Variance¶

This is a simple aggregate function which returns a variance. It is adapted from an example implementation in pysqlite.

  package variance;
  
  sub new { bless [], shift; }
  
  sub step {
      my ( $self, $value ) = @_;
  
      push @$self, $value;
  }
  
  sub finalize {
      my $self = $_[0];
  
      my $n = @$self;
  
      # Variance is NULL unless there is more than one row
      return undef unless $n || $n == 1;
  
      my $mu = 0;
      foreach my $v ( @$self ) {
          $mu += $v;
      }
      $mu /= $n;
  
      my $sigma = 0;
      foreach my $v ( @$self ) {
          $sigma += ($v - $mu)**2;
      }
      $sigma = $sigma / ($n - 1);
  
      return $sigma;
  }
  
  # NOTE: If you use an older DBI (< 1.608),
  # use $dbh->func(..., "create_aggregate") instead.
  $dbh->sqlite_create_aggregate( "variance", 1, 'variance' );

The function can then be used as:

  SELECT group_name, variance(score)
  FROM results
  GROUP BY group_name;

Variance (Memory Efficient)¶

A more efficient variance function, optimized for memory usage at the expense of precision:

  package variance2;
  
  sub new { bless {sum => 0, count=>0, hash=> {} }, shift; }
  
  sub step {
      my ( $self, $value ) = @_;
      my $hash = $self->{hash};
  
      # by truncating and hashing, we can comsume many more data points
      $value = int($value); # change depending on need for precision
                            # use sprintf for arbitrary fp precision
      if (exists $hash->{$value}) {
          $hash->{$value}++;
      } else {
          $hash->{$value} = 1;
      }
      $self->{sum} += $value;
      $self->{count}++;
  }
  
  sub finalize {
      my $self = $_[0];
  
      # Variance is NULL unless there is more than one row
      return undef unless $self->{count} > 1;
  
      # calculate avg
      my $mu = $self->{sum} / $self->{count};
  
      my $sigma = 0;
      while (my ($h, $v) = each %{$self->{hash}}) {
          $sigma += (($h - $mu)**2) * $v;
      }
      $sigma = $sigma / ($self->{count} - 1);
  
      return $sigma;
  }

The function can then be used as:

  SELECT group_name, variance2(score)
  FROM results
  GROUP BY group_name;

Variance (Highly Scalable)¶

A third variable implementation, designed for arbitrarily large data sets:

  package variance3;
  
  sub new { bless {mu=>0, count=>0, S=>0}, shift; }
  
  sub step {
      my ( $self, $value ) = @_;
      $self->{count}++;
      my $delta = $value - $self->{mu};
      $self->{mu} += $delta/$self->{count};
      $self->{S} += $delta*($value - $self->{mu});
  }
  
  sub finalize {
      my $self = $_[0];
      return $self->{S} / ($self->{count} - 1);
  }

The function can then be used as:

  SELECT group_name, variance3(score)
  FROM results
  GROUP BY group_name;

Sparing database disk space¶

As explained in <http://www.sqlite.org/fts3.html#fts4_options>, several options are available to specify how SQLite should store indexed documents.

One strategy is to use SQLite only for the fulltext index and metadata, and keep the full documents outside of SQLite; to do so, use the "content=""" option. For example, the following SQL creates an FTS4 table with three columns - "a", "b", and "c":

   CREATE VIRTUAL TABLE t1 USING fts4(content="", a, b, c);

Data can be inserted into such an FTS4 table using an INSERT statements. However, unlike ordinary FTS4 tables, the user must supply an explicit integer docid value. For example:

  -- This statement is Ok:
  INSERT INTO t1(docid, a, b, c) VALUES(1, 'a b c', 'd e f', 'g h i');
  -- This statement causes an error, as no docid value has been provided:
  INSERT INTO t1(a, b, c) VALUES('j k l', 'm n o', 'p q r');

Of course your application will need an algorithm for finding the external resource corresponding to any docid stored within SQLite. Furthermore, SQLite "offsets()" and "snippet()" functions cannot be used, so if such functionality is needed, it has to be directly programmed within the Perl application.