def gradient_it(m, eps):
cnt = 0
(A, B) = ut.split_at(m)
x0 = [0] * len(B)
r0 = ut.minus(B, ut.subst(A, x0))
p0 = r0
z0 = r0
s0 = r0
for i in range(0, 2 * len(B)):
sub = ut.subst(A, z0)
prev_p = p0
prev_r = r0
At = ut.transpose_matrix(A)
# print(At)
a = ut.scalar_product(p0, r0) / ut.scalar_product(s0, sub)
x0 = ut.plus(x0, ut.mul(a, z0))
r0 = ut.minus(r0, ut.mul(a, sub))
p0 = ut.minus(p0, ut.mul(a, ut.subst(At, s0)))
b = ut.scalar_product(p0, r0) / ut.scalar_product(prev_p, prev_r)
z0 = ut.plus(r0, ut.mul(b, z0))
s0 = ut.plus(p0, ut.mul(b, s0))
if abs(ut.norm(r0) / ut.norm(B)) < eps:
break
cnt += 1
return (x0, cnt)
def estremo_gibbs(iterations=50000,
verbose=False,
every=1000,
sigma=1,
mu=-10,
Ne=5):
nu = Ne - 1
L = 10
N = 20
code, motif = (sample_code(L=10,
sigma=1), random_motif(length=L, num_sites=N))
def log_f((code, motif)):
eps = map(lambda x: -log(x), pw_prob_sites(motif, code))
return sum(nu * log(1 / (1 + exp(ep - mu))) for ep in eps)
chain = [(code, motif[:])]
print log_f((code, motif))
for iteration in trange(iterations):
for i in range(N):
site = motif[i]
for j in range(L):
b = site[j]
log_ps = []
bps = [bp for bp in "ACGT" if not bp == b]
for bp in bps:
site_p = subst(site, bp, j)
log_ps.append(log_f((code, [site_p])))
log_ps = [p - min(log_ps) for p in log_ps]
bp = inverse_cdf_sample(bps,
map(exp, log_ps),
normalized=False)
motif[i] = subst(site, bp, j)
for k in range(L - 1):
for b1 in "ACGT":
for b2 in "ACGT":
dws = [random.gauss(0, 0.1) for _ in range(10)]
code_ps = [[d.copy() for d in code] for _ in range(10)]
for code_p, dw in zip(code_ps, dws):
code_p[k][b1, b2] += dw
log_ps = [log_f((code_p, motif)) for code_p in code_ps]
log_ps = [p - min(log_ps) for p in log_ps]
code_p = inverse_cdf_sample(code_ps,
map(exp, log_ps),
normalized=False)
code = code_p
print log_f((code, motif))
chain.append((code, motif[:]))
return chain
x0 = (sample_code(L=10, sigma=1), random_motif(length=10, num_sites=20))
chain = mh(log_f,
prop,
x0,
use_log=True,
iterations=iterations,
verbose=verbose,
every=every)
return chain
def jacobi(m, eps):
(A, f) = split_at(m)
(B, c) = to_iter(A, f)
prev = c
x = plus(subst(B, prev), c)
cnt = 1
n = norma(B)
if (n >= 1):
print("norma > 1, Jacobi error")
return ([[]], 0)
e1 = (1 - n) / n * eps
while (myNorm(minus(x, prev)) > e1):
cnt += 1
prev = x
x = plus(subst(B, prev), c)
return (x, cnt)
def maxent_site_cftp(N, beta):
top_site = ["A"]*N
bottom_site = ["T"]*N
def mutate_site(site, (ri, rdir)):
i = "ACGT".index(site[ri])
ip = max(0, min(3, i + rdir))
bp = "ACGT"[ip]
return subst(site,[bp],ri)
def maxent_site_cftp(N, beta):
top_site = ["A"] * N
bottom_site = ["T"] * N
def mutate_site(site, (ri, rdir)):
i = "ACGT".index(site[ri])
ip = max(0, min(3, i + rdir))
bp = "ACGT"[ip]
return subst(site, [bp], ri)
def sample_site_cftp_dep(matrix, mu, Ne):
L = len(matrix)
def log_phat(s):
ep = score_seq(matrix,s)
nu = Ne - 1
return -nu*log(1 + exp(ep - mu))
first_site = "A"*L
last_site = "T"*L
best_site = "".join(["ACGT"[argmin(row)] for row in matrix])
worst_site = "".join(["ACGT"[argmax(row)] for row in matrix])
trajs = [[best_site],[random_site(L)],[random_site(L)],[random_site(L)], [worst_site]]
def mutate_site(site,(ri,rb)):
return subst(site,"ACGT"[rb],ri)
def mutate_sites_spec(sites, site_mu):
n = len(sites)
L = len(sites[0])
muts = np.random.binomial(n * L, site_mu)
if muts == 0:
