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Make an editorial pass over the newly SGML-ified contrib documentation.

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Fix lots of bad markup, bad English, bad explanations.

This commit covers only about half the contrib modules, but I grow weary...
This commit is contained in:
Tom Lane
2007-12-06 04:12:10 +00:00
parent a37a0a4180
commit 53e99f57fc
21 changed files with 3713 additions and 3093 deletions
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doc/src/sgml/cube.sgml
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@@ -1,21 +1,24 @@
<!-- $PostgreSQL: pgsql/doc/src/sgml/cube.sgml,v 1.5 2007/12/06 04:12:09 tgl Exp $ -->
<sect1 id="cube">
<title>cube</title>
<indexterm zone="cube">
<primary>cube</primary>
</indexterm>
<para>
This module contains the user-defined type, CUBE, representing
multidimensional cubes.
This module implements a data type <type>cube</> for
representing multi-dimensional cubes.
</para>
<sect2>
<title>Syntax</title>
<para>
The following are valid external representations for the CUBE type:
The following are valid external representations for the <type>cube</>
type. <replaceable>x</>, <replaceable>y</>, etc denote floating-point
numbers:
</para>
<table>
@@ -23,289 +26,114 @@
<tgroup cols="2">
<tbody>
<row>
<entry>'x'</entry>
<entry>A floating point value representing a one-dimensional point or
one-dimensional zero length cubement
</entry>
</row>
<row>
<entry>'(x)'</entry>
<entry>Same as above</entry>
</row>
<row>
<entry>'x1,x2,x3,...,xn'</entry>
<entry>A point in n-dimensional space, represented internally as a zero
volume box
</entry>
</row>
<row>
<entry>'(x1,x2,x3,...,xn)'</entry>
<entry>Same as above</entry>
</row>
<row>
<entry>'(x),(y)'</entry>
<entry>1-D cubement starting at x and ending at y or vice versa; the
order does not matter
</entry>
</row>
<row>
<entry>'(x1,...,xn),(y1,...,yn)'</entry>
<entry>n-dimensional box represented by a pair of its opposite corners, no
matter which. Functions take care of swapping to achieve "lower left --
upper right" representation before computing any values
</entry>
</row>
</tbody>
</tgroup>
</table>
</sect2>
<sect2>
<title>Grammar</title>
<table>
<title>Cube Grammar Rules</title>
<tgroup cols="2">
<tbody>
<row>
<entry>rule 1</entry>
<entry>box -> O_BRACKET paren_list COMMA paren_list C_BRACKET</entry>
</row>
<row>
<entry>rule 2</entry>
<entry>box -> paren_list COMMA paren_list</entry>
</row>
<row>
<entry>rule 3</entry>
<entry>box -> paren_list</entry>
</row>
<row>
<entry>rule 4</entry>
<entry>box -> list</entry>
</row>
<row>
<entry>rule 5</entry>
<entry>paren_list -> O_PAREN list C_PAREN</entry>
</row>
<row>
<entry>rule 6</entry>
<entry>list -> FLOAT</entry>
</row>
<row>
<entry>rule 7</entry>
<entry>list -> list COMMA FLOAT</entry>
</row>
</tbody>
</tgroup>
</table>
</sect2>
<sect2>
<title>Tokens</title>
<table>
<title>Cube Grammar Rules</title>
<tgroup cols="2">
<tbody>
<row>
<entry>n</entry>
<entry>[0-9]+</entry>
</row>
<row>
<entry>i</entry>
<entry>nteger [+-]?{n}</entry>
</row>
<row>
<entry>real</entry>
<entry>[+-]?({n}\.{n}?|\.{n})</entry>
</row>
<row>
<entry>FLOAT</entry>
<entry>({integer}|{real})([eE]{integer})?</entry>
</row>
<row>
<entry>O_BRACKET</entry>
<entry>\[</entry>
</row>
<row>
<entry>C_BRACKET</entry>
<entry>\]</entry>
</row>
<row>
<entry>O_PAREN</entry>
<entry>\(</entry>
</row>
<row>
<entry>C_PAREN</entry>
<entry>\)</entry>
</row>
<row>
<entry>COMMA</entry>
<entry>\,</entry>
</row>
</tbody>
</tgroup>
</table>
</sect2>
<sect2>
<title>Examples</title>
<table>
<title>Examples</title>
<tgroup cols="2">
<tbody>
<row>
<entry>'x'</entry>
<entry>A floating point value representing a one-dimensional point
<entry><literal><replaceable>x</></literal></entry>
