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403 lines
14 KiB
C++
403 lines
14 KiB
C++
#pragma once
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#include <IO/ReadBuffer.h>
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#include <IO/VarInt.h>
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#include <IO/WriteBuffer.h>
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#include <Common/NaNUtils.h>
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#include <Common/PODArray.h>
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#include <base/sort.h>
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#include <base/types.h>
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namespace DB
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{
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struct Settings;
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namespace ErrorCodes
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{
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extern const int NOT_IMPLEMENTED;
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extern const int BAD_ARGUMENTS;
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}
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template <typename Value, typename Derived>
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struct QuantileExactBase
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{
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/// The memory will be allocated to several elements at once, so that the state occupies 64 bytes.
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static constexpr size_t bytes_in_arena = 64 - sizeof(PODArray<Value>);
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using Array = PODArrayWithStackMemory<Value, bytes_in_arena>;
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Array array;
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void add(const Value & x)
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{
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/// We must skip NaNs as they are not compatible with comparison sorting.
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if (!isNaN(x))
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array.push_back(x);
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}
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template <typename Weight>
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void add(const Value &, const Weight &)
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{
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throw Exception("Method add with weight is not implemented for QuantileExact", ErrorCodes::NOT_IMPLEMENTED);
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}
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void merge(const QuantileExactBase & rhs) { array.insert(rhs.array.begin(), rhs.array.end()); }
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void serialize(WriteBuffer & buf) const
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{
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size_t size = array.size();
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writeVarUInt(size, buf);
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buf.write(reinterpret_cast<const char *>(array.data()), size * sizeof(array[0]));
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}
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void deserialize(ReadBuffer & buf)
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{
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size_t size = 0;
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readVarUInt(size, buf);
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array.resize(size);
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buf.read(reinterpret_cast<char *>(array.data()), size * sizeof(array[0]));
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}
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Value get(Float64 level)
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{
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auto derived = static_cast<Derived*>(this);
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return derived->getImpl(level);
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}
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void getMany(const Float64 * levels, const size_t * indices, size_t size, Value * result)
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{
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auto derived = static_cast<Derived*>(this);
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return derived->getManyImpl(levels, indices, size, result);
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}
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};
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/** Calculates quantile by collecting all values into array
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* and applying n-th element (introselect) algorithm for the resulting array.
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*
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* It uses O(N) memory and it is very inefficient in case of high amount of identical values.
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* But it is very CPU efficient for not large datasets.
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*/
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template <typename Value>
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struct QuantileExact : QuantileExactBase<Value, QuantileExact<Value>>
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{
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using QuantileExactBase<Value, QuantileExact<Value>>::array;
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// Get the value of the `level` quantile. The level must be between 0 and 1.
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Value getImpl(Float64 level)
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{
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if (!array.empty())
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{
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size_t n = level < 1 ? level * array.size() : (array.size() - 1);
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nth_element(array.begin(), array.begin() + n, array.end()); /// NOTE: You can think of the radix-select algorithm.
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return array[n];
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}
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return std::numeric_limits<Value>::quiet_NaN();
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}
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/// Get the `size` values of `levels` quantiles. Write `size` results starting with `result` address.
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/// indices - an array of index levels such that the corresponding elements will go in ascending order.
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void getManyImpl(const Float64 * levels, const size_t * indices, size_t size, Value * result)
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{
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if (!array.empty())
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{
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size_t prev_n = 0;
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for (size_t i = 0; i < size; ++i)
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{
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auto level = levels[indices[i]];
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size_t n = level < 1 ? level * array.size() : (array.size() - 1);
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nth_element(array.begin() + prev_n, array.begin() + n, array.end());
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result[indices[i]] = array[n];
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prev_n = n;
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}
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}
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else
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{
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for (size_t i = 0; i < size; ++i)
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result[i] = Value();
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}
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}
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};
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/// QuantileExactExclusive is equivalent to Excel PERCENTILE.EXC, R-6, SAS-4, SciPy-(0,0)
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template <typename Value>
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/// There are no virtual-like functions. So we don't inherit from QuantileExactBase.
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struct QuantileExactExclusive : public QuantileExact<Value>
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{
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using QuantileExact<Value>::array;
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/// Get the value of the `level` quantile. The level must be between 0 and 1 excluding bounds.
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Float64 getFloat(Float64 level)
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{
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if (!array.empty())
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{
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if (level == 0. || level == 1.)
