ISO/IEC 19075-8:2021

INTERNATIONAL ISO/IEC
STANDARD 19075-8
First edition
Information technology — Guidance
for the use of database language
SQL —
Part 8:
Multidimensional arrays
PROOF/ÉPREUVE
Reference number
ISO/IEC 19075-8:2021(E)
©
ISO/IEC 2021

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ISO/IEC 19075-8:2021(E)

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ii © ISO/IEC 2021 – All rights reserved

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ISO/IEC19075-8:2021(E)
Contents Page
Foreword.vii
Introduction.ix
1 Scope.1
2 Normativereferences.2
3 Termsanddefinitions.3
4 Multidimensionalarrays(MDA)concepts.4
4.1 Contextofmultidimensionalarrays.4
4.2 Concept.4
4.3 WhyconsidersupportforMDAinSQL?.4
4.4 Arrayrepresentations.6
4.5 UsecasesforMDAsupportinSQL.6
4.5.1 Theusecases.6
4.5.2 Arraydataingestionandstorage.6
4.5.3 Integratedqueryingofarrayandrelationaldata.7
4.5.4 Updatingstoredarraydata.7
4.5.5 Exporting arrays.7
4.6 Non-Usecases:Directaccesstoexternalarraydata.7
5 SQL/MDAdatamodel.8
5.1 Datamodelconcepts.8
5.2 MD-array.8
5.3 MD-arraytypedefinition.9
5.3.1 Typedefinitionconcepts.9
5.3.2 Element type.9
5.3.3 MD-dimension.10
5.3.4 MD-axis names.10
5.3.5 MD-axislowerandupperlimits.10
5.3.6 Puttingitalltogether.11
5.4 MD-arraycreation.13
5.4.1 MD-arraycreationconcepts.13
5.4.2 Explicitelementenumeration.14
5.4.3 FromSQLtablequeryresult.15
5.4.4 Constructionbyimplicititeration.16
5.4.5 Decodingaformat-encodedarray.17
5.5 MD-arrayupdating.18
5.5.1 MD-arrayupdatingintroduction.18
5.5.2 UpdatingMD-arraysofequalMD-dimension.19
5.5.3 UpdatingMD-arraysofgreaterMD-dimension.20
5.5.4 UpdatingasingleelementofanMD-array.21
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ISO/IEC19075-8:2021(E)
5.6 Exporting MD-arrays.21
5.6.1 Encodingtoadataformat.21
5.6.2 ConvertingtoanSQLtable.23
6 SQL/MDA operations.25
6.1 IntroductiontoSQL/MDAoperations.25
6.2 MD-extentprobingoperators.25
6.3 MD-arrayelementreference.27
6.4 MD-extentmodifyingoperations.28
6.4.1 IntroductiontoMDE-extentmodifyingoperations.28
6.4.2 Subsetting.28
6.4.3 Reshaping.30
6.4.4 Shifting.32
6.4.5 MD-axisrenaming.32
6.5 MD-arrayderivingoperators.33
6.5.1 IntroductiontoMD-arrayderivingoperators.33
6.5.2 Scaling.33
6.5.3 Concatenation.35
6.5.4 Inducedoperations.35
6.5.5 JoinMD-arraysontheircoordinates.42
6.6 MD-arrayaggregation.43
6.6.1 Generalaggregationexpression.43
6.6.2 Shorthandaggregationfunctions.44
7 Remotesensingexample.46
7.1 Introductiontoremotesensingexample.46
7.2 Data setup.46
7.3 Bandmath.48
7.3.1 Introductiontobandmath.48
7.3.2 NDVI.48
7.3.3 Band Swapping.51
7.4 Histograms.52
7.5 Changedetection.53
7.6 Extracting features.54
7.7 Datasearchandfiltering.55
Bibliography.57
Index.58
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ISO/IEC19075-8:2021(E)
Tables
Table Page
1 ExamplesofMD-arraytypedefinitions.12
2 ExamplesofMD-arraysconstructedbyelementenumeration.15
