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