<entry>A one-dimensional point
(or, zero-length one-dimensional interval)
</entry>
</row>
<row>
<entry>'(x)'</entry>
<entry><literal>(<replaceable>x</>)</literal></entry>
<entry>Same as above</entry>
</row>
<row>
<entry>'x1,x2,x3,...,xn'</entry>
<entry>A point in n-dimensional space,represented internally as a zero
volume cube
<entry><literal><replaceable>x1</>,<replaceable>x2</>,...,<replaceable>xn</></literal></entry>
<entry>A point in n-dimensional space, represented internally as a
zero-volume cube
</entry>
</row>
<row>
<entry>'(x1,x2,x3,...,xn)'</entry>
<entry><literal>(<replaceable>x1</>,<replaceable>x2</>,...,<replaceable>xn</>)</literal></entry>
<entry>Same as above</entry>
</row>
<row>
<entry>'(x),(y)'</entry>
<entry>A 1-D interval starting at x and ending at y or vice versa; the
<entry><literal>(<replaceable>x</>),(<replaceable>y</>)</literal></entry>
<entry>A one-dimensional interval starting at <replaceable>x</> and ending at <replaceable>y</> or vice versa; the
order does not matter
</entry>
</row>
<row>
<entry>'[(x),(y)]'</entry>
<entry><literal>[(<replaceable>x</>),(<replaceable>y</>)]</literal></entry>
<entry>Same as above</entry>
</row>
<row>
<entry>'(x1,...,xn),(y1,...,yn)'</entry>
<entry>An n-dimensional box represented by a pair of its diagonally
opposite corners, regardless of order. Swapping is provided
by all comarison routines to ensure the
"lower left -- upper right" representation
before actaul comparison takes place.
<entry><literal>(<replaceable>x1</>,...,<replaceable>xn</>),(<replaceable>y1</>,...,<replaceable>yn</>)</literal></entry>
<entry>An n-dimensional cube represented by a pair of its diagonally
opposite corners
</entry>
</row>
<row>
<entry>'[(x1,...,xn),(y1,...,yn)]'</entry>
<entry><literal>[(<replaceable>x1</>,...,<replaceable>xn</>),(<replaceable>y1</>,...,<replaceable>yn</>)]</literal></entry>
<entry>Same as above</entry>
</row>
</tbody>
</tgroup>
</table>
<para>
White space is ignored, so '[(x),(y)]' can be: '[ ( x ), ( y ) ]'
It does not matter which order the opposite corners of a cube are
entered in. The <type>cube</> functions
automatically swap values if needed to create a uniform
<quote>lower left &mdash; upper right</> internal representation.
</para>
<para>
White space is ignored, so <literal>[(<replaceable>x</>),(<replaceable>y</>)]</literal> is the same as
<literal>[ ( <replaceable>x</> ), ( <replaceable>y</> ) ]</literal>.
</para>
</sect2>
<sect2>
<title>Defaults</title>
<para>
I believe this union:
</para>
<programlisting>
select cube_union('(0,5,2),(2,3,1)','0');
cube_union
-------------------
(0, 0, 0),(2, 5, 2)
(1 row)
</programlisting>
<para>
does not contradict to the common sense, neither does the intersection
</para>
<programlisting>
select cube_inter('(0,-1),(1,1)','(-2),(2)');
cube_inter
-------------
(0, 0),(1, 0)
(1 row)
</programlisting>
<para>
In all binary operations on differently sized boxes, I assume the smaller
one to be a cartesian projection, i. e., having zeroes in place of coordinates
omitted in the string representation. The above examples are equivalent to:
</para>
<programlisting>
cube_union('(0,5,2),(2,3,1)','(0,0,0),(0,0,0)');
cube_inter('(0,-1),(1,1)','(-2,0),(2,0)');
</programlisting>
<para>
The following containment predicate uses the point syntax,
while in fact the second argument is internally represented by a box.
This syntax makes it unnecessary to define the special Point type
and functions for (box,point) predicates.
</para>
<programlisting>
select cube_contains('(0,0),(1,1)', '0.5,0.5');
cube_contains
--------------
t
(1 row)
</programlisting>
</sect2>
<sect2>
<title>Precision</title>
<para>
Values are stored internally as 64-bit floating point numbers. This means that
numbers with more than about 16 significant digits will be truncated.
