mirror of
https://github.com/ClickHouse/ClickHouse.git
synced 2024-09-21 17:20:50 +00:00
505 lines
14 KiB
C++
505 lines
14 KiB
C++
#pragma once
|
||
|
||
#include <DB/IO/WriteHelpers.h>
|
||
#include <DB/IO/ReadHelpers.h>
|
||
#include <DB/DataTypes/DataTypesNumberFixed.h>
|
||
#include <DB/AggregateFunctions/IUnaryAggregateFunction.h>
|
||
#include <DB/AggregateFunctions/IBinaryAggregateFunction.h>
|
||
#include <DB/Columns/ColumnVector.h>
|
||
|
||
#include <cmath>
|
||
|
||
namespace DB
|
||
{
|
||
|
||
namespace
|
||
{
|
||
|
||
/// Эта функция возвращает true если оба значения велики и сравнимы.
|
||
/// Она употребляется для вычисления среднего значения путём слияния двух источников.
|
||
/// Ибо если размеры обоих источников велики и сравнимы, то надо применить особенную
|
||
/// формулу гарантирующую больше стабильности.
|
||
bool areComparable(UInt64 a, UInt64 b)
|
||
{
|
||
const Float64 sensitivity = 0.001;
|
||
const UInt64 threshold = 10000;
|
||
|
||
if ((a == 0) || (b == 0))
|
||
return false;
|
||
|
||
auto res = std::minmax(a, b);
|
||
return (((1 - static_cast<Float64>(res.first) / res.second) < sensitivity) && (res.first > threshold));
|
||
}
|
||
|
||
}
|
||
|
||
/** Статистические аггрегатные функции:
|
||
* varSamp - выборочная дисперсия
|
||
* stddevSamp - среднее выборочное квадратичное отклонение
|
||
* varPop - дисперсия
|
||
* stddevPop - среднее квадратичное отклонение
|
||
* covarSamp - выборочная ковариация
|
||
* covarPop - ковариация
|
||
* corr - корреляция
|
||
*/
|
||
|
||
/** Параллельный и инкрементальный алгоритм для вычисления дисперсии.
|
||
* Источник: "Updating formulae and a pairwise algorithm for computing sample variances"
|
||
* (Chan et al., Stanford University, 12.1979)
|
||
*/
|
||
template<typename T, typename Op>
|
||
class AggregateFunctionVarianceData
|
||
{
|
||
public:
|
||
AggregateFunctionVarianceData() = default;
|
||
|
||
void update(const IColumn & column, size_t row_num)
|
||
{
|
||
T received = static_cast<const ColumnVector<T> &>(column).getData()[row_num];
|
||
Float64 val = static_cast<Float64>(received);
|
||
Float64 delta = val - mean;
|
||
|
||
++count;
|
||
mean += delta / count;
|
||
m2 += delta * (val - mean);
|
||
}
|
||
|
||
void mergeWith(const AggregateFunctionVarianceData & source)
|
||
{
|
||
UInt64 total_count = count + source.count;
|
||
if (total_count == 0)
|
||
return;
|
||
|
||
Float64 factor = static_cast<Float64>(count * source.count) / total_count;
|
||
Float64 delta = mean - source.mean;
|
||
|
||
if (areComparable(count, source.count))
|
||
mean = (source.count * source.mean + count * mean) / total_count;
|
||
else
|
||
mean = source.mean + delta * (static_cast<Float64>(count) / total_count);
|
||
|
||
m2 += source.m2 + delta * delta * factor;
|
||
count = total_count;
|
||
}
|
||
|
||
void serialize(WriteBuffer & buf) const
|
||
{
|
||
writeVarUInt(count, buf);
|
||
writeBinary(mean, buf);
|
||
writeBinary(m2, buf);
|
||
}
|
||
|
||
void deserialize(ReadBuffer & buf)
|
||
{
|
||
readVarUInt(count, buf);
|
||
readBinary(mean, buf);
|
||
readBinary(m2, buf);
|
||
}
|
||
|
||
void publish(IColumn & to) const
|
||
{
|
||
static_cast<ColumnFloat64 &>(to).getData().push_back(Op::apply(m2, count));
|
||
}
|
||
|
||
private:
|
||
UInt64 count = 0;
|
||
Float64 mean = 0.0;
|
||
Float64 m2 = 0.0;
|
||
};
|
||
|
||
/** Основной код для реализации функций varSamp, stddevSamp, varPop, stddevPop.
