BigQuery：将矩阵乘法的直表格式转换为更传统的矩阵乘法格式？

Question

这个问题here 展示了如何将矩阵乘法转换为直表格式，例如给定 (6x1) (Path, value) 矩阵，您将得到 (36,1) 直表。现在我想得到传统的矩阵乘法格式，在示例中它是（6x6）矩阵。

如何将矩阵乘法的直表塑造成更传统的矩阵乘法格式？

--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

Answer 1

如何将其整形为 6x6 矩阵？

以下是 BigQuery 标准 SQL。几个简单的选项

选项#1

#standardSQL
SELECT ap AS row, STRING_AGG(CAST(val AS STRING), ' ' ORDER BY bp) AS cols
FROM matrixMultiplication
GROUP BY row
-- ORDER BY row   

当应用于您问题中的虚拟数据时 - 结果是

Row     row     cols     
1       1       -2 4 6 6 0 2     
2       2       3 -6 -9 -9 0 -3  
3       3       -4 8 12 12 0 4   
4       4       1 -2 -3 -3 0 -1  
5       5       0 0 0 0 0 0  
6       6       -2 4 6 6 0 2     

选项 #2

#standardSQL
SELECT row, 
  cols[OFFSET(0)] AS col1,
  cols[OFFSET(1)] AS col2,
  cols[OFFSET(2)] AS col3,
  cols[OFFSET(3)] AS col4,
  cols[OFFSET(4)] AS col5,
  cols[OFFSET(5)] AS col6
FROM (  
  SELECT ap AS row, ARRAY_AGG(val ORDER BY bp) AS cols
  FROM matrixMultiplication
  GROUP BY ap
)
-- ORDER BY row    

当应用于您问题中的虚拟数据时 - 结果是

Row row col1    col2    col3    col4    col5    col6     
1   1   -2      4       6       6       0       2    
2   2   3       -6      -9      -9      0       -3   
3   3   -4      8       12      12      0       4    
4   4   1       -2      -3      -3      0       -1   
5   5   0       0       0       0       0       0    
6   6   -2      4       6       6       0       2