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<!-- doc/src/sgml/seg.sgml -->
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<sect1 id="seg" xreflabel="seg">
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<title>seg</title>
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<indexterm zone="seg">
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<primary>seg</primary>
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</indexterm>
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<para>
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This module implements a data type <type>seg</> for
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representing line segments, or floating point intervals.
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<type>seg</> can represent uncertainty in the interval endpoints,
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making it especially useful for representing laboratory measurements.
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</para>
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<sect2>
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<title>Rationale</title>
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<para>
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The geometry of measurements is usually more complex than that of a
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point in a numeric continuum. A measurement is usually a segment of
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that continuum with somewhat fuzzy limits. The measurements come out
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as intervals because of uncertainty and randomness, as well as because
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the value being measured may naturally be an interval indicating some
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condition, such as the temperature range of stability of a protein.
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</para>
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<para>
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Using just common sense, it appears more convenient to store such data
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as intervals, rather than pairs of numbers. In practice, it even turns
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out more efficient in most applications.
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</para>
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<para>
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Further along the line of common sense, the fuzziness of the limits
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suggests that the use of traditional numeric data types leads to a
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certain loss of information. Consider this: your instrument reads
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6.50, and you input this reading into the database. What do you get
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when you fetch it? Watch:
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2010-07-29 21:34:41 +02:00
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<screen>
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test=> select 6.50 :: float8 as "pH";
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pH
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---
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6.5
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(1 row)
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</screen>
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In the world of measurements, 6.50 is not the same as 6.5. It may
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sometimes be critically different. The experimenters usually write
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down (and publish) the digits they trust. 6.50 is actually a fuzzy
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interval contained within a bigger and even fuzzier interval, 6.5,
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with their center points being (probably) the only common feature they
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share. We definitely do not want such different data items to appear the
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same.
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</para>
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<para>
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Conclusion? It is nice to have a special data type that can record the
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limits of an interval with arbitrarily variable precision. Variable in
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the sense that each data element records its own precision.
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</para>
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<para>
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Check this out:
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<screen>
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test=> select '6.25 .. 6.50'::seg as "pH";
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pH
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------------
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6.25 .. 6.50
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(1 row)
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</screen>
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</para>
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</sect2>
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<sect2>
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<title>Syntax</title>
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<para>
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The external representation of an interval is formed using one or two
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floating-point numbers joined by the range operator (<literal>..</literal>
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or <literal>...</literal>). Alternatively, it can be specified as a
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center point plus or minus a deviation.
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Optional certainty indicators (<literal><</literal>,
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<literal>></literal> or <literal>~</literal>) can be stored as well.
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(Certainty indicators are ignored by all the built-in operators, however.)
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<xref linkend="seg-repr-table"> gives an overview of allowed
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representations; <xref linkend="seg-input-examples"> shows some
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examples.
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</para>
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<para>
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In <xref linkend="seg-repr-table">, <replaceable>x</>, <replaceable>y</>, and
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<replaceable>delta</> denote
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floating-point numbers. <replaceable>x</> and <replaceable>y</>, but
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not <replaceable>delta</>, can be preceded by a certainty indicator.
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</para>
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2009-05-18 13:08:24 +02:00
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<table id="seg-repr-table">
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<title><type>seg</> External Representations</title>
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<tgroup cols="2">
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<tbody>
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<row>
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<entry><literal><replaceable>x</></literal></entry>
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<entry>Single value (zero-length interval)
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</entry>
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</row>
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<row>
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<entry><literal><replaceable>x</> .. <replaceable>y</></literal></entry>
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<entry>Interval from <replaceable>x</> to <replaceable>y</>
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</entry>
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</row>
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<row>
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<entry><literal><replaceable>x</> (+-) <replaceable>delta</></literal></entry>
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<entry>Interval from <replaceable>x</> - <replaceable>delta</> to
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<replaceable>x</> + <replaceable>delta</>
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</entry>
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</row>
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<row>
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<entry><literal><replaceable>x</> ..</literal></entry>
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<entry>Open interval with lower bound <replaceable>x</>
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</entry>
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</row>
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<row>
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<entry><literal>.. <replaceable>x</></literal></entry>
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<entry>Open interval with upper bound <replaceable>x</>
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</entry>
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</row>
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</tbody>
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</tgroup>
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</table>
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2010-08-10 22:42:01 +02:00
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<table id="seg-input-examples">
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<title>Examples of Valid <type>seg</> Input</title>
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<tgroup cols="2">
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<tbody>
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<row>
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<entry><literal>5.0</literal></entry>
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<entry>
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Creates a zero-length segment (a point, if you will)
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</entry>
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</row>
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<row>
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<entry><literal>~5.0</literal></entry>
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<entry>
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Creates a zero-length segment and records
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<literal>~</> in the data. <literal>~</literal> is ignored
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by <type>seg</> operations, but
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is preserved as a comment.