3 ExamplesofMD-arrayscreatedwiththeconstructorbyiteration.17
4 ExamplesofMD-arrayscreatedfromJSON-encodedarrays.18
5 ExamplesofMD-arraysencodedtoJSONarrays.22
6 ResultofexampleUNNESTquery.24
7 ResultofexampleUNNESTqueryspecifyingWITHORDINALITY.24
8 ExampleswithMD-extentprobingfunctions.26
9 ResultofMDEXTENT(kernel).26
10 ResultofMDMAX_EXTENT(kernel).26
11 ExamplesofreferencingasingleelementinanMD-array.27
12 ExamplesofMD-arraysubsetting.30
13 ExamplesofMD-extentreshaping.31
14 ExamplesofMD-extentshifting.32
15 ExamplesofMD-axisrenaming.33
16 InterpolationmethodsdefinedinISO19123:2005.34
17 ExamplesofMD-arrayconcatenation.35
18 ExamplesofinducedfunctionapplicationtoMD-arrays.38
19 Operationscorrespondingtothegrammarrules.40
20 ExamplesofinducedMD-arrayexpressions.40
21 ExampleofinducedMD-arraycasting.41
22 ExamplesofinducedCASEexpression.41
23 ExamplesofMDJOIN.43
24 Identityelementsforthes.43
25 ExamplesofgeneralMD-arrayaggregation.44
26 Predefinedaggregationoperators.45
27 LandsatTMbands.46
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ISO/IEC19075-8:2021(E)
Figures
Figure Page
1 Aerialgreyscaleimageofsize1024x1024(SanDiego).5
2 RelationshipsbetweenMDAandSQL/MDA.8
3 ThestructureofanMD-arrayvalueillustratedonasample3x3array.9
4 Placementofsatelliteimagesofeachcountryonaworldmap(fromGeographicBoundingBoxes).11
5 ExampleofanSQLtablethatcorrespondstoa3x3MD-array.16
6 ExampleofanSQLtableconvertedtoa3x3MD-arraywithMD-extent[i(-1:1),j(-1:1)].16
7 Exampleofarrayupdate.20
8 Updatinga3-DMD-arraywitha2-DsourceMD-array.21
9 MD-arraysubsettingexamples.28
10 MD-arrayreshapingexample.31
11 MD-arrayshiftingexample.32
12 MD-arrayscalingexample.33
13 Concatenation examples.35
14 ExampleofsummingtwoMD-arrays.36
15 Colorizedarray.42
16 Visiblecolor(RGB)bandsofaLandsatTMscene.47
17 NDVIresultstretchedtotherange(0,255).49
18 NDVIvaluesbetween0.2and0.4showninwhite,whileeverythingelseisblack.50
19 Color-mappedNDVIresult,fromdarkblue,throughgrey,todarkgreen.51
20 FalsecolorimageconstructedfromthenearIR,redandgreenbands.52
21 HistogramoftheNDVIindexofaLandsatTMscene.53
22 AcompositeimagewithanNDVIindexfromdifferentyearsineachchannel.54
23 NaturalRGBcolorofbarrierislandsarea.55
24 Binaryimageshowingisolatedislands.55
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ISO/IEC19075-8:2021(E)
Foreword
ISO(theInternationalOrganizationforStandardization)andIEC(theInternationalElectrotechnical
Commission)formthespecializedsystemforworldwidestandardization.Nationalbodiesthatare
membersofISOorIECparticipateinthedevelopmentofInternationalStandardsthroughtechnical
committeesestablishedbytherespectiveorganizationtodealwithparticularfieldsoftechnicalactivity.
ISOandIECtechnicalcommitteescollaborateinfieldsofmutualinterest.Otherinternationalorganizations,
governmentalandnon-governmental,inliaisonwithISOandIEC,alsotakepartinthework.
