How to find the MAX of a calculated value in a window? - sqlite

Question

I have a simple database table with three columns: id, x, y. x and y are just the coordinates of points in a line. I want to using the SQLite Window function to partition the table using a sliding window of three rows, and then get the y value that is the furthest from the y value of the first coordinate (row) in the window.
An example:
| id | x | y |
|----|---|---|
| 1 | 1 | .5|
| 2 | 2 | .9|
| 3 | 3 | .7|
| 4 | 4 |1.1|
| 5 | 5 | 1 |
So the first partition would consist of:
| id | x | y |
|----|---|---|
| 1 | 1 | .5|
| 2 | 2 | .9|
| 3 | 3 | .7|
And the desired result would be:
| id | x | y | d |
|----|---|---|---|
| 1 | 1 | .5| .4|
| 2 | 2 | .9|
| 3 | 3 | .7|
Since the the window with id = 1 as the CURRENT ROW would have a maximum variation of .4; the maximum distance between the y value of the first row in the partition, .5, and .9, is .4.
The final expected result:
| id | x | y | d |
|----|---|---|---|
| 1 | 1 | .5| .4|
| 2 | 2 | .9| .2|
| 3 | 3 | .7| .4|
| 4 | 4 |1.1| .1|
| 5 | 5 | 1 | |
I've tried using a window function like: WINDOW win1 AS (ROWS BETWEEN CURRENT ROW AND 2 FOLLOWING which gives me the correct window.
With the window defined, I tried doing something like:
SELECT
max(abs(y - first_value(y) OVER win1)) AS d
FROM t
WINDOW win1 AS (ROWS BETWEEN CURRENT ROW AND 2 FOLLOWING)
But I get an error for misuse of first_value.
I think the problem I have is this is not the proper approach to calculate over each row of a partition, but I could not find another solution or approach that matches what I am trying to do here.

Answer 1

For each row of your table you define a window starting from the current row up to the next 2 rows.
In your code y is the value in the current row and first_value() is the 1st value of y of the current window which is also the value of y of the current row.
So even if your code was syntactically correct the difference you calculate would always return 0.
It's easier to solve your problem with LEAD() window function:
WITH cte AS (
SELECT *,
LEAD(y, 1) OVER () AS y1,
LEAD(y, 2) OVER () AS y2
FROM tablename
)
SELECT
id, x, y,
MAX(ABS(y - y1), COALESCE(ABS(y - y2), 0)) d
FROM cte
See the demo.
Results:
id x y d
1 1 0.5 0.4
2 2 0.9 0.2
3 3 0.7 0.4
4 4 1.1 0.1
5 5 1.0