def __init__(self,cdts,Rcut,hyp,Dist,centre_init):
"""
Constructor of the logposteriorModule
"""
rad,thet = Deg2pc(cdts,centre_init,Dist)
c,r,t,self.Rmax = TruncSort(cdts,rad,thet,Rcut)
self.pro = c[:,2]
self.cdts = c[:,:2]
self.Dist = Dist
#-------------- Finds the mode of the band -------
band_all = c[:,3]
idv = np.where(np.isfinite(c[:,3]))[0]
band = c[idv,3]
kde = st.gaussian_kde(band)
x = np.linspace(np.min(band),np.max(band),num=1000)
self.mode = x[kde(x).argmax()]
print "Mode of band at ",self.mode
#---- repleace NANs by mode -----
idnv = np.setdiff1d(np.arange(len(band_all)),idv)
band_all[idnv] = self.mode
self.delta_band = band_all - self.mode
#------------- poisson ----------------
self.quadrants = [0,np.pi/2.0,np.pi,3.0*np.pi/2.0,2.0*np.pi]
self.poisson = st.poisson(len(r)/4.0)
#-------------- priors ----------------
self.Prior_0 = st.norm(loc=centre_init[0],scale=hyp[0])
self.Prior_1 = st.norm(loc=centre_init[1],scale=hyp[1])
self.Prior_2 = st.uniform(loc=-0.5*np.pi,scale=np.pi)
self.Prior_3 = st.halfcauchy(loc=0.01,scale=hyp[2])
self.Prior_4 = st.halfcauchy(loc=0.01,scale=hyp[2])
self.Prior_5 = st.truncexpon(b=hyp[3],loc=2.01,scale=hyp[4])
self.Prior_6 = st.norm(loc=hyp[5],scale=hyp[6])
print "Module Initialized"
def LogLike(self, params, ndim, nparams):
ctr = params[:2]
rc = params[2]
g = params[3]
#----- Checks if parameters' values are in the ranges
#----- only needed if prior is not properly set
# if not Support(rc,g):
# return -1e50
#------- Obtains radii and angles ---------
radii, theta = Deg2pc(self.cdts, ctr, self.Dist)
############### Radial likelihood ###################
lf = (1.0 - self.pro) * LikeField(radii, self.Rmax)
lk = radii * (self.pro) * Kernel(radii, rc, g)
# Normalisation constant
y = rc**2 + self.Rmax**2
# print rc,g
a = (1.0 / (g - 2.0)) * (1.0 - (rc**(g - 2.0)) *
(y**(1.0 - 0.5 * g))) # Truncated at Rm
# a = 1.0/(g-2.0) # No truncated
k = 1.0 / (a * (rc**2.0))
llike_r = np.sum(np.log((k * lk + lf)))
##################### POISSON ###################################
quarter = cut(theta, bins=self.quadrants, include_lowest=True)
counts = value_counts(quarter)
llike_t = self.poisson.logpmf(counts).sum()
##################################################################
llike = llike_t + llike_r
# print(llike)
return llike
def LogLike(self,params,ndim,nparams):
ctr= params[:2]
rc = params[2]
a = params[3]
b = params[4]
#----- Checks if parameters' values are in the ranges
# if not Support(rc,a,b) :
# return -1e50
#------- Obtains radii and angles ---------
radii,theta = Deg2pc(self.cdts,ctr,self.Dist)
############### Radial likelihood ###################
# Computes likelihood
lf = (1.0-self.pro)*LikeField(radii,self.Rmax)
lk = radii*(self.pro)*Kernel(radii,rc,a,b)
# Normalisation constant
x = -1.0*((rc/self.Rmax)**(-1.0/a))
c = (self.Rmax**2)*hyp2f1(2.0*a,a*b,1 + 2.0*a,x).real
k = 2.0/c
llike_r = np.sum(np.log((k*lk + lf)))
##################### POISSON ###################################
quarter = cut(theta,bins=self.quadrants,include_lowest=True)
