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Added comments; added test [#CLICKHOUSE-2].

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Alexey Milovidov 2017-12-23 02:08:57 +03:00
parent 69a7761812
commit 7e60152e72
3 changed files with 168 additions and 0 deletions
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12
dbms/src/AggregateFunctions/AggregateFunctionStatisticsSimple.h
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@ -10,6 +10,18 @@
#include <DataTypes/DataTypesNumber.h>
/** This is simple, not numerically stable
* implementations of variance/covariance/correlation functions.
*
* It is about two times faster than stable variants.
* Numerical errors may occur during summation.
*
* This implementation is selected as default,
* because "you don't pay for what you don't need" principle.
*
* For more sophisticated implementation, look at AggregateFunctionStatistics.h
*/
namespace DB
{

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dbms/tests/queries/0_stateless/00181_aggregate_functions_statistics_stable.reference Normal file
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dbms/tests/queries/0_stateless/00181_aggregate_functions_statistics_stable.sql Normal file
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DROP TABLE IF EXISTS test.series;
CREATE TABLE test.series(i UInt32, x_value Float64, y_value Float64) ENGINE = Memory;
INSERT INTO test.series(i, x_value, y_value) VALUES (1, 5.6,-4.4),(2, -9.6,3),(3, -1.3,-4),(4, 5.3,9.7),(5, 4.4,0.037),(6, -8.6,-7.8),(7, 5.1,9.3),(8, 7.9,-3.6),(9, -8.2,0.62),(10, -3,7.3);
/* varSampStable */
SELECT varSampStable(x_value) FROM (SELECT x_value FROM test.series LIMIT 0);
SELECT varSampStable(x_value) FROM (SELECT x_value FROM test.series LIMIT 1);
SELECT round(abs(res1 - res2), 6) FROM
(
SELECT
varSampStable(x_value) AS res1,
(sum(x_value * x_value) - ((sum(x_value) * sum(x_value)) / count())) / (count() - 1) AS res2
FROM test.series
);
/* stddevSampStable */
SELECT stddevSampStable(x_value) FROM (SELECT x_value FROM test.series LIMIT 0);
SELECT stddevSampStable(x_value) FROM (SELECT x_value FROM test.series LIMIT 1);
SELECT round(abs(res1 - res2), 6) FROM
(
SELECT
stddevSampStable(x_value) AS res1,
sqrt((sum(x_value * x_value) - ((sum(x_value) * sum(x_value)) / count())) / (count() - 1)) AS res2
FROM test.series
);
/* varPopStable */
SELECT varPopStable(x_value) FROM (SELECT x_value FROM test.series LIMIT 0);
SELECT varPopStable(x_value) FROM (SELECT x_value FROM test.series LIMIT 1);
SELECT round(abs(res1 - res2), 6) FROM
(
SELECT
varPopStable(x_value) AS res1,
(sum(x_value * x_value) - ((sum(x_value) * sum(x_value)) / count())) / count() AS res2
FROM test.series
);
/* stddevPopStable */
SELECT stddevPopStable(x_value) FROM (SELECT x_value FROM test.series LIMIT 0);
SELECT stddevPopStable(x_value) FROM (SELECT x_value FROM test.series LIMIT 1);
SELECT round(abs(res1 - res2), 6) FROM
(
SELECT
stddevPopStable(x_value) AS res1,
sqrt((sum(x_value * x_value) - ((sum(x_value) * sum(x_value)) / count())) / count()) AS res2
FROM test.series
);
/* covarSampStable */
SELECT covarSampStable(x_value, y_value) FROM (SELECT x_value, y_value FROM test.series LIMIT 0);
SELECT covarSampStable(x_value, y_value) FROM (SELECT x_value, y_value FROM test.series LIMIT 1);
SELECT round(abs(COVAR1 - COVAR2), 6)
FROM
(
SELECT
arrayJoin([1]) AS ID2,
covarSampStable(x_value, y_value) AS COVAR1
FROM test.series
) ANY INNER JOIN
(
SELECT
arrayJoin([1]) AS ID2,
sum(VAL) / (count() - 1) AS COVAR2
FROM
(
SELECT (X - AVG_X) * (Y - AVG_Y) AS VAL
FROM
(
SELECT
toUInt32(arrayJoin([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])) AS ID,
avg(x_value) AS AVG_X,
avg(y_value) AS AVG_Y
FROM test.series
) ANY INNER JOIN
(
SELECT
i AS ID,
x_value AS X,
y_value AS Y
FROM test.series
) USING ID
)
) USING ID2;
/* covarPopStable */
SELECT covarPopStable(x_value, y_value) FROM (SELECT x_value, y_value FROM test.series LIMIT 0);
SELECT covarPopStable(x_value, y_value) FROM (SELECT x_value, y_value FROM test.series LIMIT 1);
SELECT round(abs(COVAR1 - COVAR2), 6)
FROM
(
SELECT
arrayJoin([1]) AS ID2,
covarPopStable(x_value, y_value) AS COVAR1
FROM test.series
) ANY INNER JOIN
(
SELECT
arrayJoin([1]) AS ID2,
sum(VAL) / count() AS COVAR2
FROM
(
SELECT (X - AVG_X) * (Y - AVG_Y) AS VAL
FROM
(
SELECT
toUInt32(arrayJoin([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])) AS ID,
avg(x_value) AS AVG_X,
avg(y_value) AS AVG_Y
FROM test.series
) ANY INNER JOIN
(
SELECT
i AS ID,
x_value AS X,
y_value AS Y
FROM test.series
) USING ID
)
) USING ID2;
/* corr */
SELECT corrStable(x_value, y_value) FROM (SELECT x_value, y_value FROM test.series LIMIT 0);
SELECT corrStable(x_value, y_value) FROM (SELECT x_value, y_value FROM test.series LIMIT 1);
SELECT round(abs(corrStable(x_value, y_value) - covarPopStable(x_value, y_value) / (stddevPopStable(x_value) * stddevPopStable(y_value))), 6) FROM test.series;
DROP TABLE test.series;