Google Cloud：使用Bigquery或其他服务进行矩阵乘法？

Question

我正在使用Google Analytics（分析）并通过Bigquery处理数据，因此我需要执行matrix multiplication。

在Google Cloud中实现矩阵乘法的最可行方法是什么？可以直接在Bigquery中完成吗？

Answer 1

假设MatrixA是具有以下各列的表：

i, k, value   

和MatrixB-模式为

k, j, value    

并假设两个表中的k值范围相同：

这将模仿以下矩阵：

Matrix A
 2 -3  4
-1  0  2

Matrix B
-1  2  3
 0  1  7
 1  1 -2

以下用于乘法的代码用于BigQuery标准SQL

#standardSQL
WITH MatrixA AS (
  SELECT 1 AS i, 1 AS k, 2 AS val UNION ALL
  SELECT 1, 2, -3 UNION ALL
  SELECT 1, 3, 4 UNION ALL
  SELECT 2, 1, -1 UNION ALL
  SELECT 2, 2, 0 UNION ALL
  SELECT 2, 3, 2 
), MatrixB AS (
  SELECT 1 AS k, 1 AS j, -1 AS val UNION ALL
  SELECT 1, 2, 2 UNION ALL
  SELECT 1, 3, 3 UNION ALL
  SELECT 2, 1, 0 UNION ALL
  SELECT 2, 2, 1 UNION ALL
  SELECT 2, 3, 7 UNION ALL
  SELECT 3, 1, 1 UNION ALL
  SELECT 3, 2, 1 UNION ALL
  SELECT 3, 3, -2 
)
SELECT i, j, SUM(a.val * b.val) val
FROM MatrixA AS a
CROSS JOIN MatrixB AS b
WHERE a.k = b.k
GROUP BY i, j
ORDER BY i, j   

结果将如下所示

Row i   j   val  
1   1   1   2    
2   1   2   5    
3   1   3   -23  
4   2   1   3    
5   2   2   0    
6   2   3   -7     

代表MatrixA * MatrixB

2   5  -23
3   0   -7

注意：您可以使用

FROM MatrixA AS a
JOIN MatrixB AS b
ON a.k = b.k  

代替

FROM MatrixA AS a
CROSS JOIN MatrixB AS b
WHERE a.k = b.k   

随您的喜好

Answer 2

假设一个矩阵有两列，即路径和值列。您要获取邻接矩阵P P^t。通过6条路径，您想要获得36个值或6x6矩阵，可以通过矩阵乘法来完成。

在给定一些元组(Path, value)的情况下，我重构了Mikhail示例以用于路径邻接矩阵。该演示包含6条路径，因此生成的邻接矩阵的尺寸为6x6。现在是纯格式，但我想将其转换为6x6形式的矩阵形式或交叉表格式。

--standardSQL
WITH MatrixA AS (
  SELECT 1 AS p, 2 AS val UNION ALL
  SELECT 2, -3 UNION ALL
  SELECT 3, 4 UNION ALL
  SELECT 4, -1 UNION ALL
  SELECT 5, 0 UNION ALL
  SELECT 6, 2 
), MatrixB AS (
  SELECT 1 AS p, -1 AS val UNION ALL
  SELECT 2, 2 UNION ALL
  SELECT 3, 3 UNION ALL
  SELECT 4, 3 UNION ALL
  SELECT 5, 0 UNION ALL
  SELECT 6, 1
),
matrixMultiplication AS
(
SELECT a.p AS ap, b.p as bp, SUM(a.val * b.val) val
FROM MatrixA AS a
CROSS JOIN MatrixB AS b
GROUP BY a.p, b.p
ORDER BY a.p, b.p
)

--36 elements for the 6x6 PATHS Matrix
--TODO: how to shape it to 6x6 matrix?
SELECT * FROM matrixMultiplication

现在here的整形问题是将直线表整形为更传统的矩阵乘法格式。