Theproceduresusedtodevelopthisdocumentandthoseintendedforitsfurthermaintenanceare
describedintheISO/IECDirectives,Part1.Inparticular,thedifferentapprovalcriterianeededforthe
differenttypesofdocumentshouldbenoted.Thisdocumentwasdraftedinaccordancewiththeeditorial
rulesoftheISO/IECDirectives,Part2(seewww.iso.org/directivesorwww.iec.ch/mem-
bers_experts/refdocs).
Attentionisdrawntothepossibilitythatsomeoftheelementsofthisdocumentmaybethesubjectof
patentrights.ISOandIECshallnotbeheldresponsibleforidentifyinganyorallsuchpatentrights.Details
ofanypatentrightsidentifiedduringthedevelopmentofthedocumentwillbeintheIntroductionand/or
ontheISOlistofpatentdeclarationsreceived(seewww.iso.org/patents),ortheIEClistofpatent
declarationsreceived(seepatents.iec.ch).
Anytradenameusedinthisdocumentisinformationgivenfortheconvenienceofusersanddoesnot
constituteanendorsement.
Foranexplanationofthevoluntarynatureofstandards,themeaningofISOspecifictermsandexpressions
relatedtoconformityassessment,aswellasinformationaboutISO’sadherencetotheWorldTrade
Organization(WTO)principlesintheTechnicalBarrierstoTrade(TBT)seewww.iso.org/iso/fore-
word.html.IntheIEC,seewww.iec.ch/understanding-standards.
ThisdocumentwaspreparedbyTechnicalCommitteeISO/IECJTC1,Informationtechnology,Subcom-
mitteeSC32,Datamanagementandinterchange.
ThisfirsteditionofISO/IEC19075-8cancelsandreplacesISO/IECTR19075-8:2019.
ThisdocumentisintendedtobeusedinconjunctionwiththefollowingeditionsofthepartsoftheISO/IEC
9075series:
— ISO/IEC9075-1,sixtheditionorlater,
— ISO/IEC9075-2,sixtheditionorlater,
— ISO/IEC9075-3,sixtheditionorlater,
— ISO/IEC9075-4,seventheditionorlater,
— ISO/IEC9075-9,fiftheditionorlater,
— ISO/IEC9075-10,fiftheditionorlater,
— ISO/IEC9075-11,fiftheditionorlater,
— ISO/IEC9075-13,fiftheditionorlater,
— ISO/IEC9075-14,sixtheditionorlater,
— ISO/IEC9075-15,secondeditionorlater,
— ISO/IEC9075-16,firsteditionorlater.
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ISO/IEC19075-8:2021(E)
AlistofallpartsintheISO/IEC19075seriescanbefoundontheISOandIECwebsites.
Anyfeedbackorquestionsonthisdocumentshouldbedirectedtotheuser’snationalstandardsbody.A
completelistingofthesebodiescanbefoundatwww.iso.org/members.htmlandwww.iec.ch/-
national-committees.
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ISO/IEC19075-8:2021(E)
Introduction
ThisdocumentdescribesthedefinitionanduseofmultidimensionalarraysinSQL.Multidimensional
arraysrepresentacoreunderlyingstructureofmanifoldscienceandengineeringdata.Itisgenerally
recognizedtoday,therefore,thatarrayshaveanessentialroleinBigDataandshouldbecomeanintegral
partoftheoveralldatatypeorchestrationininformationsystems.Thisdocumentdiscussesthesyntax
andsemanticsofoperationsontheMD-arraydatatypedefinedinISO/IEC9075-15.
Theorganizationofthisdocumentisasfollows:
1) Clause1,“Scope”,specifiesthescopeofthisdocument.
2) Clause2,“Normativereferences”,identifiesstandardsthatarereferencedbythisdocument.
3) Clause3,“Termsanddefinitions”,definesthetermsanddefinitionsusedinthisdocument.
4) Clause4,“Multidimensionalarrays(MDA)concepts”,introducestheconceptofMultidimensional
Arrays.
