TSQL根据同一列中前一行的值计算行值

Question

我有一个数据集，我需要计算一个值，该值的每一行取决于同一列的前一行中的值。或者当没有上一行时最初为 1。我需要在不同的分区上执行此操作。

公式如下所示：factor = (前一个因子，如果不存在则为 1) * (1 + div / nav) 这需要通过 Inst_id 进行分区。

我宁愿避免使用光标。也许 cte 带有递归 - 但我无法理解它 - 或其他方式？

我知道这段代码不起作用，因为我无法引用同一列，但这是显示我正在尝试做的事情的另一种方式：

SELECT Dato, Inst_id, nav, div
     , (1 + div / nav ) * ISNULL(LAG(factor, 1) OVER (PARTITION BY Inst_id ORDER BY Date), 1) AS factor
FROM @tmp

因此，我需要使用我的测试数据在下面的因子列中获得这些结果。 请忽略舍入问题，因为我是在 Excel 中计算的：

date     Inst_id    nav     div     factor
11-04-2012  16  57.5700     5.7500  1.09987841
19-04-2013  16  102.8600    10.2500 1.20948130
29-04-2014  16  65.9300     16.7500 1.51675890
08-04-2013  29  111.2736    17.2500 1.15502333
10-04-2014  29  101.9650    16.3000 1.33966395
15-04-2015  29  109.5400    7.5000  1.43138825
27-04-2016  29  94.2500     0.4000  1.43746311
15-04-2015  34  159.1300    11.4000 1.07163954
27-04-2016  34  124.6100    17.6000 1.22299863
26-04-2017  34  139.7900    9.2000  1.30348784
01-04-2016  38  99.4600     0.1000  1.00100543
26-04-2017  38  102.9200    2.1000  1.02143014

测试数据：

DECLARE @tmp TABLE(Dato DATE, Inst_id INT, nav DECIMAL(26,19), div DECIMAL(26,19), factor DECIMAL(26,19))
INSERT INTO @tmp (Dato, Inst_id, nav, div) VALUES
('2012-04-11', 16, 57.57, 5.75),
('2013-04-19', 16, 102.86, 10.25),
('2014-04-29', 16, 65.93, 16.75),
('2013-04-08', 29, 111.273577, 17.25),
('2014-04-10', 29, 101.964994, 16.3),
('2015-04-15', 29, 109.54, 7.5),
('2016-04-27', 29, 94.25, 0.4),
('2015-04-15', 34, 159.13, 11.4),
('2016-04-27', 34, 124.61, 17.6),
('2017-04-26', 34, 139.79, 9.2)

我使用的是 Microsoft SQL Server Enterprise 2016（并使用 SSMS 2016）。

Answer 1

您可以使用（如果 DIV 和 NAV 始终 >0）：

SELECT A.* , EXP(SUM( LOG(1+DIV/NAV) ) OVER (PARTITION BY INST_ID ORDER BY DATO) )AS FACT_NEW
FROM @tmp A

其实你需要的是一个等价的聚合函数 MULTIPLY() OVER ...。 使用对数定理：LOG(M*N) = LOG(M) + LOG (N) 你可以做到；例如：

DECLARE @X1 NUMERIC(10,4)=5
DECLARE @X2 NUMERIC(10,4)=7
SELECT @x1*@x2 AS S1, EXP(LOG(@X1)+LOG(@X2)) AS S2

输出：

+------------+---------+-------------------------+------------------------+--------+------------------+
|    Dato    | Inst_id |           nav           |          div           | factor |     FACT_NEW     |
+------------+---------+-------------------------+------------------------+--------+------------------+
| 2012-04-11 |      16 |  57.5700000000000000000 |  5.7500000000000000000 | NULL   |   1.099878408893 |
| 2013-04-19 |      16 | 102.8600000000000000000 | 10.2500000000000000000 | NULL   | 1.20948130303111 |
| 2014-04-29 |      16 |  65.9300000000000000000 | 16.7500000000000000000 | NULL   | 1.51675889783963 |
| 2013-04-08 |      29 | 111.2735770000000000000 | 17.2500000000000000000 | NULL   |   1.155023325977 |
| 2014-04-10 |      29 | 101.9649940000000000000 | 16.3000000000000000000 | NULL   | 1.33966395090911 |
| 2015-04-15 |      29 | 109.5400000000000000000 |  7.5000000000000000000 | NULL   | 1.43138824917236 |
| 2016-04-27 |      29 |  94.2500000000000000000 |  0.4000000000000000000 | NULL   | 1.43746310646293 |
| 2015-04-15 |      34 | 159.1300000000000000000 | 11.4000000000000000000 | NULL   |   1.071639539998 |
| 2016-04-27 |      34 | 124.6100000000000000000 | 17.6000000000000000000 | NULL   | 1.22299862758278 |
| 2017-04-26 |      34 | 139.7900000000000000000 |  9.2000000000000000000 | NULL   | 1.30348784264639 |
+------------+---------+-------------------------+------------------------+--------+------------------+

Answer 2

使用递归 CTE：

WITH DataSource AS
(
    SELECT *
          ,ROW_NUMBER() OVER (PARTITION BY Inst_id ORDER BY Dato) AS [rowId]
    FROM @tmp
),
RecursiveDataSource AS
(
    SELECT *
          ,CAST((1 + div / nav ) * 1 AS DECIMAL(26,19)) as [factor_calculated]
    FROM DataSource
    WHERE [rowId] = 1
    UNION ALL
    SELECT A.*
          ,CAST((1 + A.div / A.nav ) * R.factor_calculated AS DECIMAL(26,19)) as [factor_calculated]
    FROM RecursiveDataSource R
    INNER JOIN DataSource A
        ON r.[Inst_id] = A.[Inst_id]
        AND R.[rowId] + 1 = A.[rowId]
)
SELECT *
FROM RecursiveDataSource
ORDER BY Inst_id, Dato;

我猜你在第 3 行之后在 Excel 中得到了不同的值，因为你没有在那里按Inst_id 进行分区。