How To Calculate Fibonacci Extensions using SQL?
How To Calculate Fibonacci Extensions using SQL?
1 answer
@oda.tromp
To calculate Fibonacci extensions using SQL, you will first need a table with the Fibonacci sequence. You can create this table using a common table expression (CTE) or by populating a table with the Fibonacci numbers up to a certain point.
Here is an example of how you can calculate Fibonacci extensions in SQL:
- Create a table with the Fibonacci sequence:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
WITH RECURSIVE Fibonacci AS (
SELECT 0 AS n, 0 AS f
UNION ALL
SELECT
n + 1,
CASE
WHEN n = 0 THEN 1
WHEN n = 1 THEN 1
ELSE f + LAG(f, 1) OVER (ORDER BY n)
END
FROM Fibonacci
WHERE n < 10 -- Change this to the desired number of Fibonacci numbers
)
SELECT *
FROM Fibonacci;
|
- Calculate the Fibonacci extensions using the Fibonacci numbers from the table:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 |
WITH Fibonacci AS (
SELECT 0 AS n, 0 AS f
UNION ALL
SELECT
n + 1,
CASE
WHEN n = 0 THEN 1
WHEN n = 1 THEN 1
ELSE f + LAG(f, 1) OVER (ORDER BY n)
END
FROM Fibonacci
WHERE n < 10 -- Change this to the desired number of Fibonacci numbers
),
Extensions AS (
SELECT
f1.f AS fib1,
LAG(f2.f, 1) OVER (ORDER BY f2.n) AS fib2,
LAG(f2.f, 2) OVER (ORDER BY f2.n) AS fib3,
LAG(f2.f, 3) OVER (ORDER BY f2.n) AS fib4
FROM Fibonacci f1
CROSS JOIN Fibonacci f2
)
SELECT
fib1,
fib1 + (fib1 - fib2) AS extension1,
fib1 + (fib1 - fib3) AS extension2,
fib1 + (fib1 - fib4) AS extension3
FROM Extensions;
|
In this example, the Fibonacci CTE generates the Fibonacci numbers up to 10, and the Extensions CTE calculates the first three Fibonacci extensions for each Fibonacci number. You can adjust the number of Fibonacci numbers generated and the number of extensions calculated by changing the values in the WHERE clause of the Fibonacci CTE and the LAG functions in the Extensions CTE.