5) Clause5,“SQL/MDAdatamodel”,introducesthedatamodel.
6) Clause6,“SQL/MDAoperations”,coversthesupportedoperationsonMD-arrays.
7) Clause7,“Remotesensingexample”,illustratesthesupportedfunctionalitythroughrealisticexamples.
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ISO/IEC19075-8:2021(E)
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INTERNATIONAL STANDARD ISO/IEC 19075-8:2021(E)
Informationtechnology—GuidancefortheuseofdatabaselanguageSQL—
Part8:
Multidimensionalarrays
1 Scope
ThisdocumentdescribesthedefinitionanduseofmultidimensionalarraysinSQL.Multidimensional
arraysrepresentacoreunderlyingstructureofmanifoldscienceandengineeringdata.Itisgenerally
recognizedtoday,therefore,thatarrayshaveanessentialroleinBigDataandshouldbecomeanintegral
partoftheoveralldatatypeorchestrationininformationsystems.Thisdocumentdiscussesthesyntax
andsemanticsofoperationsontheMD-arraydatatypedefinedinISO/IEC9075-15.
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ISO/IEC19075-8:2021(E)
2 Normativereferences
Thefollowingdocumentsarereferredtointhetextinsuchawaythatsomeoralloftheircontentconsti-
tutesrequirementsofthisdocument.Fordatedreferences,onlytheeditioncitedapplies.Forundated
references,thelatesteditionofthereferenceddocument(includinganyamendments)applies.
ISO/IEC9075-1,Informationtechnology—Databaselanguages—SQL—Part1:Framework
(SQL/Framework)
ISO/IEC9075-2,Informationtechnology—Databaselanguages—SQL—Part2:Foundation
(SQL/Foundation)
ISO/IEC9075-15,Informationtechnology—Databaselanguages—SQL—Part15:Multidimensional
Arrays(SQL/MDA)
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ISO/IEC19075-8:2021(E)
3 Termsanddefinitions
Forthepurposesofthisdocument,thefollowingtermsanddefinitionsapply.
ISOandIECmaintainterminologicaldatabasesforuseinstandardizationatthefollowingaddresses:
— IECElectropedia:availableathttp://www.electropedia.org/
— ISOOnlinebrowsingplatform:availableathttp://www.iso.org/obp
3.1
coordinate
non-emptyorderedlistofintegers
3.2
cardinality
numberofelementsinanMD-array
3.3
MD-array
orderedcollectionofelementsofthesametypeassociatedwithanMD-extentwhereeachelementis1:1
associatedwithsomecoordinatewithinitsMD-extent
Note1toentry:AcoordinateiswithinanMD-extentifeverycoordinatevaluefromtheintegerlistis
greaterthanorequaltothelowerlimit,andlessthanorequaltotheupperlimitoftheMD-intervalof
theMD-axisatthepositionintheMD-extentasthecoordinatevaluehaswithinthecoordinate
3.4
MD-axis
namedMD-interval
3.5
MD-dimension
numberofMD-axesintheMD-extentofanMD-array
Note1toentry:Alsoknownas“rank”outsideofSQL/MDA
3.6
MD-extent
non-emptyorderedcollectionofMD-axeswithnoduplicatenames
3.7
MD-interval
integerintervalgivenbyapairoflowerandupperintegerlimitssuchthatthelowerlimitislessthanor
equaltotheupperlimit;theintervalisclosed,i.e.,,bothlimitsarecontainedinit
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ISO/IEC19075-8:2021(E)
4 Multidimensionalarrays(MDA)concepts
4.1 Contextofmultidimensionalarrays
TherequirementsforthematerialdiscussedinthisdocumentshallbeasspecifiedinISO/IEC9075-1
andISO/IEC9075-15.
4.2 Concept
Thephrase“(Multidimensional)array,rasterdata”isusedtorefertoarraysgenerally,incontrasttothe
MD-arraytermconfinedtotherealmofSQL/MDA.Itisnottobeconfusedwiththeterm“array”inISO/IEC
9075-2.ThisdocumentusesthetermARRAYfortheoriginalSQLarraycollectiontype.
