Google Cloud: matrix multiplication with Bigquery or some other service?

Question

I am using Google Analytics and processing the data with Bigquery, I need to do a matrix multiplication.

What is the most feasible way of implementing matrix mu

Answer 1

Suppose a matrix with two columns, a path and a value column. You want to get the adjacency matrix P P^t. With 6 paths, you wanna get 36 values or 6x6 matrix that can be done with matrix multiplication.

I refactor Mikhail example for a path adjacency matrix given some tuple (Path, value). The demo contains 6 paths so the resulting adjacency matrix has dimensions 6x6. It is now in a straight format, but I would like to get it into a matrix formar or crosstab format with 6x6 form.

--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

where the shaping question is now here about shaping the straight table into more traditional matrix multiplication format.