def weight_of_partition(part):
n = sum(part)
#abstract_sequences = fac(n)/prod(fac(i) for i in part)
abstract_sequences = exp(log_fac(n) - sum(log_fac(i) for i in part))
foo = [part.count(i) for i in set(part)]
bar = fac(4)/prod(fac(i) for i in foo)
return abstract_sequences*bar
def count_partitions(n):
d = defaultdict(int)
for kmer in make_kmers(n):
d[tuple(partition_sequence(kmer))] += 1
for k,v in sorted(d.items(),key=lambda (k,v):k):
abstract_sequences = exp(log_fac(n) - sum(log_fac(i) for i in k))
assignments = choose(4,sum(1 for i in k if i > 0))
foo = [k.count(i) for i in set(k)]
bar = fac(4)/prod(fac(i) for i in foo)
print k,v,abstract_sequences*bar#,abstract_sequences,float(v)/abstract_sequences,foo,bar
return d
def counts_to_cols(counts):
"""return numer of cols associated given counts"""
N = sum(counts)
# all_cols = 4**N
metacounts = Counter(counts)
counts_to_bases = fac(4) / prod(
fac(multiplicity) for multiplicity in metacounts.values())
if N <= 170:
bases_to_pos = fac(N) / prod(fac(count) for count in counts)
else:
#print "Warning: possible numerical issues in counts_to_cols"
bases_to_pos = round(
exp(log_fac(N) - sum(log_fac(count) for count in counts)))
return counts_to_bases * bases_to_pos
def _ncp(ps,n):
"""find non-coincidence probability for n draws from ps"""
tic = time.time()
#print n,ncp_dict
if n == 0:
return 1
if n not in ncp_dict:
#print "didn't find",n
ans = sum((-1)**(i-1)*fac(n-1)/fac(n-i)
*powsum(ps,i)*_ncp(ps,n-i) for i in range(1,n+1))
ncp_dict[n] = ans
else:
#print "found",n
pass
toc = time.time()
#print "leaving call w/ %s in %1.2f sec" % (n,toc-tic)
return ncp_dict[n]
def predict_log_partition_normal_series(K,sigma,n):
Z0,norm_sig = predict_partition(K,sigma)
a = norm_sig/Z0
print a
def facfac(k):
assert k % 2 == 1
return reduce(lambda x,y:x*y,range(1,k+1,2))
return log(Z0) - sum(1/fac(k)*a**k*facfac(k-1) for k in range(2,n+1,2))
from math import exp, log, sqrt, ceil
from matplotlib import pyplot as plt
#import seaborn as sbn
import scipy
from collections import defaultdict
from sde import ou_relaxation_time_from_sample, is_stationary
n = 16
L = 5
beta = 1
K = 4**L
G = 5 * 10**6
AAS = 5
num_recognizers = AAS**L
num_motifs = 4**(n * L)
permutations = fac(L) * fac(n)
num_genotypes = num_recognizers * num_motifs / float(permutations)
log_num_genotypes = L * log(AAS) + (n * L) * log(4) - log_fac(L)
# site_mut_prob = 10**-0.5
# rec_mut_prob = 10**-0.5
def sample_code(sigma=1):
return {(i, b): random.gauss(0, sigma) for i in range(AAS) for b in "ACGT"}
def code_statistics(code):
mus = [mean([code[(aa, b)] for aa in range(AAS)]) for b in "ACGT"]
sigmas = [sd([code[(aa, b)] for aa in range(AAS)]) for b in "ACGT"]
return sum(mus), sum(sigmas)
def log_choose_approx(N,k):
return k*log(N) - log(fac(k))
def multiplicities(eps):
metacounts = Counter(eps)
substitutions = fac(n)/prod(fac(multiplicity) for multiplicity in metacounts.values())
return substitutions
def dist_configs(G,q):
"""Return all ch-configs, assuming indistinguishable particles"""
return [chi_from_tau(tau_config,G) for qp in range(q+1)
for tau_config in itertools.combinations(range(G),qp)
for degeneracy in range(int(fac(q)/fac(show(q-qp))))]
import utils
factorials = {i: utils.fac(i) for i in range(10)}
def is_factorial(n):
summ = sum([factorials[int(digit)] for digit in str(n)])
if summ == n:
return True
return False
def get_max():
num = 9
while True:
summ = sum([factorials[9] for digit in str(num)])
if num > summ:
break
num = int(str(num) + '9')
return len(str(num)) * factorials[9]
i = 10
nums = []
maxx = get_max()
print('max', maxx)
while i < maxx:
if is_factorial(i):
print(i)
nums.append(i)
i += 1
def w(eps):
"""number of ways to """
return (fac(L)**len(eps)) / prod(fac(ep) * fac(L - ep)
for ep in eps) * 3**sum(eps)
def occ_dist_poisson_ref(eps,mus):
print "computing ps"
ps = [fd(ep,mu) for ep in eps]
print "---"
lamb = sum(ps)
return [lamb**k*exp(-lamb)/fac(k) for k in range(len(ps)+1)]
def a(n,k):
"""See OEIS A111492"""
return fac(k-1)*choose(n,k)
def expm(A,n=100):
return sum(linalg.matrix_power(A,i)/fac(i) for i in range(n+1))
def ncp(ps,n):
return fac(n)*esp(ps,n)/1.0
import utils N = utils.get_N() if utils.get_N() else 100 num = utils.fac(N) print(sum([int(digit) for digit in str(num)]))
def multiplicities(eps):
metacounts = Counter(eps)
substitutions = fac(n) / prod(
fac(multiplicity) for multiplicity in metacounts.values())
return substitutions
def omega(N,q):
assert 0 <= q <= N
ks = [make_k(i) for i in range(1,N+1)]
return sum(int(fac(q)/fac(q-i))*esp(ks,i) for i in range(q+1))
from math import exp,log,sqrt,ceil
from matplotlib import pyplot as plt
#import seaborn as sbn
import scipy
from collections import defaultdict
from sde import ou_relaxation_time_from_sample,is_stationary
n = 16
L = 5
beta = 1
K = 4**L
G = 5*10**6
AAS = 5
num_recognizers = AAS**L
num_motifs = 4**(n*L)
permutations = fac(L)*fac(n)
num_genotypes = num_recognizers * num_motifs / float(permutations)
log_num_genotypes = L*log(AAS) + (n*L)*log(4) - log_fac(L)
# site_mut_prob = 10**-0.5
# rec_mut_prob = 10**-0.5
def sample_code(sigma=1):
return {(i,b):random.gauss(0,sigma) for i in range(AAS) for b in "ACGT"}
def code_statistics(code):
mus = [mean([code[(aa,b)] for aa in range(AAS)]) for b in "ACGT"]
sigmas = [sd([code[(aa,b)] for aa in range(AAS)]) for b in "ACGT"]
return sum(mus),sum(sigmas)
if not 'code' in globals():
code = sample_code()
def simplex_integrate(f, n, sigma, trials=1000):
integrand = lambda ps: f(ps) * logit_measure(ps, sigma) / fac(n - 1)
return mean(integrand(simplex_sample(n)) for i in xrange(trials))
def w(eps):
"""number of ways to """
return (fac(L)**len(eps))/prod(fac(ep)*fac(L-ep) for ep in eps)*3**sum(eps)