|
||
*/
|
||
template<typename T, typename Op>
|
||
class AggregateFunctionVariance final
|
||
: public IUnaryAggregateFunction<AggregateFunctionVarianceData<T, Op>,
|
||
AggregateFunctionVariance<T, Op> >
|
||
{
|
||
public:
|
||
String getName() const override { return Op::name; }
|
||
|
||
DataTypePtr getReturnType() const override
|
||
{
|
||
return new DataTypeFloat64;
|
||
}
|
||
|
||
void setArgument(const DataTypePtr & argument)
|
||
{
|
||
if (!argument->behavesAsNumber())
|
||
throw Exception("Illegal type " + argument->getName() + " of argument for aggregate function " + getName(),
|
||
ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT);
|
||
}
|
||
|
||
void addImpl(AggregateDataPtr place, const IColumn & column, size_t row_num) const
|
||
{
|
||
this->data(place).update(column, row_num);
|
||
}
|
||
|
||
void merge(AggregateDataPtr place, ConstAggregateDataPtr rhs) const override
|
||
{
|
||
this->data(place).mergeWith(this->data(rhs));
|
||
}
|
||
|
||
void serialize(ConstAggregateDataPtr place, WriteBuffer & buf) const override
|
||
{
|
||
this->data(place).serialize(buf);
|
||
}
|
||
|
||
void deserializeMerge(AggregateDataPtr place, ReadBuffer & buf) const override
|
||
{
|
||
AggregateFunctionVarianceData<T, Op> source;
|
||
source.deserialize(buf);
|
||
|
||
this->data(place).mergeWith(source);
|
||
}
|
||
|
||
void insertResultInto(ConstAggregateDataPtr place, IColumn & to) const override
|
||
{
|
||
this->data(place).publish(to);
|
||
}
|
||
};
|
||
|
||
namespace
|
||
{
|
||
|
||
/** Реализации функции varSamp.
|
||
*/
|
||
struct VarSampImpl
|
||
{
|
||
static constexpr auto name = "varSamp";
|
||
|
||
static inline Float64 apply(Float64 m2, UInt64 count)
|
||
{
|
||
if (count < 2)
|
||
return std::numeric_limits<Float64>::infinity();
|
||
else
|
||
return m2 / (count - 1);
|
||
}
|
||
};
|
||
|
||
/** Реализация функции stddevSamp.
|
||
*/
|
||
struct StdDevSampImpl
|
||
{
|
||
static constexpr auto name = "stddevSamp";
|
||
|
||
static inline Float64 apply(Float64 m2, UInt64 count)
|
||
{
|
||
return sqrt(VarSampImpl::apply(m2, count));
|
||
}
|
||
};
|
||
|
||
/** Реализация функции varPop.
|
||
*/
|
||
struct VarPopImpl
|
||
{
|
||
static constexpr auto name = "varPop";
|
||
|
||
static inline Float64 apply(Float64 m2, UInt64 count)
|
||
{
|
||
if (count == 0)
|
||
return std::numeric_limits<Float64>::infinity();
|
||
else if (count == 1)
|
||
return 0.0;
|
||
else
|
||
return m2 / count;
|
||
}
|
||
};
|
||
|
||
/** Реализация функции stddevPop.
