def global_align(s, t, matrix, gap):
# Score of best alignment ending with a match or mismatch.
M = [[0 for j in range(len(t)+1)] for i in range(len(s)+1)]
# Initialize the gap matrices with an arbitrarily small number.
# Score of best alignment ending with a space in X.
X = [[-9999 for j in range(len(t)+1)] for i in range(len(s)+1)]
# Score of best alignment ending with a space in Y.
Y = [[-9999 for j in range(len(t)+1)] for i in range(len(s)+1)]
for i in range(1, len(s)+1):
M[i][0] = gap
for j in range(1, len(t)+1):
M[0][j] = gap
for i in range(1, len(s)+1):
for j in range(1, len(t)+1):
X[i][j] = max([M[i-1][j] + gap,
X[i-1][j]])
Y[i][j] = max([M[i][j-1] + gap,
Y[i][j-1]])
M[i][j] = max([M[i-1][j-1] + match_score(matrix, s[i-1], t[j-1]),
X[i][j],
Y[i][j]])
# The max possible score is found at the bottom-right corner of the matrix.
return(M[-1][-1])
def global_align(s, t, matrix, gap):
# Score of best alignment ending with a match or mismatch.
M = [[0 for j in range(len(t) + 1)] for i in range(len(s) + 1)]
# Initialize the gap matrices with an arbitrarily small number.
# Score of best alignment ending with a space in X.
X = [[-9999 for j in range(len(t) + 1)] for i in range(len(s) + 1)]
# Score of best alignment ending with a space in Y.
Y = [[-9999 for j in range(len(t) + 1)] for i in range(len(s) + 1)]
for i in range(1, len(s) + 1):
M[i][0] = gap
for j in range(1, len(t) + 1):
M[0][j] = gap
for i in range(1, len(s) + 1):
for j in range(1, len(t) + 1):
X[i][j] = max([M[i - 1][j] + gap, X[i - 1][j]])
Y[i][j] = max([M[i][j - 1] + gap, Y[i][j - 1]])
M[i][j] = max([
M[i - 1][j - 1] + match_score(matrix, s[i - 1], t[j - 1]),
X[i][j], Y[i][j]
])
# The max possible score is found at the bottom-right corner of the matrix.
return M[-1][-1]
def local_align_with_affine(s, t, scores, gap, gap_e):
# Initialize the arrays that will contain the previous round of scores.
Sx = [0 for i in range(len(t)+1)]
Sy = [0 for j in range(len(t)+1)]
Sm = [0 for i in range(len(t)+1)]
# Initialize the traceback matrix.
traceback = [[0 for j in range(len(t)+1)] for i in range(len(s)+1)]
best = -1
best_pos = (0, 0)
# Fill in the Score and Traceback matrices.
for i in range(1, len(s)+1):
new_x = [0 for i in range(len(t)+1)]
new_y = [0 for i in range(len(t)+1)]
new_m = [0 for i in range(len(t)+1)]
for j in range(1, len(t)+1):
new_x[j] = max([Sm[j] + gap, Sx[j] + gap_e])
new_y[j] = max([new_m[j-1] + gap, new_y[j-1] + gap_e])
costM = [Sm[j-1] + match_score(scores, s[i-1], t[j-1]),
new_x[j],
new_y[j],
0]
new_m[j] = max(costM)
traceback[i][j] = costM.index(new_m[j])
if new_m[j] > best:
best = new_m[j]
best_pos = i, j
Sx = new_x
Sy = new_y
Sm = new_m
# Initialize the values of i, j
i, j = best_pos
# Initialize the aligned strings as the input strings.
r, u = s[:i], t[:j]
# Traceback to build alignment.
while traceback[i][j] != 3 and i*j != 0:
if traceback[i][j] == 0:
i -= 1
j -= 1
elif traceback[i][j] == 1:
i -= 1
elif traceback[i][j] == 2:
j -= 1
r = r[i:]
u = u[j:]
return str(best), r, u
def alignment_score(s, t, scores, gap):
''' Returns two matrices of the edit distance and edit alignment between
strings s and t.
