Aggregate Functions

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

Except for count(), count_if(), max_by(), min_by() and approx_distinct(), all of these aggregate functions ignore null values and 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 null values in the count. The coalesce function can be used to convert null into zero.

Some aggregate functions such as array_agg() produce different results depending on the order of input values.

General Aggregate Functions

arbitrary(x) → [same as x]

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

any_value(x) → [same as x]

This is an alias for arbitrary().

array_agg(x) → array<[same as x]>

Returns an array created from the input x elements. Ignores null inputs if presto.array_agg.ignore_nulls is set to false.

avg(x) → double | real

Returns the average (arithmetic mean) of all non-null input values. When x is of type REAL, the result type is REAL. For all other input types, the result type is DOUBLE.

bool_and(boolean) → boolean

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

bool_or(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.

count_if(x) → bigint

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

entropy(c) → double

Returns the log-2 entropy of count input-values.

\[\mathrm{entropy}(c) = \sum_i \left[ {c_i \over \sum_j [c_j]} \log_2\left({\sum_j [c_j] \over c_i}\right) \right].\]

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

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

every(boolean) → boolean

This is an alias for bool_and().

histogram(x)

Returns a map containing the count of the number of times each input value occurs. Supports integral, floating-point, boolean, timestamp, and date input types.

geometric_mean(bigint) → double

geometric_mean(double) → double

geometric_mean(real) → real

Returns the geometric mean of all input values.

max_by(x, y) → [same as x]

Returns the value of x associated with the maximum value of y over all input values. y must be an orderable type.

max_by(x, y, n) -> array([same as x])

Returns n values of x associated with the n largest values of y in descending order of y.

min_by(x, y) → [same as x]

Returns the value of x associated with the minimum value of y over all input values. y must be an orderable type.

min_by(x, y, n) -> array([same as x])

Returns n values of x associated with the n smallest values of y in ascending order of y.

max(x) → [same as x]

Returns the maximum value of all input values. x must not contain nulls when it is complex type. x must be an orderable type. Nulls are ignored if there are any non-null inputs. For REAL and DOUBLE types, NaN is considered greater than Infinity.

max(x, n) → array<[same as x]>

Returns n largest values of all input values of x. n must be a positive integer and not exceed 10’000. Currently not supported for ARRAY, MAP, and ROW input types. Nulls are not included in the output array. For REAL and DOUBLE types, NaN is considered greater than Infinity.

min(x) → [same as x]

Returns the minimum value of all input values. x must not contain nulls when it is complex type. x must be an orderable type. Nulls are ignored if there are any non-null inputs. For REAL and DOUBLE types, NaN is considered greater than Infinity.

min(x, n) → array<[same as x]>

Returns n smallest values of all input values of x. n must be a positive integer and not exceed 10’000. Currently not supported for ARRAY, MAP, and ROW input types. Nulls are not included in output array. For REAL and DOUBLE types, NaN is considered greater than Infinity.

multimap_agg(K key, V value) -> map(K, array(V))

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

reduce_agg(inputValue T, initialState S, inputFunction(S, T, S), combineFunction(S, S, S)) → S

Reduces all non-NULL input values into a single value. inputFunction will be invoked for each non-NULL input value. If all inputs are NULL, the result is NULL. In addition to taking the input value, inputFunction takes 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. Throws an error if initialState is NULL or inputFunction or combineFunction returns a NULL.

Take care when designing initialState, inputFunction and combineFunction. These need to support evaluating aggregation in a distributed manner using partial aggregation on many nodes, followed by shuffle over group-by keys, followed by final aggregation. Given a set of all possible values of state, make sure that combineFunction is commutative and associative operation with initialState as the identity value.

combineFunction(s, initialState) = s for any s

combineFunction(s1, s2) = combineFunction(s2, s1) for any s1 and s2

combineFunction(s1, combineFunction(s2, s3)) = combineFunction(combineFunction(s1, s2), s3) for any s1, s2, s3

In addition, make sure that the following holds for the inputFunction:

inputFunction(inputFunction(initialState, x), y) = combineFunction(inputFunction(initialState, x), inputFunction(initialState, y)) for any x and y

Check out blog post about reduce_agg for more context.