|
||
*/
|
||
struct StdDevPopImpl
|
||
{
|
||
static constexpr auto name = "stddevPop";
|
||
|
||
static inline Float64 apply(Float64 m2, UInt64 count)
|
||
{
|
||
return sqrt(VarPopImpl::apply(m2, count));
|
||
}
|
||
};
|
||
|
||
}
|
||
|
||
/** Если флаг compute_marginal_moments установлен, этот класс предоставялет наследнику
|
||
* CovarianceData поддержку маргинальных моментов для вычисления корреляции.
|
||
*/
|
||
template<bool compute_marginal_moments>
|
||
class BaseCovarianceData
|
||
{
|
||
protected:
|
||
void incrementMarginalMoments(Float64 left_incr, Float64 right_incr) {}
|
||
void mergeWith(const BaseCovarianceData & source) {}
|
||
void serialize(WriteBuffer & buf) const {}
|
||
void deserialize(const ReadBuffer & buf) {}
|
||
};
|
||
|
||
template<>
|
||
class BaseCovarianceData<true>
|
||
{
|
||
protected:
|
||
void incrementMarginalMoments(Float64 left_incr, Float64 right_incr)
|
||
{
|
||
left_m2 += left_incr;
|
||
right_m2 += right_incr;
|
||
}
|
||
|
||
void mergeWith(const BaseCovarianceData & source)
|
||
{
|
||
left_m2 += source.left_m2;
|
||
right_m2 += source.right_m2;
|
||
}
|
||
|
||
void serialize(WriteBuffer & buf) const
|
||
{
|
||
writeBinary(left_m2, buf);
|
||
writeBinary(right_m2, buf);
|
||
}
|
||
|
||
void deserialize(ReadBuffer & buf)
|
||
{
|
||
readBinary(left_m2, buf);
|
||
readBinary(right_m2, buf);
|
||
}
|
||
|
||
protected:
|
||
Float64 left_m2 = 0.0;
|
||
Float64 right_m2 = 0.0;
|
||
};
|
||
|
||
/** Параллельный и инкрементальный алгоритм для вычисления ковариации.
|
||
* Источник: "Numerically Stable, Single-Pass, Parallel Statistics Algorithms"
|
||
* (J. Bennett et al., Sandia National Laboratories,
|
||
* 2009 IEEE International Conference on Cluster Computing)
|
||
*/
|
||
template<typename T, typename U, typename Op, bool compute_marginal_moments>
|
||
class CovarianceData : public BaseCovarianceData<compute_marginal_moments>
|
||
{
|
||
private:
|
||
using Base = BaseCovarianceData<compute_marginal_moments>;
|
||
|
||
public:
|
||
void update(const IColumn & column_left, const IColumn & column_right, size_t row_num)
|
||
{
|
||
T left_received = static_cast<const ColumnVector<T> &>(column_left).getData()[row_num];
|
||
Float64 left_val = static_cast<Float64>(left_received);
|
||
Float64 left_delta = left_val - left_mean;
|
||
|
||
U right_received = static_cast<const ColumnVector<U> &>(column_right).getData()[row_num];
|
||
Float64 right_val = static_cast<Float64>(right_received);
|
||
Float64 right_delta = right_val - right_mean;
|
||
|
||
Float64 old_right_mean = right_mean;
|
||
|
||
++count;
|
||
|
||
left_mean += left_delta / count;
|
||
right_mean += right_delta / count;
|
||
co_moment += (left_val - left_mean) * (right_val - old_right_mean);
|
||
|
||
/// Обновить маргинальные моменты, если они есть.
