1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
|
// 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
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//
// Copyright 2005-2010 Google, Inc.
// Author: krr@google.com (Kasturi Rangan Raghavan)
// Inspiration: shumash@google.com (Masha Maria Shugrina)
// \file
// Expectation semiring as described by Jason Eisner:
// See: doi=10.1.1.22.9398
// Multiplex semiring operations and identities:
// One: <One, Zero>
// Zero: <Zero, Zero>
// Plus: <a1, b1> + <a2, b2> = < (a1 + a2) , (b1 + b2) >
// Times: <a1, b1> * <a2, b2> = < (a1 * a2) , [(a1 * b2) + (a2 * b1)] >
// Division: Undefined (currently)
//
// Usually used to store the pair <probability, random_variable> so that
// ShortestDistance[Fst<ArcTpl<ExpectationWeight<P, V> > >]
// == < PosteriorProbability, Expected_Value[V] >
#ifndef FST_LIB_EXPECTATION_WEIGHT_H_
#define FST_LIB_EXPECTATION_WEIGHT_H_
#include<string>
#include <fst/pair-weight.h>
namespace fst {
// X1 is usually a probability weight like LogWeight
// X2 is usually a random variable or vector
// see SignedLogWeight or SparsePowerWeight
//
// If X1 is distinct from X2, it is required that there is an external
// product between X1 and X2 and if both semriring are commutative, or
// left or right semirings, then result must have those properties.
template <class X1, class X2>
class ExpectationWeight : public PairWeight<X1, X2> {
public:
using PairWeight<X1, X2>::Value1;
using PairWeight<X1, X2>::Value2;
using PairWeight<X1, X2>::Reverse;
using PairWeight<X1, X2>::Quantize;
using PairWeight<X1, X2>::Member;
typedef X1 W1;
typedef X2 W2;
typedef ExpectationWeight<typename X1::ReverseWeight,
typename X2::ReverseWeight> ReverseWeight;
ExpectationWeight() : PairWeight<X1, X2>(Zero()) { }
ExpectationWeight(const ExpectationWeight<X1, X2>& w)
: PairWeight<X1, X2> (w) { }
ExpectationWeight(const PairWeight<X1, X2>& w)
: PairWeight<X1, X2> (w) { }
ExpectationWeight(const X1& x1, const X2& x2)
: PairWeight<X1, X2>(x1, x2) { }
static const ExpectationWeight<X1, X2> &Zero() {
static const ExpectationWeight<X1, X2> zero(X1::Zero(), X2::Zero());
return zero;
}
static const ExpectationWeight<X1, X2> &One() {
static const ExpectationWeight<X1, X2> one(X1::One(), X2::Zero());
return one;
}
static const ExpectationWeight<X1, X2> &NoWeight() {
static const ExpectationWeight<X1, X2> no_weight(X1::NoWeight(),
X2::NoWeight());
return no_weight;
}
static const string &Type() {
static const string type = "expectation_" + X1::Type() + "_" + X2::Type();
return type;
}
PairWeight<X1, X2> Quantize(float delta = kDelta) const {
return PairWeight<X1, X2>::Quantize();
}
ReverseWeight Reverse() const {
return PairWeight<X1, X2>::Reverse();
}
bool Member() const {
return PairWeight<X1, X2>::Member();
}
static uint64 Properties() {
uint64 props1 = W1::Properties();
uint64 props2 = W2::Properties();
return props1 & props2 & (kLeftSemiring | kRightSemiring |
kCommutative | kIdempotent);
}
};
template <class X1, class X2>
inline ExpectationWeight<X1, X2> Plus(const ExpectationWeight<X1, X2> &w,
const ExpectationWeight<X1, X2> &v) {
return ExpectationWeight<X1, X2>(Plus(w.Value1(), v.Value1()),
Plus(w.Value2(), v.Value2()));
}
template <class X1, class X2>
inline ExpectationWeight<X1, X2> Times(const ExpectationWeight<X1, X2> &w,
const ExpectationWeight<X1, X2> &v) {
return ExpectationWeight<X1, X2>(Times(w.Value1(), v.Value1()),
Plus(Times(w.Value1(), v.Value2()),
Times(w.Value2(), v.Value1())));
}
template <class X1, class X2>
inline ExpectationWeight<X1, X2> Divide(const ExpectationWeight<X1, X2> &w,
const ExpectationWeight<X1, X2> &v,
DivideType typ = DIVIDE_ANY) {
FSTERROR() << "ExpectationWeight::Divide: not implemented";
return ExpectationWeight<X1, X2>::NoWeight();
}
} // namespace fst
#endif // FST_LIB_EXPECTATION_WEIGHT_H_
|