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throw Exception("QuantileExactExclusive cannot interpolate for the percentiles 1 and 0", ErrorCodes::BAD_ARGUMENTS);
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Float64 h = level * (array.size() + 1);
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auto n = static_cast<size_t>(h);
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if (n >= array.size())
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return static_cast<Float64>(array[array.size() - 1]);
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else if (n < 1)
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return static_cast<Float64>(array[0]);
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nth_element(array.begin(), array.begin() + n - 1, array.end());
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auto nth_elem = std::min_element(array.begin() + n, array.end());
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return static_cast<Float64>(array[n - 1]) + (h - n) * static_cast<Float64>(*nth_elem - array[n - 1]);
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}
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return std::numeric_limits<Float64>::quiet_NaN();
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}
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void getManyFloat(const Float64 * levels, const size_t * indices, size_t size, Float64 * result)
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{
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if (!array.empty())
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{
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size_t prev_n = 0;
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for (size_t i = 0; i < size; ++i)
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{
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auto level = levels[indices[i]];
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if (level == 0. || level == 1.)
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throw Exception("QuantileExactExclusive cannot interpolate for the percentiles 1 and 0", ErrorCodes::BAD_ARGUMENTS);
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Float64 h = level * (array.size() + 1);
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auto n = static_cast<size_t>(h);
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if (n >= array.size())
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result[indices[i]] = static_cast<Float64>(array[array.size() - 1]);
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else if (n < 1)
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result[indices[i]] = static_cast<Float64>(array[0]);
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else
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{
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nth_element(array.begin() + prev_n, array.begin() + n - 1, array.end());
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auto nth_elem = std::min_element(array.begin() + n, array.end());
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result[indices[i]] = static_cast<Float64>(array[n - 1]) + (h - n) * static_cast<Float64>(*nth_elem - array[n - 1]);
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prev_n = n - 1;
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}
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}
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}
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else
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{
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for (size_t i = 0; i < size; ++i)
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result[i] = std::numeric_limits<Float64>::quiet_NaN();
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}
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}
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};
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/// QuantileExactInclusive is equivalent to Excel PERCENTILE and PERCENTILE.INC, R-7, SciPy-(1,1)
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template <typename Value>
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/// There are no virtual-like functions. So we don't inherit from QuantileExactBase.
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struct QuantileExactInclusive : public QuantileExact<Value>
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{
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using QuantileExact<Value>::array;
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/// Get the value of the `level` quantile. The level must be between 0 and 1 including bounds.
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Float64 getFloat(Float64 level)
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{
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if (!array.empty())
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{
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Float64 h = level * (array.size() - 1) + 1;
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auto n = static_cast<size_t>(h);
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if (n >= array.size())
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return static_cast<Float64>(array[array.size() - 1]);
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else if (n < 1)
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return static_cast<Float64>(array[0]);
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nth_element(array.begin(), array.begin() + n - 1, array.end());
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auto nth_elem = std::min_element(array.begin() + n, array.end());
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return static_cast<Float64>(array[n - 1]) + (h - n) * static_cast<Float64>(*nth_elem - array[n - 1]);
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}
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return std::numeric_limits<Float64>::quiet_NaN();
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}
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void getManyFloat(const Float64 * levels, const size_t * indices, size_t size, Float64 * result)
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{
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if (!array.empty())
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{
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size_t prev_n = 0;
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for (size_t i = 0; i < size; ++i)
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{
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auto level = levels[indices[i]];
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Float64 h = level * (array.size() - 1) + 1;
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auto n = static_cast<size_t>(h);
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if (n >= array.size())
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result[indices[i]] = static_cast<Float64>(array[array.size() - 1]);
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else if (n < 1)
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result[indices[i]] = static_cast<Float64>(array[0]);
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else
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{
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nth_element(array.begin() + prev_n, array.begin() + n - 1, array.end());
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auto nth_elem = std::min_element(array.begin() + n, array.end());
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result[indices[i]] = static_cast<Float64>(array[n - 1]) + (h - n) * (static_cast<Float64>(*nth_elem) - array[n - 1]);
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prev_n = n - 1;
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}
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}
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}
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else
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{
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for (size_t i = 0; i < size; ++i)
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result[i] = std::numeric_limits<Float64>::quiet_NaN();
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}
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}
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};
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// QuantileExactLow returns the low median of given data.
