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bm_preproc.py
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bm_preproc.py
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#!/usr/bin/env python
"""bm_preproc.py: Boyer-Moore preprocessing."""
__author__ = "Ben Langmead"
import unittest
def z_array(s):
""" Use Z algorithm (Gusfield theorem 1.4.1) to preprocess s """
assert len(s) > 1
z = [len(s)] + [0] * (len(s)-1)
# Initial comparison of s[1:] with prefix
for i in range(1, len(s)):
if s[i] == s[i-1]:
z[1] += 1
else:
break
r, l = 0, 0
if z[1] > 0:
r, l = z[1], 1
for k in range(2, len(s)):
assert z[k] == 0
if k > r:
# Case 1
for i in range(k, len(s)):
if s[i] == s[i-k]:
z[k] += 1
else:
break
r, l = k + z[k] - 1, k
else:
# Case 2
# Calculate length of beta
nbeta = r - k + 1
zkp = z[k - l]
if nbeta > zkp:
# Case 2a: zkp wins
z[k] = zkp
else:
# Case 2b: Compare characters just past r
nmatch = 0
for i in range(r+1, len(s)):
if s[i] == s[i - k]:
nmatch += 1
else:
break
l, r = k, r + nmatch
z[k] = r - k + 1
return z
def n_array(s):
""" Compile the N array (Gusfield theorem 2.2.2) from the Z array """
return z_array(s[::-1])[::-1]
def big_l_prime_array(p, n):
""" Compile L' array (Gusfield theorem 2.2.2) using p and N array.
L'[i] = largest index j less than n such that N[j] = |P[i:]| """
lp = [0] * len(p)
for j in range(len(p)-1):
i = len(p) - n[j]
if i < len(p):
lp[i] = j + 1
return lp
def big_l_array(p, lp):
""" Compile L array (Gusfield theorem 2.2.2) using p and L' array.
L[i] = largest index j less than n such that N[j] >= |P[i:]| """
l = [0] * len(p)
l[1] = lp[1]
for i in range(2, len(p)):
l[i] = max(l[i-1], lp[i])
return l
def small_l_prime_array(n):
""" Compile lp' array (Gusfield theorem 2.2.4) using N array. """
small_lp = [0] * len(n)
for i in range(len(n)):
if n[i] == i+1: # prefix matching a suffix
small_lp[len(n)-i-1] = i+1
for i in range(len(n)-2, -1, -1): # "smear" them out to the left
if small_lp[i] == 0:
small_lp[i] = small_lp[i+1]
return small_lp
def good_suffix_table(p):
""" Return tables needed to apply good suffix rule. """
n = n_array(p)
lp = big_l_prime_array(p, n)
return lp, big_l_array(p, lp), small_l_prime_array(n)
def good_suffix_mismatch(i, big_l_prime, small_l_prime):
""" Given a mismatch at offset i, and given L/L' and l' arrays,
return amount to shift as determined by good suffix rule. """
length = len(big_l_prime)
assert i < length
if i == length - 1:
return 0
i += 1 # i points to leftmost matching position of P
if big_l_prime[i] > 0:
return length - big_l_prime[i]
return length - small_l_prime[i]
def good_suffix_match(small_l_prime):
""" Given a full match of P to T, return amount to shift as
determined by good suffix rule. """
return len(small_l_prime) - small_l_prime[1]
def dense_bad_char_tab(p, amap):
""" Given pattern string and list with ordered alphabet characters, create
and return a dense bad character table. Table is indexed by offset
then by character. """
tab = []
nxt = [0] * len(amap)
for i in range(0, len(p)):
c = p[i]
assert c in amap
tab.append(nxt[:])
nxt[amap[c]] = i+1
return tab
class BoyerMoore(object):
""" Encapsulates pattern and associated Boyer-Moore preprocessing. """
def __init__(self, p, alphabet='ACGT'):
# Create map from alphabet characters to integers
self.amap = {alphabet[i]: i for i in range(len(alphabet))}
# Make bad character rule table
self.bad_char = dense_bad_char_tab(p, self.amap)
# Create good suffix rule table
_, self.big_l, self.small_l_prime = good_suffix_table(p)
def bad_character_rule(self, i, c):
""" Return # skips given by bad character rule at offset i """
assert c in self.amap
assert i < len(self.bad_char)
ci = self.amap[c]
return i - (self.bad_char[i][ci]-1)
def good_suffix_rule(self, i):
""" Given a mismatch at offset i, return amount to shift
as determined by (weak) good suffix rule. """
length = len(self.big_l)
