Can PostgreSQL LAG() function refer to itself? - postgresql

Question

I've just discovered LAG() function in PostgreSQL and I've been experimenting to see what it can achieve. I've though that I might calculate factorial with it and I wrote
SELECT i, i * lag(factorial, 1, 1) OVER (ORDER BY i, 1) as factorial FROM generate_series(1, 10) as i;
But online IDE complains that 42703 column "factorial" does not exist.
Is there any way I can access the result of previous LAG call?

Answer 1

You can't refer to the column recursively in its definition.
However, you can express the factorial calculation as:
SELECT i, EXP(SUM(LN(i)) OVER w)::int factorial
FROM generate_series(1, 10) i
WINDOW w AS (ORDER BY i ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW);
-- outputs:
i | factorial
----+-----------
1 | 1
2 | 2
3 | 6
4 | 24
5 | 120
6 | 720
7 | 5040
8 | 40320
9 | 362880
10 | 3628800
(10 rows)
Postgresql does support an advanced SQL feature called recursive query, which can also be used to express the factorial table recursively:
WITH RECURSIVE series AS (
SELECT i FROM generate_series(1, 10) i
)
, rec AS (
SELECT i, 1 factorial FROM series WHERE i = 1
UNION ALL
SELECT series.i, series.i * rec.factorial
FROM series
JOIN rec ON series.i = rec.i + 1
)
SELECT *
FROM rec;
what EXP(SUM(LN(i)) OVER w) does:
This exploits the mathematical identities that:
[1]: log(a * b * c) = log (a) + log (b) + log (c)
[2]: exp (log a) = a
[combining 1&2]: exp(log a + log b + log c) = a * b * c
SQL does not have an aggregate multiply operation, so to perform an aggregate multiply operation, we first have to take the log of each value, then we can use the sum aggregate function to give us the the log of the values' product. This we invert with the final exponentiation step.
This works as long as the values being multiplied are positive as log is undefined for 0 and negative numbers. If you have negative numbers, or zero, the trick is to check if any value is 0, then the whole aggregation is 0, and check if the number of negative values is even, then the result is positive, else it is negative. Alternatively, you could also convert the reals to the complex plane and then use the identity Log(z) = ln(r) - iπ
what ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW does
This declares an expanding window frame that includes all preceding rows, and the current row.
e.g.
when i equals 1 the values in this window frame are {1}
when i equals 2 the values in this window frame are {1,2}
when i equals 3 the values in this window frame are {1,2,3}
what is a recursive query
A recursive query lets you express recursive logic using SQL. Recursive queries are often used to generate parent-child relationships from relational data (think manager-report, or product classification hierarchy), but they can generally be used to query any tree like structure.
Here is a SO answer I wrote a while back that illustrates and explains some of the capabilities of recursive queries.
There are also a tonne of useful tutorials on recursive queries. It is a very powerful sql-language feature and solves a type of problem that are very difficult do do without recursion.
Hope this gives you more insight into what the code does. Happy learning!