Showing posts with label User defined variable. Show all posts
Showing posts with label User defined variable. Show all posts

Tuesday, September 15, 2009

MySQL: Another Ranking trick

I just read SQL: Ranking without self join, in which Shlomi Noach shares a nice MySQL-specific trick based on user-defined variables to compute rankings.

Shlomi's trick reminds me somewhat of the trick I came across little over a year ago to caclulate percentiles. At that time, several people pointed out to me too that using user-defined variables in this way can be unreliable.

The problem with user-defined variables

So what is the problem exaclty? Well, whenever a query assigns to a variable, and that same variable is read in another part of the query, you're on thin ice. That's because the result of the read is likely to differ depending on whether the assignment took place before or after the read. Not surprising when you think about it - the whole point of variable assignment is to change its value, which by definition causes a different result when subsequently reading the variable (unless you assigned the already assigned value of course, duh...).

Now watch that previous statement clearly - the word subsequently is all-important.

See, that's the problem. The semantics of a SQL SELECT statement is to obtain a (tabular) resultset - not specifying an algorithm to construct that resultset. It is the job of the RDBMS to figure out an algorithm and thus, you can't be sure in what order individual expressions (including variable evaluation and assignment) are executed.

The MySQL manual states it like this:

The order of evaluation for user variables is undefined and may change based on the elements contained within a given query. In SELECT @a, @a := @a+1 ..., you might think that MySQL will evaluate @a first and then do an assignment second, but changing the query (for example, by adding a GROUP BY, HAVING, or ORDER BY clause) may change the order of evaluation.

The general rule is never to assign a value to a user variable in one part of a statement and use the same variable in some other part of the same statement. You might get the results you expect, but this is not guaranteed.

So what good are these variables anyway?

On the one hand, this looks really lame: can't MySQL just figure out the correct order of doing the calulations? Well, that is one way of looking at it. But there is an equally valid reason not to do that. If the calculations would influence execution order, it would drastically lessen the number of ways that are available to optimize the statement.

This begs the question: Why is it possible at all to assign values to the user-defined variables? The answer is quite simple: you can use it to pass values between statetments. My hunch is the variables were created in the olden days to overcome some limitations resulting from the lack of support for subqueries. Having variables at least enables you to execute a query and assign the result temporarily for use in a subsequent statement. For example, to find the student with the highest score, you can do:

mysql> select @score:=max(score) from score;
+--------------------+
| @score:=max(score) |
+--------------------+
| 97 |
+--------------------+
1 row in set (0.00 sec)

mysql> select * from score where score = @score;
+----------+--------------+-------+
| score_id | student_name | score |
+----------+--------------+-------+
| 2 | Gromit | 97 |
+----------+--------------+-------+
1 row in set (0.03 sec)
There is nothing wrong with this approach - problems start arising only when reading and writing the same variable in one and the same statement.

Another way - serializing the set with GROUP_CONCAT


Anyway, the percentile post I just linked to contains another solution for that problem that relies on GROUP_CONCAT. It turns out we can use the same trick here.

(Some people may like to point out that using GROUP_CONCAT is not without issues either, because it may truncate the list in case the pre-assigned string buffer is not large enough. I wrote about dealing with that limitation in several places and I remain recommending to set the group_concat_max_len server variable to the value set for the max_packet_size server variable like so:
SET @@group_concat_max_len := @@max_allowed_packet;
)

The best way to understand how it works is to think of the problem in a few steps. First, we make an ordered list of all the values we want to rank. We can do this with GROUP_CONCAT like this:

mysql> SELECT GROUP_CONCAT(
-> DISTINCT score
-> ORDER BY score DESC
-> ) AS scores
-> FROM score
-> ;
+-------------+
| scores |
+-------------+
| 97,95,92,85 |
+-------------+
1 row in set (0.00 sec)

Now that we have this list, we can use the FIND_IN_SET function to look up the position of any particlar value contained in the list. Because the list is ordered in descending order (due to the ORDER BY ... DESC), and contains only unique values (due to the DISTINCT), this position is in fact the rank number. For example, if we want to know the rank of all scores with the value 92, we can do:

mysql> SELECT FIND_IN_SET(92, '97,95,92,85')
+--------------------------------+
| FIND_IN_SET(92, '97,95,92,85') |
+--------------------------------+
| 3 |
+--------------------------------+
1 row in set (0.00 sec)
So, the answer is 3 because 92 is the third entry in the list.