Note that reduce_agg doesn’t support evaluation over sorted inputs.:

-- Compute sum (for illustration purposes only; use SUM aggregate function in production queries).
SELECT id, reduce_agg(value, 0, (a, b) -> a + b, (a, b) -> a + b)
FROM (
    VALUES
        (1, 2),
        (1, 3),
        (1, 4),
        (2, 20),
        (2, 30),
        (2, 40)
) AS t(id, value)
GROUP BY id;
-- (1, 9)
-- (2, 90)

-- Compute product.
SELECT id, reduce_agg(value, 1, (a, b) -> a * b, (a, b) -> a * b)
FROM (
    VALUES
        (1, 2),
        (1, 3),
        (1, 4),
        (2, 20),
        (2, 30),
        (2, 40)
) AS t(id, value)
GROUP BY id;
-- (1, 24)
-- (2, 24000)

-- Compute avg (for illustration purposes only; use AVG aggregate function in production queries).
SELECT id, sum_and_count.sum / sum_and_count.count FROM (
  SELECT id, reduce_agg(value, CAST(row(0, 0) AS row(sum double, count bigint)),
    (s, x) -> CAST(row(s.sum + x, s.count + 1) AS row(sum double, count bigint)),
    (s, s2) -> CAST(row(s.sum + s2.sum, s.count + s2.count) AS row(sum double, count bigint))) AS sum_and_count
  FROM (
       VALUES
           (1, 2),
           (1, 3),
           (1, 4),
           (2, 20),
           (2, 30),
           (2, 40)
   ) AS t(id, value)
   GROUP BY id
);
-- (1, 3.0)
-- (2, 30.0)

set_agg(x) → array<[same as x]>

Returns an array created from the distinct input x elements. x must not contain nulls when it is complex type.

set_union(array(T)) -> array(T)

Returns an array of all the distinct values contained in each array of the input.

Returns an empty array if all input arrays are NULL.

Example:

SELECT set_union(elements)
FROM (
    VALUES
        ARRAY[1, 2, 3],
        ARRAY[2, 3, 4]
) AS t(elements);

Returns ARRAY[1, 2, 3, 4]

sum(x) → [same as x]

Returns the sum of all input values.

Bitwise Aggregate Functions

bitwise_and_agg(x) → [same as x]

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

Supported types are TINYINT, SMALLINT, INTEGER and BIGINT.

bitwise_or_agg(x) → [same as x]

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

Supported types are TINYINT, SMALLINT, INTEGER and BIGINT.

bitwise_xor_agg(x) → [same as x]

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

Supported types are TINYINT, SMALLINT, INTEGER and BIGINT.

Map Aggregate Functions

map_agg(K key, V value) -> map(K, V)

Returns a map created from the input key / value pairs. Inputs with NULL or duplicate keys are ignored.

map_union(map(K, V)) -> map(K, V)

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

map_union_sum(map(K, V)) -> map(K, V)

Returns the union of all the input maps summing the values of matching keys in all the maps. All null values in the original maps are coalesced to 0.

Approximate Aggregate Functions

approx_distinct(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 the standard deviation of the (approximately normal) error distribution over all possible sets. It does not guarantee an upper bound on the error for any specific input set.

approx_distinct(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, which is the standard deviation of the (approximately normal) error distribution over all possible sets. It does not guarantee an upper bound on the error for any specific input set. The current implementation of this function requires that e be in the range of [0.0040625, 0.26000].

approx_most_frequent(buckets, value, capacity) → map<[same as value], bigint>

Computes the top frequent values up to buckets elements approximately. Approximate estimation of the function enables us to pick up the frequent values with less memory. Larger capacity improves the accuracy of underlying algorithm with sacrificing the memory capacity. The returned value is a map containing the top elements with corresponding estimated frequency.

For BOOLEAN ‘value’, this function always returns ‘perfect’ result. ‘bucket’ and ‘capacity’ arguments are ignored in this case.

The error of the function depends on the permutation of the values and its cardinality. We can set the capacity same as the cardinality of the underlying data to achieve the least error.

buckets and capacity must be bigint. value can be numeric or string type.

