
<sect1 id="seg">
 <title>seg</title>
 
 <indexterm zone="seg">
  <primary>seg</primary>
 </indexterm>

 <para>
  The <literal>seg</literal> module contains the code for the user-defined 
  type, <literal>SEG</literal>, representing laboratory measurements as 
  floating point intervals. 
 </para>
 
 <sect2>
  <title>Rationale</title>
  <para>
   The geometry of measurements is usually more complex than that of a
   point in a numeric continuum. A measurement is usually a segment of
   that continuum with somewhat fuzzy limits. The measurements come out
   as intervals because of uncertainty and randomness, as well as because
   the value being measured may naturally be an interval indicating some
   condition, such as the temperature range of stability of a protein.
  </para>
  <para>
   Using just common sense, it appears more convenient to store such data
   as intervals, rather than pairs of numbers. In practice, it even turns
   out more efficient in most applications.
  </para>
  <para>
   Further along the line of common sense, the fuzziness of the limits
   suggests that the use of traditional numeric data types leads to a
   certain loss of information. Consider this: your instrument reads
   6.50, and you input this reading into the database. What do you get
   when you fetch it? Watch:
  </para>
  <programlisting>
test=> select 6.50 as "pH";
 pH
---
6.5
(1 row)
  </programlisting>
  <para>
   In the world of measurements, 6.50 is not the same as 6.5. It may
   sometimes be critically different. The experimenters usually write
   down (and publish) the digits they trust. 6.50 is actually a fuzzy
   interval contained within a bigger and even fuzzier interval, 6.5,
   with their center points being (probably) the only common feature they
   share. We definitely do not want such different data items to appear the
   same.
  </para>
  <para>
   Conclusion? It is nice to have a special data type that can record the
   limits of an interval with arbitrarily variable precision. Variable in
   a sense that each data element records its own precision.
  </para>
  <para>
   Check this out:
  </para>
  <programlisting>
test=> select '6.25 .. 6.50'::seg as "pH";
          pH
------------
6.25 .. 6.50
(1 row)
  </programlisting>
 </sect2>

 <sect2>
  <title>Syntax</title>
  <para>
   The external representation of an interval is formed using one or two
   floating point numbers joined by the range operator ('..' or '...'). 
   Optional certainty indicators (<, > and ~) are ignored by the internal 
   logics, but are retained in the data.
  </para>
  
  <table>
   <title>Rules</title>
   <tgroup cols="2">
    <tbody>
     <row>
      <entry>rule 1</entry>
      <entry>seg -> boundary PLUMIN deviation</entry>
     </row>
     <row>
      <entry>rule 2</entry>
      <entry>seg -> boundary RANGE boundary</entry>
     </row>
     <row>
      <entry>rule 3</entry>
      <entry>seg -> boundary RANGE</entry>
     </row>
     <row>
      <entry>rule 4</entry>
      <entry>seg -> RANGE boundary</entry>
     </row>
     <row>
      <entry>rule 5</entry>
      <entry>seg -> boundary</entry>
     </row>
     <row>
      <entry>rule 6</entry>
      <entry>boundary -> FLOAT</entry>
     </row>
     <row>
      <entry>rule 7</entry>
      <entry>boundary -> EXTENSION FLOAT</entry>
     </row>
     <row>
      <entry>rule 8</entry>
      <entry>deviation -> FLOAT</entry>
     </row>
    </tbody>
   </tgroup>
  </table>

  <table>
   <title>Tokens</title>
   <tgroup cols="2">
    <tbody>
     <row>
      <entry>RANGE</entry>
      <entry>(\.\.)(\.)?</entry>
     </row>
     <row>
      <entry>PLUMIN</entry>
      <entry>\'\+\-\'</entry>
     </row>
     <row>
      <entry>integer</entry>
      <entry>[+-]?[0-9]+</entry>
     </row>
     <row>
      <entry>real</entry>
      <entry>[+-]?[0-9]+\.[0-9]+</entry>
     </row>
     <row>
      <entry>FLOAT</entry>
      <entry>({integer}|{real})([eE]{integer})?</entry>
     </row>
     <row>
      <entry>EXTENSION</entry>
      <entry>[<>~]</entry>
     </row>
    </tbody>
   </tgroup>
  </table>
 