(If you're wondering how it's possible that we can pass the integer 92 as first argument for FIND_IN_SET: the function expects string arguments, and automatically converts whichever non-string typed value we pass to a string. In the case of the integer 92, it is silently converted to the string '92')

Of course, we are't really interested in looking up ranks for individual numbers one at a time; rather, we'd like to combine this with a query on the scores table that does it for us. Likewise, we don't really want to manually supply the list of values as a string constant, we want to substitute that with the query we wrote to generate that list.
So, we get:

mysql> SELECT score_id, student_name, score
-> , FIND_IN_SET(
-> score
-> , (SELECT GROUP_CONCAT(
-> DISTINCT score
-> ORDER BY score DESC
-> )
-> FROM score)
-> ) as rank
-> FROM score;
+----------+--------------+-------+------+
| score_id | student_name | score | rank |
+----------+--------------+-------+------+
| 1 | Wallace | 95 | 2 |
| 2 | Gromit | 97 | 1 |
| 3 | Shaun | 85 | 4 |
| 4 | McGraw | 92 | 3 |
| 5 | Preston | 92 | 3 |
+----------+--------------+-------+------+
5 rows in set (0.00 sec)

Alternatively, if you think that subqueries are for the devil, you can rewrite this to a CROSS JOIN like so:

SELECT score_id, student_name, score
, FIND_IN_SET(
score
, scores
) AS rank
FROM score
CROSS JOIN (SELECT GROUP_CONCAT(
DISTINCT score
ORDER BY score DESC
) AS scores
FROM score) scores

Now that we have a solutions, lets see how it compares to Shlomi's original method. To do this, I am using the payment table from the sakila sample database.

First, Shlomi's method:

mysql> SELECT payment_id
-> , amount
-> , @prev := @curr
-> , @curr := amount
-> , @rank := IF(@prev = @curr, @rank, @rank+1) AS rank
-> FROM sakila.payment
-> , (SELECT @curr := null, @prev := null, @rank := 0) sel1
-> ORDER BY amount DESC;
+------------+--------+----------------+-----------------+------+
| payment_id | amount | @prev := @curr | @curr := amount | rank |
+------------+--------+----------------+-----------------+------+
| 342 | 11.99 | NULL | 11.99 | 1 |
. ... . ..... . ..... . ..... . . .
| 15456 | 0.00 | 0.00 | 0.00 | 19 |
+------------+--------+----------------+-----------------+------+
16049 rows in set (0.09 sec)

Wow! It sure is fast :) Now, the GROUP_CONCAT solution, using a subquery:

mysql> SELECT payment_id, amount
-> , FIND_IN_SET(
-> amount
-> , (SELECT GROUP_CONCAT(
-> DISTINCT amount
-> ORDER BY amount DESC
-> )
-> FROM sakila.payment)
-> ) as rank
-> FROM sakila.payment
+------------+--------+------+
| payment_id | amount | rank |
+------------+--------+------+
| 1 | 2.99 | 15 |
. . . .... . .. .
| 16049 | 2.99 | 15 |
+------------+--------+------+
16049 rows in set (0.14 sec)


(In case you're wondering why the results are different, this is because the result set for Shlomi's solution is necessarily ordered by ascending rank (or descending amount - same difference. To obtain the identical result, you need to add an ORDER BY clause to my query. But since the point was to calculate the ranks, I didn't bother. Of course, adding an ORDER BY could slow things down even more.)

Quite a bit slower, bummer. But at leastt we can't run into nasties with the user variables anymore. For this data set, I get about the same performance with the CROSS JOIN, but I should warn that I did not do a real benchmark.

Conclusion

Don't fall into the trap of reading and writing the same user-defined variable in the same statement. Although it seems like a great device and can give you very good performance, you cannot really control the order of reads and writes. Even if you can, you must check it again whenever you have reason to believe the query will be solved differently by the server. This is of course the case whenever you upgrade the server. But also seemingly harmless changes like adding an index to a table may change the order of execution.

Almost all cases where people want to read and write to the same user variables within the same query, they are dealing with a kind of serialization problem. They are trying to maintain state in a variable in order to use it across rows. In many cases, the right way to do that is to use a self-join. But this may not always be feasible, as pointed out in Shlomi's original post. For example, rewriting the payment rank query using a self join is not going to make you happy.

