6.14. Aggregate Functions

Aggregate functions operate on a set of values to compute a single result.

Except for count(), count_if(), max_by(), min_by() andapprox_distinct(), all of these aggregate functions ignore null valuesand return null for no input rows or when all values are null. For example,sum() returns null rather than zero and avg() does not include nullvalues in the count. The coalesce function can be used to convert null intozero.

Some aggregate functions such as array_agg() produce different resultsdepending on the order of input values. This ordering can be specified by writingan ORDER BY Clause within the aggregate function:

  1. array_agg(x ORDER BY y DESC)
  2. array_agg(x ORDER BY x, y, z)

General Aggregate Functions

  • arbitrary(x) → [same as input]

  • Returns an arbitrary non-null value of x, if one exists.

  • arrayagg(_x) → array<[same as input]>

  • Returns an array created from the input x elements.

  • avg(x) → double

  • Returns the average (arithmetic mean) of all input values.

  • avg(time interval type) → time interval type

  • Returns the average interval length of all input values.

  • booland(_boolean) → boolean

  • Returns TRUE if every input value is TRUE, otherwise FALSE.

  • boolor(_boolean) → boolean

  • Returns TRUE if any input value is TRUE, otherwise FALSE.

  • checksum(x) → varbinary

  • Returns an order-insensitive checksum of the given values.

  • count(*) → bigint

  • Returns the number of input rows.

  • count(x) → bigint

  • Returns the number of non-null input values.

  • countif(_x) → bigint

  • Returns the number of TRUE input values.This function is equivalent to count(CASE WHEN x THEN 1 END).

  • every(boolean) → boolean

  • This is an alias for bool_and().

  • geometricmean(_x) → double

  • Returns the geometric mean of all input values.

  • maxby(_x, y) → [same as x]

  • Returns the value of x associated with the maximum value of y over all input values.

  • maxby(_x, y, n) → array<[same as x]>

  • Returns n values of x associated with the n largest of all input values of yin descending order of y.

  • minby(_x, y) → [same as x]

  • Returns the value of x associated with the minimum value of y over all input values.

  • minby(_x, y, n) → array<[same as x]>

  • Returns n values of x associated with the n smallest of all input values of yin ascending order of y.

  • max(x) → [same as input]

  • Returns the maximum value of all input values.

  • max(x, n) → array<[same as x]>

  • Returns n largest values of all input values of x.

  • min(x) → [same as input]

  • Returns the minimum value of all input values.

  • min(x, n) → array<[same as x]>

  • Returns n smallest values of all input values of x.

  • reduceagg(_inputValue T, initialState S, inputFunction(S, T, S), combineFunction(S, S, S)) → S

  • Reduces all input values into a single value. `inputFunction will be invokedfor each input value. In addition to taking the input value, inputFunctiontakes the current state, initially initialState, and returns the new state.combineFunction will be invoked to combine two states into a new state.The final state is returned:
  1. SELECT id, reduce_agg(value, 0, (a, b) -> a + b, (a, b) -> a + b)
  2. FROM (
  3.     VALUES
  4.         (1, 2)
  5.         (1, 3),
  6.         (1, 4),
  7.         (2, 20),
  8.         (2, 30),
  9.         (2, 40)
  10. ) AS t(id, value)
  11. GROUP BY id;
  12. -- (1, 9)
  13. -- (2, 90)
  14.  
  15. SELECT id, reduce_agg(value, 1, (a, b) -> a * b, (a, b) -> a * b)
  16. FROM (
  17.     VALUES
  18.         (1, 2),
  19.         (1, 3),
  20.         (1, 4),
  21.         (2, 20),
  22.         (2, 30),
  23.         (2, 40)
  24. ) AS t(id, value)
  25. GROUP BY id;
  26. -- (1, 24)
  27. -- (2, 24000)

The state type must be a boolean, integer, floating-point, or date/time/interval.

  • sum(x) → [same as input]
  • Returns the sum of all input values.

Bitwise Aggregate Functions

  • bitwiseand_agg(_x) → bigint

  • Returns the bitwise AND of all input values in 2’s complement representation.

  • bitwiseor_agg(_x) → bigint

  • Returns the bitwise OR of all input values in 2’s complement representation.

