PostgreSQL 9.6.0 Documentation | |||
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This module implements a data type `cube`
for representing multidimensional cubes.

Table F-3 shows the
valid external representations for the `cube` type. `x`,
`y`, etc. denote floating-point
numbers.

Table F-3. Cube External Representations

External Syntax | Meaning |
---|---|

x |
A one-dimensional point (or, zero-length one-dimensional interval) |

(x) |
Same as above |

x1,x2,...,xn |
A point in n-dimensional space, represented internally as a zero-volume cube |

(x1,x2,...,xn) |
Same as above |

(x),(y) |
A one-dimensional interval starting at x and ending at y or vice versa; the order does
not matter |

[(x),(y)] |
Same as above |

(x1,...,xn),(y1,...,yn) |
An n-dimensional cube represented by a pair of its diagonally opposite corners |

[(x1,...,xn),(y1,...,yn)] |
Same as above |

It does not matter which order the opposite corners of a
cube are entered in. The `cube` functions
automatically swap values if needed to create a uniform
"lower left — upper right" internal
representation. When the corners coincide, `cube` stores only one corner along with an
"is point" flag to avoid wasting
space.

White space is ignored on input, so `[( x),(y)]` is the same as

Values are stored internally as 64-bit floating point numbers. This means that numbers with more than about 16 significant digits will be truncated.

Table F-4 shows
the operators provided for type `cube`.

Table F-4. Cube Operators

Operator | Result | Description |
---|---|---|

a = b |
boolean |
The cubes a and b are identical. |

a && b |
boolean |
The cubes a and b overlap. |

a @> b |
boolean |
The cube a contains the cube b. |

a <@ b |
boolean |
The cube a is contained in the cube b. |

a < b |
boolean |
The cube a is less than the cube b. |

a <= b |
boolean |
The cube a is less than or equal to the cube b. |

a > b |
boolean |
The cube a is greater than the cube b. |

a >= b |
boolean |
The cube a is greater than or equal to the cube b. |

a <> b |
boolean |
The cube a is not equal to the cube b. |

a -> n |
float8 |
Get n-th coordinate
of cube (counting from 1). |

a ~> n |
float8 |
Get n-th coordinate
in "normalized" cube
representation, in which the coordinates have been
rearranged into the form "lower
left — upper right"; that is, the smaller
endpoint along each dimension appears first. |

a <-> b |
float8 |
Euclidean distance between a and b. |

a <#> b |
float8 |
Taxicab (L-1 metric) distance between a and b. |

a <=> b |
float8 |
Chebyshev (L-inf metric) distance between a and b. |

(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 data types!)

The scalar ordering operators (`<`, `>=`, 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
`cube`, which can be useful for example if
you would like a UNIQUE constraint on a `cube` column.

The `cube` module also provides a
GiST index operator class for `cube`
values. A `cube` GiST index can be used to
search for values using the `=`,
`&&`, `@>`, and `<@`
operators in `WHERE` clauses.

In addition, a `cube` GiST index can be
used to find nearest neighbors using the metric operators
`<->`, `<#>`, and `<=>` in `ORDER BY`
clauses. For example, the nearest neighbor of the 3-D point
(0.5, 0.5, 0.5) could be found efficiently with:

SELECT c FROM test ORDER BY c <-> cube(array[0.5,0.5,0.5]) LIMIT 1;

The `~>` 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:

SELECT c FROM test ORDER BY c ~> 1 LIMIT 5;

And to get 2-D cubes ordered by the first coordinate of the upper right corner descending:

SELECT c FROM test ORDER BY c ~> 3 DESC LIMIT 5;

Table F-5 shows the available functions.

Table F-5. Cube Functions

Function | Result | Description | Example |
---|---|---|---|

cube(float8) |
cube |
Makes a one dimensional cube with both coordinates the same. | cube(1) == '(1)' |

cube(float8, float8) |
cube |
Makes a one dimensional cube. | cube(1,2) ==
'(1),(2)' |

cube(float8[]) |
cube |
Makes a zero-volume cube using the coordinates defined by the array. | cube(ARRAY[1,2]) ==
'(1,2)' |

cube(float8[],
float8[]) |
cube |
Makes a cube with upper right and lower left coordinates as defined by the two arrays, which must be of the same length. | cube(ARRAY[1,2], ARRAY[3,4]) ==
'(1,2),(3,4)' |