Values are stored internally as 64-bit floating point numbers. This means
that numbers with more than about 16 significant digits will be truncated.
</para>
</sect2>
<sect2>
<title>Usage</title>
<para>
The access method for CUBE is a GiST index (gist_cube_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/seg).
</para>
<para>
The operators supported by the GiST access method include:
The <filename>cube</> module includes a GiST index operator class for
<type>cube</> values.
The operators supported by the GiST opclass include:
</para>
<programlisting>
a = b Same as
</programlisting>
<para>
The cubements a and b are identical.
</para>
<programlisting>
<itemizedlist>
<listitem>
<programlisting>
a = b Same as
</programlisting>
<para>
The cubes a and b are identical.
</para>
</listitem>
<listitem>
<programlisting>
a &amp;&amp; b Overlaps
</programlisting>
<para>
The cubements a and b overlap.
</para>
<programlisting>
</programlisting>
<para>
The cubes a and b overlap.
</para>
</listitem>
<listitem>
<programlisting>
a @&gt; b Contains
</programlisting>
<para>
The cubement a contains the cubement b.
</para>
</programlisting>
<para>
The cube a contains the cube b.
</para>
</listitem>
<listitem>
<programlisting>
a &lt;@ b Contained in
</programlisting>
<para>
The cubement a is contained in b.
</para>
<para>
The cube a is contained in the cube b.
</para>
</listitem>
</itemizedlist>
<para>
(Before PostgreSQL 8.2, the containment operators @&gt; and &lt;@ were
@@ -316,26 +144,18 @@ a &lt;@ b Contained in
</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>
The standard B-tree operators are also provided, for example
<programlisting>
[a, b] &lt; [c, d] Less than
[a, b] &gt; [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
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
you want to use ORDER BY with this type.
</para>
<para>
@@ -343,49 +163,35 @@ a &lt;@ b Contained in
</para>
<table>
<title>Functions available</title>
<title>Cube functions</title>
<tgroup cols="2">
<tbody>
<row>
<entry><literal>cube_distance(cube, cube) returns double</literal></entry>
<entry>cube_distance returns the distance between two cubes. If both
cubes are points, this is the normal distance function.
</entry>
</row>
<row>
<entry><literal>cube(text)</literal></entry>
<entry>Takes text input and returns a cube. This is useful for making
cubes from computed strings.
</entry>
</row>
<row>
<entry><literal>cube(float8) returns cube</literal></entry>
<entry>This makes a one dimensional cube with both coordinates the same.
If the type of the argument is a numeric type other than float8 an
explicit cast to float8 may be needed.
<entry>Makes a one dimensional cube with both coordinates the same.
<literal>cube(1) == '(1)'</literal>
</entry>
</row>
<row>
<entry><literal>cube(float8, float8) returns cube</literal></entry>
<entry>
This makes a one dimensional cube.
<entry>Makes a one dimensional cube.
<literal>cube(1,2) == '(1),(2)'</literal>
</entry>
</row>
<row>
<entry><literal>cube(float8[]) returns cube</literal></entry>
<entry>This makes a zero-volume cube using the coordinates
defined by thearray.<literal>cube(ARRAY[1,2]) == '(1,2)'</literal>
<entry>Makes a zero-volume cube using the coordinates
defined by the array.
<literal>cube(ARRAY[1,2]) == '(1,2)'</literal>
</entry>
</row>
<row>
<entry><literal>cube(float8[], float8[]) returns cube</literal></entry>
<entry>This makes a cube, with upper right and lower left
coordinates as defined by the 2 float arrays. Arrays must be of the
<entry>Makes a cube with upper right and lower left
coordinates as defined by the two arrays, which must be of the
same length.
<literal>cube('{1,2}'::float[], '{3,4}'::float[]) == '(1,2),(3,4)'
</literal>
@@ -394,8 +200,8 @@ a &lt;@ b Contained in
<row>
<entry><literal>cube(cube, float8) returns cube</literal></entry>
<entry>This builds a new cube by adding a dimension on to an
existing cube with the same values for both parts of the new coordinate.
<entry>Makes a new cube by adding a dimension on to an
existing cube with the same values for both parts of the new coordinate.
This is useful for building cubes piece by piece from calculated values.
