def prob_coal_counts(u, v, t, n):
"""
The probabiluty of going from 'u' lineages to 'v' lineages in time 't'
with population size 'n'
"""
T = t / n
s = 0.0
for k in xrange(v, u+1):
a = exp(-k*(k-1)*T/2.0) * (2*k-1)*(-1)**(k-v) / stats.factorial(v) / \
stats.factorial(k-v) / (k+v-1) * \
stats.prod((v+y)*(u-y)/(u+y) for y in xrange(k))
s += a
return s
def prob_coal_counts_slow(a, b, t, n):
"""
The probabiluty of going from 'a' lineages to 'b' lineages in time 't'
with population size 'n'
Implemented more directly, but slower. Good for testing against.
"""
s = 0.0
for k in range(b, a + 1):
i = exp(-k*(k-1)*t/2.0/n) * \
float(2*k-1)*(-1)**(k-b) / stats.factorial(b) / \
stats.factorial(k-b) / (k+b-1) * \
stats.prod((b+y)*(a-y)/float(a+y) for y in range(k))
s += i
return s
def prob_coal_counts(a, b, t, n):
"""
The probability of going from 'a' lineages to 'b' lineages in time 't'
with population size 'n'
"""
try:
terms = []
C = stats.prod((b + y) * (a - y) / float(a + y) for y in xrange(b)) / float(stats.factorial(b))
terms.append(exp(-b * (b - 1) * t / 2.0 / n) * C)
for k in xrange(b + 1, a + 1):
k1 = k - 1
C = (b + k1) * (a - k1) / float(a + k1) / float(b - k) * C
terms.append(exp(-k * k1 * t / 2.0 / n) * (2 * k - 1) / float(k1 + b) * C)
terms.sort(key=abs)
return kahan_sum(terms)
except:
print a, b, t, n
raise
def prob_coal_counts_slow(a, b, t, n):
"""
The probabiluty of going from 'a' lineages to 'b' lineages in time 't'
with population size 'n'
Implemented more directly, but slower. Good for testing against.
"""
s = 0.0
for k in xrange(b, a + 1):
i = (
exp(-k * (k - 1) * t / 2.0 / n)
* float(2 * k - 1)
* (-1) ** (k - b)
/ stats.factorial(b)
/ stats.factorial(k - b)
/ (k + b - 1)
* stats.prod((b + y) * (a - y) / float(a + y) for y in xrange(k))
)
s += i
return s
def prob_coal_counts(a, b, t, n):
"""
The probability of going from 'a' lineages to 'b' lineages in time 't'
with population size 'n'
"""
try:
terms = []
C = stats.prod((b+y)*(a-y)/float(a+y) for y in range(b)) \
/ float(stats.factorial(b))
terms.append(exp(-b * (b - 1) * t / 2.0 / n) * C)
for k in range(b + 1, a + 1):
k1 = k - 1
C = (b + k1) * (a - k1) / float(a + k1) / float(b - k) * C
terms.append(
exp(-k * k1 * t / 2.0 / n) * (2 * k - 1) / float(k1 + b) * C)
terms.sort(key=abs)
return kahan_sum(terms)
except:
print(a, b, t, n)
raise