'''
# Initialize the similarity and traceback matrices.
S = [[0 for j in range(len(t)+1)] for i in range(len(s)+1)]
traceback = [[3 for j in range(len(t)+1)] for i in range(len(s)+1)]
best = 0
best_pos = (0, 0)
# Fill in the matrices.
for i in range(1, len(s)+1):
for j in range(1, len(t)+1):
cost = [ S[i-1][j-1] + match_score(scores, s[i-1], t[j-1]),
S[i-1][j] + gap,
S[i][j-1] + gap,
0 ]
S[i][j] = max(cost)
traceback[i][j] = cost.index(S[i][j])
if S[i][j] >= best:
best = S[i][j]
best_pos = (i, j)
# Initialize the values of i,j as the index of the highest score.
i, j = best_pos
# Initialize the aligned strings as the prefix of the best position.
r, u = s[:i], t[:j]
# Trace back to the edge of the matrix starting at the best position.
while traceback[i][j] != 3 and i*j != 0:
if traceback[i][j] == 0: # a match
i -= 1
j -= 1
elif traceback[i][j] == 1: # an insertion
i -= 1
elif traceback[i][j] == 2: # a deletion
j -= 1
# The optimal alignment is then the suffix of the end of the traceback.
r = r[i:]
u = u[j:]
return str(best), r, u
def global_align(s, t, scores, gap):
# Initialize the similarity matrix.
S = [[0 for j in range(len(t) + 1)] for i in range(len(s) + 1)]
for i in range(1, len(s) + 1):
S[i][0] = i * gap
for j in range(1, len(t) + 1):
S[0][j] = j * gap
for i in range(1, len(s) + 1):
for j in range(1, len(t) + 1):
S[i][j] = max([
S[i - 1][j - 1] + match_score(scores, s[i - 1], t[j - 1]),
S[i - 1][j] + gap, S[i][j - 1] + gap
])
return S[-1][-1]
def global_align(s, t, scores, gap):
# Initialize the similarity matrix.
S = [[0 for j in range(len(t)+1)] for i in range(len(s)+1)]
# Each cell in the first row and column recieves a gap penalty.
for i in range(1, len(s)+1):
S[i][0] = i * gap
for j in range(1, len(t)+1):
S[0][j] = j * gap
# Fill in the similarity matrix.
for i in range(1, len(s)+1):
for j in range(1, len(t)+1):
S[i][j] = max([ S[i-1][j-1] + match_score(scores, s[i-1], t[j-1]),
S[i-1][j] + gap,
S[i][j-1] + gap ])
# The max possible score is the last cell of the similarity matrix.
return S[-1][-1]
def global_align_with_affine(s, t, scores, gap, gap_e):
''' Returns two matrices of the edit distance and edit alignment between
strings s and t.
'''
# Initialize the three score matrices...
M = [[0 for j in range(len(t) + 1)]
for i in range(len(s) + 1)] # a (mis)match
X = [[0 for j in range(len(t) + 1)]
for i in range(len(s) + 1)] # a gap in X
Y = [[0 for j in range(len(t) + 1)]
for i in range(len(s) + 1)] # a gap in Y
# ...and the traceback matrices.
traceM = [[0 for j in range(len(t) + 1)] for i in range(len(s) + 1)]
traceX = [[0 for j in range(len(t) + 1)] for i in range(len(s) + 1)]
traceY = [[0 for j in range(len(t) + 1)] for i in range(len(s) + 1)]
# Initialize the edges of the X and Y matrices with an arbitrarily
# large number (closer to negative infinity, the better) so it doesn't
# affect calculations.
for i in range(1, len(s) + 1):
M[i][0] = gap + gap_e * (i - 1)
X[i][0] = -9999
Y[i][0] = -9999
for j in range(1, len(t) + 1):
M[0][j] = gap + gap_e * (j - 1)
X[0][j] = -9999
Y[0][j] = -9999
# Fill in the matrices.
for i in range(1, len(s) + 1):
for j in range(1, len(t) + 1):
costX = [M[i - 1][j] + gap, X[i - 1][j] + gap_e]
X[i][j] = max(costX)
traceX[i][j] = costX.index(X[i][j])
costY = [M[i][j - 1] + gap, Y[i][j - 1] + gap_e]
Y[i][j] = max(costY)
traceY[i][j] = costY.index(Y[i][j])
costM = [
M[i - 1][j - 1] + match_score(scores, s[i - 1], t[j - 1]),
X[i][j], Y[i][j]
]
M[i][j] = max(costM)
traceM[i][j] = costM.index(M[i][j])
# The max possible score is found at the bottom-right of the match matrix
max_score = M[-1][-1]
