def test_relative_entropy(self):
alpha = (2.0, 10.0, 1.0, 1.0)
d = Dirichlet(alpha)
pvec = (0.1, 0.2, 0.3, 0.4)
rent = d.mean_relative_entropy(pvec)
vrent = d.variance_relative_entropy(pvec)
low, high = d.interval_relative_entropy(pvec, 0.95)
# print()
# print('> ', rent, vrent, low, high)
# This test can fail randomly, but the precision from a few
# thousand samples is low. Increasing samples, 1000->2000
samples = 2000
sent = zeros((samples,), float64)
for s in range(samples):
post = d.sample()
e = -entropy(post)
for k in range(4):
e += -post[k] * log(pvec[k])
sent[s] = e
sent.sort()
self.assertTrue(abs(sent.mean() - rent) < 4.0 * sqrt(vrent))
self.assertAlmostEqual(sent.std(), sqrt(vrent), 1)
self.assertTrue(abs(low - sent[int(samples * 0.025)]) < 0.2)
self.assertTrue(abs(high - sent[int(samples * 0.975)]) < 0.2)
def test_relative_entropy(self):
alpha = (2.0, 10.0, 1.0, 1.0)
d = Dirichlet(alpha)
pvec = (0.1, 0.2, 0.3, 0.4)
rent = d.mean_relative_entropy(pvec)
vrent = d.variance_relative_entropy(pvec)
low, high = d.interval_relative_entropy(pvec, 0.95)
# print()
# print('> ', rent, vrent, low, high)
# This test can fail randomly, but the precision from a few
# thousand samples is low. Increasing samples, 1000->2000
samples = 2000
sent = zeros((samples, ), float64)
for s in range(samples):
post = d.sample()
e = -entropy(post)
for k in range(4):
e += -post[k] * log(pvec[k])
sent[s] = e
sent.sort()
self.assertTrue(abs(sent.mean() - rent) < 4. * sqrt(vrent))
self.assertAlmostEqual(sent.std(), sqrt(vrent), 1)
self.assertTrue(abs(low - sent[int(samples * 0.025)]) < 0.2)
self.assertTrue(abs(high - sent[int(samples * 0.975)]) < 0.2)
def do_test(alpha, samples=1000):
ent = zeros((samples,), float64)
# alpha = ones( ( K,), Float64 ) * A/K
# pt = zeros( (len(alpha) ,), Float64)
d = Dirichlet(alpha)
for s in range(samples):
p = d.sample()
# print(p)
# pt +=p
ent[s] = entropy(p)
# print(pt/samples)
m = mean(ent)
v = var(ent)
dm = d.mean_entropy()
dv = d.variance_entropy()
# print(alpha, ':', m, v, dm, dv)
error = 4.0 * sqrt(v / samples)
self.assertTrue(abs(m - dm) < error)
self.assertTrue(abs(v - dv) < error) # dodgy error estimate
def do_test(alpha, samples=1000):
ent = zeros((samples, ), float64)
# alpha = ones( ( K,), Float64 ) * A/K
# pt = zeros( (len(alpha) ,), Float64)
d = Dirichlet(alpha)
for s in range(samples):
p = d.sample()
# print(p)
# pt +=p
ent[s] = entropy(p)
# print(pt/samples)
m = mean(ent)
v = var(ent)
dm = d.mean_entropy()
dv = d.variance_entropy()
# print(alpha, ':', m, v, dm, dv)
error = 4. * sqrt(v / samples)
self.assertTrue(abs(m - dm) < error)
self.assertTrue(abs(v - dv) < error) # dodgy error estimate
def mask_low_complexity(seq, width =12, trigger=1.8, extension=2.0, mask='X') :
""" Mask low complexity regions in protein sequences.
Uses the method of Seg [1] by Wootton & Federhen [2] to divide a sequence
into regions of high and low complexity. The sequence is divided into
overlapping windows. Low complexity windows either have a sequence entropy
less than the trigger complexity, or have an entropy less than the extension
complexity and neighbor other low-complexity windows. The sequence within
a low complexity region is replaced with the mask character (default 'X'),
and the masked alphabetic sequence is returned.
The default parameters, width=12, trigger=1.8, extension=2.0, mask='X' are
suitable for masking protein sequences before a database search. The
standard default seg parameters are width=12, trigger=2.2, extension=2.5
Arguments:
Seq seq -- An alphabetic sequence
int width -- Window width
float trigger -- Entropy in bits between 0 and 4.3.. ( =log_2(20) )
float extension -- Entropy in bits between 0 and 4.3.. ( =log_2(20) )
char mask -- The mask character (default: 'X')
Returns :
Seq -- A masked alphabetic sequence
Raises :
ValueError -- On invalid arguments
Refs:
[1] seg man page:
http://bioportal.weizmann.ac.il/education/materials/gcg/seg.html
[2] Wootton & Federhen (Computers and Chemistry 17; 149-163, (1993))
Authors:
GEC 2005
Future :
- Optional mask character.
