def zinb(value=sna, mu=lambduh, alpha=delta, psi=pzero):
# Initialise likeihood
like = 0.0
# Add zero component; zero probability + P(NB==0); value flags for non-zeros to cancel out
like += np.sum((np.log(psi + (1.-psi)*(alpha/(mu+alpha))**alpha))*Iz)
# Add count component; non-zero probability + P(NB>0); value flags for zeros to cancel out
like += np.sum((np.log(1.-psi) + np.log(gammaf(alpha+value))-np.log((ft(value)*gammaf(alpha))) + alpha*np.log(alpha/(mu+alpha)) + value*np.log(mu/(mu+alpha)))*Ic)
return like
import numpy as np from scipy.stats import norm, gamma, rv_discrete, beta from scipy.special import digamma from scipy.special import gamma as gammaf lgamma = lambda x: np.log(gammaf(x)) """ DIAGONAL COVARIANCE Code to check analytical derivations of ELBO in Variational_Inference_in_DPGMM_derivation.pdf against Monte Carlo estimates python bound_check.py [email protected], october 2018 """ np.random.seed(0) D = 3 K = 2 nu = np.random.randn(K, D) omega = np.random.random([K]) + 1 zeta = np.array([0.2, 0.8]) a = np.ones([K], dtype=np.float32) b = 1.5 * np.ones([K], dtype=np.float32) lambda1 = np.ones(K, dtype=np.float32) lambda2 = 2. * np.ones(K, dtype=np.float32)
def fitted(x, a, b):
fx = gammaf(a+b)/gammaf(a)/gammaf(b)*x**(a-1)*(1-x)**(b-1) # pdf of beta
return fx
def loop(inputFile='.dat'):
# vals = ["1","5", "10", "15", "20", "30", "40", "50", "100"]
vals = ["20"]
overall = [["Beam energy", "mean", "beta"]]
counter = 0
for v in vals:
totalDistance = 0.
start_x = 0
start_y = 0
start_z = 0
allDistances = []
rangeDistances = []
counter += 1
f = open(v + inputFile, 'r')
for line in f:
words = line.strip().split()
isint = True
if len(words) > 0:
try:
first = float(words[0])
except ValueError:
isint = False
if isint == True:
if len(words) > 6:
if float(words[6]) <= 0.05:
thisDistance = math.sqrt(
(float(words[0]) - start_x)**2 +
(float(words[1]) - start_y)**2 +
(float(words[2]) - start_z)**2)
# totalDistance += thisDistance
allDistances.append(thisDistance / 1000)
if float(v) > 10:
rangeDistances.append(
round(thisDistance / 1000, 1))
else:
rangeDistances.append(
round(thisDistance / 1000, 2))
elif float(words[6]) == float(v):
start_x = float(words[0])
start_y = float(words[1])
start_z = float(words[2])
f.close()
std_numpy = numpy.std(allDistances, ddof=1)
var = std_numpy**2
beta = (std_numpy * math.sqrt(6)) / math.pi
mean_numpy = numpy.mean(allDistances)
mode = max(set(rangeDistances), key=rangeDistances.count)
length = len(allDistances)
PDF = [None] * length
PDFGumbel = [None] * length
PDFGumbelEst = [None] * length
pdf_manual_beta = [None] * length
# PDFGenLog = [None] * length
plt.figure(counter)
n, bins, patches = plt.hist(allDistances, 20, normed=1)
allDistances.sort()
median = (allDistances[(length / 2) - 1] +
allDistances[length / 2]) / 2
the_max = max(allDistances)
#manual beta
alpha1, beta1, loc, scale = stats.beta.fit(allDistances)
# alpha1 = mean_numpy ** 2 * (1 - mean_numpy) / var - mean_numpy
#alpha1 = 246.2
# alpha1 = (mean_numpy*(2*mode - the_max))/(the_max*(mode-mean_numpy))
# beta1 = alpha1 * (1 - mean_numpy) / mean_numpy
# beta1 = 15.2
# beta1 = (alpha1*(the_max-mean_numpy))/mean_numpy
denominator = (gammaf(alpha1) * gammaf(beta1)) / gammaf(alpha1 + beta1)
#loc = -65.0
#scale = 74.4
