@ -75,8 +75,8 @@
entered in. The <type>cube</> functions
automatically swap values if needed to create a uniform
<quote>lower left — upper right</> internal representation.
When corners coincide cube stores only one corner along with a
special flag in order to reduce size wasted .
When the corners coincide, <type> cube</> stores only one corner
along with an <quote>is point</> flag to avoid wasting space .
</para>
<para>
@ -98,17 +98,17 @@
<title>Usage</title>
<para>
The <filename>cube</> module includes a GiST index operator class for
<type>cube</> values.
The operators supported by the GiST operator class are shown in <xref linkend="cube-gist-operators">.
<xref linkend="cube-operators"> shows the operators provided for type
<type>cube</>.
</para>
<table id="cube-gist- operators">
<title>Cube GiST Operators</title>
<tgroup cols="2 ">
<table id="cube-operators">
<title>Cube Operators</title>
<tgroup cols="3 ">
<thead>
<row>
<entry>Operator</entry>
<entry>Result</entry>
<entry>Description</entry>
</row>
</thead>
@ -116,160 +116,149 @@
<tbody>
<row>
<entry><literal>a = b</></entry>
<entry><type>boolean</></entry>
<entry>The cubes a and b are identical.</entry>
</row>
<row>
<entry><literal>a && b</></entry>
<entry><type>boolean</></entry>
<entry>The cubes a and b overlap.</entry>
</row>
<row>
<entry><literal>a @> b</></entry>
<entry><type>boolean</></entry>
<entry>The cube a contains the cube b.</entry>
</row>
<row>
<entry><literal>a <@ b</></entry>
<entry><type>boolean</></entry>
<entry>The cube a is contained in the cube b.</entry>
</row>
<row>
<entry><literal>a -> n</></entry>
<entry>Get n-th coordinate of cube.</entry>
<entry><literal>a < b</></entry>
<entry><type>boolean</></entry>
<entry>The cube a is less than the cube b.</entry>
</row>
<row>
<entry><literal>a ~> n</></entry>
<entry>
Get n-th coordinate in 'normalized' cube representation. Noramlization
means coordinate rearrangement to form (lower left, upper right).
</entry>
<entry><literal>a <= b</></entry>
<entry><type>boolean</></entry>
<entry>The cube a is less than or equal to the cube b.</entry>
</row>
</tbody>
</tgroup>
</table>
<para>
(Before PostgreSQL 8.2, the containment operators <literal>@></> and <literal><@</> were
respectively called <literal>@</> and <literal>~</>. 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
data types!)
</para>
<row>
<entry><literal>a > b</></entry>
<entry><type>boolean</></entry>
<entry>The cube a is greater than the cube b.</entry>
</row>
<para>
GiST index can be used to retrieve nearest neighbours via several metric
operators. As always any of them can be used as ordinary function.
</para>
<row>
<entry><literal>a >= b</></entry>
<entry><type>boolean</></entry>
<entry>The cube a is greater than or equal to the cube b.</entry>
</row>
<table id="cube-gistknn-operators">
<title>Cube GiST-kNN Operators</title>
<tgroup cols="2">
<thead>
<row>
<entry>Operator</entry>
<entry>Description</entry>
<entry><literal>a <> b</></entry>
<entry><type>boolean</></entry>
<entry>The cube a is not equal to the cube b.</entry>
</row>
</thead>
<tbody>
<row>
<entry><literal>a -> n</></entry>
<entry><type>float8</></entry>
<entry>Get <replaceable>n</>-th coordinate of cube (counting from 1).</entry>
</row>
<row>
<entry><literal>a ~> n</></entry>
<entry><type>float8</></entry>
<entry>
Get <replaceable>n</>-th coordinate in <quote>normalized</> cube
representation, in which the coordinates have been rearranged into
the form <quote>lower left — upper right</>; that is, the
smaller endpoint along each dimension appears first.
