PostgreSQL 9.1
业务情况
每个月都有一批特定流程的新帐户。每个批次都可以按月份，帐户数量和帐户总余额来描述。该过程的目标是从客户那里恢复一些平衡。 每个批次都按月单独跟踪（自批次转移到流程以来每月回收的金额）。
目标
我的目标是预测将来会收回多少金额。
数据定义
create table vintage_data (
granularity date, /* Month when account entered process*/
distance_in_months integer, /* Distance in months from date when accounts entered process*/
entry_accounts integer, /* Number of accounts that entered process in a given month*/
entry_amount numeric, /* Total amount for account that entered process in a given month*/
recovery_amount numeric /* Amount recovered in Nth month on accounts that entered process in a given month */
);
示例数据
insert into vintage_data values('2012-01-31',1,200,100000,1000);
insert into vintage_data values('2012-01-31',2,200,100000,2000);
insert into vintage_data values('2012-01-31',3,200,100000,3000);
insert into vintage_data values('2012-01-31',4,200,100000,3500);
insert into vintage_data values('2012-01-31',5,200,100000,3400);
insert into vintage_data values('2012-01-31',6,200,100000,3300);
insert into vintage_data values('2012-02-28',1,250,150000,1200);
insert into vintage_data values('2012-02-28',2,250,150000,1600);
insert into vintage_data values('2012-02-28',3,250,150000,1800);
insert into vintage_data values('2012-02-28',4,250,150000,1200);
insert into vintage_data values('2012-02-28',5,250,150000,1600);
insert into vintage_data values('2012-03-31',1,200,90000,1300);
insert into vintage_data values('2012-03-31',2,200,90000,1200);
insert into vintage_data values('2012-03-31',3,200,90000,1400);
insert into vintage_data values('2012-03-31',4,200,90000,1000);
insert into vintage_data values('2012-04-30',1,300,180000,1600);
insert into vintage_data values('2012-04-30',2,300,180000,1500);
insert into vintage_data values('2012-04-30',3,300,180000,4000);
insert into vintage_data values('2012-05-31',1,400,225000,2200);
insert into vintage_data values('2012-05-31',2,400,225000,6000);
insert into vintage_data values('2012-06-30',1,100,60000,1000);
计算流程
您可以将数据想象为三角矩阵（X值将被预测）：
distance_in_months 1 2 3 4 5 6
granularity entry_accounts entry_amount
2012-01-31 200 100000 1000 2000 3000 3500 3400 3300
2012-02-28 250 150000 1200 1600 1800 1200 1600 (X-1)
2012-03-31 200 90000 1300 1200 1400 1000 (X0) (X4)
2012-04-30 300 180000 1600 1500 4000 (X1) (X5) (X8)
2012-05-31 400 225000 2200 6000 (X2) (X6) (X9) (X11)
2012-06-30 100 60000 1000 (X3) (X7) (X10) (X12 (X13)
算法
我的目标是预测所有缺失点（未来）。为了说明这个过程，这是X1点的计算
1）使用距离最多为4来获取前三个月的行总数：
2012-01-31 1000+2000+3000+3500=9500 (d4m3)
2012-02-28 1200+1600+1800+1200=5800 (d4m2)
2012-03-31 1300+1200+1400+1000=4900 (d4m1)
2）使用距离最远为3来获取前三个月的行总数：
2012-01-31 1000+2000+3000=6000 (d3m3)
2012-02-28 1200+1600+1800=4600 (d3m2)
2012-03-31 1300+1200+1400=3800 (d3m1)
3）计算距离3和距离4的加权平均运行率（由entry_amount加权）：
(d4m3+d4m2+d4m1)/(100000+150000+90000) = (9500+5800+4900)/(100000+150000+90000) = 20200/340000 = 0.0594
(d3m3+d3m2+d3m1)/(100000+150000+90000) = (6000+4600+3800)/(100000+150000+90000) = 14400/340000 = 0.0424
4）计算距离3和距离4之间的变化
((d4m3+d4m2+d4m1)/(100000+150000+90000))/((d3m3+d3m2+d3m1)/(100000+150000+90000)) =
= (20200/340000)/(14400/340000) =
= 0.0594/0.0424 = 1.403 (PredictionRateForX1)
5）使用距离最多3来计算预测月份的行总数：
2012-04-30 1600+1500+4000=7100
6）使用entry_amount计算预测月份的费率
7100/180000 = 0.0394
7）计算X1预测的速率
0.0394 * PredictionRateForX1 = 0.05534
8）计算X1的数量
(0.05534-0.0394)*180000 = 2869.2
问题
问题是如何使用SQL语句计算矩阵的其余部分（从x-1到x13）。很明显，这需要某种递归算法。
答案 0 :(得分：2)
这是一项艰巨的任务，将其拆分以使其更易于管理。我会把它放在一个带RETURN TABLE的plpgsql函数中：
使用交叉表查询为“计算过程”矩阵创建临时表
您需要为此安装tablefunc模块。运行（每个数据库一次）：
CREATE EXTENSION tablefunc;
按字段更新临时表字段。
以下演示功能齐全，并使用PostgreSQL 9.1.4进行了测试。基于问题中提供的表定义：
-- DROP FUNCTION f_forcast();
CREATE OR REPLACE FUNCTION f_forcast()
RETURNS TABLE (
granularity date
,entry_accounts numeric
,entry_amount numeric
,d1 numeric
,d2 numeric
,d3 numeric
,d4 numeric
,d5 numeric
,d6 numeric) AS
$BODY$
BEGIN
--== Create temp table with result of crosstab() ==--
CREATE TEMP TABLE matrix ON COMMIT DROP AS
SELECT *
FROM crosstab (
'SELECT granularity, entry_accounts, entry_amount
,distance_in_months, recovery_amount
FROM vintage_data
ORDER BY 1, 2',
'SELECT DISTINCT distance_in_months
FROM vintage_data
ORDER BY 1')
AS tbl (
granularity date
,entry_accounts numeric
,entry_amount numeric
,d1 numeric
,d2 numeric
,d3 numeric
,d4 numeric
,d5 numeric
,d6 numeric
);
ANALYZE matrix; -- update statistics to help calculations
--== Calculations ==--
-- I implemented the first calculation for X1 and leave the rest to you.