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// Implementation is as per "medium_low" function from python:
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// https://docs.python.org/3/library/statistics.html#statistics.median_low
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template <typename Value>
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struct QuantileExactLow : public QuantileExactBase<Value, QuantileExactLow<Value>>
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{
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using QuantileExactBase<Value, QuantileExactLow<Value>>::array;
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Value getImpl(Float64 level)
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{
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if (!array.empty())
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{
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// sort inputs in ascending order
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std::sort(array.begin(), array.end());
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// if level is 0.5 then compute the "low" median of the sorted array
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// by the method of rounding.
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if (level == 0.5)
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{
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auto s = array.size();
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if (s % 2 == 1)
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{
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return array[static_cast<size_t>(floor(s / 2))];
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}
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else
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{
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return array[static_cast<size_t>((floor(s / 2)) - 1)];
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}
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}
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else
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{
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// else quantile is the nth index of the sorted array obtained by multiplying
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// level and size of array. Example if level = 0.1 and size of array is 10,
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// then return array[1].
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size_t n = level < 1 ? level * array.size() : (array.size() - 1);
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return array[n];
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}
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}
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return std::numeric_limits<Value>::quiet_NaN();
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}
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void getManyImpl(const Float64 * levels, const size_t * indices, size_t size, Value * result)
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{
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if (!array.empty())
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{
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// sort inputs in ascending order
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std::sort(array.begin(), array.end());
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for (size_t i = 0; i < size; ++i)
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{
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auto level = levels[indices[i]];
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// if level is 0.5 then compute the "low" median of the sorted array
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// by the method of rounding.
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if (level == 0.5)
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{
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auto s = array.size();
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if (s % 2 == 1)
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{
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result[indices[i]] = array[static_cast<size_t>(floor(s / 2))];
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}
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else
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{
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result[indices[i]] = array[static_cast<size_t>(floor((s / 2) - 1))];
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}
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}
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else
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{
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// else quantile is the nth index of the sorted array obtained by multiplying
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// level and size of array. Example if level = 0.1 and size of array is 10.
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size_t n = level < 1 ? level * array.size() : (array.size() - 1);
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result[indices[i]] = array[n];
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}
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}
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}
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else
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{
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for (size_t i = 0; i < size; ++i)
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result[i] = Value();
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}
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}
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};
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// QuantileExactLow returns the high median of given data.
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// Implementation is as per "medium_high function from python:
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// https://docs.python.org/3/library/statistics.html#statistics.median_high
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template <typename Value>
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struct QuantileExactHigh : public QuantileExactBase<Value, QuantileExactHigh<Value>>
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{
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using QuantileExactBase<Value, QuantileExactHigh<Value>>::array;
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Value getImpl(Float64 level)
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{
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if (!array.empty())
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{
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// sort inputs in ascending order
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std::sort(array.begin(), array.end());
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// if level is 0.5 then compute the "high" median of the sorted array
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// by the method of rounding.
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if (level == 0.5)
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{
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auto s = array.size();
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return array[static_cast<size_t>(floor(s / 2))];
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}
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else
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{
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// else quantile is the nth index of the sorted array obtained by multiplying
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// level and size of array. Example if level = 0.1 and size of array is 10.
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size_t n = level < 1 ? level * array.size() : (array.size() - 1);
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return array[n];
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}
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}
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return std::numeric_limits<Value>::quiet_NaN();
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}
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void getManyImpl(const Float64 * levels, const size_t * indices, size_t size, Value * result)
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{
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if (!array.empty())
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{
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// sort inputs in ascending order
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std::sort(array.begin(), array.end());
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for (size_t i = 0; i < size; ++i)
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{
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auto level = levels[indices[i]];
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// if level is 0.5 then compute the "high" median of the sorted array
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// by the method of rounding.
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if (level == 0.5)
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{
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auto s = array.size();
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result[indices[i]] = array[static_cast<size_t>(floor(s / 2))];
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}
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else
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{
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// else quantile is the nth index of the sorted array obtained by multiplying
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// level and size of array. Example if level = 0.1 and size of array is 10.
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size_t n = level < 1 ? level * array.size() : (array.size() - 1);
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result[indices[i]] = array[n];
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}
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}
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}
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else
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{
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for (size_t i = 0; i < size; ++i)
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result[i] = Value();
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}
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}
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};
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}
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