<literal>cube('(1)',2) == '(1,2),(1,2)'</literal>
</entry>
@@ -403,133 +209,194 @@ a &lt;@ b Contained in
<row>
<entry><literal>cube(cube, float8, float8) returns cube</literal></entry>
<entry>This builds a new cube by adding a dimension on to an
existing cube. This is useful for building cubes piece by piece from
<entry>Makes a new cube by adding a dimension on to an
existing cube. This is useful for building cubes piece by piece from
calculated values. <literal>cube('(1,2)',3,4) == '(1,3),(2,4)'</literal>
</entry>
</row>
<row>
<entry><literal>cube_dim(cube) returns int</literal></entry>
<entry>cube_dim returns the number of dimensions stored in the
the data structure
for a cube. This is useful for constraints on the dimensions of a cube.
<entry>Returns the number of dimensions of the cube
</entry>
</row>
<row>
<entry><literal>cube_ll_coord(cube, int) returns double </literal></entry>
<entry>
cube_ll_coord returns the nth coordinate value for the lower left
corner of a cube. This is useful for doing coordinate transformations.
<entry>Returns the n'th coordinate value for the lower left
corner of a cube
</entry>
</row>
<row>
<entry><literal>cube_ur_coord(cube, int) returns double
</literal></entry>
<entry>cube_ur_coord returns the nth coordinate value for the
upper right corner of a cube. This is useful for doing coordinate
transformations.
<entry>Returns the n'th coordinate value for the
upper right corner of a cube
</entry>
</row>
<row>
<entry><literal>cube_is_point(cube) returns bool</literal></entry>
<entry>Returns true if a cube is a point, that is,
the two defining corners are the same.</entry>
</row>
<row>
<entry><literal>cube_distance(cube, cube) returns double</literal></entry>
<entry>Returns the distance between two cubes. If both
cubes are points, this is the normal distance function.
</entry>
</row>
<row>
<entry><literal>cube_subset(cube, int[]) returns cube
</literal></entry>
<entry>Builds a new cube from an existing cube, using a list of
dimension indexes
from an array. Can be used to find both the ll and ur coordinate of single
dimenion, e.g.: cube_subset(cube('(1,3,5),(6,7,8)'), ARRAY[2]) = '(3),(7)'
Or can be used to drop dimensions, or reorder them as desired, e.g.:
cube_subset(cube('(1,3,5),(6,7,8)'), ARRAY[3,2,1,1]) =
'(5, 3, 1, 1),(8, 7, 6, 6)'
<entry>Makes a new cube from an existing cube, using a list of
dimension indexes from an array. Can be used to find both the LL and UR
coordinates of a single dimension, e.g.
<literal>cube_subset(cube('(1,3,5),(6,7,8)'), ARRAY[2]) = '(3),(7)'</>.
Or can be used to drop dimensions, or reorder them as desired, e.g.
<literal>cube_subset(cube('(1,3,5),(6,7,8)'), ARRAY[3,2,1,1]) = '(5, 3,
1, 1),(8, 7, 6, 6)'</>.
</entry>
</row>
<row>
<entry><literal>cube_is_point(cube) returns bool</literal></entry>
<entry>cube_is_point returns true if a cube is also a point.
This is true when the two defining corners are the same.</entry>
<entry><literal>cube_union(cube, cube) returns cube</literal></entry>
<entry>Produces the union of two cubes
</entry>
</row>
<row>
<entry><literal>cube_enlarge(cube, double, int) returns cube</literal></entry>
<entry>
cube_enlarge increases the size of a cube by a specified
radius in at least
n dimensions. If the radius is negative the box is shrunk instead. This
<entry><literal>cube_inter(cube, cube) returns cube</literal></entry>
<entry>Produces the intersection of two cubes
</entry>
</row>
<row>
<entry><literal>cube_enlarge(cube c, double r, int n) returns cube</literal></entry>
<entry>Increases the size of a cube by a specified radius in at least
n dimensions. If the radius is negative the cube is shrunk instead. This
is useful for creating bounding boxes around a point for searching for
nearby points. All defined dimensions are changed by the radius. If n
is greater than the number of defined dimensions and the cube is being
increased (r &gt;= 0) then 0 is used as the base for the extra coordinates.
LL coordinates are decreased by r and UR coordinates are increased by r.
