def LogLike(self, params, ndim, nparams):
ctr = params[:2]
dlt = params[2]
rca = params[3]
rcb = params[4]
a = params[5]
b = params[6]
g = params[7]
slp = params[8]
#----- Checks if parameters' values are in the ranges
if not Support(rca, rcb, a, b, g):
return -1e50
#------- Obtains radii and angles ---------
radii, theta = RotRadii(self.cdts, ctr, self.Dist, dlt)
rc = (rca * rcb) / np.sqrt((rcb * np.cos(theta))**2 +
(rca * np.sin(theta))**2)
# Include mass segregation with linear relation
rcs = rc + (slp * self.delta_band)
#----- Checks if parameters' values are in the ranges
if np.min(rcs) <= 0:
return -1e50
############### Radial likelihood ###################
# Computes likelihood
lf = (1.0 - self.pro) * LikeField(radii, self.Rmax)
lk = radii * (self.pro) * Kernel(radii, rcs, a, b, g)
# Normalisation constant
x = -1.0 * ((rcs / self.Rmax)**(-1.0 / a))
u = -a * (g - 2.0)
v = 1.0 + a * (g - b)
w = (((x + 0j)**u) / u)
z = ((-1.0 + 0j)**(a * (g - 2.0))) * a * (rcs**2)
h = hyp2f1(u, 1.0 - v, u + 1.0, x)
cte = np.abs(z * h * w)
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
# if not np.isfinite(llike):
# ids = np.where(np.isnan(k))[0]
# print h[ids],u,v,a,b,g
# sys.exit()
# return -1e50
# print(llike)
return llike
def LogLike(self, params, ndim, nparams):
ctr = params[:2]
dlt = params[2]
rca = params[3]
rta = params[4]
rcb = params[5]
rtb = params[6]
slp = params[7]
#----- Checks if parameters' values are in the ranges
if not Support(rca, rta, rcb, rtb):
return -1e50
#------- Obtains radii and angles ---------
radii, theta = RotRadii(self.cdts, ctr, self.Dist, dlt)
rc = (rca * rcb) / np.sqrt((rcb * np.cos(theta))**2 +
(rca * np.sin(theta))**2)
rts = (rta * rtb) / np.sqrt((rtb * np.cos(theta))**2 +
(rta * np.sin(theta))**2)
# Include mass segregation with linear relation
rcs = rc + (slp * self.delta_band)
#----- Checks if parameters' values are in the ranges
if np.min(rcs) <= 0 or np.greater(rcs, rts).any():
return -1e50
############### Radial likelihood ###################
# Computes likelihood
lf = (1.0 - self.pro) * LikeField(radii, self.Rmax)
lk = radii * (self.pro) * Kernel(radii, rcs, rts)
# In king's profile no objects is larger than tidal radius
idBad = np.where(radii > rts)[0]
lk[idBad] = 0.0
# Normalisation constant
ups = self.Rmax * np.ones_like(rts)
ids = np.where(rts < self.Rmax)[0]
ups[ids] = rts[ids]
cte = np.array(map(NormCte, np.c_[rcs, rts, ups]))
k = 2.0 / 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]
dlt = params[2]
rca = params[3]
rcb = params[4]
a = params[5]
b = params[6]
slp = params[7]
#----- Checks if parameters' values are in the ranges
if not Support(rca, rcb, a, b):
return -1e50
#------- Obtains radii and angles ---------
radii, theta = RotRadii(self.cdts, ctr, self.Dist, dlt)
rc = (rca * rcb) / np.sqrt((rcb * np.cos(theta))**2 +
(rca * np.sin(theta))**2)
# Include mass segregation with linear relation
rcs = rc + (slp * self.delta_band)
if np.min(rcs) <= 0:
return -1e50
############### Radial likelihood ###################
# Computes likelihood
lf = (1.0 - self.pro) * LikeField(radii, self.Rmax)
lk = radii * (self.pro) * Kernel(radii, rcs, a, b)
# Normalisation constant
x = -((rcs / 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
if np.isnan(k).any():
return -1e50
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
return llike
def LogLike(self, params, ndim, nparams):
ctr = params[:2]
dlt = params[2]
rca = params[3]
rcb = params[4]
g = params[5]
slp = params[6]
#----- Checks if parameters' values are in the ranges
if not Support(rca, rcb):
return -1e50
#------- Obtains radii and angles ---------
radii, theta = RotRadii(self.cdts, ctr, self.Dist, dlt)
rc = (rca * rcb) / np.sqrt((rcb * np.cos(theta))**2 +
(rca * np.sin(theta))**2)
# Include mass segregation with linear relation
rcs = rc + (slp * self.delta_band)
#----- Checks if parameters' values are in the ranges
if np.min(rcs) <= 0:
return -1e50
############### Radial likelihood ###################
lf = (1.0 - self.pro) * LikeField(radii, self.Rmax)
lk = radii * (self.pro) * Kernel(radii, rcs, g)
# Normalisation constant
y = rcs**2 + self.Rmax**2
a = (1.0 / (g - 2.0)) * (1.0 - (rcs**(g - 2.0)) *
(y**(1.0 - 0.5 * g))) # Truncated at Rm
# a = 1.0/(g-2.0) # No truncated
k = 1.0 / (a * (rcs**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_r + llike_t
# print(llike)
return llike
############### 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)
plt.plot(x,mod.Number(x,MAP,Rmax,np.max(Nr)), lw=1,color="red",zorder=4)
plt.ylim((0,1.1*max(Nr)))
plt.xlim((0,1.1*Rmax))
plt.ylabel("Number of stars")