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</entry>
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</row>
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<row>
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<entry><literal><5.0</literal></entry>
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<entry>
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Creates a point at 5.0. <literal><</literal> is ignored but
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is preserved as a comment.
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</entry>
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</row>
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<row>
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<entry><literal>>5.0</literal></entry>
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<entry>
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Creates a point at 5.0. <literal>></literal> is ignored but
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is preserved as a comment.
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</entry>
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</row>
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<row>
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<entry><literal>5(+-)0.3</literal></entry>
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<entry>
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Creates an interval <literal>4.7 .. 5.3</literal>.
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Note that the <literal>(+-)</> notation isn't preserved.
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</entry>
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</row>
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<row>
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<entry><literal>50 .. </literal></entry>
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<entry>Everything that is greater than or equal to 50</entry>
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</row>
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<row>
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<entry><literal>.. 0</literal></entry>
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<entry>Everything that is less than or equal to 0</entry>
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</row>
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<row>
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<entry><literal>1.5e-2 .. 2E-2 </literal></entry>
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<entry>Creates an interval <literal>0.015 .. 0.02</literal></entry>
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</row>
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<row>
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<entry><literal>1 ... 2</literal></entry>
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<entry>
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The same as <literal>1...2</literal>, or <literal>1 .. 2</literal>,
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or <literal>1..2</literal>
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(spaces around the range operator are ignored)
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</entry>
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</row>
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</tbody>
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</tgroup>
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</table>
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<para>
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Because <literal>...</> is widely used in data sources, it is allowed
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as an alternative spelling of <literal>..</>. Unfortunately, this
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creates a parsing ambiguity: it is not clear whether the upper bound
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in <literal>0...23</> is meant to be <literal>23</> or <literal>0.23</>.
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This is resolved by requiring at least one digit before the decimal
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point in all numbers in <type>seg</> input.
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</para>
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<para>
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As a sanity check, <type>seg</> rejects intervals with the lower bound
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greater than the upper, for example <literal>5 .. 2</>.
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</para>
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2007-11-11 00:30:46 +01:00
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</sect2>
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<sect2>
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<title>Precision</title>
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<para>
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<type>seg</> values are stored internally as pairs of 32-bit floating point
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numbers. This means that numbers with more than 7 significant digits
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will be truncated.
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</para>
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<para>
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Numbers with 7 or fewer significant digits retain their
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original precision. That is, if your query returns 0.00, you will be
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sure that the trailing zeroes are not the artifacts of formatting: they
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reflect the precision of the original data. The number of leading
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zeroes does not affect precision: the value 0.0067 is considered to
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have just 2 significant digits.
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</para>
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</sect2>
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<sect2>
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<title>Usage</title>
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2007-11-11 00:30:46 +01:00
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<para>
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The <filename>seg</> module includes a GiST index operator class for
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<type>seg</> values.
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The operators supported by the GiST operator class are shown in <xref linkend="seg-gist-operators">.