If a LL coordinate is increased to larger than the corresponding UR
coordinate (this can only happen when r &lt; 0) than both coordinates are
set to their average. To make it harder for people to break things there
is an effective maximum on the dimension of cubes of 100. This is set
in cubedata.h if you need something bigger.
nearby points. All defined dimensions are changed by the radius r.
LL coordinates are decreased by r and UR coordinates are increased by r.
If a LL coordinate is increased to larger than the corresponding UR
coordinate (this can only happen when r &lt; 0) than both coordinates
are set to their average. If n is greater than the number of defined
dimensions and the cube is being increased (r &gt;= 0) then 0 is used
as the base for the extra coordinates.
</entry>
</row>
</tbody>
</tgroup>
</table>
</sect2>
<sect2>
<title>Defaults</title>
<para>
There are a few other potentially useful functions defined in cube.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.
I believe this union:
</para>
<programlisting>
select cube_union('(0,5,2),(2,3,1)', '0');
cube_union
-------------------
(0, 0, 0),(2, 5, 2)
(1 row)
</programlisting>
<para>
does not contradict common sense, neither does the intersection
</para>
<programlisting>
select cube_inter('(0,-1),(1,1)', '(-2),(2)');
cube_inter
-------------
(0, 0),(1, 0)
(1 row)
</programlisting>
<para>
In all binary operations on differently-dimensioned cubes, I assume the
lower-dimensional one to be a cartesian projection, i. e., having zeroes
in place of coordinates omitted in the string representation. The above
examples are equivalent to:
</para>
<programlisting>
cube_union('(0,5,2),(2,3,1)','(0,0,0),(0,0,0)');
cube_inter('(0,-1),(1,1)','(-2,0),(2,0)');
</programlisting>
<para>
The following containment predicate uses the point syntax,
while in fact the second argument is internally represented by a box.
This syntax makes it unnecessary to define a separate point type
and functions for (box,point) predicates.
</para>
<programlisting>
select cube_contains('(0,0),(1,1)', '0.5,0.5');
cube_contains
--------------
t
(1 row)
</programlisting>
</sect2>
<sect2>
<title>Notes</title>
<para>
For examples of usage, see the regression test <filename>sql/cube.sql</>.
</para>
<para>
For examples of usage, see sql/cube.sql
To make it harder for people to break things, there
is a limit of 100 on the number of dimensions of cubes. This is set
in <filename>cubedata.h</> if you need something bigger.
</para>
</sect2>
<sect2>
<title>Credits</title>
<para>
This code is essentially based on the example written for
Illustra, <ulink url="http://garcia.me.berkeley.edu/~adong/rtree"></ulink>
Original author: Gene Selkov, Jr. <email>selkovjr@mcs.anl.gov</email>,
Mathematics and Computer Science Division, Argonne National Laboratory.
</para>
<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>), and
to his former student, Andy Dong
(<ulink url="http://best.me.berkeley.edu/~adong/"></ulink>), for his exemplar.
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.
(<ulink url="http://db.cs.berkeley.edu/~jmh/"></ulink>) for elucidating the
gist of the GiST (<ulink url="http://gist.cs.berkeley.edu/"></ulink>), and
to his former student, Andy Dong (<ulink
url="http://best.me.berkeley.edu/~adong/"></ulink>), for his example
written for Illustra,
<ulink url="http://garcia.me.berkeley.edu/~adong/rtree"></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>
<para>
Gene Selkov, Jr.
Computational Scientist
Mathematics and Computer Science Division
Argonne National Laboratory
9700 S Cass Ave.
Building 221
Argonne, IL 60439-4844
<email>selkovjr@mcs.anl.gov</email>
</para>
<para>
Minor updates to this package were made by Bruno Wolff III
<email>bruno@wolff.to</email> in August/September of 2002. These include
changing the precision from single precision to double precision and adding
Minor updates to this package were made by Bruno Wolff III
<email>bruno@wolff.to</email> in August/September of 2002. These include
changing the precision from single precision to double precision and adding
some new functions.
</para>
<para>
Additional updates were made by Joshua Reich <email>josh@root.net</email> in
July 2006. These include <literal>cube(float8[], float8[])</literal> and
cleaning up the code to use the V1 call protocol instead of the deprecated V0
form.
Additional updates were made by Joshua Reich <email>josh@root.net</email> in
July 2006. These include <literal>cube(float8[], float8[])</literal> and
cleaning up the code to use the V1 call protocol instead of the deprecated
V0 protocol.
</para>
</sect2>
</sect1>
</sect1>