|
||
if (compute_marginal_moments)
|
||
{
|
||
Float64 left_incr = left_delta * (left_val - left_mean);
|
||
Float64 right_incr = right_delta * (right_val - right_mean);
|
||
Base::incrementMarginalMoments(left_incr, right_incr);
|
||
}
|
||
}
|
||
|
||
void mergeWith(const CovarianceData & source)
|
||
{
|
||
UInt64 total_count = count + source.count;
|
||
if (total_count == 0)
|
||
return;
|
||
|
||
Float64 factor = static_cast<Float64>(count * source.count) / total_count;
|
||
Float64 left_delta = left_mean - source.left_mean;
|
||
Float64 right_delta = right_mean - source.right_mean;
|
||
|
||
if (areComparable(count, source.count))
|
||
{
|
||
left_mean = (source.count * source.left_mean + count * left_mean) / total_count;
|
||
right_mean = (source.count * source.right_mean + count * right_mean) / total_count;
|
||
}
|
||
else
|
||
{
|
||
left_mean = source.left_mean + left_delta * (static_cast<Float64>(count) / total_count);
|
||
right_mean = source.right_mean + right_delta * (static_cast<Float64>(count) / total_count);
|
||
}
|
||
|
||
co_moment += source.co_moment + left_delta * right_delta * factor;
|
||
count = total_count;
|
||
|
||
/// Обновить маргинальные моменты, если они есть.
|
||
if (compute_marginal_moments)
|
||
{
|
||
Float64 left_incr = left_delta * left_delta * factor;
|
||
Float64 right_incr = right_delta * right_delta * factor;
|
||
Base::mergeWith(source);
|
||
Base::incrementMarginalMoments(left_incr, right_incr);
|
||
}
|
||
}
|
||
|
||
void serialize(WriteBuffer & buf) const
|
||
{
|
||
writeVarUInt(count, buf);
|
||
writeBinary(left_mean, buf);
|
||
writeBinary(right_mean, buf);
|
||
writeBinary(co_moment, buf);
|
||
Base::serialize(buf);
|
||
}
|
||
|
||
void deserialize(ReadBuffer & buf)
|
||
{
|
||
readVarUInt(count, buf);
|
||
readBinary(left_mean, buf);
|
||
readBinary(right_mean, buf);
|
||
readBinary(co_moment, buf);
|
||
Base::deserialize(buf);
|
||
}
|
||
|
||
template<bool compute = compute_marginal_moments>
|
||
void publish(IColumn & to, typename std::enable_if<compute>::type * = nullptr) const
|
||
{
|
||
static_cast<ColumnFloat64 &>(to).getData().push_back(Op::apply(co_moment, Base::left_m2, Base::right_m2, count));
|
||
}
|
||
|
||
template<bool compute = compute_marginal_moments>
|
||
void publish(IColumn & to, typename std::enable_if<!compute>::type * = nullptr) const
|
||
{
|
||
static_cast<ColumnFloat64 &>(to).getData().push_back(Op::apply(co_moment, count));
|
||
}
|
||
|
||
private:
|
||
UInt64 count = 0;
|
||
Float64 left_mean = 0.0;
|
||
Float64 right_mean = 0.0;
|
||
Float64 co_moment = 0.0;
|
||
};
|
||
|
||
template<typename T, typename U, typename Op, bool compute_marginal_moments = false>
|
||
class AggregateFunctionCovariance final
|
||
: public IBinaryAggregateFunction<
|
||
CovarianceData<T, U, Op, compute_marginal_moments>,
|
||
AggregateFunctionCovariance<T, U, Op, compute_marginal_moments> >
|
||
{
|
||
public:
|
||
String getName() const override { return Op::name; }
|
||
|
||
DataTypePtr getReturnType() const override
|
||
{
|
||
return new DataTypeFloat64;
|
||
}
|
||
|
||
void setArgumentsImpl(const DataTypes & arguments)
|
||
{
|
||
if (!arguments[0]->behavesAsNumber())
|
||