-- Can probably be generalized in a loop or even a single statement.
UPDATE matrix m
SET d4 = (
SELECT (sum(x.d1) + sum(x.d2) + sum(x.d3) + sum(x.d4))
/(sum(x.d1) + sum(x.d2) + sum(x.d3)) - 1
-- removed redundant sum(entry_amount) from equation
FROM (
SELECT *
FROM matrix a
WHERE a.granularity < m.granularity
ORDER BY a.granularity DESC
LIMIT 3
) x
) * (m.d1 + m.d2 + m.d3)
WHERE m.granularity = '2012-04-30';
--- Next update X2 ..
--== Return results ==--
RETURN QUERY
TABLE matrix
ORDER BY 1;
END;
$BODY$ LANGUAGE plpgsql;
呼叫：
SELECT * FROM f_forcast();
我已经简化了一点，删除了计算中的一些冗余步骤 该解决方案采用了各种先进技术。你需要了解PostgreSQL的方法来解决这个问题。
答案 1 :(得分：1)
--
-- rank the dates.
-- , also fetch the the fields that seem to depend on them.
-- (this should have been done in the data model)
--
CREATE VIEW date_rank AS (
SELECT uniq.granularity,uniq.entry_accounts,uniq.entry_amount
, row_number() OVER(ORDER BY 0) AS zrank
FROM ( SELECT DISTINCT granularity, entry_accounts, entry_amount FROM vintage_data)
AS uniq
);
-- SELECT * FROM date_rank ORDER BY granularity;
--
-- transform to an x*y matrix, avoiding the date key and the slack columns
--
CREATE VIEW matrix_data AS (
SELECT vd.distance_in_months AS xxx
, dr.zrank AS yyy
, vd.recovery_amount AS val
FROM vintage_data vd
JOIN date_rank dr ON dr.granularity = vd.granularity
);
-- SELECT * FROM matrix_data;
--
-- In order to perform the reversed transformation:
-- make the view insertable.
-- INSERTS to matrix_data will percolate back into the vintage_data table
-- (don't try this at home ;-)
--
CREATE RULE magic_by_the_plasser AS
ON INSERT TO matrix_data
DO INSTEAD (
INSERT INTO vintage_data (granularity,distance_in_months,entry_accounts,entry_amount,recovery_amount)
SELECT dr.granularity, new.xxx, dr.entry_accounts, dr.entry_amount, new.val
FROM date_rank dr
WHERE dr.zrank = new.yyy
;
);
--
-- This CTE creates the weights for a Pascal-triangle
--
-- EXPLAIN -- ANALYZE
WITH RECURSIVE pascal AS (
WITH empty AS (
--
-- "cart" is a cathesian product of X*Y
-- its function is similar to a "calendar table":
-- filling in the missing X,Y pairs, making the matrix "square".
-- (well: rectangular, but in the given case nX==nY)
--
WITH cart AS (
WITH mmx AS (
WITH xx AS ( SELECT MIN(xxx) AS x0 , MAX(xxx) AS x1 FROM matrix_data)
SELECT generate_series(xx.x0,xx.x1) AS xxx
FROM xx
)
, mmy AS (
WITH yy AS ( SELECT MIN(yyy) AS y0 , MAX(yyy) AS y1 FROM matrix_data)
SELECT generate_series(yy.y0,yy.y1) AS yyy
FROM yy
)
SELECT * FROM mmx
JOIN mmy ON (1=1) -- Carthesian product here!
