ClickHouse/src/AggregateFunctions/AggregateFunctionStatistics.h
2021-05-30 13:57:30 +00:00

478 lines
14 KiB
C++

#pragma once
#include <IO/WriteHelpers.h>
#include <IO/ReadHelpers.h>
#include <DataTypes/DataTypesNumber.h>
#include <AggregateFunctions/IAggregateFunction.h>
#include <Columns/ColumnsNumber.h>
#include <Common/assert_cast.h>
#include <cmath>
namespace DB
{
struct Settings;
namespace detail
{
/// This function returns true if both values are large and comparable.
/// It is used to calculate the mean value by merging two sources.
/// It means that if the sizes of both sources are large and comparable, then we must apply a special
/// formula guaranteeing more stability.
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));
}
}
/** Statistical aggregate functions
* varSamp - sample variance
* stddevSamp - mean sample quadratic deviation
* varPop - variance
* stddevPop - standard deviation
* covarSamp - selective covariance
* covarPop - covariance
* corr - correlation
*/
/** Parallel and incremental algorithm for calculating variance.
* Source: "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:
void update(const IColumn & column, size_t row_num)
{
T received = assert_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 (detail::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
{
assert_cast<ColumnFloat64 &>(to).getData().push_back(Op::apply(m2, count));
}
private:
UInt64 count = 0;
Float64 mean = 0.0;
Float64 m2 = 0.0;
};
/** The main code for the implementation of varSamp, stddevSamp, varPop, stddevPop.
*/
template <typename T, typename Op>
class AggregateFunctionVariance final
: public IAggregateFunctionDataHelper<AggregateFunctionVarianceData<T, Op>, AggregateFunctionVariance<T, Op>>
{
public:
AggregateFunctionVariance(const DataTypePtr & arg)
: IAggregateFunctionDataHelper<AggregateFunctionVarianceData<T, Op>, AggregateFunctionVariance<T, Op>>({arg}, {}) {}
String getName() const override { return Op::name; }
DataTypePtr getReturnType() const override
{
return std::make_shared<DataTypeFloat64>();
}
bool allocatesMemoryInArena() const override { return false; }
void add(AggregateDataPtr __restrict place, const IColumn ** columns, size_t row_num, Arena *) const override
{
this->data(place).update(*columns[0], row_num);
}
void merge(AggregateDataPtr __restrict place, ConstAggregateDataPtr rhs, Arena *) const override
{
this->data(place).mergeWith(this->data(rhs));
}
void serialize(ConstAggregateDataPtr __restrict place, WriteBuffer & buf, std::optional<size_t> /* version */) const override
{
this->data(place).serialize(buf);
}
void deserialize(AggregateDataPtr __restrict place, ReadBuffer & buf, std::optional<size_t> /* version */, Arena *) const override
{
this->data(place).deserialize(buf);
}
void insertResultInto(AggregateDataPtr __restrict place, IColumn & to, Arena *) const override
{
this->data(place).publish(to);
}
};
/** Implementing the varSamp function.
*/
struct AggregateFunctionVarSampImpl
{
static constexpr auto name = "varSampStable";
static inline Float64 apply(Float64 m2, UInt64 count)
{
if (count < 2)
return std::numeric_limits<Float64>::infinity();
else
return m2 / (count - 1);
}
};
/** Implementing the stddevSamp function.
*/
struct AggregateFunctionStdDevSampImpl
{
static constexpr auto name = "stddevSampStable";
static inline Float64 apply(Float64 m2, UInt64 count)
{
return sqrt(AggregateFunctionVarSampImpl::apply(m2, count));
}
};
/** Implementing the varPop function.
*/
struct AggregateFunctionVarPopImpl
{
static constexpr auto name = "varPopStable";
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;
}
};
/** Implementing the stddevPop function.
*/
struct AggregateFunctionStdDevPopImpl
{
static constexpr auto name = "stddevPopStable";
static inline Float64 apply(Float64 m2, UInt64 count)
{
return sqrt(AggregateFunctionVarPopImpl::apply(m2, count));
}
};
/** If `compute_marginal_moments` flag is set this class provides the successor
* CovarianceData support of marginal moments for calculating the correlation.
