Implement the stored procedure iterative approach in a SQL manner - sql

Question

I am trying to implement convolution between two vectors v1 and v2. As part of that I have written a stored procedure with an iterative approach using while loops. Here is the below code as below. I am not able to think through how to do it using SQL as the stored procedure is inefficient w.r.t performance. Can somebody share your thoughts on this? Any inputs would be appreciated.
Idea behind writing the stored procedure:
https://software.intel.com/en-us/ipp-dev-reference-convolve
Table schema and sample input data:
CREATE TABLE AIRWork..TableA (idx INT, val INT);
CREATE TABLE AIRWork..TableB (idx INT, val INT);
INSERT INTO AIRWork..TableA
VALUES (0, -2), (1, 0), (2, 1), (3, -1), (4, 3);
INSERT INTO AIRWork..TableB
VALUES (0, 0), (1, 1);
Stored procedure:
ALTER PROCEDURE Calc_Convolved_Values_Test
AS
BEGIN
DECLARE #srclen1 INT
DECLARE #srclen2 INT
DECLARE #n INT = 0
DECLARE #k INT
DECLARE #m INT
DECLARE #SQL NVARCHAR(1000)
DECLARE #x int
DECLARE #xx int = 0
DECLARE #sum INT = 0
DECLARE #y int
DECLARE #yy int = 0
DECLARE #a INT = 0
DECLARE #b INT = 0
SELECT #srclen1 = COUNT(*) FROM AIRWork..TableA;
SELECT #srclen2 = COUNT(*) FROM AIRWork..TableB;
SET #m = #srclen1 + #srclen2 -1
WHILE #n < #m
BEGIN
SET #k = 0
SET #sum = 0
WHILE #k <= #n
BEGIN
SET #SQL = 'SELECT #x=val FROM AIRWork..TableA WHERE idx ='+CONVERT(VARCHAR(5),#k)
EXEC sp_executesql #SQL, N'#x int out', #xx out
SET #a = #xx
IF #n-#k < #srclen2
BEGIN
SET #SQL = 'SELECT #y=val FROM AIRWork..TableB WHERE idx ='+CONVERT(VARCHAR(5),#n-#k)
EXEC sp_executesql #SQL, N'#y int out', #yy out
SET #b = #yy
END
ELSE
BEGIN
SET #b = 0
END
SET #sum = #sum + #a*#b
SET #k = #k + 1
END
PRINT #sum
SET #n = #n + 1
END
END
GO
Sample output:
pDst[n] --> Please check the formula in the beginning of the question.
0
-2
0
1
-1
3

Answer 1

This procedure should do it:
ALTER PROCEDURE Calc_Convolved_Values_Test
AS
;WITH AllRows AS
(
SELECT idx, val, 0 as tbl FROM AIRWork..TableA
UNION ALL SELECT idx, val, 1 as tbl FROM AIRWork..TableB
)
, CombinedRows As
(
SELECT *,
ROW_NUMBER() OVER(ORDER BY tbl, idx)-1 As k,
COUNT(*) OVER(PARTITION BY 1) - 1 As n
FROM AllRows
)
SELECT ABDest.k As idx, SUM(A.val * B.val) As val
FROM CombinedRows AS ABDest
JOIN CombinedRows AS AB ON AB.k <= ABDest.k
LEFT JOIN AIRWork..TableA As A ON A.idx = AB.k
LEFT JOIN AIRWork..TableB As B ON B.idx = ABDest.k - AB.k
WHERE ABDest.k < ABDest.n
GROUP BY ABDest.k
ORDER BY ABDest.k
GO
FYI, I would not recommend using a whole table to store a single vector. You would be much better off storing all of your vectors in the same table and using a name or ID key column to separate them.