如何计算clickhouse中的累积产品

Question

在python中计算累积积，我可以使用numpy.cumprod

>>> a = [2, 3, 4, 5]
>>> numpy.cumprod(a)
[2, 6, 24, 120]
# this is result i want.  [2, 3, 4, 5] => [2, 2*3, 2*3*4, 2*3*4*5] => [2, 6, 24, 120]

但我不知道如何在 CLICKHOUSE
中编写 sql 表A：

row rate
1    2
2    3
3    4
4    5

列率是我想要的结果，如何使用CLICKHOUSE SQL语句实现。

row rate
1    2
2    6
3    24
4    120

Answer 1

没有简单的方法。我会在 CH arrayCumProd 中添加（实现）一个新函数

SELECT
    i, pow(2,arraySum(z->log2(z),n))
FROM
(
    SELECT
        ig,
        arrayMap( i -> arraySlice(ng, 1, i), arrayEnumerate(groupArray(x) AS ng) as ig) xx
    FROM ( SELECT arrayJoin([2, 3, 4, 5]) AS x )
)
ARRAY JOIN
    ig AS i,
    xx AS n

┌─i─┬─pow(2, arraySum(lambda(tuple(z), log2(z)), n))─┐
│ 1 │                                              2 │
│ 2 │                                              6 │
│ 3 │                                             24 │
│ 4 │                             119.99999999999994 │
└───┴────────────────────────────────────────────────┘

嗯，看来是我把它弄复杂了。

SELECT x FROM
(
    SELECT
        arrayMap(i -> pow(2,i), arrayCumSum(groupArray(log2(x)))) z
    FROM ( SELECT arrayJoin([2, 3, 4, 5]) AS x )
)
ARRAY JOIN z as x

Answer 2

我只是扩展了@Denis Zhuravlev 的答案。

CH 没有专门的函数来计算累积乘法（或任何除加法之外的任意数学运算符），此外，由于这种计算的“累积”性质，无法应用现有函数来获得所需的结果。

因此需要使用对数将乘法转换为加法：

log_a x*y = log_a x + log_a y

x*y = a^{(log_a x + log_a y)}

SELECT r.1.1 row, r.1.2 rate, r.2 value, round(r.2, 2) rounded_value
FROM (
  SELECT 
    groupArray((row, rate, rate_log)) data,
    arrayMap(log -> exp10(log), arrayCumSum(data_item -> data_item.3, data)) rate_cumulative_values,
    arrayJoin(arrayZip(data, rate_cumulative_values)) r  
  FROM (
    SELECT row, rate, log10(rate) AS rate_log
    FROM (
      /* emulate the origin dataset */
      SELECT data.1 row, data.2 rate
      FROM (SELECT arrayJoin([
        (1, 2), (2, 3), (3, 4), (4, 5),
        (5, 1), (6, 0), (7, -1)]) AS data))
    ORDER BY row));
/*
┌─row─┬─rate─┬──────────────value─┬─rounded_value─┐
│   1 │    2 │                  2 │             2 │
│   2 │    3 │                  6 │             6 │
│   3 │    4 │ 23.999999999999993 │            24 │
│   4 │    5 │ 119.99999999999996 │           120 │
│   5 │    1 │ 119.99999999999996 │           120 │
│   6 │    0 │                  0 │             0 │
│   7 │   -1 │                nan │           nan │
└─────┴──────┴────────────────────┴───────────────┘
*/

---

同样的逻辑可以应用于计算累加除法：

x/y = a^{(log_a x - log_a y)}

累计除法：

SELECT r.1.1 row, r.1.2 rate, r.2 value, round(r.2, 2) rounded_value
FROM (
  SELECT 
    groupArray((row, rate, rate_log)) data,
    arrayMap(log -> exp10(log), arrayCumSum((data_item, index) -> index = 1 ? data_item.3 : - data_item.3, data, arrayEnumerate(data))) rate_cumulative_values,
    arrayJoin(arrayZip(data, rate_cumulative_values)) r  
  FROM (
    SELECT row, rate, log10(rate) AS rate_log
    FROM (
      /* emulate the origin dataset */
      SELECT data.1 row, data.2 rate
      FROM (SELECT arrayJoin([
        (1, 100), (2, 2), (3, 10), (4, 2)]) AS data))
    ORDER BY row));
/*
┌─row─┬─rate─┬──────────────value─┬─rounded_value─┐
│   1 │  100 │                100 │           100 │
│   2 │    2 │  49.99999999999999 │            50 │
│   3 │   10 │  4.999999999999999 │             5 │
│   4 │    2 │ 2.4999999999999996 │           2.5 │
└─────┴──────┴────────────────────┴───────────────┘
*/