11th October 2018: PostgreSQL 11 RC 1 Released!

PostgreSQL 9.6.10 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 of cube in
following way: n = 2 * k - 1 means lower bound of k-th dimension, n = 2 * k means upper bound
of k-th dimension. This operator is
designed for KNN-GiST support. |

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.