def rate(partition):
b, k_vec, s = computeSignature(partition)
partition_multiset = re.partitionToMultiset(partition)
mergerRate = mergerRatesCoalescent(b, k_vec, s)
factorSizes = np.prod(map(mp.fac, partition))
factorCounts = np.prod(map(mp.fac, partition_multiset))
# print factorSizes, factorCounts, mergerRate
return (mp.fac(n) / factorSizes*factorCounts ) * mergerRate
def p_recursions(N, coalescentType, args):
if coalescentType == 'xi_beta':
alpha = args[0]
def lambdaMergerRate(b, k):
return betaMergerRate(b, k, alpha)
def fourwayMergerRate(b, k_vec, s):
return fourWayMergerRate(b, k_vec, s, lambdaMergerRate)
L = [transitionRatesNumberPartitions(n, fourwayMergerRate, 4) for n in range(1, N+1)]
Q = Q_matrix_Xi([[]]+L)
P = P_matrix(Q)
g = g_matrix(P, Q)
p = np.zeros((N+1, N+1, N+1), dtype=mp.mpf)
p[1, 1, 1] = mp.mpf('1')
# print L, "\n"
for n, jumpsFrom_n in enumerate(L[1:], start=2):
p[n, n, 1] = mp.mpf('1')
for n1, jumpsFrom_n_to_n1 in enumerate(jumpsFrom_n[1:-1], start=1):
# print n, n1, jumpsFrom_n_to_n1
for lam_multi, rate in [( re.partitionToMultiset(x[0]), x[2] ) for x in jumpsFrom_n_to_n1]:
jumpProb = -rate/Q[n, n]
for b1 in range(1, n1):
for lamSub, b in re.subpartitionsMultiset(lam_multi, b1):
lamSubFactor = re.subpartitionProb(lam_multi, lamSub, n1, b1)
for k in range(2, min(n1-b1+1, n-b+1) +1):
kFactor = p[n1, k, b1] * g[n1, k]/g[n, k]
p[n, k, b] += jumpProb * kFactor * lamSubFactor
print n,n1,k,b,b1,'\n',lam_multi,'\n',lamSub,'\n'
# print '\n'
#for testing if things add up
# for n, l1 in enumerate(p):
# for k, l2 in enumerate(l1):
# if sum(l2)>0:
# print (n, k, sum(l2))
return p, g, Q, P,L