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</para>
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2007-12-06 05:12:10 +01:00
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2010-07-29 21:34:41 +02:00
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<table id="seg-gist-operators">
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<title>Seg GiST Operators</title>
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<tgroup cols="2">
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<thead>
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<row>
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<entry>Operator</entry>
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<entry>Description</entry>
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</row>
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</thead>
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<tbody>
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<row>
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<entry><literal>[a, b] << [c, d]</literal></entry>
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<entry>[a, b] is entirely to the left of [c, d]. That is, [a,
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b] << [c, d] is true if b < c and false otherwise.</entry>
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</row>
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<row>
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<entry><literal>[a, b] >> [c, d]</literal></entry>
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<entry>[a, b] is entirely to the right of [c, d]. That is, [a,
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b] >> [c, d] is true if a > d and false otherwise.</entry>
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</row>
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<row>
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<entry><literal>[a, b] &< [c, d]</literal></entry>
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<entry>Overlaps or is left of — This might be better read
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as <quote>does not extend to right of</quote>. It is true when
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b <= d.</entry>
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</row>
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<row>
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<entry><literal>[a, b] &> [c, d]</literal></entry>
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<entry>Overlaps or is right of — This might be better read
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as <quote>does not extend to left of</quote>. It is true when
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a >= c.</entry>
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</row>
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<row>
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<entry><literal>[a, b] = [c, d]</literal></entry>
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<entry>Same as — The segments [a, b] and [c, d] are
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identical, that is, a = c and b = d.</entry>
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</row>
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<row>
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<entry><literal>[a, b] && [c, d]</literal></entry>
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<entry>The segments [a, b] and [c, d] overlap.</entry>
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</row>
|
|
|
|
|
|
|
|
<row>
|
|
|
|
<entry><literal>[a, b] @> [c, d]</literal></entry>
|
|
|
|
<entry>The segment [a, b] contains the segment [c, d], that is,
|
|
|
|
a <= c and b >= d.</entry>
|
|
|
|
</row>
|
|
|
|
|
|
|
|
<row>
|
|
|
|
<entry><literal>[a, b] <@ [c, d]</literal></entry>
|
|
|
|
<entry>The segment [a, b] is contained in [c, d], that is, a
|
|
|
|
>= c and b <= d.</entry>
|
|
|
|
</row>
|
|
|
|
</tbody>
|
|
|
|
</tgroup>
|
|
|
|
</table>
|
2007-12-06 05:12:10 +01:00
|
|
|
|
2007-11-11 00:30:46 +01:00
|
|
|
<para>
|
2010-07-29 21:34:41 +02:00
|
|
|
(Before PostgreSQL 8.2, the containment operators <literal>@></> and <literal><@</> were
|
|
|
|
respectively called <literal>@</> and <literal>~</>. These names are still available, but are
|
2007-11-11 00:30:46 +01:00
|
|
|
deprecated and will eventually be retired. Notice that the old names
|
|
|
|
are reversed from the convention formerly followed by the core geometric
|
2010-08-17 06:37:21 +02:00
|
|
|
data types!)
|
2007-11-11 00:30:46 +01:00
|
|
|
</para>
|
2007-12-06 05:12:10 +01:00
|
|
|
|
2007-11-11 00:30:46 +01:00
|
|
|
<para>
|
2007-12-06 05:12:10 +01:00
|
|
|
The standard B-tree operators are also provided, for example
|
2007-11-11 00:30:46 +01:00
|
|
|
|
2010-07-29 21:34:41 +02:00
|
|
|
<informaltable>
|
|
|
|
<tgroup cols="2">
|
|
|
|
<thead>
|
|
|
|
<row>
|
|
|
|
<entry>Operator</entry>
|
|
|
|
<entry>Description</entry>
|
|
|
|
</row>
|
|
|
|
</thead>
|
|
|
|
|
|
|
|
<tbody>
|
|
|
|
<row>
|
|
|
|
<entry><literal>[a, b] < [c, d]</literal></entry>
|
|
|
|
<entry>Less than</entry>
|
|
|
|
</row>
|
|
|
|
|
|
|
|
<row>
|
|
|
|
<entry><literal>[a, b] > [c, d]</literal></entry>
|
|
|
|
<entry>Greater than</entry>
|
|
|
|
</row>
|
|
|
|
</tbody>
|
|
|
|
</tgroup>
|
|
|
|
</informaltable>
|
2007-12-06 05:12:10 +01:00
|
|
|
|
2007-11-11 00:30:46 +01:00
|
|
|
These operators do not make a lot of sense for any practical
|
|
|
|
purpose but sorting. These operators first compare (a) to (c),
|
2007-12-06 05:12:10 +01:00
|
|
|
and if these are equal, compare (b) to (d). That results in
|
2007-11-11 00:30:46 +01:00
|
|
|
reasonably good sorting in most cases, which is useful if
|
2007-12-06 05:12:10 +01:00
|
|
|
you want to use ORDER BY with this type.
