是否有人用T-SQL编写了Theil-Sen回归函数？
我发现一个用Perl编写的，但无法将其重新编码为SQL。
是否有人用T-SQL编写了Theil-Sen回归函数？
我发现一个用Perl编写的，但无法将其重新编码为SQL。
Answers:
我在撒谎时说，我无法将其重新编码为SQL。我太懒了。这是带有用法示例的代码。
该代码基于TheiSen perl库，使用QuickMedian。让我们定义一个新的表类型，以轻松地将数据传递给过程。
CREATE TYPE dbo.TheilSenInputDataTableType AS TABLE
(
ID INT IDENTITY(1,1),
x REAL,
y REAL
)请注意ID列，这在这里很重要，因为我们的解决方案使用CROSS APPLY语句来正确解释TheilSen.pm中的内部循环。
my ($x1,$x2,$y1,$y2);
foreach my $i(0 .. $n-2){
$y1 = $y->[$i];
$x1 = $x->[$i];
foreach my $j($i+1 .. $n-1){
$y2 = $y->[$j];
$x2 = $x->[$j];我们还需要一种新的数据类型来存储实型值数组。
CREATE TYPE [dbo].[RealArray] AS TABLE(
[val] [real] NULL
)这是f_QuickMedian函数，返回给定数组的中值。值得赞扬的是Itzik Ben-Gan。
CREATE FUNCTION [dbo].[f_QuickMedian](@RealArray RealArray READONLY)
RETURNS REAL
AS
BEGIN
DECLARE @Median REAL;
DECLARE @QMedian REAL;
SELECT @Median = AVG(1.0 * val)
FROM
(
SELECT o.val, rn = ROW_NUMBER() OVER (ORDER BY o.val), c.c
FROM @RealArray AS o
CROSS JOIN (SELECT c = COUNT(*) FROM @RealArray) AS c
) AS x
WHERE rn IN ((c + 1)/2, (c + 2)/2);
SELECT TOP 1 @QMedian = val FROM @RealArray
ORDER BY ABS(val - @Median) ASC, val DESC
RETURN @QMedian
END和p_TheilSen估计器：
CREATE PROCEDURE [dbo].[p_TheilSen](
@TheilSenInput TheilSenInputDataTableType READONLY
, @m Real OUTPUT
, @c Real OUTPUT
)
AS
BEGIN
DECLARE
@m_arr RealArray
, @c_arr RealArray;
INSERT INTO @m_arr
SELECT m
FROM
(
SELECT
t1.x as x1
, t1.y as y1
, t2o.x as x2
, t2o.y as y2
, t2o.y-t1.y as [y2 - y1]
, t2o.x-t1.x as [x2 - x1]
, CASE WHEN (t2o.x <> t1.x) THEN CAST((t2o.y-t1.y) AS Real)/(t2o.x-t1.x) ELSE NULL END AS [($y2-$y1)/($x2-$x1)]
, CASE WHEN t1.y = t2o.y THEN 0
ELSE
CASE WHEN t1.x = t2o.x THEN NULL
ELSE
-- push @M, ($y2-$y1)/($x2-$x1);
CAST((t2o.y-t1.y) AS Real)/(t2o.x-t1.x)
END
END as m
FROM @TheilSenInput t1
CROSS APPLY
(
SELECT t2.x, t2.y
FROM @TheilSenInput t2
WHERE t2.ID > t1.ID
) t2o
) t
WHERE m IS NOT NULL
SELECT @m = dbo.f_QuickMedian(@m_arr)
INSERT INTO @c_arr
SELECT y - (@m * x)
FROM @TheilSenInput
SELECT @c = dbo.f_QuickMedian(@c_arr)
END例：
DECLARE
@in TheilSenInputDataTableType
, @m Real
, @c Real
INSERT INTO @in(x,y) VALUES (10.79,118.99)
INSERT INTO @in(x,y) VALUES (10.8,120.76)
INSERT INTO @in(x,y) VALUES (10.86,122.71)
INSERT INTO @in(x,y) VALUES (10.93,125.48)
INSERT INTO @in(x,y) VALUES (10.99,127.31)
INSERT INTO @in(x,y) VALUES (10.96,130.06)
INSERT INTO @in(x,y) VALUES (10.98,132.41)
INSERT INTO @in(x,y) VALUES (11.03,135.89)
INSERT INTO @in(x,y) VALUES (11.08,139.02)
INSERT INTO @in(x,y) VALUES (11.1,140.25)
INSERT INTO @in(x,y) VALUES (11.19,145.61)
INSERT INTO @in(x,y) VALUES (11.25,153.45)
INSERT INTO @in(x,y) VALUES (11.4,158.03)
INSERT INTO @in(x,y) VALUES (11.61,162.72)
INSERT INTO @in(x,y) VALUES (11.69,167.67)
INSERT INTO @in(x,y) VALUES (11.91,172.86)
INSERT INTO @in(x,y) VALUES (12.07,177.52)
INSERT INTO @in(x,y) VALUES (12.32,182.09)
EXEC p_TheilSen @in, @m = @m OUTPUT, @c = @c OUTPUT
SELECT @m
SELECT @c返回值：
m = 52.7079
c = -448.4853只是为了比较，perl版本针对同一数据集返回以下值：
m = 52.7078651685394
c = -448.484943820225我使用TheilSen估计器来计算文件系统的DaysToFill指标。请享用！