def each_chisq(para, m1_obs, m1_sig):
a, mbh_max, mbh_min = para
if 1.1 < a < 3 and 50 < mbh_max < 100 and 2 < mbh_min < 8:
x = np.logspace(
np.log10(m1_obs.min() / np.exp(m_noise_level)**5 / 1.1),
np.log10(m1_obs.max() * np.exp(m_noise_level)**5 * 1.1), 300)
y = cov_twofun(x,
a=a,
mbh_max=mbh_max,
mbh_min=mbh_min,
sigma=m_noise_level)
f = interpolate.interp1d(x, y)
poss_m1_i = f(m1_obs)
return poss_m1_i
else:
return np.inf
def point_Chisq(para, m1_obs, m_noise_level):
a, mbh_max, mbh_min = para
if 1.1 < a < 3 and 50 < mbh_max < 100 and 2 < mbh_min < 8:
x = np.logspace(np.log10(m1_obs.min() / 1.1),
np.log10(m1_obs.max() * 1.1), 300)
y = cov_twofun(x,
a=a,
mbh_max=mbh_max,
mbh_min=mbh_min,
sigma=m_noise_level)
f = interpolate.interp1d(x, y)
# poss_m1_i = likelihood(m1_obs,m1_sig, a=a, mbh_max=mbh_max, mbh_min=mbh_min, use_method='med',f=f)
poss_m1_i = f(m1_obs)
chisq = -np.sum(np.log(poss_m1_i))
# print a, mbh_max, mbh_min, chisq
return chisq
else:
return np.inf
def each_likeli(para, m1_obs, m1_sig, prior):
a, mbh_max, mbh_min = para
if 1.1 < a < 3 and 50 < mbh_max < 100 and 2 < mbh_min < 8:
x = np.logspace(
np.log10(m1_obs.min() / np.exp(m_noise_level)**5 / 1.1),
np.log10(m1_obs.max() * np.exp(m_noise_level)**5 * 1.1), 300)
y = cov_twofun(x,
a=a,
mbh_max=mbh_max,
mbh_min=mbh_min,
sigma=m_noise_level)
f = interpolate.interp1d(x, y)
# poss_m1_i = likelihood(m1_obs,m1_sig, a=a, mbh_max=mbh_max, mbh_min=mbh_min, use_method='med', f=f)
poss_m1_i = f(m1_obs)
post = poss_m1_i #(1/ prior)
# print a, mbh_max, mbh_min, chisq
return post
else:
return np.inf
def posterior(para, m1_obs, m_noise_level, sf_factor, z):
a0, a1, mbh_max, mbh_min = para
# a_z = a0 + a1 * z
# if 1.1 < a0 < 3 and -0.5 < a1 < 0.5 and 50 < mbh_max < 100 and 2 < mbh_min < 8:
a_z = a0 + a1 * z / (1 + z)
if 1.1 < a0 < 3 and -0.5 < a1 < 1.5 and 50 < mbh_max < 100 and 2 < mbh_min < 8:
x = np.logspace(np.log10(m1_obs.min() / 1.1),
np.log10(m1_obs.max() * 1.1),
50) #!!! 50 could be big enough?
post, az_lib, y_lib = [], [], []
for i in range(len(z)):
if a_z[i] not in az_lib:
y = cov_twofun(x,
a=a_z[i],
mbh_max=mbh_max,
mbh_min=mbh_min,
sigma=m_noise_level) #!!!