cube(cube, float8) |
cube |
Makes a new cube by adding a dimension on to an existing cube, with the same values for both endpoints of the new coordinate. This is useful for building cubes piece by piece from calculated values. | cube('(1,2),(3,4)'::cube, 5) ==
'(1,2,5),(3,4,5)' |

cube(cube, float8,
float8) |
cube |
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. | cube('(1,2),(3,4)'::cube, 5, 6)
== '(1,2,5),(3,4,6)' |

cube_dim(cube) |
integer |
Returns the number of dimensions of the cube. | cube_dim('(1,2),(3,4)') ==
'2' |

cube_ll_coord(cube,
integer) |
float8 |
Returns the n-th
coordinate value for the lower left corner of the
cube. |
cube_ll_coord('(1,2),(3,4)', 2)
== '2' |

cube_ur_coord(cube,
integer) |
float8 |
Returns the n-th
coordinate value for the upper right corner of the
cube. |
cube_ur_coord('(1,2),(3,4)', 2)
== '4' |

cube_is_point(cube) |
boolean |
Returns true if the cube is a point, that is, the two defining corners are the same. | |

cube_distance(cube,
cube) |
float8 |
Returns the distance between two cubes. If both cubes are points, this is the normal distance function. | |

cube_subset(cube,
integer[]) |
cube |
Makes a new cube from an existing cube, using a list of dimension indexes from an array. Can be used to extract the endpoints of a single dimension, or to drop dimensions, or to reorder them as desired. | cube_subset(cube('(1,3,5),(6,7,8)'),
ARRAY[2]) == '(3),(7)' cube_subset(cube('(1,3,5),(6,7,8)'),
ARRAY[3,2,1,1]) == '(5,3,1,1),(8,7,6,6)' |

cube_union(cube,
cube) |
cube |
Produces the union of two cubes. | |

cube_inter(cube,
cube) |
cube |
Produces the intersection of two cubes. | |

cube_enlarge(c cube, r double,
n integer) |
cube |
Increases the size of the cube by the specified
radius r in at least
n dimensions. If the
radius is negative the cube is shrunk instead. All
defined dimensions are changed by the radius r. Lower-left coordinates are
decreased by r and
upper-right coordinates are increased by r. If a lower-left coordinate is
increased to more than the corresponding upper-right
coordinate (this can only happen when r < 0) than both coordinates
are set to their average. If n is greater than the number of
defined dimensions and the cube is being enlarged
(r > 0), then extra
dimensions are added to make n altogether; 0 is used as the
initial value for the extra coordinates. This function
is useful for creating bounding boxes around a point
for searching for nearby points. |
cube_enlarge('(1,2),(3,4)',
0.5, 3) == '(0.5,1.5,-0.5),(3.5,4.5,0.5)' |

I believe this union:

select cube_union('(0,5,2),(2,3,1)', '0'); cube_union ------------------- (0, 0, 0),(2, 5, 2) (1 row)

does not contradict common sense, neither does the intersection

select cube_inter('(0,-1),(1,1)', '(-2),(2)'); cube_inter ------------- (0, 0),(1, 0) (1 row)

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:

cube_union('(0,5,2),(2,3,1)','(0,0,0),(0,0,0)'); cube_inter('(0,-1),(1,1)','(-2,0),(2,0)');

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.

select cube_contains('(0,0),(1,1)', '0.5,0.5'); cube_contains -------------- t (1 row)

For examples of usage, see the regression test `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 `cubedata.h` if you need something
bigger.

Original author: Gene Selkov, Jr. `<selkovjr@mcs.anl.gov>`

,
Mathematics and Computer Science Division, Argonne National
Laboratory.

My thanks are primarily to Prof. Joe Hellerstein (http://db.cs.berkeley.edu/jmh/) for elucidating the gist of the GiST (http://gist.cs.berkeley.edu/), and to his former student Andy Dong for his example written for Illustra. 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.

Minor updates to this package were made by Bruno Wolff III
`<bruno@wolff.to>`

in
August/September of 2002. These include changing the precision
from single precision to double precision and adding some new
functions.

Additional updates were made by Joshua Reich `<josh@root.net>`

in July
2006. These include `cube(float8[],
float8[])` and cleaning up the code to use the V1 call
protocol instead of the deprecated V0 protocol.

If you see anything in the documentation that is not correct, does not match your experience with the particular feature or requires further clarification, please use this form to report a documentation issue.