assert i < length
if i == length - 1:
return 0
i += 1 # i points to leftmost matching position of P
if self.big_l[i] > 0:
return length - self.big_l[i]
return length - self.small_l_prime[i]
def match_skip(self):
""" Return amount to shift in case where P matches T """
return len(self.small_l_prime) - self.small_l_prime[1]
class TestBoyerMoorePreproc(unittest.TestCase):
def test_z_1(self):
s = 'abb'
# -00
z = z_array(s)
self.assertEqual([3, 0, 0], z)
def test_z_2(self):
s = 'abababab'
# 00604020
z = z_array(s)
self.assertEqual([8, 0, 6, 0, 4, 0, 2, 0], z)
def test_z_3(self):
s = 'abababab'
# 00604020
z = z_array(s)
self.assertEqual([8, 0, 6, 0, 4, 0, 2, 0], z)
def test_n_1(self):
s = 'abb'
# 01-
n = n_array(s)
self.assertEqual([0, 1, 3], n)
def test_n_2(self):
s = 'abracadabra'
# 1004010100-
n = n_array(s)
self.assertEqual([1, 0, 0, 4, 0, 1, 0, 1, 0, 0, 11], n)
def test_n_3(self):
s = 'abababab'
# 0204060-
n = n_array(s)
self.assertEqual([0, 2, 0, 4, 0, 6, 0, 8], n)
def test_big_l_prime_1(self):
s = 'abb'
# 001
big_l_prime = big_l_prime_array(s, n_array(s))
self.assertEqual([0, 0, 2], big_l_prime)
def test_big_l_prime_2(self):
s = 'abracadabra'
# 01234567890
# L' 00000003007
# L 00000003337
big_l_prime = big_l_prime_array(s, n_array(s))
self.assertEqual([0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 8], big_l_prime)
def test_small_l_prime_1(self):
s = 'abracadabra'
# N 1004010100-
# l' 1
# l' 4
# l' 44444444111
small_l_prime = small_l_prime_array(n_array(s))
self.assertEqual([11, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1], small_l_prime)
def test_good_suffix_match_mismatch_1(self):
p = 'GGTAGGT'
big_l_prime, big_l, small_l_prime = good_suffix_table(p)
self.assertEqual([0, 0, 0, 0, 3, 0, 0], big_l_prime)
self.assertEqual([0, 0, 0, 0, 3, 3, 3], big_l)
self.assertEqual([7, 3, 3, 3, 3, 0, 0], small_l_prime)
self.assertEqual(0, good_suffix_mismatch(6, big_l_prime, small_l_prime))
self.assertEqual(0, good_suffix_mismatch(6, big_l, small_l_prime))
# t: xT
# p: GGTAGGT
# L': -000300
# L: -000333
self.assertEqual(7, good_suffix_mismatch(5, big_l_prime, small_l_prime))
self.assertEqual(4, good_suffix_mismatch(5, big_l, small_l_prime))
# t: xGT
# p: GGTAGGT
# L': -000300
# L: -000333
self.assertEqual(7, good_suffix_mismatch(4, big_l_prime, small_l_prime))
self.assertEqual(4, good_suffix_mismatch(4, big_l, small_l_prime))
# t: xGGT
# p: GGTAGGT
# L': -000300
# L: -000333
self.assertEqual(4, good_suffix_mismatch(3, big_l_prime, small_l_prime))
self.assertEqual(4, good_suffix_mismatch(3, big_l, small_l_prime))
# t: xAGGT
# p: GGTAGGT
# L': -000300
# L: -000333
self.assertEqual(4, good_suffix_mismatch(2, big_l_prime, small_l_prime))
self.assertEqual(4, good_suffix_mismatch(2, big_l, small_l_prime))
# t: xTAGGT
# p: GGTAGGT
# L': -000300
# L: -000333
self.assertEqual(4, good_suffix_mismatch(1, big_l_prime, small_l_prime))
self.assertEqual(4, good_suffix_mismatch(1, big_l, small_l_prime))
# t: xGTAGGT
# p: GGTAGGT
# L': -000300
# L: -000333
self.assertEqual(4, good_suffix_mismatch(0, big_l_prime, small_l_prime))
self.assertEqual(4, good_suffix_mismatch(0, big_l, small_l_prime))
def test_good_suffix_table_1(self):
s = 'abb'
# 001
big_l_prime, big_l, small_l_prime = good_suffix_table(s)
self.assertEqual([0, 0, 2], big_l_prime)
self.assertEqual([0, 0, 2], big_l)
self.assertEqual([3, 0, 0], small_l_prime)
def test_good_suffix_table_2(self):
s = 'abracadabra'
# 01234567890
# L' 00000003007
# L 00000003337
# l' -4444444111
big_l_prime, big_l, small_l_prime = good_suffix_table(s)
self.assertEqual([0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 8], big_l_prime)
self.assertEqual([0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 8], big_l)
self.assertEqual([11, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1], small_l_prime)
if __name__ == '__main__':
unittest.main()