Map Aggregate Functions

  • histogram(x) -> map(K, bigint)

  • Returns a map containing the count of the number of times each input value occurs.

  • mapagg(_key, value) -> map(K, V)

  • Returns a map created from the input key / value pairs.

  • mapunion(_x(K, V)) -> map(K, V)

  • Returns the union of all the input maps. If a key is found in multipleinput maps, that key’s value in the resulting map comes from an arbitrary input map.

  • multimapagg(_key, value) -> map(K, array(V))

  • Returns a multimap created from the input key / value pairs.Each key can be associated with multiple values.

Approximate Aggregate Functions

  • approxdistinct(_x) → bigint
  • Returns the approximate number of distinct input values.This function provides an approximation of count(DISTINCT x).Zero is returned if all input values are null.

This function should produce a standard error of 2.3%, which is thestandard deviation of the (approximately normal) error distribution overall possible sets. It does not guarantee an upper bound on the error forany specific input set.

  • approxdistinct(_x, e) → bigint
  • Returns the approximate number of distinct input values.This function provides an approximation of count(DISTINCT x).Zero is returned if all input values are null.

This function should produce a standard error of no more than e, whichis the standard deviation of the (approximately normal) error distributionover all possible sets. It does not guarantee an upper bound on the errorfor any specific input set. The current implementation of this functionrequires that e be in the range of [0.0040625, 0.26000].

  • approxpercentile(_x, percentage) → [same as x]

  • Returns the approximate percentile for all input values of x at thegiven percentage. The value of percentage must be between zero andone and must be constant for all input rows.

  • approxpercentile(_x, percentages) → array<[same as x]>

  • Returns the approximate percentile for all input values of x at each ofthe specified percentages. Each element of the percentages array must bebetween zero and one, and the array must be constant for all input rows.

  • approxpercentile(_x, w, percentage) → [same as x]

  • Returns the approximate weighed percentile for all input values of xusing the per-item weight w at the percentage p. The weight must bean integer value of at least one. It is effectively a replication count forthe value x in the percentile set. The value of p must be betweenzero and one and must be constant for all input rows.

  • approxpercentile(_x, w, percentage, accuracy) → [same as x]

  • Returns the approximate weighed percentile for all input values of xusing the per-item weight w at the percentage p, with a maximum rankerror of accuracy. The weight must be an integer value of at least one.It is effectively a replication count for the value x in the percentileset. The value of p must be between zero and one and must be constantfor all input rows. accuracy must be a value greater than zero and lessthan one, and it must be constant for all input rows.

  • approxpercentile(_x, w, percentages) → array<[same as x]>

  • Returns the approximate weighed percentile for all input values of xusing the per-item weight w at each of the given percentages specifiedin the array. The weight must be an integer value of at least one. It iseffectively a replication count for the value x in the percentile set.Each element of the array must be between zero and one, and the array mustbe constant for all input rows.

  • approxset(_x) → HyperLogLog

  • See HyperLogLog Functions.

  • merge(x) → HyperLogLog

  • See HyperLogLog Functions.

  • merge(qdigest(T)) -> qdigest(T)

  • See Quantile Digest Functions.

  • qdigestagg(_x) → qdigest<[same as x]>

  • See Quantile Digest Functions.

  • qdigestagg(_x, w) → qdigest<[same as x]>

  • See Quantile Digest Functions.

  • qdigestagg(_x, w, accuracy) → qdigest<[same as x]>

  • See Quantile Digest Functions.

  • numerichistogram(_buckets, value, weight) → map

  • Computes an approximate histogram with up to buckets number of bucketsfor all values with a per-item weight of weight. The keys of thereturned map are roughly the center of the bin, and the entry is the totalweight of the bin. The algorithm is based loosely on:
  1. Yael Ben-Haim and Elad Tom-Tov, "A streaming parallel decision tree algorithm",
  2. J. Machine Learning Research 11 (2010), pp. 849--872.

buckets must be a bigint. value and weight must be numeric.

  • numerichistogram(_buckets, value) → map
  • Computes an approximate histogram with up to buckets number of bucketsfor all values. This function is equivalent to the variant ofnumeric_histogram() that takes a weight, with a per-item weight of 1.In this case, the total weight in the returned map is the count of items in the bin.

