def score(self,n_ijk,alpha_ijk_in):
alpha_ijk = copy.deepcopy(alpha_ijk_in)
prod_k = sum22(subtract(matrixGammaLog(add(n_ijk,alpha_ijk)),matrixGammaLog(alpha_ijk)))
alpha_ij = sum22(alpha_ijk_in)
n_ij = sum22(n_ijk)
prod_ij = subtract(matrixGammaLog(alpha_ij), matrixGammaLog(add(alpha_ij,n_ij)))
return sum2(add(prod_ij,prod_k))
def multiply_karatsuba(x, y):
"""
Multiplies two numbers represented as arrays
using the Karatsuba algorithm, falling back
on grade school algorithm for the base case
:param x: []int
:param y: []int
:rtype []int
"""
x, y = match_padding(x, y)
a, b = split(x)
c, d = split(y)
if len(x) == 1:
return multiply_simple(x, y)
res_1 = multiply_karatsuba(a, c)
res_2 = multiply_karatsuba(b, d)
partial = multiply_karatsuba(add(a, b), add(c, d))
# res_3 is partial - res_1 - res_2.
# To simplify, just add res_1 and res_2 then subtract that sum from partial
res_3 = subtract(partial, add(res_1, res_2))
res = add(pad(res_1, len(x), 'right'), res_2,
pad(res_3, (len(x) + 1) // 2, 'right'))
return res
def multiply_karatsuba_parallel(x, y, key=None):
"""
Multiplies two numbers represented as arrays
using the Karatsuba algorithm, falling back
on grade school algorithm for the base case
:param x: []int
:param y: []int
:rtype []int
"""
x, y = match_padding(x, y)
a, b = split(x)
c, d = split(y)
# for base case, go simple
if len(x) == 1:
return multiply_simple(x, y)
# for big numbers, go parallel
if len(x) > 300:
# generate random ids for the subprocess outputs
r1 = random.random()
r2 = random.random()
r3 = random.random()
# run the sub-multiplications in parallel
p1 = Process(target=multiply_karatsuba_parallel, args=[a, c, r1])
p2 = Process(target=multiply_karatsuba_parallel, args=[b, d, r2])
p3 = Process(target=multiply_karatsuba_parallel,
args=[add(a, b), add(c, d), r3])
p1.start()
p2.start()
p3.start()
p1.join()
p2.join()
p3.join()
# get the results
res_1 = return_dict[r1]
res_2 = return_dict[r2]
partial = return_dict[r3]
# for smaller numbers, don't bother parallelizing
else:
res_1 = multiply_karatsuba_parallel(a, c)
res_2 = multiply_karatsuba_parallel(b, d)
partial = multiply_karatsuba_parallel(add(a, b), add(c, d))
# do the karatsuba shuffle
res_3 = subtract(partial, add(res_1, res_2))
res = add(pad(res_1, len(x), 'right'), res_2,
pad(res_3, (len(x) + 1) // 2, 'right'))
# if we are in parallel mode, write the result to the global dict
if key is not None:
return_dict[key] = res
return res
def distance_along_edge_to_point(edge, distance_along_edge):
edge_start, edge_end = edge
edge_vector = util.subtract(edge_end, edge_start)
edge_length = util.norm(edge_vector)
scale_factor = distance_along_edge / edge_length
scaled_vector = util.scale(scale_factor, edge_vector)
point = util.add(scaled_vector, edge_start)
return point
def compute_edge_length(self, tube_point_a, tube_point_b):
tube_coords_a = [tube_point_a.geospatial[0], tube_point_b.geospatial[1],
tube_point_a.tube_elevation]
tube_coords_b = [tube_point_b.geospatial[0], tube_point_b.geospatial[1],
tube_point_b.tube_elevation]
edge_vector = util.subtract(tube_coords_a, tube_coords_b)
edge_length = np.linalg.norm(edge_vector)
return edge_length
def get_alignment(self):
"""
:return: alignment represented as a tuple of aligned strings
"""
# start from point with maximum value
result = ("", "",
np.unravel_index(self.scores.argmax(), self.scores.shape))
self.alignment_points = []
# add candidates according to scores matrix
while True:
aligned1, aligned2, point = result
self.alignment_points.append(point)
if self.scores[point] == 0:
return result[0:2]
else:
letter1 = self.string1[point[1] - 1]
letter2 = self.string2[point[0] - 1]
if self.scores[point] - self.scores[subtract(
point, (1, 1))] == self.subs[letter1][letter2]:
result = (letter1 + aligned1, letter2 + aligned2,
subtract(point, (1, 1)))
elif self.scores[point] - self.scores[subtract(
point, (1, 0))] == self.gap_penalty:
result = ("-" + aligned1, letter2 + aligned2,
subtract(point, (1, 0)))
elif self.scores[point] - self.scores[subtract(
point, (0, 1))] == self.gap_penalty:
result = (letter1 + aligned1, "-" + aligned2,
subtract(point, (0, 1)))
def get_alignments(self):
"""
:return: list of alignments, where each alignment is represented
as a tuple of aligned strings
"""
# keep candidates in stack
stack = [("", "", (self.rows - 1, self.cols - 1))]
alignments = []
# loop candidates until stack is empty
while stack:
aligned1, aligned2, point = stack.pop()
if point == (0, 0):
# stop condition
alignments.append((aligned1, aligned2))
continue
letter1 = self.string1[point[1] - 1]
letter2 = self.string2[point[0] - 1]
# add candidates according to scores matrix
if self.scores[point] - self.scores[subtract(
point, (1, 1))] == self.subs[letter1][letter2]:
stack.append((letter1 + aligned1, letter2 + aligned2,
subtract(point, (1, 1))))
if self.scores[point] - self.scores[subtract(
point, (1, 0))] == self.gap_penalty:
stack.append(("-" + aligned1, letter2 + aligned2,
subtract(point, (1, 0))))
if self.scores[point] - self.scores[subtract(
point, (0, 1))] == self.gap_penalty:
stack.append((letter1 + aligned1, "-" + aligned2,
subtract(point, (0, 1))))
return alignments
import torch