ISO IEC 19075-8 pdf – Information technology — Guidance for the use of database language SQL — Part 8: Multidimensional arrays
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:-IEC Electropedia: available at http : / / www.electropedia.org/
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coordinate
non-empty ordered list of integers3.2
cardinality
number of elements in an MD-array3.3
MD-array
ordered collection of elements of the same type associated with an MD-extent where each element is 1:1associated with some coordinate within its MD-extent
Note 1 to entry: A coordinate is within an MD-extent if every coordinate value from the integer list isgreater than or equal to the lower limit, and less than or equal to the upper limit of the MD-interval ofthe MD-axis at the position in the MD-extent as the coordinate value has within the coordinate
3.4
MD-axis
named MD-interval3.5
MD-dimension
number of MD-axes in the MD-extent of an MD-array
Note 1 to entry: Also known as “rank” outside of sQL/MDA3.6
MD-extent
non-empty ordered collection of MD-axes with no duplicate names3.7
MD-interval
integer interval given by a pair of lower and upper integer limits such that the lower limit is less than orequal to the upper limit; the interval is closed, i.e., both limits are contained in it
4Multidimensional arrays (MDA) concepts
4.1Context of multidimensional arrays
The requirements for the material discussed in this document shall be as specified in ISO/IEC 9075-1and IsO/IEC9075-15.
4.2concept
The phrase “(Multidimensional) array, raster data” is used to refer to arrays generally, in contrast to theMD-array term confined to the realm of SQL/MDA.It is not to be confused with the term “array” in ISO/IEC9075-2.This document uses the term ARRAY for the original SQL array collection type.
The array concept is a simple and efficient data representation that finds its use in a wide array of fields,business-relatedas well as scientificandengineering.Many sensors, images, image time-series,simulationprocesses, statistical models, and so on, produce raw data that can immediately be classified as arraydata.These data may be naturally arranged along more than one axis: position and time, for example.A multidimensional array (MDA) is a set of elements ordered in a multidimensional space.The spaceconsidered here is discretized(also called rasterized or gridded), that is, only integer coordinates areadmitted as positions of the individual array elements. The number of integers needed to refer to a par-ticular position in this space is the array’s dimension(sometimes also referred to as its dimensionality).An element can be a single value (such as an intensity value in case of greyscale images) or a compositevalue (such as integertriples for the red, green, and blue components of a true-color image).All elementsof an array share the same structure, referred to as the array’s element type.
4.3why consider support for MDA in sQL?
Large multidimensional arraysin particular representa prevalent data type acrossmost scientificdomains,with examples including 1-D sensor data,2-D satellite images and microscope scans, 3-D x/y/t imagetime-series and x/y/z voxel models, as well as 4-D and 5-D climate models.
In array terms, the image in Figure 1, “Aerial greyscale image of size 1024×1024 (San Diego)”, is a 2- dimensional array of unsigned 8-bit integer elements positioned at coordinates in {0, 1, …, 1023} space. Arrays rarely occur isolated in practice and are typically ornamented with metadata and embedded in larger overall information structures. Supporting them in narrowly specialized ad hoc tools or dedicated array DBMS is thus insufficient when it comes to building modern, complex services and applications. This suggests that integration of array querying into a standardized framework like SQL is a logical next step that will benefit the communities dealing with multidimensional array data in one way or the other. SQL has had basic support for 1-dimensional arrays since 1999. Instead of attempting to extend the existing 1-dimensional array model to address the needs of multidimensional array manipulation, SQL/MDA addresses those needs with a new feature set integrated into SQL.