以 SQL 方式实施存储过程迭代方法

Question

我正在尝试实现两个向量 v1 和 v2 之间的卷积。作为其中的一部分，我编写了一个使用 while 循环的迭代方法的存储过程。下面是下面的代码。我无法考虑如何使用 SQL 来完成它，因为存储过程效率低下 w.r.t 性能。有人可以分享您对此的看法吗？如有任何意见，我们将不胜感激。

编写存储过程的思路：

https://software.intel.com/en-us/ipp-dev-reference-convolve

Table 架构和示例输入数据：

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);

存储过程：

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

示例输出：

pDst[n] --> 请检查问题开头的公式

Answer 1

这个程序应该可以做到：

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

仅供参考，我不建议使用整个 table 来存储单个向量。最好将所有向量存储在同一个 table 中并使用名称或 ID 键列来分隔它们。

以 SQL 方式实施存储过程迭代方法

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