CREATE TABLE sessions
(
  user_id integer NOT NULL,
  start_at timestamp without time zone,
  end_at timestamp without time zone,
  duration double precision,
  views integer
)

I thought for sure the next step would be to dump some data, then write some Ruby or R to scan through sessions and see how many sessions were open at a time.

Until I came up with a nice solution in SQL (Postgres). Stepping back, if I can sample from sessions at say, one-minute intervals, I can count the number of distinct sessions open at each minute. What I need is a row per session per minute spanned. Generate_series is a “set returning function” that can do just that. In the snippet below, I use generate_series to generate a set of (whole) minutes from the start of the session to the end of the session. That essentially multiplies the session row into n rows, one for each of the minutes the session spans.

From there, it’s easy to do a straight forward group by, counting distinct user_id:

with rounded_sessions as (
select user_id, start_at, end_at,
generate_series(date_trunc('minute',start_at), end_at, '1 minute') to_the_minute from sessions
where start_at between '2012-01-21' and '2012-01-28'
)
select to_the_minute, count(distinct user_id) from rounded_sessions group by 1

The date_trunc call is important so that session rows are aligned to whole minutes, if that’s not done, then none of the rows will align for the counts.

That set won’t include rows that had no users logged in. To do that, the query below will use generate_series again to generate all the minutes from the first minute present to the last, then left join the counts to that set, coalescing missing entries to zero.

with rounded_sessions as (
select plm_users.user_id, start_at, end_at,
generate_series(date_trunc('minute',start_at), end_at, '1 minute') as to_the_minute
from sessions
where start_at between '2012-01-21' and '2012-01-28'
),
counts_by_minute as (
select to_the_minute, count(distinct user_id) from rounded_sessions
group by 1
),
all_the_minutes as (
select generate_series(min(to_the_minute), max(to_the_minute), '1 minute') as minute_fu from rounded_sessions
)

select to_the_minute , coalesce(count, 0) as users from all_the_minutes
left join counts_by_minute on all_the_minutes.minute_fu = counts_by_minute.to_the_minute

One day at a time

First, a simplified example table:

create table events (
  user_id integer,
  event varchar,
  date date
)

Getting unique user counts by event on any given day is easy. Below, we’ll get the counts of unique users by events for the 7 days leading up to Valentine’s day:

select count(distinct user_id), event from events
where date between '2011-02-07' and '2011-02-14'
group by 2

Now Do That For Every Day

The simplest thing that could possibly work is to just issue that query to compute the stats for the time span desired. We’re looking for something faster, and a bit more elegant.

Stepping back a bit, for a seven day time window, we’re asking that an event on 2/7/2011 count for that day, and also count for the 6 following days – effectively we’re mapping the events of each day onto itself and 6 other days. That sounds like a SQL join waiting to happen. Once the join happens, its easy to group by the mapped date, and do a distinct count.

With a table like the one below

This SQL becomes easy.

select to_date, event, count(distinct user_id) from events
join dates_plus_7 on events.date = dates_plus_7.from_date
group by 1,2

You’ll then need to trim the ends of your data to adjust for where the windows ran off the edge of the data.
That works for me on Postgresql 8.4. Your mileage may vary with other brands.

How Do I Get One of Those?
A dates table like that is a one-liner using the generate_series method:

select date::date as from_date, date::date+plus_day as to_date from
 generate_series('2011-01-01'::date, '2011-02-28'::date, '1 day') as date,
 generate_series(0,6,1) as plus_day ;

There we get the cartesian product of the set of dates in the desired range, and the set of numbers from 0 to 6. Sum the two, treating the numbers as offsets and you’re done.

That’s all well and good, but I can’t shake the feeling every time legislation comes out to do some activity (retire, save for education, health care) the only winner is the financial services industry.

Here’s why: all of these activities requires one to maroon a slice of money into an account designated for that purpose. What comes with accounts? That’s right, fees to the bank. The Wells-Fargo HSA we’ve got is $4.25 a month (paid, for now, by work). That’s $51 a year to hold money. The interest rate is a paltry 0.1%, so with $2000 in that account (the minimum cash balance before we’re allowed to invest), I’d make about $2.00, (net -$49 if I was paying the fees, as I will one day) Thanks for nothing. Further, while some banks graciously waive fees for meeting minimum balances, it’s harder for many people to meet the balance since their money is split so many ways.