Thearrayconceptisasimpleandefficientdatarepresentationthatfindsitsuseinawidearrayoffields,
business-relatedaswellasscientificandengineering.Manysensors,images,imagetime-series,simulation
processes,statisticalmodels,andsoon,producerawdatathatcanimmediatelybeclassifiedasarray
data.Thesedatamaybenaturallyarrangedalongmorethanoneaxis:positionandtime,forexample.
Amultidimensionalarray(MDA)isasetofelementsorderedinamultidimensionalspace.Thespace
consideredhereisdiscretized(alsocalledrasterizedorgridded),thatis,onlyintegercoordinatesare
admittedaspositionsoftheindividualarrayelements.Thenumberofintegersneededtorefertoapar-
ticularpositioninthisspaceisthearray’sdimension(sometimesalsoreferredtoasitsdimensionality).
Anelementcanbeasinglevalue(suchasanintensityvalueincaseofgreyscaleimages)oracomposite
value(suchasintegertriplesforthered,green,andbluecomponentsofatrue-colorimage).Allelements
ofanarraysharethesamestructure,referredtoasthearray’selementtype.
4.3 WhyconsidersupportforMDAinSQL?
Largemultidimensionalarraysinparticularrepresentaprevalentdatatypeacrossmostscientificdomains,
withexamplesincluding1-Dsensordata,2-Dsatelliteimagesandmicroscopescans,3-Dx/y/timage
time-seriesandx/y/zvoxelmodels,aswellas4-Dand5-Dclimatemodels.
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ISO/IEC19075-8:2021(E)
4.3 WhyconsidersupportforMDAinSQL?
Figure1—Aerialgreyscaleimageofsize1024x1024(SanDiego)
Inarrayterms,theimageinFigure1,“Aerialgreyscaleimageofsize1024x1024(SanDiego)”,isa2-
2
dimensionalarrayofunsigned8-bitintegerelementspositionedatcoordinatesin{0,1,.,1023} space.
Arraysrarelyoccurisolatedinpracticeandaretypicallyornamentedwithmetadataandembeddedin
largeroverallinformationstructures.Supportingtheminnarrowlyspecializedadhoctoolsordedicated
arrayDBMSisthusinsufficientwhenitcomestobuildingmodern,complexservicesandapplications.
ThissuggeststhatintegrationofarrayqueryingintoastandardizedframeworklikeSQLisalogicalnext
stepthatwillbenefitthecommunitiesdealingwithmultidimensionalarraydatainonewayortheother.
SQLhashadbasicsupportfor1-dimensionalarrayssince1999.Insteadofattemptingtoextendthe
existing1-dimensionalarraymodeltoaddresstheneedsofmultidimensionalarraymanipulation,
SQL/MDAaddressesthoseneedswithanewfeaturesetintegratedintoSQL.
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ISO/IEC19075-8:2021(E)
4.4 Arrayrepresentations
4.4 Arrayrepresentations
Theencodinganddecodingfunctionsemanticsforotherexternalrepresentationsareimplementation-
defined.ExamplesmayincludedatainsuchrepresentationsasPDF,JPEG,PNG,andXML.
4.5 UsecasesforMDAsupportinSQL
4.5.1 Theusecases
Thequestionposedbythisusecaseis“HowisarraydataacquiredusingSQL?”
FollowingaretheprimaryusecasesthatsupportformultidimensionalarraysintheSQL-environment
isrequiredtosatisfy.
— Arraydataingestionandstorage.
— Integratedqueryingofarrayandrelationaldata,
— Updatingstoredarraydata.
— Exportingarrays.
ThefollowingSubclausesdiscusstheseusecasesingreaterdetail,andhowSQL/MDAaddressesthem.
4.5.2 Arraydataingestionandstorage
Thequestionposedbythisusecaseis“HowisarraydataacquiredusingSQL?”
