mirror of https://github.com/explosion/spaCy.git
176 lines
4.5 KiB
Cython
176 lines
4.5 KiB
Cython
# cython: infer_types=True
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'''Do Levenshtein alignment, for evaluation of tokenized input.
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Random notes:
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r i n g
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0 1 2 3 4
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r 1 0 1 2 3
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a 2 1 1 2 3
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n 3 2 2 1 2
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g 4 3 3 2 1
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0,0: (1,1)=min(0+0,1+1,1+1)=0 S
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1,0: (2,1)=min(1+1,0+1,2+1)=1 D
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2,0: (3,1)=min(2+1,3+1,1+1)=2 D
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3,0: (4,1)=min(3+1,4+1,2+1)=3 D
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0,1: (1,2)=min(1+1,2+1,0+1)=1 D
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1,1: (2,2)=min(0+1,1+1,1+1)=1 S
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2,1: (3,2)=min(1+1,1+1,2+1)=2 S or I
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3,1: (4,2)=min(2+1,2+1,3+1)=3 S or I
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0,2: (1,3)=min(2+1,3+1,1+1)=2 I
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1,2: (2,3)=min(1+1,2+1,1+1)=2 S or I
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2,2: (3,3)
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3,2: (4,3)
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At state (i, j) we're asking "How do I transform S[:i+1] to T[:j+1]?"
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We know the costs to transition:
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S[:i] -> T[:j] (at D[i,j])
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S[:i+1] -> T[:j] (at D[i+1,j])
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S[:i] -> T[:j+1] (at D[i,j+1])
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Further, we now we can tranform:
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S[:i+1] -> S[:i] (DEL) for 1,
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T[:j+1] -> T[:j] (INS) for 1.
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S[i+1] -> T[j+1] (SUB) for 0 or 1
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Therefore we have the costs:
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SUB: Cost(S[:i]->T[:j]) + Cost(S[i]->S[j])
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i.e. D[i, j] + S[i+1] != T[j+1]
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INS: Cost(S[:i+1]->T[:j]) + Cost(T[:j+1]->T[:j])
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i.e. D[i+1,j] + 1
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DEL: Cost(S[:i]->T[:j+1]) + Cost(S[:i+1]->S[:i])
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i.e. D[i,j+1] + 1
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Source string S has length m, with index i
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Target string T has length n, with index j
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Output two alignment vectors: i2j (length m) and j2i (length n)
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# function LevenshteinDistance(char s[1..m], char t[1..n]):
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# for all i and j, d[i,j] will hold the Levenshtein distance between
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# the first i characters of s and the first j characters of t
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# note that d has (m+1)*(n+1) values
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# set each element in d to zero
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ring rang
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- r i n g
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- 0 0 0 0 0
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r 0 0 0 0 0
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a 0 0 0 0 0
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n 0 0 0 0 0
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g 0 0 0 0 0
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# source prefixes can be transformed into empty string by
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# dropping all characters
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# d[i, 0] := i
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ring rang
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- r i n g
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- 0 0 0 0 0
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r 1 0 0 0 0
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a 2 0 0 0 0
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n 3 0 0 0 0
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g 4 0 0 0 0
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# target prefixes can be reached from empty source prefix
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# by inserting every character
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# d[0, j] := j
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- r i n g
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- 0 1 2 3 4
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r 1 0 0 0 0
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a 2 0 0 0 0
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n 3 0 0 0 0
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g 4 0 0 0 0
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'''
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import numpy
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cimport numpy as np
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from .compat import unicode_
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from murmurhash.mrmr cimport hash32
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def align(S, T):
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cdef int m = len(S)
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cdef int n = len(T)
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cdef np.ndarray matrix = numpy.zeros((m+1, n+1), dtype='int32')
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cdef np.ndarray i2j = numpy.zeros((m,), dtype='i')
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cdef np.ndarray j2i = numpy.zeros((n,), dtype='i')
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cdef np.ndarray S_arr = _convert_sequence(S)
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cdef np.ndarray T_arr = _convert_sequence(T)
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fill_matrix(<int*>matrix.data,
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<const int*>S_arr.data, m, <const int*>T_arr.data, n)
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fill_i2j(i2j, matrix)
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fill_j2i(j2i, matrix)
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return matrix[-1,-1], i2j, j2i, matrix
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def _convert_sequence(seq):
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if isinstance(seq, numpy.ndarray):
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return numpy.ascontiguousarray(seq, dtype='i')
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cdef np.ndarray output = numpy.zeros((len(seq),), dtype='i')
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cdef bytes item_bytes
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for i, item in enumerate(seq):
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if isinstance(item, unicode):
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item_bytes = item.encode('utf8')
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else:
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item_bytes = item
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output[i] = hash32(<void*><char*>item_bytes, len(item_bytes), 0)
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return output
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cdef void fill_matrix(int* D,
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const int* S, int m, const int* T, int n) nogil:
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m1 = m+1
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n1 = n+1
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for i in range(m1*n1):
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D[i] = 0
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for i in range(m1):
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D[i*n1] = i
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for j in range(n1):
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D[j] = j
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cdef int sub_cost, ins_cost, del_cost
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for j in range(n):
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for i in range(m):
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i_j = i*n1 + j
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i1_j1 = (i+1)*n1 + j+1
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i1_j = (i+1)*n1 + j
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i_j1 = i*n1 + j+1
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if S[i] != T[j]:
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sub_cost = D[i_j] + 1
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else:
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sub_cost = D[i_j]
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del_cost = D[i_j1] + 1
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ins_cost = D[i1_j] + 1
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best = min(min(sub_cost, ins_cost), del_cost)
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D[i1_j1] = best
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cdef void fill_i2j(np.ndarray i2j, np.ndarray D) except *:
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j = D.shape[1]-2
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cdef int i = D.shape[0]-2
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while i >= 0:
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while D[i+1, j] < D[i+1, j+1]:
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j -= 1
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if D[i, j+1] < D[i+1, j+1]:
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i2j[i] = -1
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else:
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i2j[i] = j
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j -= 1
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i -= 1
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cdef void fill_j2i(np.ndarray j2i, np.ndarray D) except *:
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i = D.shape[0]-2
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cdef int j = D.shape[1]-2
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while j >= 0:
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while D[i, j+1] < D[i+1, j+1]:
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i -= 1
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if D[i+1, j] < D[i+1, j+1]:
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j2i[j] = -1
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else:
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j2i[j] = i
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i -= 1
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j -= 1
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