These accounts limit my flexibility to spend as life events occur, limit the returns on my money, and cost me fees, and headaches. More statements to read, cards to carry, and fine print to decode.

If costs are to be tax-deductible, why not fix the tax code instead, so that all medical expenses, instead of those over a certain amount, are tax deductible, instead of these shameless handouts to the banks? Let me deduct things come tax time.

Wukong is a great library to write map/reduce jobs for Hadoop from ruby.

Together they can be really great, because problems unsolvable in pig without resorting writing a custom function in Java can be solved by streaming data through an external script, which Wukong nicely wraps. The Data Chef blog has a great example of using Pig to choreograph the data flow, and ruby/wukong to compute Jaccard Similarity of sets.

Working with Wukong on Elastic Map Reduce

Elastic map reduce is a great resource – it’s very easy to quickly have a small hadoop cluster at your disposal to process some data. Getting wukong working requires an extra step: installing the wukong gem on all the machines in the cluster.

Fortunately, elastic map reduce allows the use of bootstrap scripts located on S3, which run on boot for all the machines in the cluster. I used the following script (based on an example on stackoverflow):

sudo apt-get update
sudo apt-get -y install rubygems
sudo gem install wukong --no-rdoc --no-ri

Using Amazon’s command line utility, starting the cluster ready to use in pig interactive mode looks like this

elastic-mapreduce –create –bootstrap-action [S3 path to wukong-bootstrap.sh] –num-instances [a number] –slave-instance-type [ machine type ] –pig-interactive -ssh

The web tool for creating clusters has a space for specifying the path to a bootstrap script.

Next step: upload your pig script and it accompanying wukong script to the name node, and launch the job. (It’s also possible to do all of that when starting the cluster with more arguments to elastic-map, with the added advantage that the cluster will terminate with your job)

Solution: check the monitor’s settings. In my ViewSonic VX2453 the HDMI inputs have 2 settings “AV” and “PC”. Switching it to PC solved the problem, and now the picture is exactly the right size and crisp.

I spent some time futzing around with SwitchRes and several fruitless reboots before discovering the setting, so I hope this saves someone time!

From the docs

A multicolumn B-tree index can be used with query conditions that involve any subset of the index’s columns, but the index is most efficient when there are constraints on the leading (leftmost) columns.

Performance

If you click around that section of the docs, you’ll surely come across the section on multi-column indexing and performance, in particular this section (bold emphasis mine):

You could also create a multicolumn index on (x, y). This index would typically be more efficient than index combination for queries involving both columns, but as discussed in Section 11.3, it would be almost useless for queries involving only y, so it should not be the only index. A combination of the multicolumn index and a separate index on y would serve reasonably well. For queries involving only x, the multicolumn index could be used, though it would be larger and hence slower than an index on x alone

Life is full of tradeoffs performance wise, so we should explore just how much slower it is to use a multi-column index for single column queries.

First, lets create a dummy table:

CREATE TABLE foos_and_bars
(
  id serial NOT NULL,
  foo_id integer,
  bar_id integer,
  CONSTRAINT foos_and_bars_pkey PRIMARY KEY (id)
)

Then, using R, we’ll create 3 million rows of nicely distributed data:

rows = 3000000
foo_ids = seq(1,250000,1)
bar_ids = seq(1,20,1)
data = data.frame(foo_id = sample(foo_ids, rows,TRUE), bar_id= sample(bar_ids,rows,TRUE))

Dump that to a text file and load it up with \copy and we’re good to go.

Create the compound index

CREATE INDEX foo_id_and_bar_id_index
  ON foos_and_bars
  USING btree
  (foo_id, bar_id);

Run a simple query to make sure the index is used:

test_foo=# explain analyze select * from foos_and_bars where foo_id = 123;
                                                           QUERY PLAN
---------------------------------------------------------------------------------------------------------------------------------
 Bitmap Heap Scan on foos_and_bars  (cost=4.68..55.74 rows=13 width=12) (actual time=0.026..0.038 rows=8 loops=1)
   Recheck Cond: (foo_id = 123)
   ->  Bitmap Index Scan on foo_id_and_bar_id_index  (cost=0.00..4.68 rows=13 width=0) (actual time=0.020..0.020 rows=8 loops=1)
         Index Cond: (foo_id = 123)
 Total runtime: 0.072 ms
(5 rows)