The function uses the stream summary data structure proposed in the paper Efficient computation of frequent and top-k elements in data streams by A. Metwally, D. Agrawal and A. Abbadi.

approx_percentile(x, percentage) → [same as x]

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

approx_percentile(x, percentage, accuracy) → [same as x]

As approx_percentile(x, percentage), but with a maximum rank error of accuracy. The value of accuracy must be between zero and one (exclusive) and must be constant for all input rows. Note that a lower “accuracy” is really a lower error threshold, and thus more accurate. The default accuracy is 0.0133. The underlying implementation is KLL sketch thus has a stronger guarantee for accuracy than T-Digest.

approx_percentile(x, percentages) → array<[same as x]>

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

approx_percentile(x, percentages, accuracy) → array<[same as x]>

As approx_percentile(x, percentages), but with a maximum rank error of accuracy.

approx_percentile(x, w, percentage) → [same as x]

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

approx_percentile(x, w, percentage, accuracy) → [same as x]

As approx_percentile(x, w, percentage), but with a maximum rank error of accuracy.

approx_percentile(x, w, percentages) → array<[same as x]>

Returns the approximate weighed percentile for all input values of x using the per-item weight w at each of the given percentages specified in the array. The weight must be an integer value of at least one. It is effectively 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 must be constant for all input rows.

approx_percentile(x, w, percentages, accuracy) → array<[same as x]>

As approx_percentile(x, w, percentages), but with a maximum rank error of accuracy.

Classification Metrics Aggregate Functions

The following functions each measure how some metric of a binary confusion matrix changes as a function of classification thresholds. They are meant to be used in conjunction.

For example, to find the precision-recall curve, use

WITH
    recall_precision AS (
        SELECT
            CLASSIFICATION_RECALL(10000, correct, pred) AS recalls,
            CLASSIFICATION_PRECISION(10000, correct, pred) AS precisions
        FROM
           classification_dataset
    )
SELECT
    recall,
    precision
FROM
    recall_precision
CROSS JOIN UNNEST(recalls, precisions) AS t(recall, precision)

To get the corresponding thresholds for these values, use

WITH
    recall_precision AS (
        SELECT
            CLASSIFICATION_THRESHOLDS(10000, correct, pred) AS thresholds,
            CLASSIFICATION_RECALL(10000, correct, pred) AS recalls,
            CLASSIFICATION_PRECISION(10000, correct, pred) AS precisions
        FROM
           classification_dataset
    )
SELECT
    threshold,
    recall,
    precision
FROM
    recall_precision
CROSS JOIN UNNEST(thresholds, recalls, precisions) AS t(threshold, recall, precision)

To find the ROC curve, use

WITH
    fallout_recall AS (
        SELECT
            CLASSIFICATION_FALLOUT(10000, correct, pred) AS fallouts,
            CLASSIFICATION_RECALL(10000, correct, pred) AS recalls
        FROM
           classification_dataset
    )
SELECT
    fallout
    recall,
FROM
    recall_fallout
CROSS JOIN UNNEST(fallouts, recalls) AS t(fallout, recall)

classification_miss_rate(buckets, y, x, weight) → array<double>

Computes the miss-rate with up to buckets number of buckets. Returns an array of miss-rate values.

y should be a boolean outcome value; x should be predictions, each between 0 and 1; weight should be non-negative values, indicating the weight of the instance.

The miss-rate is defined as a sequence whose \(j\)-th entry is

\[{ \sum_{i \;|\; x_i \leq t_j \bigwedge y_i = 1} \left[ w_i \right] \over \sum_{i \;|\; x_i \leq t_j \bigwedge y_i = 1} \left[ w_i \right] + \sum_{i \;|\; x_i > t_j \bigwedge y_i = 1} \left[ w_i \right] },\]

where \(t_j\) is the \(j\)-th smallest threshold, and \(y_i\), \(x_i\), and \(w_i\) are the \(i\)-th entries of y, x, and weight, respectively.

classification_miss_rate(buckets, y, x) → array<double>

This function is equivalent to the variant of classification_miss_rate() that takes a weight, with a per-item weight of 1.

classification_fall_out(buckets, y, x, weight) → array<double>

Computes the fall-out with up to buckets number of buckets. Returns an array of fall-out values.

y should be a boolean outcome value; x should be predictions, each between 0 and 1; weight should be non-negative values, indicating the weight of the instance.

