SQL COUNT items and GROUP over multiple categories with 0 totals for missing entries

I have a table in BigQuery I would like to aggregate over a number of different categories (columns in the table) to produce a summary of the data, which is a simple COUNT and GROUP BY statement. However, for this project I would like to produce a “complete” count of every permutation of the categories (the possible values of the categories are known ahead of time) with 0 totals for combinations without any entries for that permutation.

Here is the simple initial COUNT and GROUP statement:

SELECT
  COUNT(item.id) as total,
  TIMESTAMP_TRUNC(item.date, WEEK) as week,
  item.attribute_1,
  item.attribute_2,
FROM item
GROUP BY week, attribute_1, attribute_2
ORDER BY week DESC, attribute_1, attribute_2

where attribute_1 has possible values ('A', 'B', 'C') and attribute_2 has possible values ('X', 'Y', 'Z') which produces something like this:

Row | total | week                    | attribute_1 | attribute_2
-----------------------------------------------------------------
1   | 1     | 2020-07-12 00:00:00 UTC | A           | X
2   | 2     | 2020-07-12 00:00:00 UTC | A           | Z
3   | 1     | 2020-07-12 00:00:00 UTC | B           | X
4   | 1     | 2020-07-12 00:00:00 UTC | B           | Y
5   | 3     | 2020-07-12 00:00:00 UTC | B           | Z
6   | 1     | 2020-07-12 00:00:00 UTC | C           | Y
7   | 1     | 2020-07-12 00:00:00 UTC | C           | Z
etc.

However my goal is to end up with a result like this:

Row | total | week                    | attribute_1 | attribute_2
-----------------------------------------------------------------
1   | 1     | 2020-07-12 00:00:00 UTC | A           | X
2   | 0     | 2020-07-12 00:00:00 UTC | A           | Y
3   | 2     | 2020-07-12 00:00:00 UTC | A           | Z
4   | 1     | 2020-07-12 00:00:00 UTC | B           | X
5   | 1     | 2020-07-12 00:00:00 UTC | B           | Y
6   | 3     | 2020-07-12 00:00:00 UTC | B           | Z
7   | 0     | 2020-07-12 00:00:00 UTC | C           | X
8   | 1     | 2020-07-12 00:00:00 UTC | C           | Y
9   | 1     | 2020-07-12 00:00:00 UTC | C           | Z
etc.

I found similar problems for a single category, so I can solve for that case by holding the other attributes constant with the following statement:

WITH data AS (
  SELECT
    item.id as item_id,
    TIMESTAMP_TRUNC(item.date, WEEK) as week,
    item.attribute_1,
    item.attribute_2,
  FROM item
  GROUP BY week, attribute_1, attribute_2
  ORDER BY week DESC, attribute_1, attribute_2
),
category_1 as (
 select 'A' as name union all
 select 'B' union all
 select 'C'
)
SELECT
  category_1.name,
  (
    SELECT COUNT(item_id) as total
    FROM data
    WHERE data.attribute_1 = category_1.name
    AND data.attribute_2 = 'X'
    AND data.week > TIMESTAMP('2020-07-10')
  ) as total
FROM category_1

which produces:

Row | name | total
------------------
1   | A    | 1
2   | B    | 1
3   | C    | 0

Is it possible to solve for the general case I am interested in?

Answer

If I understand correctly, you can generate the rows using a cross join and then match to the existing values:

SELECT COALESCE(SUM(i.total), 0) as total,
       w.week, a1.attribute_1, a2.attribute_2
FROM (SELECT distinct TIMESTAMP_TRUNC(date, WEEK) as week FROM item) w CROSS JOIN
     (SELECT distinct attribute_1 FROM item) a1 CROSS JOIN
     (SELECT distinct attribute_2 FROM item) a2 LEFT JOIN   
     item i
     ON TIMESTAMP_TRUNC(i.date, WEEK) = w.week AND
        i.attribute_1 = a1.attribute_1 AND
        i.attribute_2 = a2.attribute_2
GROUP BY w.week, a1.attribute_1, a2.attribute_2
ORDER BY week DESC, attribute_1, attribute_2;

Here is a db<>fiddle. It uses Postgres, so there are some syntax tweaks for Postgres.