</entry>
</row>
<row>
<entry><literal>a <-> b</></entry>
<entry>Euclidean distance between a and b</entry>
<entry><type>float8</></entry>
<entry>Euclidean distance between a and b.</entry>
</row>
<row>
<entry><literal>a <#> b</></entry>
<entry>Taxicab (L-1 metric) distance between a and b</entry>
<entry><type>float8</></entry>
<entry>Taxicab (L-1 metric) distance between a and b.</entry>
</row>
<row>
<entry><literal>a <=> b</></entry>
<entry>Chebyshev (L-inf metric) distance between a and b</entry>
<entry><type>float8</></entry>
<entry>Chebyshev (L-inf metric) distance between a and b.</entry>
</row>
</tbody>
</tgroup>
</table>
<para>
Selection of nearing neigbours can be done in the following way:
(Before PostgreSQL 8.2, the containment operators <literal>@></> and <literal><@</> were
respectively called <literal>@</> and <literal>~</>. 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
data types!)
</para>
<programlisting>
SELECT c FROM test
ORDER BY cube(array[0.5,0.5,0.5])<->c
LIMIT 1;
</programlisting>
<para>
Also kNN framework allows us to cheat with metrics in order to get results
sorted by selected coodinate directly from the index without extra sorting
step. That technique significantly faster on small values of LIMIT, however
with bigger values of LIMIT planner will switch automatically to standart
index scan and sort.
That behavior can be achieved using coordinate operator
(cube c)~>(int offset).
The scalar ordering operators (<literal><</>, <literal>>=</>, etc)
do not make a lot of sense for any practical purpose but sorting. These
operators first compare the first coordinates, and if those are equal,
compare the second coordinates, etc. They exist mainly to support the
b-tree index operator class for <type>cube</>, which can be useful for
example if you would like a UNIQUE constraint on a <type>cube</> column.
</para>
<programlisting>
=> select cube(array[0.41,0.42,0.43])~>2 as coord;
coord
-------
0.42
(1 row)
</programlisting>
<para>
So using that operator as kNN metric we can obtain cubes sorted by it's
coordinate.
The <filename>cube</> module also provides a GiST index operator class for
<type>cube</> values.
A <type>cube</> GiST index can be used to search for values using the
<literal>=</>, <literal>&&</>, <literal>@></>, and
<literal><@</> operators in <literal>WHERE</> clauses.
</para>
<para>
To get cubes ordered by first coordinate of lower left corner ascending
one can use the following query:
</para>
In addition, a <type>cube</> GiST index can be used to find nearest
neighbors using the metric operators
<literal><-></>, <literal><#></>, and
<literal><=></> in <literal>ORDER BY</> clauses.
For example, the nearest neighbor of the 3-D point (0.5, 0.5, 0.5)
could be found efficiently with:
<programlisting>
SELECT c FROM test ORDER BY c~>1 LIMIT 5;
SELECT c FROM test
ORDER BY cube(array[0.5,0.5,0.5]) <-> c
LIMIT 1;
</programlisting>
<para>
And to get cubes descending by first coordinate of upper right corner
of 2d-cube:
</para>
<programlisting>
SELECT c FROM test ORDER BY c~>3 DESC LIMIT 5;
</programlisting>
<para>
The standard B-tree operators are also provided, for example
<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>
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 results in
reasonably good sorting in most cases, which is useful if
you want to use ORDER BY with this type.
The <literal>~></> operator can also be used in this way to
efficiently retrieve the first few values sorted by a selected coordinate.
For example, to get the first few cubes ordered by the first coordinate
(lower left corner) ascending one could use the following query:
<programlisting>
SELECT c FROM test ORDER BY c ~> 1 LIMIT 5;
</programlisting>
And to get 2-D cubes ordered by the first coordinate of the upper right
corner descending:
<programlisting>
SELECT c FROM test ORDER BY c ~> 3 DESC LIMIT 5;
</programlisting>
</para>
<para>
Tom Lane
10 years ago