else:
j = np.where(np.asarray(az_lib) == a_z[i])[0][0]
y = y_lib[j]
az_lib.append(a_z[i])
y_lib.append(y)
f = interpolate.interp1d(x, y)
poss_m1_i = f(m1_obs[i])
post.append(poss_m1_i)
if i / 300 > (i - 1) / 300:
print i
post = np.array(post)
chisq = -0.5 * np.sum(np.log(post) * sf_factor)
t2 = time.time()
t_cost = (t2 - t1)
t_per_cost = t_cost / step
t_remain = t_per_cost * (step_total - step)
step = np.sum(sampler.flatchain != 0) / (ndim * nwalkers)
if step != 0:
print "step:", step, "percent", round(
step / (step_total / 100),
2), "%", "\r", "para:", para, "time remain:", round(t_remain /
60), 'mins'
return chisq
else:
return np.inf
def posterior(para, m1_obs, m_noise_level, sf_factor):
a, mbh_max, mbh_min = para
if 1.1 < a < 3 and 50 < mbh_max < 100 and 2 < mbh_min < 8:
x = np.logspace(np.log10(m1_obs.min() / 1.1),
np.log10(m1_obs.max() * 1.1), 300)
y = cov_twofun(x,
a=a,
mbh_max=mbh_max,
mbh_min=mbh_min,
sigma=m_noise_level)
f = interpolate.interp1d(x, y)
poss_m1_i = f(m1_obs)
post = poss_m1_i
# if prior_true is not None:
# prior[np.where(prior<prior_true.min())] = prior_true.min()
# sf_factor[np.where(sf_factor>75)] = 75 # Do it in other place
chisq = -0.5 * np.sum(np.log(post) * sf_factor)
return chisq
else:
return np.inf
def posterior(para, m1_obs, m_noise_level, sf_factor, z):
a0, a1, mbh_max, mbh_min = para
# a_z = a0 + a1 * z
# if 1.1 < a0 < 3 and -0.5 < a1 < 0.5 and 50 < mbh_max < 100 and 2 < mbh_min < 8:
a_z = a0 + a1 * z / (1 + z)
if 0.1 < a0 < 3.5 and -3. < a1 < 3.0 and 30 < mbh_max < 115 and 2 < mbh_min < 8:
post = []
for i in range(len(z)):
poss_m1_i = cov_twofun(m1_obs[i],
a=a_z[i],
mbh_max=mbh_max,
mbh_min=mbh_min,
sigma=m_noise_level)
post.append(poss_m1_i)
post = np.array(post)
chisq = -0.5 * np.sum(np.log(post) * sf_factor)
# print para, chisq
global mini_count
if mini_count / 50 > (mini_count - 1) / 50:
print "State of count {0}".format(mini_count), para, chisq
mini_count = mini_count + 1
return chisq
else:
return np.inf
def posterior(para, m1_obs, m_noise_level, sf_factor, z, r_detail=False):
a0, a1, mbh_max, mbh_min = para
a_z = a0 + a1 * z
if 1.1 < a0 < 3 and -0.5 < a1 < 0.5 and 50 < mbh_max < 100 and 2 < mbh_min < 8:
# a_z = a0 + a1 * z/(1+z)
# if 1.1 < a0 < 3 and -0.5 < a1 < 1.5 and 50 < mbh_max < 100 and 2 < mbh_min < 8:
x = np.logspace(np.log10(m1_obs.min() / 1.1),
np.log10(m1_obs.max() * 1.1),
50) #!!! 50 could be big enough?
post, az_lib, y_lib = [], [], []
for i in range(len(z)):
if a_z[i] not in az_lib:
y = cov_twofun(x,
a=a_z[i],
mbh_max=mbh_max,
mbh_min=mbh_min,
sigma=m_noise_level) #!!!
else:
j = np.where(np.asarray(az_lib) == a_z[i])[0][0]
y = y_lib[j]
az_lib.append(a_z[i])
y_lib.append(y)
f = interpolate.interp1d(x, y)
poss_m1_i = f(m1_obs[i])
post.append(poss_m1_i)
if i / 300 > (i - 1) / 300:
print i
post = np.array(post)
chisq = -0.5 * np.sum(np.log(post) * sf_factor)
print para, ": Chisq:", chisq
if r_detail == False:
return chisq
elif r_detail == True:
return chisq, -0.5 * np.log(post) * sf_factor
else:
return np.inf