Question

I’m trying to implement a custom aggregate function in Postgres which will average directions in degrees – i.e. I want to able to do:

SELECT circavg(direction) FROM sometable;

This can be done using the formula:

xbar = atan2(sum(sin(xi), sum(cos(xi)))

I think I need to define an sfunc which will take a direction, and add the sine and cosine of that into two accumulators. The final function then converts the two components back into a direction using atan2.

I can’t work out how to define the sfunc so that the current state consists of two components e.g. (float, float). The documentation is a bit short on concrete examples, so any help is appreciated.

Answer 1

You can make use of an ARRAY type internally. Argument type can still be any numeric type. Demonstrating with float (= double precision):

CREATE OR REPLACE FUNCTION f_circavg (float[], float)
  RETURNS float[] LANGUAGE sql STRICT AS
'SELECT ARRAY[$1[1] + sin($2), $1[2] + cos($2), 1]';

CREATE OR REPLACE FUNCTION f_circavg_final (float[])
  RETURNS float  LANGUAGE sql AS
'SELECT CASE WHEN $1[3] > 0 THEN atan2($1[1], $1[2]) END';

CREATE AGGREGATE circavg (float) (
   sfunc     = f_circavg
 , stype     = float[]
 , finalfunc = f_circavg_final
 , initcond  = '{0,0,0}'
);

The transition function f_circavg() is defined STRICT, so it ignores rows with NULL input. It also sets a third array element to identify sets with one or more input rows – else the CASE the final function returns NULL.

Temporary table for testing:

CREATE TEMP TABLE t (x float);
INSERT INTO t VALUES (2), (NULL), (3), (4), (5);

I threw in a NULL value to also test the STRICT magic. Call:

SELECT circavg(x) FROM t;

       circavg
-------------------
 -2.78318530717959

Cross check:

SELECT atan2(sum(sin(x)), sum(cos(x))) FROM t;

       atan2
-------------------
 -2.78318530717959

Returns the same. Seems to work. In test with a bigger table the last expression with regular aggregate functions was 4x faster than the custom aggregate.

Test for zero input rows / only NULL input:

SELECT circavg(x) FROM t WHERE false;     -- no input rows
SELECT circavg(x) FROM t WHERE x IS NULL; -- only NULL input

Returns NULL in both cases.