)
--
-- The (x,y) pairs that are not present in the current matrix
--
SELECT * FROM cart ca
WHERE NOT EXISTS (
SELECT *
FROM matrix_data nx
WHERE nx.xxx = ca.xxx
AND nx.yyy = ca.yyy
)
)
SELECT md.yyy AS src_y
, md.xxx AS src_x
, md.yyy AS dst_y
, md.xxx AS dst_x
-- The filled-in matrix cells have weight 1
, 1::numeric AS weight
FROM matrix_data md
UNION ALL
SELECT pa.src_y AS src_y
, pa.src_x AS src_x
, em.yyy AS dst_y
, em.xxx AS dst_x
-- the derived matrix cells inherit weight/2 from both their parents
, (pa.weight/2) AS weight
FROM pascal pa
JOIN empty em
ON ( em.yyy = pa.dst_y+1 AND em.xxx = pa.dst_x)
OR ( em.yyy = pa.dst_y AND em.xxx = pa.dst_x+1 )
)
INSERT INTO matrix_data(yyy,xxx,val)
SELECT pa.dst_y,pa.dst_x
,SUM(ma.val*pa.weight)
FROM pascal pa
JOIN matrix_data ma ON pa.src_y = ma.yyy AND pa.src_x = ma.xxx
-- avoid the filled-in matrix cells (which map to themselves)
WHERE NOT (pa.src_y = pa.dst_y AND pa.src_x = pa.dst_x)
GROUP BY pa.dst_y,pa.dst_x
;
--
-- This will also get rid of the matrix_data view and the rule.
--
DROP VIEW date_rank CASCADE;
-- SELECT * FROM matrix_data ;
SELECT * FROM vintage_data ORDER BY granularity, distance_in_months;
结果：
NOTICE: CREATE TABLE / PRIMARY KEY will create implicit index "vintage_data_pkey" for table "vintage_data"
CREATE TABLE
NOTICE: ALTER TABLE / ADD UNIQUE will create implicit index "mx_xy" for table "vintage_data"
ALTER TABLE
INSERT 0 21
VACUUM
CREATE VIEW
CREATE VIEW
CREATE RULE
INSERT 0 15
NOTICE: drop cascades to view matrix_data
DROP VIEW
granularity | distance_in_months | entry_accounts | entry_amount | recovery_amount
-------------+--------------------+----------------+--------------+---------------------------
2012-01-31 | 1 | 200 | 100000 | 1000
2012-01-31 | 2 | 200 | 100000 | 2000
2012-01-31 | 3 | 200 | 100000 | 3000
2012-01-31 | 4 | 200 | 100000 | 3500
2012-01-31 | 5 | 200 | 100000 | 3400
2012-01-31 | 6 | 200 | 100000 | 3300
2012-02-28 | 1 | 250 | 150000 | 1200
2012-02-28 | 2 | 250 | 150000 | 1600
2012-02-28 | 3 | 250 | 150000 | 1800
2012-02-28 | 4 | 250 | 150000 | 1200
2012-02-28 | 5 | 250 | 150000 | 1600
2012-02-28 | 6 | 250 | 150000 | 2381.25000000000000000000
2012-03-31 | 1 | 200 | 90000 | 1300
2012-03-31 | 2 | 200 | 90000 | 1200
2012-03-31 | 3 | 200 | 90000 | 1400
2012-03-31 | 4 | 200 | 90000 | 1000
2012-03-31 | 5 | 200 | 90000 | 2200.00000000000000000000
2012-03-31 | 6 | 200 | 90000 | 2750.00000000000000000000
2012-04-30 | 1 | 300 | 180000 | 1600
2012-04-30 | 2 | 300 | 180000 | 1500
2012-04-30 | 3 | 300 | 180000 | 4000
2012-04-30 | 4 | 300 | 180000 | 2500.00000000000000000000
2012-04-30 | 5 | 300 | 180000 | 2350.00000000000000000000
2012-04-30 | 6 | 300 | 180000 | 2550.00000000000000000000
2012-05-31 | 1 | 400 | 225000 | 2200
2012-05-31 | 2 | 400 | 225000 | 6000
2012-05-31 | 3 | 400 | 225000 | 5000.00000000000000000000
2012-05-31 | 4 | 400 | 225000 | 3750.00000000000000000000
2012-05-31 | 5 | 400 | 225000 | 3050.00000000000000000000
2012-05-31 | 6 | 400 | 225000 | 2800.00000000000000000000
2012-06-30 | 1 | 100 | 60000 | 1000
2012-06-30 | 2 | 100 | 60000 | 3500.00000000000000000000
2012-06-30 | 3 | 100 | 60000 | 4250.00000000000000000000
2012-06-30 | 4 | 100 | 60000 | 4000.00000000000000000000
2012-06-30 | 5 | 100 | 60000 | 3525.00000000000000000000
2012-06-30 | 6 | 100 | 60000 | 3162.50000000000000000000
(36 rows)