aggs_for_vecs

This is a C-based Postgres extension offering various aggregate functions like min, max, avg, and var_samp that operate on arrays instead of scalars. It treats each array as a "vector" and handles each element independently. So suppose you have 3 rows each with a 4-element array like so:

id	vals
1	{1,2,3,4}
2	{5,0,-5,0}
3	{3,6,0,9}

Then SELECT vec_to_min(vals) will pick the minimum item in each array position, giving you {1,0,-5,0}.

Note that the functions here are true aggregate functions. If you want something that provides aggregate-like behavior by computing stats from a single array, take a look at my other extension aggs_for_arrays. You could say that this extension follows a row-based format and the other a column-based.

Details

Functions support arrays of any numeric type: SMALLINT, INTEGER, BIGINT, REAL, or DOUBLE PRECISION (aka FLOAT). They either return an array of the same type (e.g. vec_to_min) or an array of FLOAT (e.g. vec_to_mean).

All input arrays must be the same length, or you get an error. The output array will have the same length as the inputs.

NULLs are ignored, and NULL elements are also skipped. Basically you get the same result as if you could do MIN on the first elements, then MIN on the second elements, etc. If all your inputs are simply NULL, then you'll get a NULL in return. But if the inputs are arrays of NULLs, then you'll get an array of NULLs in return (of the same length).

Note that when input arrays have NULL in some positions but not others, you still get correct results for things like mean. That is, we keep a count for each position separately and divide by the appropriate amount.

Installing

This package installs like any Postgres extension. First say:

make && sudo make install

You will need to have pg_config in your path, but normally that is already the case. You can check with which pg_config. (If you have multiple Postgresses installed, make sure that pg_config points to the right one.)

Then in the database of your choice say:

CREATE EXTENSION aggs_for_vecs;

You can also run tests and benchmarks yourself with make test and make bench, respectively, but first you'll have to set up databases for those to use. If you run the commands and they can't find a database, they'll give you instructions how to make one.

Aggregate functions

vec_to_count(ANYARRAY) RETURNS BIGINT[]

Returns the count of non-nulls in each array position.

vec_to_sum(ANYARRAY) RETURNS ANYARRAY

Returns the sum of non-nulls in each array position.

vec_to_min(ANYARRAY) RETURNS ANYARRAY

Returns the minimum in each array position.

vec_to_max(ANYARRAY) RETURNS ANYARRAY

Returns the maximum in each array position.

vec_to_mean(ANYARRAY) RETURNS FLOAT[]

Returns the average (mean) in each array position.

vec_to_weighted_mean(ANYARRAY, ANYARRAY) RETURNS FLOAT[]

Returns the weighted average (mean) in each array position, using the first parameter for the values and the second for the weights. The two arrays should have the same length.

vec_to_var_samp(ANYARRAY) RETURNS FLOAT[]

Returns the sample variance in each array position. The code is very similar to the built-in var_samp function, so if it works there it should work here (or it's a bug).

hist_2d(x ANYELEMENT, y ANYELEMENT, x_bucket_start ANYELEMENT, y_bucket_start ANYELEMENT, x_bucket_width ANYELEMENT, y_bucket_width ANYELEMENT, x_bucket_count INTEGER, y_bucket_count INTEGER)

Aggregate function that takes a bunch of x and y values, and plots them on a 2-D histogram. The other parameters determine the shape of the histogram (number of buckets on each axis, start of the buckets, width of each bucket).

hist_md(vals ANYARRAY, indexes INTEGER[], bucket_starts ANYARRAY, bucket_widths ANYARRAY, bucket_counts INTEGER[])

Aggregate function to compute an n-dimensional histogram. It takes a vector of values, and it uses indexes to pick one or more elements from that vector and treat them as x, y, z, etc. If you want 2 dimensions, there should be two values for indexes, two for bucket_starts, two for bucket_widths, and two for bucket_counts. Or if you want 3 dimensions, you need three values for each of those.

