Best way to interpolate values in SQL - sql

Question

I have a table with rate at certain date :
Rates
Id | Date | Rate
----+---------------+-------
1 | 01/01/2011 | 4.5
2 | 01/04/2011 | 3.2
3 | 04/06/2011 | 2.4
4 | 30/06/2011 | 5
I want to get the output rate base on a simple linear interpolation.
So if I enter 17/06/2011:
Date Rate
---------- -----
01/01/2011 4.5
01/04/2011 3.2
04/06/2011 2.4
17/06/2011
30/06/2011 5.0
the linear interpolation is (5 + 2,4) / 2 = 3,7
Is there a way to do a simple query (SQL Server 2005), or this kind of stuff need to be done in a programmatic way (C#...) ?

Answer 1

Something like this (corrected):
SELECT CASE WHEN next.Date IS NULL THEN prev.Rate
WHEN prev.Date IS NULL THEN next.Rate
WHEN next.Date = prev.Date THEN prev.Rate
ELSE ( DATEDIFF(d, prev.Date, #InputDate) * next.Rate
+ DATEDIFF(d, #InputDate, next.Date) * prev.Rate
) / DATEDIFF(d, prev.Date, next.Date)
END AS interpolationRate
FROM
( SELECT TOP 1
Date, Rate
FROM Rates
WHERE Date <= #InputDate
ORDER BY Date DESC
) AS prev
CROSS JOIN
( SELECT TOP 1
Date, Rate
FROM Rates
WHERE Date >= #InputDate
ORDER BY Date ASC
) AS next

Answer 2

As #Mark already pointed out, the CROSS JOIN has its limitations. As soon as the target value falls outside the range of defined values no records will be returned.
Also the above solution is limited to one result only. For my project I needed an interpolation for a whole list of x values and came up with the following solution. Maybe it is of interested to other readers too?
-- generate some grid data values in table #ddd:
CREATE TABLE #ddd (id int,x float,y float, PRIMARY KEY(id,x));
INSERT INTO #ddd VALUES (1,3,4),(1,4,5),(1,6,3),(1,10,2),
(2,1,4),(2,5,6),(2,6,5),(2,8,2);
SELECT * FROM #ddd;
-- target x-values in table #vals (results are to go into column yy):
CREATE TABLE #vals (xx float PRIMARY KEY,yy float null, itype int);
INSERT INTO #vals (xx) VALUES (1),(3),(4.3),(9),(12);
-- do the actual interpolation
WITH valstyp AS (
SELECT id ii,xx,
CASE WHEN min(x)<xx THEN CASE WHEN max(x)>xx THEN 1 ELSE 2 END ELSE 0 END flag,
min(x) xmi,max(x) xma
FROM #vals INNER JOIN #ddd ON id=1 GROUP BY xx,id
), ipol AS (
SELECT v.*,(b.x-xx)/(b.x-a.x) f,a.y ya,b.y yb
FROM valstyp v
INNER JOIN #ddd a ON a.id=ii AND a.x=(SELECT max(x) FROM #ddd WHERE id=ii
AND (flag=0 AND x=xmi OR flag=1 AND x<xx OR flag=2 AND x<xma))
INNER JOIN #ddd b ON b.id=ii AND b.x=(SELECT min(x) FROM #ddd WHERE id=ii
AND (flag=0 AND x>xmi OR flag=1 AND x>xx OR flag=2 AND x=xma))
)
UPDATE v SET yy=ROUND(f*ya+(1-f)*yb,8),itype=flag FROM #vals v INNER JOIN ipol i ON i.xx=v.xx;
-- list the interpolated results table:
SELECT * FROM #vals
When running the above script you will get the following data grid points in table #ddd
id x y
-- -- -
1 3 4
1 4 5
1 6 3
1 10 2
2 1 4
2 5 6
2 6 5
2 8 2
[[ The table contains grid points for two identities (id=1 and id=2). In my example I referenced only the 1-group by using where id=1 in the valstyp CTE. This can be changed to suit your requirements. ]]
and the results table #vals with the interpolated data in column yy:
xx yy itype
--- ---- -----
1 2 0
3 4 0
4.3 4.7 1
9 2.25 1
12 1.5 2
The last column itype indicates the type of interpolation/extrapolation that was used to calculate the value:
0: extrapolation to lower end
1: interpolation within given data range
2: extrapolation to higher end
This working example can be found here.

Answer 3

The trick with CROSS JOIN here is it wont return any records if either of the table does not have rows (1 * 0 = 0) and the query may break. Better way to do is use FULL OUTER JOIN with inequality condition (to avoid getting more than one row)
( SELECT TOP 1
Date, Rate
FROM Rates
WHERE Date <= #InputDate
ORDER BY Date DESC
) AS prev
FULL OUTER JOIN
( SELECT TOP 1
Date, Rate
FROM Rates
WHERE Date >= #InputDate
ORDER BY Date ASC
) AS next
ON (prev.Date <> next.Date) [or Rate depending on what is unique]