*/
template <bool compute_marginal_moments>
class BaseCovarianceData
{
protected:
void incrementMarginalMoments(Float64, Float64) {}
void mergeWith(const BaseCovarianceData &) {}
void serialize(WriteBuffer &) const {}
void deserialize(const ReadBuffer &) {}
};
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;
};
/** Parallel and incremental algorithm for calculating covariance.
* Source: "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 = assert_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 = assert_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);
/// Update the marginal moments, if any.
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 (detail::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;
/// Update the marginal moments, if any.
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);
}
void publish(IColumn & to) const
{
if constexpr (compute_marginal_moments)
assert_cast<ColumnFloat64 &>(to).getData().push_back(Op::apply(co_moment, Base::left_m2, Base::right_m2, count));
else
assert_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 IAggregateFunctionDataHelper<
CovarianceData<T, U, Op, compute_marginal_moments>,
AggregateFunctionCovariance<T, U, Op, compute_marginal_moments>>
{
public:
AggregateFunctionCovariance(const DataTypes & args) : IAggregateFunctionDataHelper<
CovarianceData<T, U, Op, compute_marginal_moments>,
AggregateFunctionCovariance<T, U, Op, compute_marginal_moments>>(args, {}) {}
String getName() const override { return Op::name; }
DataTypePtr getReturnType() const override
{
return std::make_shared<DataTypeFloat64>();
}
bool allocatesMemoryInArena() const override { return false; }
void add(AggregateDataPtr __restrict place, const IColumn ** columns, size_t row_num, Arena *) const override
{
this->data(place).update(*columns[0], *columns[1], row_num);
}
void merge(AggregateDataPtr __restrict place, ConstAggregateDataPtr rhs, Arena *) const override
{
this->data(place).mergeWith(this->data(rhs));
}
void serialize(ConstAggregateDataPtr __restrict place, WriteBuffer & buf, std::optional<size_t> /* version */) const override
{
this->data(place).serialize(buf);
}
void deserialize(AggregateDataPtr __restrict place, ReadBuffer & buf, std::optional<size_t> /* version */, Arena *) const override
{
this->data(place).deserialize(buf);
}
void insertResultInto(AggregateDataPtr __restrict place, IColumn & to, Arena *) const override
{
this->data(place).publish(to);
}
};
/** Implementing the covarSamp function.
*/
struct AggregateFunctionCovarSampImpl
{
static constexpr auto name = "covarSampStable";
static inline Float64 apply(Float64 co_moment, UInt64 count)
{
if (count < 2)
return std::numeric_limits<Float64>::infinity();
else
return co_moment / (count - 1);
}
};
/** Implementing the covarPop function.
*/
struct AggregateFunctionCovarPopImpl
{
static constexpr auto name = "covarPopStable";
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;
}
};
/** `corr` function implementation.
*/
struct AggregateFunctionCorrImpl
{
static constexpr auto name = "corrStable";
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 AggregateFunctionVarSampStable = AggregateFunctionVariance<T, AggregateFunctionVarSampImpl>;
template <typename T>
using AggregateFunctionStddevSampStable = AggregateFunctionVariance<T, AggregateFunctionStdDevSampImpl>;
template <typename T>
using AggregateFunctionVarPopStable = AggregateFunctionVariance<T, AggregateFunctionVarPopImpl>;
template <typename T>
using AggregateFunctionStddevPopStable = AggregateFunctionVariance<T, AggregateFunctionStdDevPopImpl>;
template <typename T, typename U>
using AggregateFunctionCovarSampStable = AggregateFunctionCovariance<T, U, AggregateFunctionCovarSampImpl>;
template <typename T, typename U>
using AggregateFunctionCovarPopStable = AggregateFunctionCovariance<T, U, AggregateFunctionCovarPopImpl>;
template <typename T, typename U>
using AggregateFunctionCorrStable = AggregateFunctionCovariance<T, U, AggregateFunctionCorrImpl, true>;
}