counts = value_counts(quarter)
llike_t = self.poisson.logpmf(counts).sum()
##################################################################
llike = llike_t + llike_r
# print(llike)
return llike
def __init__(self, cdts, Rcut, hyp, Dist, centre_init):
"""
Constructor of the logposteriorModule
"""
rad, thet = Deg2pc(cdts, centre_init, Dist)
c, r, t, self.Rmax = TruncSort(cdts, rad, thet, Rcut)
self.pro = c[:, 2]
self.cdts = c[:, :2]
self.Dist = Dist
#------------- poisson ----------------
self.quadrants = [
0, np.pi / 2.0, np.pi, 3.0 * np.pi / 2.0, 2.0 * np.pi
]
self.poisson = st.poisson(len(r) / 4.0)
#-------------- priors ----------------
self.Prior_0 = st.norm(loc=centre_init[0], scale=hyp[0])
self.Prior_1 = st.norm(loc=centre_init[1], scale=hyp[1])
self.Prior_2 = st.uniform(loc=-0.5 * np.pi, scale=np.pi)
self.Prior_3 = st.halfcauchy(loc=0.01, scale=hyp[2])
self.Prior_4 = st.halfcauchy(loc=0.01, scale=hyp[3])
self.Prior_5 = st.halfcauchy(loc=0.01, scale=hyp[2])
self.Prior_6 = st.halfcauchy(loc=0.01, scale=hyp[3])
self.Prior_7 = st.truncexpon(b=hyp[4], loc=0.01, scale=hyp[5])
self.Prior_8 = st.truncexpon(b=hyp[4], loc=0.01, scale=hyp[5])
print("Module Initialized")
def __init__(self, cdts, Rcut, hyp, Dist, centre):
"""
Constructor of the logposteriorModule
"""
rad, thet = Deg2pc(cdts, centre, Dist)
c, r, t, self.Rmax = TruncSort(cdts, rad, thet, Rcut)
self.pro = c[:, 2]
self.rad = r
# -------- Priors --------
self.Prior_0 = st.halfcauchy(loc=0, scale=hyp[0])
self.Prior_1 = st.halfcauchy(loc=0, scale=hyp[1])
print("Module Initialized")
def LogLike(self,params,ndim,nparams):
ctr= params[:2]
rc = params[2]
rt = params[3]
a = params[4]
b = params[5]
#----- Checks if parameters' values are in the ranges
if not Support(rc,rt,a,b) :
return -1e50
#------- Obtains radii and angles ---------
radii,theta = Deg2pc(self.cdts,ctr,self.Dist)
############### Radial likelihood ###################
# Computes likelihood
lf = (1.0-self.pro)*LikeField(radii,self.Rmax)
lk = radii*(self.pro)*Kernel(radii,rc,rt,a,b)
# In king's profile no objects is larger than tidal radius
idBad = np.where(radii > rt)[0]
lk[idBad] = 0.0
# Normalisation constant
if rt < self.Rmax:
up = rt
else:
up = self.Rmax
cte = NormCte(np.array([rc,rt,a,b,up]))
k = 1.0/cte
llike_r = np.sum(np.log((k*lk + lf)))
##################### POISSON ###################################
quarter = cut(theta,bins=self.quadrants,include_lowest=True)
counts = value_counts(quarter)
llike_t = self.poisson.logpmf(counts).sum()
##################################################################
llike = llike_t + llike_r
# print(llike)
return llike
def LogLike(self, params, ndim, nparams):
ctr = params[:2]
rc = params[2]
rt = params[3]
#----- Checks if parameters' values are in the ranges
if not Support(rc, rt):
return -1e50
#------- Obtains radii and angles ---------
radii, theta = Deg2pc(self.cdts, ctr, self.Dist)
############### Radial likelihood ###################
# Computes likelihood
lf = (1.0 - self.pro) * LikeField(radii, self.Rmax)