# Initialize the aligned strings as the input strings.
s_align, t_align = s, t
# Get the traceback starting position, i.e. the greatest value.
scores = [X[i][j], Y[i][j], M[i][j]]
max_score = max(scores)
traceback = scores.index(max_score)
# Initialize the values of i,j
i, j = len(s), len(t)
# Traceback to build alignment.
while i > 0 and j > 0:
if traceback == 0:
if traceX[i][j] == 0:
traceback = 2
i -= 1
t_align = t_align[:j] + '-' + t_align[j:]
elif traceback == 1:
if traceY[i][j] == 0:
traceback = 2
j -= 1
s_align = s_align[:i] + '-' + s_align[i:]
elif traceback == 2:
if traceM[i][j] == 1:
traceback = 0
elif traceM[i][j] == 2:
traceback = 1
else:
i -= 1
j -= 1
# Fill in any leading gaps.
for remaining in range(i):
t_align = t_align[:0] + '-' + t_align[0:]
for remaining in range(j):
s_align = s_align[:0] + '-' + s_align[0:]
return (str(max_score), s_align, t_align)
def global_align_with_affine(s, t, scores, gap, gap_e):
''' Returns two matrices of the edit distance and edit alignment between
strings s and t.
'''
# Initialize the three score matrices...
M = [[0 for j in range(len(t)+1)] for i in range(len(s)+1)] # a (mis)match
X = [[0 for j in range(len(t)+1)] for i in range(len(s)+1)] # a gap in X
Y = [[0 for j in range(len(t)+1)] for i in range(len(s)+1)] # a gap in Y
# ...and the traceback matrices.
traceM = [[0 for j in range(len(t)+1)] for i in range(len(s)+1)]
traceX = [[0 for j in range(len(t)+1)] for i in range(len(s)+1)]
traceY = [[0 for j in range(len(t)+1)] for i in range(len(s)+1)]
# Initialize the edges of the X and Y matrices with an arbitrarily
# large number (closer to negative infinity, the better) so it doesn't
# affect calculations.
for i in range(1, len(s)+1):
M[i][0] = gap + gap_e*(i-1)
X[i][0] = -9999
Y[i][0] = -9999
for j in range(1, len(t)+1):
M[0][j] = gap + gap_e*(j-1)
X[0][j] = -9999
Y[0][j] = -9999
# Fill in the matrices.
for i in range(1, len(s)+1):
for j in range(1, len(t)+1):
costX = [M[i-1][j] + gap,
X[i-1][j] + gap_e]
X[i][j] = max(costX)
traceX[i][j] = costX.index(X[i][j])
costY = [M[i][j-1] + gap,
Y[i][j-1] + gap_e]
Y[i][j] = max(costY)
traceY[i][j] = costY.index(Y[i][j])
costM = [M[i-1][j-1] + match_score(scores, s[i-1], t[j-1]),
X[i][j],
Y[i][j]]
M[i][j] = max(costM)
traceM[i][j] = costM.index(M[i][j])
# The max possible score is found at the bottom-right of the match matrix
max_score = M[-1][-1]
# Initialize the aligned strings as the input strings.
s_align, t_align = s, t
# Get the traceback starting position, i.e. the greatest value.
scores = [X[i][j], Y[i][j], M[i][j]]
max_score = max(scores)
traceback = scores.index(max_score)
# Initialize the values of i,j
i, j = len(s), len(t)
# Traceback to build alignment.
while i>0 and j>0:
if traceback == 0:
if traceX[i][j] == 0:
traceback = 2
i -= 1
t_align = t_align[:j] + '-' + t_align[j:]
elif traceback == 1:
if traceY[i][j] == 0:
traceback = 2
j -= 1
s_align = s_align[:i] + '-' + s_align[i:]
elif traceback == 2:
if traceM[i][j] == 1:
traceback = 0
elif traceM[i][j] == 2:
traceback = 1
else:
i -= 1
j -= 1
# Fill in any leading gaps.
for remaining in range(i):
t_align = t_align[:0] + '-' + t_align[0:]
for remaining in range(j):
s_align = s_align[:0] + '-' + s_align[0:]
return str(max_score), s_align, t_align
