(10**J,i,j)
interp_Like_ra = interp(ra_array,LikeJra) # build the profile likelihood along ra
eval_Like_ra = np.logspace(log10(ra_array.min()),log10(ra_array.max()),1e3)
min_Like_ra = interp_Like_ra(eval_Like_ra).min()
min_ra = eval_Like_ra[np.where(interp_Like_ra(eval_Like_ra)==min_Like_ra)[0][0]]
if ra_array[1]<min_ra<ra_array[-2]:
LikeJr0 = np.append(LikeJr0,min_Like_ra)
ra_new = np.append(ra_new,min_ra)
r0_new = np.append(r0_new,r0)
if LikeJr0.size>3:
interp_ra = interp(r0_new,ra_new)
interp_r0 = interp(r0_new,LikeJr0) # build the profile likelihood along r0
eval_Like_r0 = np.logspace(log10(r0_new.min()),log10(r0_new.max()),1e3)
min_Like_r0 = interp_r0(eval_Like_r0).min()
min_r0 = eval_Like_r0[np.where(interp_r0(eval_Like_r0)==min_Like_r0)[0][0]]
if r0_new[1]<min_r0<r0_new[-2]:
min_ra_arr = np.append(min_ra_arr,interp_ra(min_r0))
min_r0_arr = np.append(min_r0_arr,min_r0)
min_LikeJ = np.append(min_LikeJ,min_Like_r0)
J_new = np.append(J_new,J)
##########################################################################################################################################################
# minimum and C.I. determination
interp_Like_J = interp(J_new,min_LikeJ)
interp_Like_ra = interp(J_new,min_ra_arr)
interp_Like_r0 = interp(J_new,min_r0_arr)
eval_Like_J = np.linspace(J_new.min(),J_new.max(),1e3)
min_Like_J = interp_Like_J(eval_Like_J).min()
J_min = eval_Like_J[np.where(interp_Like_J(eval_Like_J)==min_Like_J)[0][0]]
J_r0 = float(interp_Like_r0(J_min))
J_ra = float(interp_Like_ra(J_min))
J_rho0 = 10**sciopt.minimize_scalar(lambda log10rho0 : abs(J_min-np.log10(Jfactor(D,np.inf,J_r0,1.,theta))-2*log10rho0)).x
J1sL = round(sciopt.minimize_scalar(lambda J : np.abs(interp_Like_J(J)-interp_Like_J(J_min)-0.5),method='Bounded',bounds=(J_new[0],J_min)).x-J_min,2)
J1sR = round(sciopt.minimize_scalar(lambda J : np.abs(interp_Like_J(J)-interp_Like_J(J_min)-0.5),method='Bounded',bounds=(J_min,J_new[-1])).x-J_min,2)
J2sL = round(sciopt.minimize_scalar(lambda J : np.abs(interp_Like_J(J)-interp_Like_J(J_min)-2.),method='Bounded',bounds=(J_new[0],J_min)).x-J_min,2)
J2sR = round(sciopt.minimize_scalar(lambda J : np.abs(interp_Like_J(J)-interp_Like_J(J_min)-2.),method='Bounded',bounds=(J_min,J_new[-1])).x-J_min,2)
J3sL = round(sciopt.minimize_scalar(lambda J : np.abs(interp_Like_J(J)-interp_Like_J(J_min)-4.),method='Bounded',bounds=(J_new[0],J_min)).x-J_min,2)
J3sR = round(sciopt.minimize_scalar(lambda J : np.abs(interp_Like_J(J)-interp_Like_J(J_min)-4.),method='Bounded',bounds=(J_min,J_new[-1])).x-J_min,2)
if J_min+J3sL-0.1>J_new[0]: J_i = J_min+J3sL-0.1
else: J_i = J_new[0]
if J_min+J3sR+0.1<J_new[-1]: J_f = J_min+J3sR+0.1
else: J_f = J_new[-1]
J_plt = np.linspace(J_i,J_f,100)
np.save('results/LikeJ_%s'%case,np.vstack((J_plt,interp_Like_J(J_plt)-interp_Like_J(J_min))))
yaml.dump({'Nstars':R.size,'Jmin':J_min,'r0':J_r0,'rho0':J_rho0,'ra':J_ra,'J1sL':J1sL,'J1sR':J1sR,
'J2sL':J2sL,'J2sR':J2sR,'J3sL':J3sL,'J3sR':J3sR},open('results/results_%s.yaml'%case,'w'))