  <table>
   <title>Examples of valid <literal>SEG</literal> representations</title>
   <tgroup cols="2">
    <tbody>
     <row>
      <entry>Any number</entry>
      <entry>
       (rules 5,6) -- creates a zero-length segment (a point,
       if you will)
      </entry>
     </row>
     <row>
      <entry>~5.0</entry>
      <entry>
       (rules 5,7) -- creates a zero-length segment AND records 
       '~' in the data. This notation reads 'approximately 5.0', 
       but its meaning is not recognized by the code. It is ignored 
       until you get the value back. View it is a short-hand comment.
      </entry>
     </row> 
     <row>
      <entry><5.0</entry>
      <entry>
       (rules 5,7) -- creates a point at 5.0; '<' is ignored but 
       is preserved as a comment
      </entry>
     </row>
     <row>
      <entry>>5.0</entry>
      <entry>
       (rules 5,7) -- creates a point at 5.0; '>' is ignored but
       is preserved as a comment
      </entry>
     </row>
     <row>
      <entry><para>5(+-)0.3</para><para>5'+-'0.3</para></entry>
      <entry>
       <para>
        (rules 1,8) -- creates an interval '4.7..5.3'. As of this 
        writing (02/09/2000), this mechanism isn't completely accurate 
        in determining the number of significant digits for the 
        boundaries. For example, it adds an extra digit to the lower
        boundary if the resulting interval includes a power of ten:
       </para>
       <programlisting>
postgres=> select '10(+-)1'::seg as seg;
      seg
---------
9.0 .. 11 -- should be: 9 .. 11
       </programlisting>
       <para>
        Also, the (+-) notation is not preserved: 'a(+-)b' will 
        always be returned as '(a-b) .. (a+b)'. The purpose of this 
        notation is to allow input from certain data sources without 
        conversion.
       </para>
      </entry>
     </row>
     <row>
      <entry>50 .. </entry>
      <entry>(rule 3) -- everything that is greater than or equal to 50</entry>
     </row>
     <row>
      <entry>.. 0</entry>
      <entry>(rule 4) -- everything that is less than or equal to 0</entry>
     </row>
     <row>
      <entry>1.5e-2 .. 2E-2 </entry>
      <entry>(rule 2) -- creates an interval (0.015 .. 0.02)</entry>
     </row>
     <row>
      <entry>1 ... 2</entry>
      <entry>
       The same as 1...2, or 1 .. 2, or 1..2 (space is ignored).
       Because of the widespread use of '...' in the data sources,
       I decided to stick to is as a range operator. This, and
       also the fact that the white space around the range operator
       is ignored, creates a parsing conflict with numeric constants 
       starting with a decimal point.
      </entry>
     </row>
    </tbody>
   </tgroup>
  </table>

  <table>
   <title>Examples</title>
   <tgroup cols="2">
    <tbody>
     <row>
      <entry>.1e7</entry>
      <entry>should be: 0.1e7</entry>
     </row>
     <row>
      <entry>.1 .. .2</entry>
      <entry>should be: 0.1 .. 0.2</entry>
     </row>
     <row>
      <entry>2.4 E4</entry>
      <entry>should be: 2.4E4</entry>
     </row>
    </tbody>
   </tgroup>
  </table>
  <para>
   The following, although it is not a syntax error, is disallowed to improve
   the sanity of the data:
  </para>
  <table>
   <title></title>
   <tgroup cols="2">
    <tbody>
     <row>
      <entry>5 .. 2</entry>
      <entry>should be: 2 .. 5</entry>
     </row>
    </tbody>
   </tgroup>
  </table>
 </sect2>

 <sect2>
  <title>Precision</title>
  <para>
   The segments are stored internally as pairs of 32-bit floating point
   numbers. It means that the numbers with more than 7 significant digits
   will be truncated.
  </para>
  <para>
   The numbers with less than or exactly 7 significant digits retain their
   original precision. That is, if your query returns 0.00, you will be
   sure that the trailing zeroes are not the artifacts of formatting: they
   reflect the precision of the original data. The number of leading
   zeroes does not affect precision: the value 0.0067 is considered to
   have just 2 significant digits.
  </para>
 </sect2>

