def freq_pdf_old(x, p, n, t, k=8):
if x > 0.5:
return freq_pdf2(1.0-x, 1.0-p, n, t, k)
q = 1.0 - p
prob = -util.INF
sgn = 1
t4n = t / (4*n)
for i in xrange(1, k+1):
#term = (p * q * i * (i+1) * (2*i+1) *
# hypergeo(1-i,i+2,2,p) * hypergeo(1-i,i+2,2,x) *
# exp(-t * i * (i+1) / (4*n)))
lcoff = log(p * q * i * (i+1) * (2*i+1))
h1 = hypergeo(1-i,i+2,2,p, i+2)
h2 = hypergeo(1-i,i+2,2,x, i+2)
sgn2 = util.sign(h1) * util.sign(h2)
if sgn2 != 0:
term = (lcoff + log(abs(h1)) + log(abs(h2)) +
(- i * (i+1) * t4n))
sgn, prob = stats.logadd_sign(sgn, prob, sgn2, term)
return sgn * exp(prob)
def hypergeo(a, b, c, z, k=100):
"""Hypergeometric function"""
terms = [0.0]
signs = [1.0]
for i in xrange(1, k+1):
term = float((i+a-1)*(i+b-1)*z)/(i+c-1)/i
signs.append(util.sign(term) * signs[-1])
if term == 0.0:
break
terms.append(log(abs(term)) + terms[i-1])
return sum(s*exp(i) for s, i in zip(signs, terms))
def loghypergeo(a, b, c, z, k=100):
"""
Hypergeometric function
Performs computation in log-space
"""
terms = [0.0]
signs = [1.0]
for i in xrange(1, k+1):
term = float((i+a-1)*(i+b-1)*z)/(i+c-1)/i
signs.append(util.sign(term) * signs[-1])
if term == 0.0:
break
terms.append(log(abs(term)) + terms[i-1])
sgn = 1
tot = -util.INF
for s, t in zip(signs, terms):
sgn, tot = stats.logadd_sign(sgn, tot, s, t)
return sgn, tot