Postgres custom aggregate functions

custome_aggregate_functions.sql

-- See: https://stackoverflow.com/questions/48770517/take-first-second-third-last-value-and-selecting-rows-window-function-wit
----- N = 1
-- State transition function
-- agg_state: the current state, el: new element
create or replace function lag_agg_sfunc_1(agg_state point, el float)
    returns point
    immutable
    language plpgsql
    as $$
declare
    i integer;
    stored_value float;
begin
    i := agg_state[0];
    stored_value := agg_state[1];

    i := i + 1; -- First row i=1
    if i = 1 then
        stored_value := el;
    end if;
    return point(i, stored_value);
end;
$$;

-- Final function
--DROP FUNCTION lag_agg_ffunc_1(point) CASCADE;
create or replace function lag_agg_ffunc_1(agg_state point)
    returns float
    immutable
    strict
    language plpgsql
    as $$
begin
  return agg_state[1];
end;
$$;

-- Aggregate function
drop aggregate if exists lag_agg_1(double precision);
create aggregate lag_agg_1 (float) (
    sfunc = lag_agg_sfunc_1,
    stype = point,
    finalfunc = lag_agg_ffunc_1,
    initcond = '(0,0)'
);