 <sect2>
  <title>Usage</title>
  <para>
   The access method for SEG is a GiST index (gist_seg_ops), which is a
   generalization of R-tree. GiSTs allow the postgres implementation of
   R-tree, originally encoded to support 2-D geometric types such as
   boxes and polygons, to be used with any data type whose data domain
   can be partitioned using the concepts of containment, intersection and
   equality. In other words, everything that can intersect or contain
   its own kind can be indexed with a GiST. That includes, among other
   things, all geometric data types, regardless of their dimensionality
   (see also contrib/cube).
  </para>
  <para>
   The operators supported by the GiST access method include:
  </para>
  <itemizedlist>
   <listitem>
    <programlisting>
[a, b] << [c, d]        Is left of
    </programlisting>
    <para>
     The left operand, [a, b], occurs entirely to the left of the
     right operand, [c, d], on the axis (-inf, inf). It means,
     [a, b] << [c, d] is true if b < c and false otherwise
    </para>
   </listitem>
   <listitem>
    <programlisting>
[a, b] >> [c, d]        Is right of
    </programlisting>
    <para>
        [a, b] is occurs entirely to the right of [c, d]. 
        [a, b] >> [c, d] is true if a > d and false otherwise
    </para>
   </listitem>
   <listitem>
    <programlisting>
[a, b] &< [c, d]        Overlaps or is left of
    </programlisting>
    <para>
        This might be better read as "does not extend to right of".
        It is true when b <= d.
    </para>
   </listitem>
   <listitem>
    <programlisting>
[a, b] &> [c, d]        Overlaps or is right of
    </programlisting>
    <para>
        This might be better read as "does not extend to left of".
        It is true when a >= c.
    </para>
   </listitem>
   <listitem>
    <programlisting>
[a, b] = [c, d]                Same as
    </programlisting>
    <para>
        The segments [a, b] and [c, d] are identical, that is, a == b
        and c == d
    </para>
   </listitem>
   <listitem>
    <programlisting>
[a, b] && [c, d]        Overlaps
    </programlisting>
    <para>
        The segments [a, b] and [c, d] overlap.
    </para>
   </listitem>
   <listitem>
    <programlisting>
[a, b] @> [c, d]                Contains
    </programlisting>
    <para>
        The segment [a, b] contains the segment [c, d], that is, 
        a <= c and b >= d
    </para>
   </listitem>
   <listitem>
    <programlisting>
[a, b] <@ [c, d]                Contained in
    </programlisting>
    <para>
        The segment [a, b] is contained in [c, d], that is, 
        a >= c and b <= d
    </para>
   </listitem>
  </itemizedlist>
  <para>
   (Before PostgreSQL 8.2, the containment operators @> and <@ were
   respectively called @ and ~.  These names are still available, but are
   deprecated and will eventually be retired.  Notice that the old names
   are reversed from the convention formerly followed by the core geometric
   datatypes!)
  </para>
  <para>
   Although the mnemonics of the following operators is questionable, I
   preserved them to maintain visual consistency with other geometric
   data types defined in Postgres.
  </para>
  <para>
   Other operators:
  </para>

  <programlisting>
[a, b] < [c, d]                Less than
[a, b] > [c, d]                Greater than
  </programlisting>
  <para>
   These operators do not make a lot of sense for any practical
   purpose but sorting. These operators first compare (a) to (c),
   and if these are equal, compare (b) to (d). That accounts for
   reasonably good sorting in most cases, which is useful if
   you want to use ORDER BY with this type
  </para>

  <para>
   There are a few other potentially useful functions defined in seg.c 
   that vanished from the schema because I stopped using them. Some of 
   these were meant to support type casting. Let me know if I was wrong: 
   I will then add them back to the schema. I would also appreciate 
   other ideas that would enhance the type and make it more useful.
  </para>
  <para>
   For examples of usage, see sql/seg.sql
  </para>
  <para>
   NOTE: The performance of an R-tree index can largely depend on the
   order of input values. It may be very helpful to sort the input table
   on the SEG column (see the script sort-segments.pl for an example)
  </para>
 </sect2>

 <sect2>
  <title>Credits</title>
  <para>
   My thanks are primarily to Prof. Joe Hellerstein
   (<ulink url="http://db.cs.berkeley.edu/~jmh/"></ulink>) for elucidating the 
   gist of the GiST (<ulink url="http://gist.cs.berkeley.edu/"></ulink>). I am 
   also grateful to all postgres developers, present and past, for enabling 
   myself to create my own world and live undisturbed in it. And I would like 
   to acknowledge my gratitude to Argonne Lab and to the U.S. Department of 
   Energy for the years of faithful support of my database research.
  </para>
  <programlisting>
   Gene Selkov, Jr.
   Computational Scientist
   Mathematics and Computer Science Division
   Argonne National Laboratory
   9700 S Cass Ave.
   Building 221
   Argonne, IL 60439-4844
  </programlisting>
  <para>
   <email>selkovjr@mcs.anl.gov</email>
  </para>
 </sect2>

</sect1>