return sites
# else...
new_sites = sites[:]
for mut in range(muts):
i = random.randrange(n)
j = random.randrange(L)
site = new_sites[i]
b = site[j]
new_b = random.choice([c for c in "ACGT" if not c == b])
new_sites[i] = subst(site, new_b, j)
return new_sites
def mutate_sites_spec(sites,site_mu):
n = len(sites)
L = len(sites[0])
muts = np.random.binomial(n*L,site_mu)
if muts == 0:
return sites
# else...
new_sites = sites[:]
for mut in range(muts):
i = random.randrange(n)
j = random.randrange(L)
site = new_sites[i]
b = site[j]
new_b = random.choice([c for c in "ACGT" if not c == b])
new_sites[i] = subst(site,new_b,j)
return new_sites
def mutate_motif_k_times(motif, k):
motif_ = motif[:]
n = len(motif)
L = len(motif[0])
N = n * L
rs = range(N)
choices = []
for _ in range(k):
r = random.choice(rs)
choices.append(r)
rs.remove(r)
for r in choices:
i = r / L
j = r % L
b = motif[i][j]
new_b = random.choice([c for c in "ACGT" if not c == b])
motif_[i] = subst(motif_[i], new_b, j)
return motif_
def mutate_motif_k_times_ref(motif, k):
motif_ = motif[:]
n = len(motif)
L = len(motif[0])
N = n * L
k_so_far = 0
choices = []
while k_so_far < k:
i = random.randrange(n)
j = random.randrange(L)
if (i, j) in choices:
continue
else:
choices.append((i, j))
k_so_far += 1
b = motif[i][j]
new_b = random.choice([c for c in "ACGT" if not c == b])
motif_[i] = subst(motif_[i], new_b, j)
return motif_
def sample_site_cftp(matrix, mu, Ne):
L = len(matrix)
f = seq_scorer(matrix)
def log_phat(s):
ep = f(s)
nu = Ne - 1
return -nu*log(1 + exp(ep - mu))
first_site = "A"*L
last_site = "T"*L
best_site = "".join(["ACGT"[argmin(row)] for row in matrix])
worst_site = "".join(["ACGT"[argmax(row)] for row in matrix])
#middle_sites = [[random_site(L)] for i in range(10)]
#trajs = [[best_site]] + middle_sites + [[worst_site]]
trajs = [[best_site],[worst_site]]
ords = [rslice("ACGT",sorted_indices(row)) for row in matrix]
def mutate_site(site,(ri,direction)):
b = (site[ri])
idx = ords[ri].index(b)
idxp = min(max(idx + direction,0),3)
bp = ords[ri][idxp]
return subst(site,bp,ri)
def do_query(self, q):
"""
Query solution.
Consider the following example;
> f(1) := 1.
> f(2) := 4.
There a few versions of query:
- `vquery` shows variable bindings
> vquery f(X)
1 where {X=1}
4 where {X=1}
- `query` shows variable bindings applied to query
> query f(X)
f(1) = 1.
f(2) = 4.
- `trace` is an introspection tool for visualizing the derivation of an
item and its value. Type `help trace` for more information.
"""
results = self._query(q)
if results is None:
return
if len(results) == 0:
print 'No results.'
return
print
for term, result in sorted(
(subst(q, result), result) for result in results):
print '%s = %s.' % (term, _repr(todyna(result['$val'])))
print
def do_query(self, q):
"""
Query solution.
Consider the following example;
> f(1) := 1.
> f(2) := 4.
There a few versions of query:
- `vquery` shows variable bindings
> vquery f(X)
1 where {X=1}
4 where {X=1}
- `query` shows variable bindings applied to query
> query f(X)
f(1) = 1.
f(2) = 4.
- `trace` is an introspection tool for visualizing the derivation of an
item and its value. Type `help trace` for more information.
"""
results = self._query(q)
if results is None:
return
if len(results) == 0:
print "No results."
return
print
for term, result in sorted((subst(q, result), result) for result in results):
print "%s = %s." % (term, _repr(todyna(result["$val"])))
print