lk = radii * (self.pro) * Kernel(radii, rc, rt)
# In king's profile no objects is larger than tidal radius
idBad = np.where(radii > rt)[0]
lk[idBad] = 0.0
# Normalisation constant
# w = rc**2 + r**2
y = rc**2 + self.Rmax**2
z = rc**2 + rt**2
a = (self.Rmax**2) / z + 4 * (rc - np.sqrt(y)) / np.sqrt(z) + np.log(
y) - 2 * np.log(rc) # Truncated at Rm
# a = (rt**2)/z - 4.0 + 4.0*(rc/np.sqrt(z)) + np.log(z) - 2*np.log(rc) # Truncated at Rt (i.e. No truncated)
k = 2.0 / (a * (rc**2.0))
llike_r = np.sum(np.log((k * lk + lf)))
##################### POISSON ###################################
quarter = cut(theta, bins=self.quadrants, include_lowest=True)
counts = value_counts(quarter)
llike_t = self.poisson.logpmf(counts).sum()
##################################################################
llike = llike_t + llike_r
# print(llike)
return llike
def __init__(self, cdts, Rcut, hyp, Dist, centre_init):
"""
Constructor of the logposteriorModule
"""
rad, thet = Deg2pc(cdts, centre_init, Dist)
c, r, t, self.Rmax = TruncSort(cdts, rad, thet, Rcut)
self.pro = c[:, 2]
self.cdts = c[:, :2]
self.Dist = Dist
print "There are ", len(self.cdts), " observations."
# sys.exit()
#------------- poisson ----------------
self.quadrants = [
0, np.pi / 2.0, np.pi, 3.0 * np.pi / 2.0, 2.0 * np.pi
]
self.poisson = st.poisson(len(r) / 4.0)
#-------------- priors ----------------
self.Prior_0 = st.norm(loc=centre_init[0], scale=hyp[0])
self.Prior_1 = st.norm(loc=centre_init[1], scale=hyp[1])
self.Prior_2 = st.halfcauchy(loc=0.01, scale=hyp[2])
self.Prior_3 = st.truncexpon(b=hyp[3], loc=2.01, scale=hyp[4])
print "Module Initialized"
def LogLike(self,params,ndim,nparams):
ctr= params[:2]
rc = params[0]
a = params[1]
g = params[2]
#----- Checks if parameters' values are in the ranges
if not Support(rc,a,g) :
return -1e50
#------- Obtains radii and angles ---------
radii,theta = Deg2pc(self.cdts,ctr,self.Dist)
############### Radial likelihood ###################
# Computes likelihood
lf = (1.0-self.pro)*LikeField(radii,self.Rmax)
lk = radii*(self.pro)*Kernel(radii,rc,a,g)
# Normalisation constant
x = -1.0*((rc/self.Rmax)**(-1.0/a))
u = -a*(g-2.0)
v = 1.0+ a*g
z = ((-1.0+0j)**(a*(g-2.0)))*a*(rc**2)
betainc = (((x+0j)**u)/u)*hyp2f1(u,1.0-v,1.0+u,x)
k = 1.0/np.abs(z*betainc)
llike_r = np.sum(np.log((k*lk + lf)))
##################### POISSON ###################################
quarter = cut(theta,bins=self.quadrants,include_lowest=True)
counts = value_counts(quarter)
llike_t = self.poisson.logpmf(counts).sum()
##################################################################
llike = llike_t + llike_r
# print(llike)
return llike
# extracts coordinates
cdtsT = np.c_[tycho['RAJ2000'], tycho['DEJ2000'], tycho['Jmag']]
cdtsD = np.c_[dance['RA'], dance['Dec'], dance["J"]]
cdts = np.vstack([cdtsT, cdtsD])
#---- removes duplicateds --------
sumc = np.sum(cdts[:, :2], axis=1)
idx = np.unique(sumc, return_index=True)[1]
cdts = cdts[idx]
sumc = np.sum(cdts[:, :2], axis=1)
if len(sumc) != len(list(set(sumc))):
sys.exit("Duplicated entries in Coordinates!")