The fall-out is defined as a sequence whose \(j\)-th entry is

\[{ \sum_{i \;|\; x_i > t_j \bigwedge y_i = 0} \left[ w_i \right] \over \sum_{i \;|\; y_i = 0} \left[ w_i \right] },\]

where \(t_j\) is the \(j\)-th smallest threshold, and \(y_i\), \(x_i\), and \(w_i\) are the \(i\)-th entries of y, x, and weight, respectively.

classification_fall_out(buckets, y, x) → array<double>

This function is equivalent to the variant of classification_fall_out() that takes a weight, with a per-item weight of 1.

classification_precision(buckets, y, x, weight) → array<double>

Computes the precision with up to buckets number of buckets. Returns an array of precision values.

y should be a boolean outcome value; x should be predictions, each between 0 and 1; weight should be non-negative values, indicating the weight of the instance.

The precision is defined as a sequence whose \(j\)-th entry is

\[{ \sum_{i \;|\; x_i > t_j \bigwedge y_i = 1} \left[ w_i \right] \over \sum_{i \;|\; x_i > t_j} \left[ w_i \right] },\]

where \(t_j\) is the \(j\)-th smallest threshold, and \(y_i\), \(x_i\), and \(w_i\) are the \(i\)-th entries of y, x, and weight, respectively.

classification_precision(buckets, y, x) → array<double>

This function is equivalent to the variant of classification_precision() that takes a weight, with a per-item weight of 1.

classification_recall(buckets, y, x, weight) → array<double>

Computes the recall with up to buckets number of buckets. Returns an array of recall values.

y should be a boolean outcome value; x should be predictions, each between 0 and 1; weight should be non-negative values, indicating the weight of the instance.

The recall is defined as a sequence whose \(j\)-th entry is

\[{ \sum_{i \;|\; x_i > t_j \bigwedge y_i = 1} \left[ w_i \right] \over \sum_{i \;|\; y_i = 1} \left[ w_i \right] },\]

where \(t_j\) is the \(j\)-th smallest threshold, and \(y_i\), \(x_i\), and \(w_i\) are the \(i\)-th entries of y, x, and weight, respectively.

classification_recall(buckets, y, x) → array<double>

This function is equivalent to the variant of classification_recall() that takes a weight, with a per-item weight of 1.

classification_thresholds(buckets, y, x) → array<double>

Computes the thresholds with up to buckets number of buckets. Returns an array of threshold values.

y should be a boolean outcome value; x should be predictions, each between 0 and 1.

The thresholds are defined as a sequence whose \(j\)-th entry is the \(j\)-th smallest threshold.

Statistical Aggregate Functions

corr(y, x) → double

Returns correlation coefficient of input values.

covar_pop(y, x) → double

Returns the population covariance of input values.

covar_samp(y, x) → double

Returns the sample covariance of input values.

kurtosis(x) → double

Returns the excess kurtosis of all input values. Unbiased estimate using the following expression:

\[\mathrm{kurtosis}(x) = {n(n+1) \over (n-1)(n-2)(n-3)} { \sum[(x_i-\mu)^4] \over \sigma^4} -3{ (n-1)^2 \over (n-2)(n-3) },\]

where \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

regr_avgx(y, x) → double

Returns the average of the independent value in a group. y is the dependent value. x is the independent value.

regr_avgy(y, x) → double

Returns the average of the dependent value in a group. y is the dependent value. x is the independent value.

regr_count(y, x) → double

Returns the number of non-null pairs of input values. y is the dependent value. x is the independent value.

regr_intercept(y, x) → double

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

regr_r2(y, x) → double

Returns the coefficient of determination of the linear regression. y is the dependent value. x is the independent value. If regr_sxx(y, x) is 0, result is null. If regr_syy(y, x) is 0 and regr_sxx(y, x) isn’t 0, result is 1.

regr_slope(y, x) → double

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

regr_sxx(y, x) → double

Returns the sum of the squares of the independent values in a group. y is the dependent value. x is the independent value.

regr_sxy(y, x) → double

Returns the sum of the product of the dependent and independent values in a group. y is the dependent value. x is the independent value.

regr_syy(y, x) → double

Returns the sum of the squares of the dependent values in a group. y is the dependent value. 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().

stddev_pop(x) → double

Returns the population standard deviation of all input values.

stddev_samp(x) → double

Returns the sample standard deviation of all input values.

variance(x) → double

This is an alias for var_samp().

var_pop(x) → double

Returns the population variance of all input values.

var_samp(x) → double

Returns the sample variance of all input values.

Miscellaneous

max_data_size_for_stats(x) → bigint

Returns an estimate of the the maximum in-memory size in bytes of x.

sum_data_size_for_stats(x) → bigint

Returns an estimate of the sum of in-memory size in bytes of x.