Compute trace of matrix in database - sql

Question

I have a table in a Postgres that stores 10x10 matrices, where each row has it's own entry, defined as:
id, matrix_id, row_id, col1, col2, col3...
I'd like to compute the trace (sum of main diagonal) for every matrix identified by its matrix_id, that is, for every matrix_id, I would like to get (col1 where row_id=1) + (col2 where row_id=2) + (col3 where row_id=3)...
I've tried grouping it by matrix_id but then I cannot use subqueries, something like:
select matrix_id, (select col1 where row_id=1) + (col2 where row_id=2) +
(col3 where row_id=3) ... from matrix group by matrix_id;
but it doesn't work this way.
How could I do that?

Answer 1

So long as they are all 10x10 matrices, use a case statement like so:
select matrix_id,
sum(
case row_id
when 1 then col1
when 2 then col2
when 3 then col3
when 4 then col4
when 5 then col5
when 6 then col6
when 7 then col7
when 8 then col8
when 9 then col9
when 10 then col10
end
) as trace
from matrix
group by matrix_id;
Had variable-sized matrices been allowed, you could transpose columns to rows via to_jsonb() and then sum where row_id = <column suffix>.
EDIT TO ADD
Based on your comment, you really should update your version of PostgreSQL. That said, try a CTE to filter on the new trace column:
with traces as (
select matrix_id,
sum(
case row_id
when 1 then col1
when 2 then col2
when 3 then col3
when 4 then col4
when 5 then col5
when 6 then col6
when 7 then col7
when 8 then col8
when 9 then col9
when 10 then col10
end
) as trace
from matrix
group by matrix_id
)
select *
from traces
where trace > 100;