Question

I have a 1000×1000 matrix, with some data in each entry.

Is it possible to store it sequentially (ie, a row next to the previous one) in a table? I mean, if I could just access the table “by offset” (just like an array), given I won’t add/delete any entry, I would save space for the key, which is blatantly redundant here.

Is it possible? Thanks!

Answer 1

Tables don’t have an order. There is no sequence to them. The key is not redundant because it tells you how to access your data. If I were to model this I would do it like so:

CREATE TABLE My_Matrix AS (
    row_num    SMALLINT    NOT NULL,
    col_num    SMALLINT    NOT NULL,
    value      INT         NOT NULL, -- Or whatever data type is appropriate
    CONSTRAINT PK_My_Matrix PRIMARY KEY CLUSTERED (row_num, col_num),
    CONSTRAINT My_Matrix_row_num_chk CHECK (row_num BETWEEN 1 AND 1000),
    CONSTRAINT My_Matrix_col_num_chk CHECK (col_num BETWEEN 1 AND 1000)
)

Now, if you want to get a value by row number and column number then you can quickly get that with:

SELECT value FROM My_Matrix WHERE row_num = @row_num AND col_num = @col_num

If you want to get it by an offset then you could use something like:

SELECT
    value
FROM
    My_Matrix
WHERE
    row_num = @value%1000 AND
    col_num = @value/1000

As for saving storage, you’re talking about 4 bytes per row here, with a matrix that has a maximum of 1M rows. For any serious RDBMS that’s pretty irrelevant.