- Option to lower case masked symbols.
- Remove arbitary restriction to protein.
"""
lg20 = log2(20)
if trigger<0 or trigger>lg20 :
raise ValueError("Invalid trigger complexity: %f"% trigger)
if extension<0 or extension>lg20 or extension<trigger:
raise ValueError("Invalid extension complexity: %f"% extension)
if width<0 :
raise ValueError("Invalid width: %d"% width)
if width > len(seq) : return seq
s = seq.ords()
X = seq.alphabet.ord(mask)
nwindows = len(seq)- width +1
ent = [ 0 for x in range(0, nwindows)]
count = [ 0 for x in range(0, len(seq.alphabet) )]
for c in s[0:width] : count[c] +=1
ent[0] = entropy(count,2)
for i in range(1, nwindows) :
count[ s[i-1] ] -= 1
count[ s[i+width-1] ] +=1
ent[i] = entropy(count,2)
prev_segged = False
for i in range(0, nwindows) :
if ((prev_segged and ent[i]< extension) or
ent[i]< trigger) :
for j in range(0, width) : s[i+j]=X
prev_segged=True
else :
prev_segged = False
# Redo, only backwards
prev_segged = False
for i in range(nwindows-1, -1, -1) :
if ((prev_segged and ent[i]< extension) or
ent[i]< trigger) :
for j in range(0, width) : s[i+j]=X
prev_segged=True
else :
prev_segged = False
segged = seq.alphabet.chrs(s)
segged.name =seq.name
segged.description = seq.description
return segged
def mask_low_complexity(seq, width=12, trigger=1.8, extension=2.0, mask='X'):
""" Mask low complexity regions in protein sequences.
Uses the method of Seg [1] by Wootton & Federhen [2] to divide a sequence
into regions of high and low complexity. The sequence is divided into
overlapping windows. Low complexity windows either have a sequence entropy
less than the trigger complexity, or have an entropy less than the extension
complexity and neighbor other low-complexity windows. The sequence within
a low complexity region is replaced with the mask character (default 'X'),
and the masked alphabetic sequence is returned.
The default parameters, width=12, trigger=1.8, extension=2.0, mask='X' are
suitable for masking protein sequences before a database search. The
standard default seg parameters are width=12, trigger=2.2, extension=2.5
Arguments:
Seq seq -- An alphabetic sequence
int width -- Window width
float trigger -- Entropy in bits between 0 and 4.3.. ( =log_2(20) )
float extension -- Entropy in bits between 0 and 4.3.. ( =log_2(20) )
char mask -- The mask character (default: 'X')
Returns :
Seq -- A masked alphabetic sequence
Raises :
ValueError -- On invalid arguments
Refs:
[1] seg man page:
http://bioportal.weizmann.ac.il/education/materials/gcg/seg.html
[2] Wootton & Federhen (Computers and Chemistry 17; 149-163, (1993))
Authors:
GEC 2005
Future :
- Optional mask character.
- Option to lower case masked symbols.
- Remove arbitary restriction to protein.
"""
lg20 = log2(20)
if trigger < 0 or trigger > lg20:
raise ValueError("Invalid trigger complexity: %f" % trigger)
if extension < 0 or extension > lg20 or extension < trigger:
raise ValueError("Invalid extension complexity: %f" % extension)
if width < 0:
raise ValueError("Invalid width: %d" % width)
if width > len(seq): return seq
s = seq.ords()
X = seq.alphabet.ord(mask)
nwindows = len(seq) - width + 1
ent = [0 for x in range(0, nwindows)]
count = [0 for x in range(0, len(seq.alphabet))]
for c in s[0:width]:
count[c] += 1
ent[0] = entropy(count, 2)
for i in range(1, nwindows):
count[s[i - 1]] -= 1
count[s[i + width - 1]] += 1
ent[i] = entropy(count, 2)
prev_segged = False
for i in range(0, nwindows):
if ((prev_segged and ent[i] < extension) or ent[i] < trigger):
for j in range(0, width):
s[i + j] = X
prev_segged = True
else:
prev_segged = False
# Redo, only backwards
prev_segged = False
for i in range(nwindows - 1, -1, -1):
if ((prev_segged and ent[i] < extension) or ent[i] < trigger):
for j in range(0, width):
s[i + j] = X
prev_segged = True
else:
prev_segged = False
segged = seq.alphabet.chrs(s)
segged.name = seq.name
segged.description = seq.description
return segged
