// util/edit-distance-inl.h
// Copyright 2009-2011 Microsoft Corporation; Haihua Xu; Yanmin Qian
// See ../../COPYING for clarification regarding multiple authors
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
// http://www.apache.org/licenses/LICENSE-2.0
// THIS CODE IS PROVIDED *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
// KIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED
// WARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR PURPOSE,
// MERCHANTABLITY OR NON-INFRINGEMENT.
// See the Apache 2 License for the specific language governing permissions and
// limitations under the License.
#ifndef KALDI_UTIL_EDIT_DISTANCE_INL_H_
#define KALDI_UTIL_EDIT_DISTANCE_INL_H_
#include "util/stl-utils.h"
namespace kaldi {
template<class T>
int32 LevenshteinEditDistance(const std::vector<T> &a,
const std::vector<T> &b) {
// Algorithm:
// write A and B for the sequences, with elements a_0 ..
// let |A| = M and |B| = N be the lengths, and have
// elements a_0 ... a_{M-1} and b_0 ... b_{N-1}.
// We are computing the recursion
// E(m, n) = min( E(m-1, n-1) + (1-delta(a_{m-1}, b_{n-1})),
// E(m-1, n),
// E(m, n-1) ).
// where E(m, n) is defined for m = 0..M and n = 0..N and out-of-
// bounds quantities are considered to be infinity (i.e. the
// recursion does not visit them).
// We do this computation using a vector e of size N+1.
// The outer iterations range over m = 0..M.
int M = a.size(), N = b.size();
std::vector<int32> e(N+1);
std::vector<int32> e_tmp(N+1);
// initialize e.
for (size_t i = 0; i < e.size(); i++)
e[i] = i;
for (int32 m = 1; m <= M; m++) {
// computing E(m, .) from E(m-1, .)
// handle special case n = 0:
e_tmp[0] = e[0] + 1;
for (int32 n = 1; n <= N; n++) {
int32 term1 = e[n-1] + (a[m-1] == b[n-1] ? 0 : 1);
int32 term2 = e[n] + 1;
int32 term3 = e_tmp[n-1] + 1;
e_tmp[n] = std::min(term1, std::min(term2, term3));
}
e = e_tmp;
}
return e.back();
}
//
struct error_stats{
int32 ins_num;
int32 del_num;
int32 sub_num;
int32 total_cost; // minimum total cost to the current alignment.
};
// Note that both hyp and ref should not contain noise word in
// the following implementation.
template<class T>
int32 LevenshteinEditDistance(const std::vector<T> &ref,
const std::vector<T> &hyp,
int32 *ins, int32 *del, int32 *sub) {
// temp sequence to remember error type and stats.
std::vector<error_stats> e(ref.size()+1);
std::vector<error_stats> cur_e(ref.size()+1);
// initialize the first hypothesis aligned to the reference at each
// position:[hyp_index =0][ref_index]
for (size_t i =0; i < e.size(); i ++) {
e[i].ins_num = 0;
e[i].sub_num = 0;
e[i].del_num = i;
e[i].total_cost = i;
}
// for other alignments
for (size_t hyp_index = 1; hyp_index <= hyp.size(); hyp_index ++) {
cur_e[0] = e[0];
cur_e[0].ins_num ++;
cur_e[0].total_cost ++;
for (size_t ref_index = 1; ref_index <= ref.size(); ref_index ++) {
int32 ins_err = e[ref_index].total_cost + 1;
int32 del_err = cur_e[ref_index-1].total_cost + 1;
int32 sub_err = e[ref_index-1].total_cost;
if (hyp[hyp_index-1] != ref[ref_index-1])
sub_err ++;
if (sub_err < ins_err && sub_err < del_err) {
cur_e[ref_index] =e[ref_index-1];
if (hyp[hyp_index-1] != ref[ref_index-1])
cur_e[ref_index].sub_num ++; // substitution error should be increased
cur_e[ref_index].total_cost = sub_err;
}else if (del_err < ins_err ) {
cur_e[ref_index] = cur_e[ref_index-1];
cur_e[ref_index].total_cost = del_err;
cur_e[ref_index].del_num ++; // deletion number is increased.
}else{
cur_e[ref_index] = e[ref_index];
cur_e[ref_index].total_cost = ins_err;
cur_e[ref_index].ins_num ++; // insertion number is increased.
}
}
e = cur_e; // alternate for the next recursion.
}
size_t ref_index = e.size()-1;
*ins = e[ref_index].ins_num, *del = e[ref_index].del_num, *sub = e[ref_index].sub_num;
return e[ref_index].total_cost;
}
template<class T>
int32 LevenshteinAlignment(const std::vector<T> &a,
const std::vector<T> &b,
T eps_symbol,
std::vector<std::pair<T, T> > *output) {
// Check inputs:
{
KALDI_ASSERT(output != NULL);
for (size_t i = 0; i < a.size(); i++) KALDI_ASSERT(a[i] != eps_symbol);
for (size_t i = 0; i < b.size(); i++) KALDI_ASSERT(b[i] != eps_symbol);
}
output->clear();
// This is very memory-inefficiently implemented using a vector of vectors.
size_t M = a.size(), N = b.size();
size_t m, n;
std::vector<std::vector<int32> > e(M+1);
for (m = 0; m <=M; m++) e[m].resize(N+1);
for (n = 0; n <= N; n++)
e[0][n] = n;
for (m = 1; m <= M; m++) {
e[m][0] = e[m-1][0] + 1;
for (n = 1; n <= N; n++) {
int32 sub_or_ok = e[m-1][n-1] + (a[m-1] == b[n-1] ? 0 : 1);
int32 del = e[m-1][n] + 1; // assumes a == ref, b == hyp.
int32 ins = e[m][n-1] + 1;
e[m][n] = std::min(sub_or_ok, std::min(del, ins));
}
}
// get time-reversed output first: trace back.
m = M; n = N;
while (m != 0 || n != 0) {
size_t last_m, last_n;
if (m == 0) { last_m = m; last_n = n-1; }
else if (n == 0) { last_m = m-1; last_n = n; }
else {
int32 sub_or_ok = e[m-1][n-1] + (a[m-1] == b[n-1] ? 0 : 1);
int32 del = e[m-1][n] + 1; // assumes a == ref, b == hyp.
int32 ins = e[m][n-1] + 1;
if (sub_or_ok <= std::min(del, ins)) { // choose sub_or_ok if all else equal.
last_m = m-1; last_n = n-1;
} else {
if (del <= ins) { // choose del over ins if equal.
last_m = m-1; last_n = n;
} else {
last_m = m; last_n = n-1;
}
}
}
T a_sym, b_sym;
a_sym = (last_m == m ? eps_symbol : a[last_m]);
b_sym = (last_n == n ? eps_symbol : b[last_n]);
output->push_back(std::make_pair(a_sym, b_sym));
m = last_m;
n = last_n;
}
ReverseVector(output);
return e[M][N];
}
} // end namespace kaldi
#endif // KALDI_UTIL_EDIT_DISTANCE_INL_H_