Now we’ll make 100 queries by foo_id with this index, and then repeat with the single index installed using this code:

require 'rubygems'
require 'benchmark'
require 'pg'

TEST_IDS = [...] #randomly selected 100 ids in R

conn = PGconn.open(:dbname => 'test_foo')
def perform_test(conn,foo_id)
  time = Benchmark.realtime do
    res = conn.exec("select * from foos_and_bars where foo_id = #{foo_id}")
    res.clear
  end
end

TEST_IDS.map {|id| perform_test(conn,id)} #warm things up?
data = TEST_IDS.map {|id| perform_test(conn,id)}

data.each do |d|
puts d
end

How do things stack up? I’d say about evenly:

Remember: Indexing isn’t free, and Postgres is pretty good at using (and reusing) your indexes, so you may not need to create as many as you think.

This usually happens to me after a long time between reboots, and a reboot usually allows me to successfully connect again. Rebooting when I’m in the middle of something can be a pain, so I did some research and found a better way. There’s a process called “racoon” – it performs key exchange operations to set up IPSec tunnels. Kill it (using kill or activity monitor) and your VPN will start working again.

Works on OSX 10.6.5 and 10.6.6

While simple belongs_to relationships are easy to fix with :include, lets take a look at a concrete example where that won’t work:

class User < ActiveRecord::Base
  has_many :likes
end

class Item < ActiveRecord::Base
  has_many :likes
  def liked_by?(user)
     likes.by_user(user).present?
  end
end

class Like < ActiveRecord::Base
  belongs_to :user
  belongs_to :item
end

A view presenting a set of items that called Item#liked_by? would be an n+1 problem that wouldn’t be well solved by :include. Instead, we’d have to come up with a query to get the Likes for the set of items by this user:

Like.of_item(@items).by_user(user)

Then we’d have to store that in a controller instance variable, and change all the views that called item.liked_by?(user) to access the instance variable instead.

Active Support’s memoize functionality stores the results of function calls so they’re only evaluated once. What if we could trick the method into thinking it’s already been called? We can do just that by writing data into the instance variables that memoize uses to save results on each of the model instances. First, we memoize liked_by:

  memoize :liked_by?

Then bulk load the relevant likes and stash them into memoize’s internal state:

def precompute_data(items, user)
  likes = Like.of_item(items).by_user(user).index_by {|like| like.item_id}
  items.each do |item|
    item.write_memo(:liked_by?,likes[item.id].present?,user)
  end
end

The write_memo method is implemented as follows.

  def write_memo(method, return_value, args=nil)
    ivar = ActiveSupport::Memoizable.memoized_ivar_for(method)
    if args
      if hash = instance_variable_get(ivar)
        hash[Array(args)] = return_value
      else
        instance_variable_set(ivar, {Array(args) => return_value})
      end
    else
      instance_variable_set(ivar, [return_value])
    end
  end

This problem described here could be solved with some crafty left joins added to the query that fetched the items in the first place, but when there’s several different hard to prefetch properties, such a query would likely become unmanageable, if not terribly slow.

Inspired by the tweet by @doctorzaius referencing a URL to Twitter’s search page for “your an idiot”, I used Twitter’s streaming API to download a sample of 6581 tweets containing the word “idiot” overnight, for about 12 hours.

Of these 6581 tweets, 65 contained our friend “your an idiot”. 161, two and a half times as many, contained “you’re an idiot”. Additionally, there were 2 tweets with “your such an idiot”, and just one “you’re such an idiot”. The forces of good grammar have won this round?

Note: This is a very small sample. It may be interesting to compare Facebook status updates to see what the you’re/your ratio looks like there one day…

The files on first inspection are a bit strange, because although they spring from a csv export button, they’re tab-delimited, but with CSV-style quoting conventions. That’s easy enough to work around, but R and Ruby both barfed reading the files. I cottoned on to the fact that the files had some odd characters in them, so I recruited JRuby and ruby 1.9 to try to load them, due to better unicode support, but still couldn’t quite get the parameters right.

Then I thought of iconv, the character set converting utility. Since in this case, the only special characters was the ellipsis character, I was happy to strip those out, and the following command does the trick:

iconv -f UTF-16LE -t US-ASCII -c responses.csv > converted_responses.csv

And, as they say, Bob’s your uncle