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Put Welford's online algorithm everywhere

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mariadb-AndreyPiskunov
2022-09-06 18:45:56 +03:00
committed by Leonid Fedorov
parent 14b976991b
commit 14810d87ba
8 changed files with 531 additions and 227 deletions
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115
utils/regr/regr_intercept.cpp
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@ -39,10 +39,10 @@ static Add_regr_intercept_ToUDAFMap addToMap;
struct regr_intercept_data
{
uint64_t cnt;
long double sumx;
long double sumx2; // sum of (x squared)
long double sumy;
long double sumxy; // sum of x * y
long double avgx;
long double cx;
long double avgy;
long double cxy;
};
mcsv1_UDAF::ReturnCode regr_intercept::init(mcsv1Context* context, ColumnDatum* colTypes)
@ -75,10 +75,10 @@ mcsv1_UDAF::ReturnCode regr_intercept::reset(mcsv1Context* context)
{
struct regr_intercept_data* data = (struct regr_intercept_data*)context->getUserData()->data;
data->cnt = 0;
data->sumx = 0.0;
data->sumx2 = 0.0;
data->sumy = 0.0;
data->sumxy = 0.0;
data->avgx = 0.0;
data->cx = 0.0;
data->avgy = 0.0;
data->cxy = 0.0;
return mcsv1_UDAF::SUCCESS;
}
@ -88,12 +88,27 @@ mcsv1_UDAF::ReturnCode regr_intercept::nextValue(mcsv1Context* context, ColumnDa
double valx = toDouble(valsIn[1]);
struct regr_intercept_data* data = (struct regr_intercept_data*)context->getUserData()->data;
data->sumy += valy;
data->sumx += valx;
data->sumx2 += valx * valx;
data->sumxy += valx * valy;
long double avgyPrev = data->avgy;
long double avgxPrev = data->avgx;
long double cxPrev = data->cx;
long double cxyPrev = data->cxy;
++data->cnt;
uint64_t cnt = data->cnt;
long double dx = valx - avgxPrev;
long double dy = valy - avgyPrev;
avgyPrev += dy / cnt;
avgxPrev += dx / cnt;
cxPrev += dx * (valx - avgxPrev);
cxyPrev += dx * (valy - avgyPrev);
data->avgx = avgxPrev;
data->avgy = avgyPrev;
data->cx = cxPrev;
data->cxy = cxyPrev;
return mcsv1_UDAF::SUCCESS;
}
@ -108,11 +123,34 @@ mcsv1_UDAF::ReturnCode regr_intercept::subEvaluate(mcsv1Context* context, const
struct regr_intercept_data* outData = (struct regr_intercept_data*)context->getUserData()->data;
struct regr_intercept_data* inData = (struct regr_intercept_data*)userDataIn->data;
outData->sumx += inData->sumx;
outData->sumx2 += inData->sumx2;
outData->sumy += inData->sumy;
outData->sumxy += inData->sumxy;
outData->cnt += inData->cnt;
uint64_t outCnt = outData->cnt;
long double outAvgx = outData->avgx;
long double outAvgy = outData->avgy;
long double outCx = outData->cx;
long double outCxy = outData->cxy;
uint64_t inCnt = inData->cnt;
long double inAvgx = inData->avgx;
long double inAvgy = inData->avgy;
long double inCx = inData->cx;
long double inCxy = inData->cxy;
uint64_t resCnt = inCnt + outCnt;
long double deltax = outAvgx - inAvgx;
long double deltay = outAvgy - inAvgy;
long double resAvgx = inAvgx + deltax * outCnt / resCnt;
long double resAvgy = inAvgy + deltay * outCnt / resCnt;
long double resCx = outCx + inCx + deltax * deltax * inCnt * outCnt / resCnt;
long double resCxy = outCxy + inCxy + deltax * deltay * inCnt * outCnt / resCnt;
outData->avgx = resAvgx;
outData->avgy = resAvgy;
outData->cx = resCx;
outData->cxy = resCxy;
outData->cnt = resCnt;
return mcsv1_UDAF::SUCCESS;
}
@ -123,18 +161,14 @@ mcsv1_UDAF::ReturnCode regr_intercept::evaluate(mcsv1Context* context, static_an
long double N = data->cnt;
if (N > 1)
{
long double sumx = data->sumx;
long double sumy = data->sumy;
long double sumx2 = data->sumx2;
long double sumxy = data->sumxy;
long double avgx = data->avgx;
long double avgy = data->avgy;
long double cx = data->cx;
long double cxy = data->cxy;
// regr_intercept is AVG(y) - slope(y,x)*avg(x)
// We do some algebra and we can get a slightly smaller calculation
long double numerator = sumy * sumx2 - sumx * sumxy;
long double var_pop =
(N * sumx2) - (sumx * sumx); // Not realy var_pop, but sort of after some reductions
if (var_pop > 0)
if (cx > 0)
{
valOut = static_cast<double>(numerator / var_pop);
valOut = static_cast<double>(avgy - cxy / cx * avgx);
}
}
return mcsv1_UDAF::SUCCESS;
@ -146,12 +180,27 @@ mcsv1_UDAF::ReturnCode regr_intercept::dropValue(mcsv1Context* context, ColumnDa
double valx = toDouble(valsDropped[1]);
struct regr_intercept_data* data = (struct regr_intercept_data*)context->getUserData()->data;
data->sumy -= valy;
data->sumx -= valx;
data->sumx2 -= valx * valx;
data->sumxy -= valx * valy;
long double avgyPrev = data->avgy;
long double avgxPrev = data->avgx;
long double cxPrev = data->cx;
long double cxyPrev = data->cxy;
--data->cnt;
uint64_t cnt = data->cnt;
long double dx = valx - avgxPrev;
long double dy = valy - avgyPrev;
avgyPrev -= dy / cnt;
avgxPrev -= dx / cnt;
cxPrev -= dx * (valx - avgxPrev);
cxyPrev -= dx * (valy - avgyPrev);
data->avgx = avgxPrev;
data->avgy = avgyPrev;
data->cx = cxPrev;
data->cxy = cxyPrev;
return mcsv1_UDAF::SUCCESS;
}