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#include "tdigest.h"
#include <library/cpp/tdigest/tdigest.pb.h>
#include <cmath>
// TODO: rewrite to https://github.com/tdunning/t-digest/blob/master/src/main/java/com/tdunning/math/stats/MergingDigest.java
TDigest::TDigest(double delta, double k)
: N(0)
, Delta(delta)
, K(k)
{
}
TDigest::TDigest(double delta, double k, double firstValue)
: TDigest(delta, k)
{
AddValue(firstValue);
}
TDigest::TDigest(TStringBuf serializedDigest)
: N(0)
{
NTDigest::TDigest digest;
Y_ABORT_UNLESS(digest.ParseFromArray(serializedDigest.data(), serializedDigest.size()));
Delta = digest.delta();
K = digest.k();
for (int i = 0; i < digest.centroids_size(); ++i) {
const NTDigest::TDigest::TCentroid& centroid = digest.centroids(i);
Update(centroid.mean(), centroid.weight());
}
}
TDigest::TDigest(const TDigest* digest1, const TDigest* digest2)
: N(0)
, Delta(std::min(digest1->Delta, digest2->Delta))
, K(std::max(digest1->K, digest2->K))
{
Add(*digest1);
Add(*digest2);
}
void TDigest::Add(const TDigest& otherDigest) {
for (auto& it : otherDigest.Centroids)
Update(it.Mean, it.Count);
for (auto& it : otherDigest.Unmerged)
Update(it.Mean, it.Count);
}
TDigest TDigest::operator+(const TDigest& other) {
TDigest T(Delta, K);
T.Add(*this);
T.Add(other);
return T;
}
TDigest& TDigest::operator+=(const TDigest& other) {
Add(other);
return *this;
}
void TDigest::AddCentroid(const TCentroid& centroid) {
Unmerged.push_back(centroid);
N += centroid.Count;
}
double TDigest::GetThreshold(double q) {
return 4 * N * Delta * q * (1 - q);
}
void TDigest::MergeCentroid(TVector<TCentroid>& merged, double& sum, const TCentroid& centroid) {
if (merged.empty()) {
merged.push_back(centroid);
sum += centroid.Count;
return;
}
// Use quantile that has the tightest k
double q1 = (sum - merged.back().Count * 0.5) / N;
double q2 = (sum + centroid.Count * 0.5) / N;
double k = GetThreshold(q1);
double k2 = GetThreshold(q2);
if (k > k2) {
k = k2;
}
if (merged.back().Count + centroid.Count <= k) {
merged.back().Update(centroid.Mean, centroid.Count);
} else {
merged.push_back(centroid);
}
sum += centroid.Count;
}
void TDigest::Update(double x, double w) {
AddCentroid(TCentroid(x, w));
if (Unmerged.size() >= K / Delta) {
Compress();
}
}
void TDigest::Compress() {
if (Unmerged.empty())
return;
// Merge Centroids and Unmerged into Merged
std::stable_sort(Unmerged.begin(), Unmerged.end());
Merged.clear();
double sum = 0;
iter_t i = Centroids.begin();
iter_t j = Unmerged.begin();
while (i != Centroids.end() && j != Unmerged.end()) {
if (i->Mean <= j->Mean) {
MergeCentroid(Merged, sum, *i++);
} else {
MergeCentroid(Merged, sum, *j++);
}
}
while (i != Centroids.end()) {
MergeCentroid(Merged, sum, *i++);
}
while (j != Unmerged.end()) {
MergeCentroid(Merged, sum, *j++);
}
swap(Centroids, Merged);
Unmerged.clear();
}
void TDigest::Clear() {
Centroids.clear();
Unmerged.clear();
N = 0;
}
void TDigest::AddValue(double value) {
Update(value, 1);
}
double TDigest::GetPercentile(double percentile) {
Compress();
if (Centroids.empty())
return 0.0;
// This algorithm uses C=1/2 with 0.5 optimized away
// See https://en.wikipedia.org/wiki/Percentile#First_Variant.2C
double x = percentile * N;
double sum = 0.0;
double prev_x = 0;
double prev_mean = Centroids.front().Mean;
for (const auto& C : Centroids) {
double current_x = sum + C.Count * 0.5;
if (x <= current_x) {
double k = (x - prev_x) / (current_x - prev_x);
return prev_mean + k * (C.Mean - prev_mean);
}
sum += C.Count;
prev_x = current_x;
prev_mean = C.Mean;
}
return Centroids.back().Mean;
}
double TDigest::GetRank(double value) {
Compress();
if (Centroids.empty()) {
return 0.0;
}
if (value < Centroids.front().Mean) {
return 0.0;
}
if (value == Centroids.front().Mean) {
return Centroids.front().Count * 0.5 / N;
}
double sum = 0.0;
double prev_x = 0.0;
double prev_mean = Centroids.front().Mean;
for (const auto& C : Centroids) {
double current_x = sum + C.Count * 0.5;
if (value <= C.Mean) {
double k = (value - prev_mean) / (C.Mean - prev_mean);
return (prev_x + k * (current_x - prev_x)) / N;
}
sum += C.Count;
prev_mean = C.Mean;
prev_x = current_x;
}
return 1.0;
}
TString TDigest::Serialize() {
Compress();
NTDigest::TDigest digest;
digest.set_delta(Delta);
digest.set_k(K);
for (const auto& it : Centroids) {
NTDigest::TDigest::TCentroid* centroid = digest.add_centroids();
centroid->set_mean(it.Mean);
centroid->set_weight(it.Count);
}
return digest.SerializeAsString();
}
i64 TDigest::GetCount() const {
return std::llround(N);
}
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