|
2007-11-11 00:30:46 +01:00
|
|
|
</para>
|
2007-12-06 05:12:10 +01:00
|
|
|
</sect2>
|
|
|
|
|
|
|
|
<sect2>
|
|
|
|
<title>Notes</title>
|
2007-11-11 00:30:46 +01:00
|
|
|
|
|
|
|
<para>
|
2007-12-06 05:12:10 +01:00
|
|
|
For examples of usage, see the regression test <filename>sql/seg.sql</>.
|
2007-11-11 00:30:46 +01:00
|
|
|
</para>
|
2007-12-06 05:12:10 +01:00
|
|
|
|
2007-11-11 00:30:46 +01:00
|
|
|
<para>
|
2007-12-06 05:12:10 +01:00
|
|
|
The mechanism that converts <literal>(+-)</> to regular ranges
|
|
|
|
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:
|
|
|
|
|
2010-07-29 21:34:41 +02:00
|
|
|
<screen>
|
2007-12-06 05:12:10 +01:00
|
|
|
postgres=> select '10(+-)1'::seg as seg;
|
|
|
|
seg
|
|
|
|
---------
|
|
|
|
9.0 .. 11 -- should be: 9 .. 11
|
2010-07-29 21:34:41 +02:00
|
|
|
</screen>
|
2007-11-11 00:30:46 +01:00
|
|
|
</para>
|
2007-12-06 05:12:10 +01:00
|
|
|
|
2007-11-11 00:30:46 +01:00
|
|
|
<para>
|
2007-12-06 05:12:10 +01:00
|
|
|
The performance of an R-tree index can largely depend on the initial
|
2007-11-11 00:30:46 +01:00
|
|
|
order of input values. It may be very helpful to sort the input table
|
2007-12-06 05:12:10 +01:00
|
|
|
on the <type>seg</> column; see the script <filename>sort-segments.pl</>
|
|
|
|
for an example.
|
2007-11-11 00:30:46 +01:00
|
|
|
</para>
|
|
|
|
</sect2>
|
|
|
|
|
|
|
|
<sect2>
|
|
|
|
<title>Credits</title>
|
2007-12-06 05:12:10 +01:00
|
|
|
|
2007-11-11 00:30:46 +01:00
|
|
|
<para>
|
2007-12-06 05:12:10 +01:00
|
|
|
Original author: Gene Selkov, Jr. <email>selkovjr@mcs.anl.gov</email>,
|
|
|
|
Mathematics and Computer Science Division, Argonne National Laboratory.
|
2007-11-11 00:30:46 +01:00
|
|
|
</para>
|
2007-12-06 05:12:10 +01:00
|
|
|
|
2007-11-11 00:30:46 +01:00
|
|
|
<para>
|
2007-12-06 05:12:10 +01:00
|
|
|
My thanks are primarily to Prof. Joe Hellerstein
|
2009-12-08 21:08:30 +01:00
|
|
|
(<ulink url="http://db.cs.berkeley.edu/jmh/"></ulink>) for elucidating the
|
2007-12-06 05:12:10 +01:00
|
|
|
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.
|
2007-11-11 00:30:46 +01:00
|
|
|
</para>
|
2007-12-06 05:12:10 +01:00
|
|
|
|
2007-11-11 00:30:46 +01:00
|
|
|
</sect2>
|
|
|
|
|
|
|
|
</sect1>
|