MySQL matrix multiplication - mysql

Question

I am trying to write matrix multiplication for MySQL and am kinda stuck:
basically, my matrices are stored in format
[row#, column#, matrixID, value], so for example matrix [3 x 2] would be something like:
[row#, column#, matrixID, value]
1 1 mat01 1
1 2 mat01 2
1 3 mat01 3
2 1 mat01 4
2 2 mat01 5
2 3 mat01 6
being equivalent to: [[1 2 3],[4 5 6]]
following does calculation of single element of matrix1 * matrix2 quite well:
SELECT SUM(row1.`val` * col2.`val`)
FROM matValues row1
INNER JOIN `matValues` col2
WHERE row1.`row` = 1 AND row1.`mID`='matrix1' AND
col2.`mID`='matrix2' AND col2.`col` = 1 AND row1.col = col2.row
wrapping this into function and then using another function to iterate over row and column numbers might work, but I have problems with generating this set of numbers and iterating over them using SQL.
Any advice / suggestions are welcome

Answer 1

Try:
select m1.`row#`, m2.`column#`, sum(m1.value*m2.value)
from matValues m1
join matValues m2 on m2.`row#` = m1.`column#`
where m1.matrixID = 'mat01' and m2.matrixID = 'mat02'
group by m1.`row#`, m2.`column#`
Example here.
(Replace 'mat01' and 'mat02' with suitable matrixID values.)

Answer 2

You can do the entire calculation in SQL. You only give an example with a single matrix, which because it is not square, cannot be multiplied by itself.
Here is the idea:
SELECT mout.row, mout.col, SUM(m1.value*m2.value)
FROM (select distinct row from matValues cross join
select distinct COL from matValues
) mout left outer join
matValues m1
on m1.row = mout.row left outer join
matValues m2
on m2.col = mout.col and
m2.row = m1.col

Answer 3

I know this is SQL-Server syntax, but it should give you a start on the corresponding MySql syntax. The sparse matrix nature seems to handle well.
with I as (
select * from ( values
(1,1, 1),
(2,2, 1),
(3,3, 1)
) data(row,col,value)
)
,z_90 as (
select * from ( values
(1,2, 1),
(2,1,-1),
(3,3, 1)
) data(row,col,value)
)
,xy as (
select * from ( values
(1,2, 1),
(2,1, 1),
(3,3, 1)
) data(row,col,value)
)
,x_90 as (
select * from ( values
(1,1, 1),
(2,3, 1),
(3,2,-1)
) data(row,col,value)
)
select
'I * z_90' as instance,
a.row,
b.col,
sum( case when a.value is null then 0 else a.value end
* case when b.value is null then 0 else b.value end ) as value
from I as a
join z_90 as b on a.col = b.row
group by a.row, b.col
union all
select
'z_90 * xy' as instance,
a.row,
b.col,
sum( case when a.value is null then 0 else a.value end
* case when b.value is null then 0 else b.value end ) as value
from z_90 as a
join xy as b on a.col = b.row
group by a.row, b.col
union all
select
'z_90 * x_90' as instance,
a.row,
b.col,
sum( case when a.value is null then 0 else a.value end
* case when b.value is null then 0 else b.value end ) as value
from z_90 as a
join x_90 as b on a.col = b.row
group by a.row, b.col
order by instance, a.row, b.col
yields:
instance row col value
----------- ----------- ----------- -----------
I * z_90 1 2 1
I * z_90 2 1 -1
I * z_90 3 3 1
z_90 * x_90 1 3 1
z_90 * x_90 2 1 -1
z_90 * x_90 3 2 -1
z_90 * xy 1 1 1
z_90 * xy 2 2 -1
z_90 * xy 3 3 1
However, I suggest you also check out performing this on your graphics card. NVIDIA has a good example of implementing matrix multiplication in theri C Programming Guide.