AsdiscussedearlierinSubclause4.4,“Arrayrepresentations”,arraysexistinawidevarietyofformats.
InordertoworkwiththeminagenericwayinSQL,itisnecessarytobuildanabstractdatamodelthat
fitswiththeSQLphilosophy.TheMD-arrayasdefinedbySQL/MDAprovidesexactlysuchadatamodel,
implementedasanewattributetypeMDARRAY.Ingestionofarraydataencodedinanexternalformat
intoSQLinvolvestransformingitordecodingitintoaninstanceoftheinternalMD-arraydatamodel,
whichistheninsertedintoanMDARRAYcolumnofanappropriatetype.
What“decode”meansinpracticedependsonmanyfactors,includingthedataformat,thedetailsof
physicalstorageofMD-arraysinaspecificDBMS,systemarchitecture,etc.Thisdocumentandthestandard
donotdiveintothesetechnicaldetailsofarraydataingestionbeyondprovidingadefaultspecification
forJSONencodedarraysandasuitableinterfaceforimplementationstoattachtheiringestionextensions.
Itisworthdiscussingthestoragedatamodelhere.Theseveralpossibilitiesare:
— MD-arrayasafirst-classobjectinthesamewaythatSQLtablesare.
— DirectmappingofSQLtablesintoMD-arrays.
— Storewithinanopaquedatatype(SQLstringorLargeObjectforexample).
— Adedicatedcolumndatatypewithwell-definedsemantics.
MD-arrayisasimpledatastructuredefinedbyalistofMD-axes,eachspecifyinganame,lowerandupper
limits,pairedwithanelementtype.Thisledtoadoptionofthelastoption,followingtheexampleof
ARRAYandMULTISETcollectiondatatypes.Datatransformationishandledduringingestionwithspecial
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ISO/IEC19075-8:2021(E)
4.5 UsecasesforMDAsupportinSQL
functions,allowingworkingwithvalueswithclearlydefinedsemanticswithintheSQL-environment.It
isminimallyintrusivetotheSQLstandard,whileitneverthelesssupportsalloftherequirementsidentified
inthisdocument.
4.5.3 Integratedqueryingofarrayandrelationaldata
AswasintroducedinthepreviousSubclause,MD-arraysarestoredwithinanewcollectiondatatype
MDARRAYthatismanipulatedthroughafunctionalandoperationalinterfacedescribedinthisdocument.
ThisissimilartotheexistingARRAYandMULTISETcollectiondatatypes,exceptthattheoperationset
isricher.Integrationwithotherdatatypesisseamless(e.g.,,multiplyingthevaluesofallelementsofa
numericMD-arraycolumnAwiththesinglevalueofanumericcolumnCissimplyA * C),andthegeneral
SQLquerymechanicsareunchanged.Inaddition,itispossibletogenerateanSQLtablefromanMD-array
andvice-versa,anMD-arrayfromanSQLtablewiththeappropriatestructure.
4.5.4 Updatingstoredarraydata
Read-onlyaccesstoMD-arraydataisclearlyinsufficient.Arraydataisveryoftencontinuouslyandregularly
produced,e.g.,,atemperaturesensortakingareadingeveryhour,orasatelliteperiodicallytakingearth-
observationimagesasitorbitsaroundtheEarth.Inaddition,asinglearraycanexceedterabytesinsize,
andforpracticalreasonsitmightbesplitintomultiplesmallerarrays;ingestingthemallintoasingle
MD-arraycolumnrequirespiece-wiseextensionandupdatingofthecolumn.Therefore,SQL/MDAallows
updatingofentireMD-arrayvalues,aswellasspecificsubsetsofanMD-array.
4.5.5 Exportingarrays
FrequentlytheresultofoperationsonMD-arrayswillbeanMDarray,whichneedstobeexportedusing
someexternalrepresentation.Thisisthecounterpartofarraydataingestiondiscussedpreviouslyin
Subclause4.5.2,“Arraydataingestionandstorage”.