for x in range(len(allDistances)):
m = (allDistances[x] - loc) / scale
pdf_manual_beta[x] = (1 / scale) * ((m**(alpha1 - 1)) * ((1 - (
(m))**(beta1 - 1))) / denominator)
'''
#work out Gayther dist
z = (allDistances[x]-mean_numpy)/beta
PDF[x] = ((1/beta)*(math.exp((z-math.exp(z)))))
#work out gumbel
z = (allDistances[x] - mode) / beta
PDFGumbel[x] = ((1 / beta) * (math.exp(-(z + math.exp(-z)))))
#z = (allDistances[x] - (mean_numpy - beta+0/5772)) / beta
#PDFGumbelEst[x] = ((1 / beta) * (math.exp(-(z + math.exp(-z)))))
#work out genlog
PDFGenLog[x] = (median * math.exp(-allDistances[x]))/((1+math.exp(-allDistances[x]))**(median+1))
# gamma
ag, bg, cg = stats.gamma.fit(allDistances)
pdf_gamma = stats.gamma.pdf(allDistances, ag, bg, cg)
green_line = plt.plot(allDistances, pdf_gamma, color = 'g', label="Gamma")
'''
# gumbel_l
agl, bgl = gumbel_l.fit(allDistances)
print(agl)
print(bgl)
# pdf_gumbel_l = gumbel_l.pdf(allDistances, agl, bgl)
pdf_gumbel_best = gumbel_l.pdf(allDistances, agl, bgl)
pdf_gumbel_l = [None] * length
for x in range(len(allDistances)):
#z = (allDistances[x]-agl)/bgl
#pdf_gumbel_l[x] = (1/bgl) * math.exp(-(z + math.exp(-z)))
#agl = mean_numpy
z = (allDistances[x] - agl) / bgl
pdf_gumbel_l[x] = (1 / bgl) * math.exp(z - math.exp(z))
magenta_line, = plt.plot(allDistances,
pdf_gumbel_l,
color='m',
label="gumbel_l")
blue_line, = plt.plot(allDistances,
pdf_gumbel_best,
color='b',
label="gumbel_best")
'''
#gumbel_r
agr, bgr = gumbel_r.fit(allDistances)
pdf_gumbel_r = gumbel_r.pdf(allDistances, agr, bgr)
cyan_line, = plt.plot(allDistances, pdf_gumbel_r, color='c', label="gumbel_r")
#gamma
ag, bg, cg = stats.gamma.fit(allDistances)
pdf_gamma = stats.gamma.pdf(allDistances, ag, bg, cg)
#beta
ab, bb, cb, db = stats.beta.fit(allDistances)
print(ab)
print(bb)
print(cb)
print(db)
pdf_beta = stats.beta.pdf(allDistances, ab, bb, cb, db)
yellow_line, = plt.plot(allDistances, pdf_beta, color = 'y', label="Beta")
#normal
pdf_g = stats.norm.pdf(allDistances, mean_numpy, std_numpy) # now get theoretical values in our interval
black_line, = plt.plot(allDistances, pdf_g, color='k', label="Norm") # plot it
#manual beta
'''
# red_line, = plt.plot(allDistances, PDF, color='r', label='Gayther')
red_line, = plt.plot(allDistances,
pdf_manual_beta,
color='r',
label='manual beta')
# blue_line, = plt.plot(allDistances, PDFGumbel, color = 'b', label='Gumbel')
# green_line, = plt.plot(allDistances, PDFGenLog, color = 'g', label='GenLog')
# green_line, = plt.plot(allDistances, PDFGumbelEst, color='b', label='GumbelEst')
# green_line, = plt.plot(allDistances, pdf_gamma, color = 'g', label="Gamma")
# plt.legend(handles=[blue_line, red_line, green_line])
# plt.legend(handles=[black_line, green_line, cyan_line, magenta_line, yellow_line, red_line])
plt.legend(handles=[magenta_line, blue_line, red_line])
plt.xlabel('Path length')
plt.ylabel('Probability density')
plt.title(v + 'keV')
plt.show()
# meanDistance = totalDistance / counter
'''
def compute_normalgamma_pdf(mu, llambda, a, b):
return lambda x, tau: b**a * sqrt(llambda) / (gammaf(a) * sqrt(
2 * pi)) * (tau**
(a - 0.5)) * (e**(-b * tau)) * (e**-(llambda * tau *
(x - mu)**2 / 2))
def betafun(x, a, b):
return gammaf(a + b) / gammaf(a) / gammaf(b) * x**(a - 1) * (1 - x)**(b -
1)