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/* 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 funcionality 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"
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