4.6 Non-Usecases:Directaccesstoexternalarraydata
AllaccesstoarraydatarequiresthatthearraydataisfirstimportedintotheSQLenvironment.Inorder
toqueryexternalarraydatausingSQL,applicationsarerequiredtoaccessexternalarraysthemselves,
theninsertthosedataintoMD-arrayvalues,perhapsbyusingtheMDDECODEfunction.
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ISO/IEC19075-8:2021(E)
5 SQL/MDAdatamodel
5.1 Datamodelconcepts
TheSQL/MDAmodelisessentiallyrepresentedbytheconceptofMD-array.Itisnecessarytoclearly
distinguishbetweenarrayvalues“outside”theDBMS,andtheiranalogs“inside”theDBMS.Thethefol-
lowingconventionisused:
— Theterms“array”,“multidimensionalarray”,and“MDA”refertoarrayvaluesexternaltotheSQL-
environment,encodedinaparticularformatlikeTIFF,netCDF,HDF5,JSON,etc.
— Theterms“MD-array”and“SQL/MDA”refertoconstructswithintheSQL-environment.
Therelationshipbetween“MDA”and“SQL/MDA”isillustratedinFigure2,“RelationshipsbetweenMDA
andSQL/MDA”.
Figure2—RelationshipsbetweenMDAandSQL/MDA
5.2 MD-array
MD-arrayvaluesareinputsofallSQL/MDAoperations,andmostoftentheoutputs.Figure3,“The
structureofanMD-arrayvalueillustratedonasample3x3array”,showsthestructureofasampleMD-
arrayvalue.
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ISO/IEC19075-8:2021(E)
5.2 MD-array
Figure3—ThestructureofanMD-arrayvalueillustratedonasample3x3array
5.3 MD-arraytypedefinition
5.3.1 Typedefinitionconcepts
ThedefinitionofanMD-array(seeClause3,“Termsanddefinitions”)isagoodstartingpointinorderto
understandwhatcomponentsareneededforthetypeofanMD-array:
1) “AnMD-arrayisanorderedcollectionofelementsofthesametype.”So,onethingneededtospecify
thetypeofanMD-arrayisthetypeofitselements,morespecificallyknownastheelementtype.This
isnodifferentfromtheexistingARRAYandMULTISET.
2) “.whereeachelementis1:1associatedwithsomecoordinatewithinitsMD-extent.”Hence,the
otherpartneededisanMD-extentthatdelimitsthecoordinatesoftheelementsinanMD-array.
5.3.2 Elementtype
MD-arraysstandoutfromthespectrumofcollectiontypesinthatthestoragelocationofanelementcan
bederiveddirectlyfromitscoordinates,whichmakesstorageandaccessparticularlyefficient.This
requiresthatallelementsareofthesamelength.Therefore,variable-sizecollectionelementslikesets
andmultisetsdonotqualifyaselementtypes.MD-arraysaselementtypeisdisallowedaswellforthe
followingreasons:
1) NestinganMD-arrayofMD-dimensiond intoanMD-arrayofMD-dimensiond canequivalentlybe
1 2
modeledasasingleMD-arrayofMD-dimensiond+d.
1 2
2) Itkeepsthedatamodelsimplerandmoreconsistentinthatallcollectiontypesaredisallowed,and
nohandlingspecificallyofMD-arraysisneeded.
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ISO/IEC19075-8:2021(E)
5.3 MD-arraytypedefinition
Allinall,anySQLdatatypeisallowedtobeanelementtypeofanMD-array,exceptforcollection-con-
tainingtypes.AdatatypeTYiscollection-containingifexactlyoneofthefollowingconditionsistrue:
— TYisacollectiontype.
— TYisarowtype,andthedeclaredtypeofsomefieldofTYisacollection-containingtype.
— TYisdistincttype,andthesourcetypeofTYisacollection-containingtype.
— TYisastructuredtypeandthedeclaredtypeofsome
...