#------- Real distances and position angles
radii, theta = Deg2pc(cdts, centre, Dist)
id_17 = np.where(cdts[:, 2] <= 17)[0]
id_18 = np.where(cdts[:, 2] <= 18)[0]
id_19 = np.where(cdts[:, 2] <= 19)[0]
id_20 = np.where(cdts[:, 2] <= 20)[0]
id_21 = np.where(cdts[:, 2] <= 21)[0]
rad_17, the_17 = Deg2pc(cdts[id_17, :], centre, Dist)
rad_18, the_18 = Deg2pc(cdts[id_18, :], centre, Dist)
rad_19, the_19 = Deg2pc(cdts[id_19, :], centre, Dist)
rad_20, the_20 = Deg2pc(cdts[id_20, :], centre, Dist)
rad_21, the_21 = Deg2pc(cdts[id_21, :], centre, Dist)
pdf = PdfPages(fout)
plt.figure()
# ----- select only 100 parameters to plot
samp = samples[np.random.choice(np.arange(len(samples)),size=100,replace=False)]
############### Stores the covariance matrix ##############
print("Finding covariance matrix around MAP ...")
covar = fCovar(samples,MAP)
np.savetxt(dir_out+"/"+model+"_covariance.txt",covar,
fmt=str('%2.3f'),delimiter=" & ",newline=str("\\\ \n"))
# ------ establish new centre (if needed) ------
if not exte == "None":
centre = MAP[:2]
# -------- prepare data for plots ---------
rad,thet = Deg2pc(cdts,centre,Dist)
cdts,radii,theta,Rmax = TruncSort(cdts,rad,thet,Rcut)
if exte == "Ell":
radii,theta = RotRadii(cdts,centre,Dist,MAP[3])
Nr,bins,dens = DenNum(radii,Rmax)
x = np.linspace(0.01,Rmax,50)
pdf = PdfPages(dir_out+"/"+model+'_fit.pdf')
plt.figure()
for s,par in enumerate(samp):
plt.plot(x,mod.Number(x,par,Rmax,np.max(Nr)),lw=1,color="orange",alpha=0.2,zorder=1)
plt.fill_between(radii, Nr+np.sqrt(Nr), Nr-np.sqrt(Nr), facecolor='grey', alpha=0.5,zorder=2)
plt.plot(radii,Nr,lw=1,color="black",zorder=3)
mag_labs = ["Y [mag]", "i-K [mag]", "J [mag]", "H [mag]", "K [mag]"]
# extracts coordinates
cdts = np.c_[dance['RA'], dance['Dec'], dance['Y'], dance['i'], dance['J'],
dance['H'], dance['K']]
cdts[:, 3] = cdts[:, 3] - cdts[:, 6]
#---- removes duplicateds --------
sumc = np.sum(cdts[:, :2], axis=1)
idx = np.unique(sumc, return_index=True)[1]
cdts = cdts[idx]
sumc = np.sum(cdts[:, :2], axis=1)
if len(sumc) != len(list(set(sumc))):
sys.exit("Duplicated entries in Coordinates!")
radii, theta = Deg2pc(cdts, centre, Dist)
#----- plot distributions ------
pdf = PdfPages(fout)
plt.figure()
for i in range(5):
# compute 2D density PM
X = np.c_[radii.copy(), cdts[:, 2 + i].copy()]
X = X[np.where(np.sum(np.isfinite(X), axis=1) == 2)[0]]
Y, x_bins, y_bins = np.histogram2d(X[:, 0],
X[:, 1], (nbins, nbins),
normed=True)
plt.imshow(Y.T,
