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
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
|
/* Copyright 2012 10gen Inc.
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU Affero General Public License, version 3,
* as published by the Free Software Foundation.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Affero General Public License for more details.
*
* You should have received a copy of the GNU Affero General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*
* As a special exception, the copyright holders give permission to link the
* code of portions of this program with the OpenSSL library under certain
* conditions as described in each individual source file and distribute
* linked combinations including the program with the OpenSSL library. You
* must comply with the GNU Affero General Public License in all respects
* for all of the code used other than as permitted herein. If you modify
* file(s) with this exception, you may extend this exception to your
* version of the file(s), but you are not obligated to do so. If you do not
* wish to do so, delete this exception statement from your version. If you
* delete this exception statement from all source files in the program,
* then also delete it in the license file.
*/
#pragma once
#include <cmath>
#include "mongo/db/jsobj.h"
#include "mongo/util/assert_util.h"
/**
* These classes provide online descriptive statistics estimator capable
* of computing the mean, standard deviation and quantiles.
* Exactness is traded for the ability to obtain reasonable estimates
* without the need to store all the samples or perform multiple passes
* over the data.
*
* NOTEs on the estimator accessors provide information about accuracy
* of the approximation.
*
* The implementation of the estimators is heavily inspired by the algorithms used in
* boost.accumulators (www.boost.org/libs/accumulators/).
* It differs by being tailored for typical descriptive statistics use cases
* thus providing a simpler (even though less flexible) interface.
*/
namespace mongo {
/**
* Collects count, minimum and maximum, calculates mean and standard deviation.
*
* The 'Sample' template parameter is the type of the samples. It does not affect the calculated
* mean and standard deviation as all values are converted to double.
* However, setting the correct sample type prevents unnecessary casting or precision loss
* for min and max.
*/
template <class Sample>
class BasicEstimators {
public:
BasicEstimators();
/**
* Update estimators with another observed value.
*/
BasicEstimators& operator <<(const Sample sample);
/**
* @return number of observations so far
*/
inline size_t count() const { return _count; }
/**
* @return mean of the observations seen so far
* NOTE: exact (within the limits of IEEE floating point precision).
*/
inline double mean() const { return _sum / _count; }
/**
* @return standard deviation of the observations so far
* NOTE: exact (within the limits of IEEE floating point precision).
*/
inline double stddev() const { return std::sqrt(_diff / _count); }
/**
* @return minimum observed value so far
* NOTE: exact.
*/
inline Sample min() const { return _min; }
/**
* @return maximum observed value so far
* NOTE: exact.
*/
inline Sample max() const { return _max; }
/**
* Appends the basic estimators to the provided BSONObjBuilder.
*/
void appendBasicToBSONObjBuilder(BSONObjBuilder& b) const;
private:
size_t _count;
double _sum;
double _diff; // sum of squares of differences from the (then-current) mean
Sample _min;
Sample _max;
};
/**
* Computes 'NumQuantiles' quantiles.
*
* The quantiles at probability 0 and 1 (minimum and maximum observations) are always computed.
* Thus DistributionEstimators<3> computes the the 1st, 2nd and 3rd quartiles (probabilities
* .25, .50, .75) and the default 0th and 5th (min and max).
*
* The quantile estimators are mean square consistent (they become a better approximation of the
* actual quantiles as the sample size grows).
*/
template <std::size_t NumQuantiles>
class DistributionEstimators {
public:
DistributionEstimators();
DistributionEstimators& operator <<(const double sample);
/**
* Number of computed quantiles, excluding minimum and maximum.
*/
static const size_t numberOfQuantiles = NumQuantiles;
/**
* Updates the estimators with another observed value.
*/
inline double quantile(std::size_t i) const {
massert(16476, "the requested value is out of the range of the computed quantiles",
i <= NumQuantiles + 1);
return this->_heights[2 * i];
}
/**
* @return true when enough value has been observed to output sensible quantiles
*/
inline bool quantilesReady() const {
return _count >= NumMarkers;
}
/**
* @return estimated minimum
*
* NOTE: use SimpleEstimators::min for an exact value.
*/
inline double min() const {
return quantile(0);
}
/**
* @return estimated maximum
*
* NOTE: use SimpleEstimators::max for an exact value.
*/
inline double max() const {
return quantile(NumQuantiles + 1);
}
/**
* @return estimated median (2nd quartile)
*/
inline double median() const {
return icdf(.5);
}
/**
* @return probability associated with the i-th quantile
*/
inline double probability(std::size_t i) const {
return i * 1. / (NumQuantiles + 1);
}
/**
* @return value for the nearest available quantile for probability 'prob'
*/
inline double icdf(double prob) const {
int quant = static_cast<int>(prob * (NumQuantiles + 1) + 0.5);
return quantile(quant);
}
/**
* Appends the quantiles to the provided BSONArrayBuilder.
* REQUIRES e.quantilesReady() == true
*/
void appendQuantilesToBSONArrayBuilder(BSONArrayBuilder& arr) const;
private:
inline double _positions_increments(std::size_t i) const;
int _count;
enum { NumMarkers = 2 * NumQuantiles + 3 };
double _heights[NumMarkers]; // q_i
double _actual_positions[NumMarkers]; // n_i
double _desired_positions[NumMarkers]; // d_i
};
/**
* Provides the functionality of both BasicEstimators and DistributionEstimators.
*/
template <class Sample, std::size_t NumQuantiles>
class SummaryEstimators :
// Multiple-inheritance
public BasicEstimators<Sample>,
public DistributionEstimators<NumQuantiles> {
public:
// Dispatch samples to the inherited estimators
inline SummaryEstimators& operator<<(const Sample sample) {
this->BasicEstimators<Sample>::operator<<(sample);
this->DistributionEstimators<NumQuantiles>::operator<<(sample);
return *this;
}
// Expose the exact values
inline Sample min() const {
return this->BasicEstimators<Sample>::min();
}
inline Sample max() const {
return this->BasicEstimators<Sample>::max();
}
/**
* @return a summary of the computed estimators as a BSONObj.
*/
BSONObj statisticSummaryToBSONObj() const;
};
} // namespace mongo
#include "mongo/util/descriptive_stats-inl.h"
|