Since the values in indexes should follow Postgres's convention of 1-indexed arrays, so that if indexes is {1,4}, then we will use vals[1] and vals[4] as the histogram x and y.

vec_to_first(ANYARRAY) RETURNS ANYARRAY

Returns an array containing the first non-null value in each array position. Designed to be used as an ordered set aggregate like vec_to_first(nums ORDER BY ts).

vec_to_last(ANYARRAY) RETURNS ANYARRAY

Returns an array containing the last non-null value in each array position. Designed to be used as an ordered set aggregate like vec_to_last(nums ORDER BY ts).

Non-aggregate math functions

The following functions are not aggregate functions, and accept two arguments (l, r) in the following forms:

1. array, array
2. array, number
3. number, array

If number is provided instead of array, it is treated as if it were an array of the same length as the other argument, where every element has this value. In all cases the argument value types must be the same (for example both the integer type), and when two arrays are provided they must be of the same length. Each function returns an array of the same length as the input array(s) of the same type.

vec_add(l, r) RETURNS ANYARRAY

Returns each array position in the first argument added to the same position in the second argument.

vec_div(l, r) RETURNS ANYARRAY

Returns each array position in the first argument divided by the same position in the second argument.

vec_mul(l, r) RETURNS ANYARRAY

Returns each array position in the first argument multiplied by the same position in the second argument.

vec_sub(l, r) RETURNS ANYARRAY

Returns each array position in the second argument subtracted from the same position in the first argument.

Non-aggregate utility functions

The following are other non-arrgregate functions that are useful in combination with the other functions provided by this extension.

pad_vec(ANYRARRAY, INTEGER) RETURNS ANYARRAY

Return an array with the same elements as the given array, but extended to have the length of the second argument if necessary. Any added elements will be set to NULL. If the given array is already the given length, it is returned directly.

vec_coalesce(ANYARRAY, ANYELEMENT) RETURNS ANYARRAY

Return an array with the same elements as the given array, execept all NULL elements are replaced by the given second argument.

vec_trim_scale(NUMERIC[]) RETURNS NUMERIC[]

Trims trailing zeros from NUMERIC elements, for example on the results of a vec_to_mean() operation. In Postgres 13 or later the built-in trim_scale function will be applied to each array element, which adjusts the scale of each numeric such that trailing zeros are dropped. For Postgres 12 or older a polyfill implementation of that function is used.

vec_without_outliers(ANYARRAY, ANYARRAY, ANYARRAY) RETURNS ANYARRAY

Useful to trim down the inputs to the other functions here. You pass it three arrays all of the same length and type. The first array has the actual values. The second array gives the minimum amount allowed in each position; the third array, the maximum. The function returns an array where each element is either the input value (if within the min/max) or NULL (if an outlier). You can include NULLs in the min/max arrays to indicate an unbounded limit there, or pass a simple NULL for either to indicate no bounds at all.

Testing

These tests follow the PGXS and pg_regress framework used for Postgres extensions, including Postgres's own contrib package. To run the tests, first install the extension somewhere then say make installcheck. You can use standard libpq envvars to control the database connection, e.g. PGPORT=5436 make installcheck.

Limitations/TODO

• Lots of functions are still left to implement:

  • vec_to_min_max
  • vec_to_median
  • vec_to_mode
  • vec_to_percentile
  • vec_to_percentiles
  • vec_to_skewness
  • vec_to_kurtosis

Author

Paul A. Jungwirth

Benchmarks

You can get the same behavior as this extension by using UNNEST to break up the input arrays, and then array_agg to put the results back together. But these benchmarks show that aggs_for_vecs functions are 9-10 times faster:

function	SQL	aggs_for_vecs
vec_to_min	14150.7 ms	1468.14 ms
vec_to_max	14062.4 ms	1549.66 ms
vec_to_mean	14341.5 ms	1586.62 ms
vec_to_var_samp	14196.7 ms	1578.92 ms