throw Exception("Illegal type " + arguments[0]->getName() + " of first argument to function " + getName(),
|
||
ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT);
|
||
|
||
if (!arguments[1]->behavesAsNumber())
|
||
throw Exception("Illegal type " + arguments[1]->getName() + " of second argument to function " + getName(),
|
||
ErrorCodes::ILLEGAL_TYPE_OF_ARGUMENT);
|
||
}
|
||
|
||
void addImpl(AggregateDataPtr place, const IColumn & column_left, const IColumn & column_right, size_t row_num) const
|
||
{
|
||
this->data(place).update(column_left, column_right, row_num);
|
||
}
|
||
|
||
void merge(AggregateDataPtr place, ConstAggregateDataPtr rhs) const override
|
||
{
|
||
this->data(place).mergeWith(this->data(rhs));
|
||
}
|
||
|
||
void serialize(ConstAggregateDataPtr place, WriteBuffer & buf) const override
|
||
{
|
||
this->data(place).serialize(buf);
|
||
}
|
||
|
||
void deserializeMerge(AggregateDataPtr place, ReadBuffer & buf) const override
|
||
{
|
||
CovarianceData<T, U, Op, compute_marginal_moments> source;
|
||
source.deserialize(buf);
|
||
this->data(place).mergeWith(source);
|
||
}
|
||
|
||
void insertResultInto(ConstAggregateDataPtr place, IColumn & to) const override
|
||
{
|
||
this->data(place).publish(to);
|
||
}
|
||
};
|
||
|
||
namespace
|
||
{
|
||
|
||
/** Реализация функции covarSamp.
|
||
*/
|
||
struct CovarSampImpl
|
||
{
|
||
static constexpr auto name = "covarSamp";
|
||
|
||
static inline Float64 apply(Float64 co_moment, UInt64 count)
|
||
{
|
||
if (count < 2)
|
||
return std::numeric_limits<Float64>::infinity();
|
||
else
|
||
return co_moment / (count - 1);
|
||
}
|
||
};
|
||
|
||
/** Реализация функции covarPop.
|
||
*/
|
||
struct CovarPopImpl
|
||
{
|
||
static constexpr auto name = "covarPop";
|
||
|
||
static inline Float64 apply(Float64 co_moment, UInt64 count)
|
||
{
|
||
if (count == 0)
|
||
return std::numeric_limits<Float64>::infinity();
|
||
else if (count == 1)
|
||
return 0.0;
|
||
else
|
||
return co_moment / count;
|
||
}
|
||
};
|
||
|
||
/** Реализация функции corr.
|
||
*/
|
||
struct CorrImpl
|
||
{
|
||
static constexpr auto name = "corr";
|
||
|
||
static inline Float64 apply(Float64 co_moment, Float64 left_m2, Float64 right_m2, UInt64 count)
|
||
{
|
||
if (count < 2)
|
||
return std::numeric_limits<Float64>::infinity();
|
||
else
|
||
return co_moment / sqrt(left_m2 * right_m2);
|
||
}
|
||
};
|
||
|
||
}
|
||
|
||
template<typename T>
|
||
using AggregateFunctionVarSamp = AggregateFunctionVariance<T, VarSampImpl>;
|
||
|
||
template<typename T>
|
||
using AggregateFunctionStdDevSamp = AggregateFunctionVariance<T, StdDevSampImpl>;
|
||
|
||
template<typename T>
|
||
using AggregateFunctionVarPop = AggregateFunctionVariance<T, VarPopImpl>;
|
||
|
||
template<typename T>
|
||
using AggregateFunctionStdDevPop = AggregateFunctionVariance<T, StdDevPopImpl>;
|
||
|
||
template<typename T, typename U>
|
||
using AggregateFunctionCovarSamp = AggregateFunctionCovariance<T, U, CovarSampImpl>;
|
||
|
||
template<typename T, typename U>
|
||
using AggregateFunctionCovarPop = AggregateFunctionCovariance<T, U, CovarPopImpl>;
|
||
|
||
template<typename T, typename U>
|
||
using AggregateFunctionCorr = AggregateFunctionCovariance<T, U, CorrImpl, true>;
|
||
|
||
}
|