Often, there is a way out. You can use GROUP_CONCAT to serialize a set of rows. Granted, you need at least one pass for that, and another one to do something useful with the result, but this still a lot better than dealing with semi-cartesian self join issues.

Wednesday, July 09, 2008

A fast, single pass method to calculate the median in MySQL

After stepping off of the GROUP_CONCAT() solution for calculating quantiles I figured it would be nice to find a better way to calculate the median too.

Solution


I previously wrote on how to calculate the median using GROUP_CONCAT(), but I think that this is a better way:

SELECT AVG(length) AS median -- take the average of left and right median
, MIN(length) AS left_median --
, MAX(length) AS right_median --
, @l AS left_median_position --
, @r AS right_median_position --
FROM (
SELECT @n, length -- @n is just here to facilitate debug
FROM film
CROSS JOIN (
SELECT @n:=0
, @r := COUNT(*) DIV 2 + 1 -- right median or true median
, @l := COUNT(*) DIV 2 -- left median, or true medain
+ IF(
COUNT(*) % 2 -- even or odd?
, 1 -- odd, need next value
, 0 -- even, need true left median
)
FROM film
) ``
WHERE (@n:=@n+1) -- row number
BETWEEN @l AND @r -- select two middle ones
ORDER BY length -- need to sort to get middle values
) ``

Apart from not relying on setting the buffer size for group_concat_max_len, this solution is also faster than the GROUP_CONCAT() solution. For example, calculating the median amount from the payment table in the sakila database takes some 0.12 seconds using the GROUP_CONCAT() solution and about 0.03 seconds with this method.

Explanation


At the heart of the solution are the user-defined variables:

  • @n: the row number

  • @l: the position of the 'left median' that is the row number with the highest value in the lower half of all rows

  • @r: the position of the 'right median', that is the row number with the lowest value in the higher half of all rows


These are initialized in the inmost subquery:

SELECT @n:=0
, @r := COUNT(*) DIV 2 + 1 -- right median or true median
, @l := COUNT(*) DIV 2 -- left median, or true medain
+ IF(
COUNT(*) % 2 -- even or odd?
, 1 -- odd, need next value
, 0 -- even, need true left median
)
FROM film

Note that this yields one row, initializing the row number @n to zero. We can calculate the position for the right median immediately by doing

COUNT(*) DIV 2 + 1

You see, first we divide the total number of rows by two. If there is an even number of rows, COUNT(*) DIV 2 will give us the left median, and adding 1 is then by definition the right median. If COUNT(*) is an odd number, it still holds: the integer division rounds down to the nearest integer value, and adding 1 then gives us the position of the true median in that case.

The calculation of the left median is along the same lines:

@l := COUNT(*) DIV 2 -- left median, or true medain
+ IF(
COUNT(*) % 2 -- even or odd?
, 1 -- odd, need next value
, 0 -- even, need true left median
)

We just have to take care that in case we do have an odd number of rows, we need to pick the true median position here too.

To do that we first find out if there is an odd number of rows using COUNT(*) % 2. This calculates the remainder of dividing the total number of rows by two. In case of an odd number of rows, the remainder is 1 which is considered to be TRUE by the IF function. In this case, 1 is added, effectively making @l equal to @r (that is, both hold the position of the true median). In case of an even number of rows, we add 0 as COUNT(*) % 2 is already the desired position of the left median.

Now that we have these values, we can use @n to generate a rownumber, which we can compare against the calculated @l and @r values:

WHERE (@n:=@n+1) -- row number
BETWEEN @l AND @r -- select two middle ones
ORDER BY length -- need to sort to get middle values

And this will give us at most two rows in case of an even number of rows, and one row for an odd number of rows.

The final step is to average the values from the rows, which is required to calculate the median in case of an even number of rows:

SELECT AVG(length) AS median -- take the average of left and right median
...
FROM (
...
) ``

Monday, July 07, 2008

Calculating Percentiles with MySQL, Round 2

My previous post on calculating percentiles with MySQL generated some comments and good discussion. In particular, I got some very interesting comments from Vladimir.