Statistical Aggregate Functions

  • corr(y, x) → double

  • Returns correlation coefficient of input values.

  • covarpop(_y, x) → double

  • Returns the population covariance of input values.

  • covarsamp(_y, x) → double

  • Returns the sample covariance of input values.

  • entropy(c) → double

  • Returns the log-2 entropy of count input-values.
  1. entropy(c) = \sum_i [ c_i / \sum_j [c_j] \log_2(\sum_j [c_j] / c_i) ]

c must be a bigint column of non-negative values.

The function ignores any NULL count. If the sum of non-NULL counts is 0,it returns 0.

  • kurtosis(x) → double
  • Returns the excess kurtosis of all input values. Unbiased estimate usingthe following expression:
  1. kurtosis(x) = n(n+1)/((n-1)(n-2)(n-3))sum[(x_i-mean)^4]/stddev(x)^4-3(n-1)^2/((n-2)(n-3))
  • classificationmiss_rate(_buckets, y, x, weight) → array
  • Computes the miss-rate part of the receiver operator curve with up to buckets number of buckets. Returnsan array of miss-rate values. y should be a boolean outcome value; x should be predictions, eachbetween 0 and 1; weight should be non-negative values, indicating the weight of the instance.

To get an ROC map, use this in conjunction with classification_recall():

  1. MAP(classification_recall(200, outcome, prediction), classification_miss_rate(200, outcome, prediction))

  • classificationprecision(_buckets, y, x) → array
  • This function is equivalent to the variant ofclassification_precision() that takes a weight, with a per-item weight of 1.
  • classificationprecision(_buckets, y, x, weight) → array
  • Computes the precision part of the precision-recall curve with up to buckets number of buckets. Returnsan array of precision values. y should be a boolean outcome value; x should be predictions, eachbetween 0 and 1; weight should be non-negative values, indicating the weight of the instance.

To get a map of recall to precision, use this in conjunction with classification_recall():

  1. MAP(classification_recall(200, outcome, prediction), classification_precision(200, outcome, prediction))

  • classificationprecision(_buckets, y, x) → array
  • This function is equivalent to the variant ofclassification_precision() that takes a weight, with a per-item weight of 1.
  • classificationrecall(_buckets, y, x, weight) → array
  • Computes the recall part of the precision-recall curve or the receiver operator charateristic curvewith up to buckets number of buckets. Returns an array of recall values.y should be a boolean outcome value; x should be predictions, eachbetween 0 and 1; weight should be non-negative values, indicating the weight of the instance.

To get a map of recall to precision, use this in conjunction with classification_recall():

  1. MAP(classification_recall(200, outcome, prediction), classification_precision(200, outcome, prediction))

  • classificationrecall(_buckets, y, x) → array
  • This function is equivalent to the variant ofclassification_recall() that takes a weight, with a per-item weight of 1.
  • classificationthresholds(_buckets, y, x) → array
  • Computes the thresholds part of the precision-recall curve with up to buckets number of buckets. Returnsan array of thresholds. y should be a boolean outcome value; x should be predictions, eachbetween 0 and 1.

To get a map of thresholds to precision, use this in conjunction with classification_precision():

  1. MAP(classification_thresholds(200, outcome, prediction), classification_precision(200, outcome, prediction))

To get a map of thresholds to recall, use this in conjunction with classification_recall():

  1. MAP(classification_thresholds(200, outcome, prediction), classification_recall(200, outcome, prediction))

  • regrintercept(_y, x) → double

  • Returns linear regression intercept of input values. y is the dependentvalue. x is the independent value.

  • regrslope(_y, x) → double

  • Returns linear regression slope of input values. y is the dependentvalue. x is the independent value.

  • skewness(x) → double

  • Returns the skewness of all input values.

  • stddev(x) → double

  • This is an alias for stddev_samp().

  • stddevpop(_x) → double

  • Returns the population standard deviation of all input values.

  • stddevsamp(_x) → double

  • Returns the sample standard deviation of all input values.

  • variance(x) → double

  • This is an alias for var_samp().

  • varpop(_x) → double

  • Returns the population variance of all input values.

  • varsamp(_x) → double

  • Returns the sample variance of all input values.