Basically, Vladimir was doubtful whether the GROUP_CONCAT() solution would be optimal in comparison to a JOIN. His proposal is to solve it like this:

SELECT SUM(g1.r) sr
, g2.length l
, SUM(g1.r)/(SELECT COUNT(*) FROM film) p
FROM (SELECT COUNT(*) r, length FROM film GROUP BY length) g1
JOIN (SELECT COUNT(*) r, length FROM film GROUP BY length) g2
ON g1.length < g2.length
GROUP BY g2.length
HAVING p > 0.9
ORDER BY p
LIMIT 1

First, this query sets up two identical subqueries in the FROM list using GROUP BY and COUNT() to calculate the number of occurrences of each distinct value. Then, these are joined and GROUP BY is again applied to calculate the total number of rows having a lower value. Finally, HAVING is used to find the groups in the upper percentiles, and LIMIT and ORDER BY are used to single out the one desired percentile value.

As it turns out, this solution is slower for moderately small data sets, but much faster for large data sets. He benchmarked it for a total of 999 distinct values on varying number of rows. Here are his slightly rounded numbers:

#rows: group_concat: groupby-join:
4M 1 min 6 sec 5.3 sec
1M 5 sec 2.5 sec
100K 0.5 sec 1.6 sec

Although GROUP_CONCAT() seems to break down pretty soon, he also writes:

I must admit that when N of distinct rows reaches approx. 10K I get pretty the opposite results if the total number of rows is relatively small. Basically we get into the same situation as with joining the whole tables.

He concluded by saying:

But what I think is the right solution is having something like this on the server side:

SELECT COUNT(INC length)/(SELECT COUNT(*) FROM film) p, length
FROM film
GROUP BY length
HAVING p >= 0.9 ORDER BY p LIMIT 1

Where "INC" is a flag that tells the server to not reset per-group counters in the aggregate functions. This would be quite a trivial change in the Item_sum class and would make sense not only for SUM, but maybe also for MIN, MAX, AVG, COUNT and maybe some other aggregate functions.

So, COUNT(INC length) would be the cumulative count, or a running total of counts. The fun thing is, you can already do exactly that using user-defined variables. Look:

-- allow statement batching
DELIMITER go

-- initialize
SELECT 0, COUNT(*)
INTO @cum_cnt, @cnt
FROM sakila.payment;

-- calculate percentiles
SELECT @cum_cnt:=@cum_cnt + COUNT(*) / @cnt as p, -- running fraction of #rows per distinct amount
amount
FROM sakila.payment
GROUP BY amount
HAVING p >= 0.9
LIMIT 1;

go

and this gets us the result:

Query OK, 1 row affected (0.01 sec)

+-------------+--------+
| p | amount |
+-------------+--------+
| 0.904542334 | 6.99 |
+-------------+--------+
1 row in set (0.03 sec)

Here is the equivalent GROUP_CONCAT solution:

SELECT SUBSTRING_INDEX(
SUBSTRING_INDEX(
GROUP_CONCAT(
p.amount
ORDER BY p.amount
SEPARATOR ','
)
, ','
, 90/100 * COUNT(*) + 1
)
, ','
, -1
) AS `90th Percentile`
FROM sakila.payment AS p;

...and it is considerably slower:

+-----------------+
| 90th Percentile |
+-----------------+
| 6.99 |
+-----------------+
1 row in set (0.08 sec)

(sakila.payment has 16049 rows and 19 distinct values for amount)

So, the sane thing to do would be to forget about that GROUP_CONCAT idea, and use this method. It does not have the nasty drawbacks of having to mess with group_concat_max_len and I am pretty sure Vladimir's method will be faster across the board anyway.

The one thing you could object about is the extra query to initialize the user-defined variables. You can get around that by initializing those in a single row subquery in the FROM clause, a technique described by Baron Schwartz (see for example this post)

SELECT @cum_cnt:=@cum_cnt + COUNT(*) / @cnt as p,
amount
FROM sakila.payment
CROSS JOIN (SELECT @cum_cnt:=0
, @cnt:=COUNT(*)
FROM sakila.payment) p
GROUP BY amount
HAVING p >= 0.9
LIMIT 1;

This has the advantage that the variables are initialized in one go with the entire query, ensuring you are not accidentally working with uninitialized or garbage variables.

(BTW: If you want to do more with these user-defined variables, I can highly recommend more from Baron's site, see for example his article on advanced user defined variable techniques.)

DuckDb Performance: min, max, and median vs quantile

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