<s>
In	O
computer	O
programming	O
contexts	O
,	O
a	O
data	B-Algorithm
cube	I-Algorithm
(	O
or	O
datacube	B-Algorithm
)	O
is	O
a	O
multi-dimensional	O
(	O
"	O
n-D	O
"	O
)	O
array	O
of	O
values	O
.	O
</s>
<s>
Typically	O
,	O
the	O
term	O
data	B-Algorithm
cube	I-Algorithm
is	O
applied	O
in	O
contexts	O
where	O
these	O
arrays	O
are	O
massively	O
larger	O
than	O
the	O
hosting	O
computer	O
's	O
main	O
memory	O
;	O
examples	O
include	O
multi-terabyte/petabyte	O
data	O
warehouses	O
and	O
time	O
series	O
of	O
image	O
data	O
.	O
</s>
<s>
The	O
data	B-Algorithm
cube	I-Algorithm
is	O
used	O
to	O
represent	O
data	O
(	O
sometimes	O
called	O
facts	O
)	O
along	O
some	O
dimensions	O
of	O
interest	O
.	O
</s>
<s>
For	O
example	O
,	O
in	O
online	B-Application
analytical	I-Application
processing	I-Application
(	O
OLAP	B-Application
)	O
such	O
dimensions	O
could	O
be	O
the	O
subsidiaries	O
a	O
company	O
has	O
,	O
the	O
products	O
the	O
company	O
offers	O
,	O
and	O
time	O
;	O
in	O
this	O
setup	O
,	O
a	O
fact	O
would	O
be	O
a	O
sales	O
event	O
where	O
a	O
particular	O
product	O
has	O
been	O
sold	O
in	O
a	O
particular	O
subsidiary	O
at	O
a	O
particular	O
time	O
.	O
</s>
<s>
Even	O
though	O
it	O
is	O
called	O
a	O
cube	O
(	O
and	O
the	O
examples	O
provided	O
above	O
happen	O
to	O
be	O
3-dimensional	O
for	O
brevity	O
)	O
,	O
a	O
data	B-Algorithm
cube	I-Algorithm
generally	O
is	O
a	O
multi-dimensional	O
concept	O
which	O
can	O
be	O
1-dimensional	O
,	O
2-dimensional	O
,	O
3-dimensional	O
,	O
or	O
higher-dimensional	O
.	O
</s>
<s>
Fortran	B-Application
offers	O
arbitrarily-indexed	O
1-D	O
arrays	O
and	O
arrays	O
of	O
arrays	O
,	O
which	O
allows	O
the	O
construction	O
of	O
higher-dimensional	O
arrays	O
,	O
up	O
to	O
15	O
dimensions	O
.	O
</s>
<s>
APL	B-Language
supports	O
n-D	O
arrays	O
with	O
a	O
rich	O
set	O
of	O
operations	O
.	O
</s>
<s>
All	O
these	O
have	O
in	O
common	O
that	O
arrays	O
must	O
fit	O
into	O
the	O
main	O
memory	O
and	O
are	O
available	O
only	O
while	O
the	O
particular	O
program	O
maintaining	O
them	O
(	O
such	O
as	O
image	B-Algorithm
processing	I-Algorithm
software	O
)	O
is	O
running	O
.	O
</s>
<s>
Examples	O
include	O
MDX	B-Language
for	O
statistical	O
(	O
in	O
particular	O
,	O
business	O
)	O
data	O
,	O
Hierarchical	B-Application
Data	I-Application
Format	I-Application
for	O
general	O
scientific	O
data	O
,	O
and	O
TIFF	O
for	O
imagery	O
.	O
</s>
<s>
In	O
1992	O
,	O
Peter	O
Baumann	O
introduced	O
management	O
of	O
massive	O
data	B-Algorithm
cubes	I-Algorithm
with	O
high-level	O
user	O
functionality	O
combined	O
with	O
an	O
efficient	O
software	O
architecture	O
.	O
</s>
<s>
Datacube	B-Algorithm
operations	O
include	O
subset	O
extraction	O
,	O
processing	O
,	O
fusion	O
,	O
and	O
in	O
general	O
queries	O
in	O
the	O
spirit	O
of	O
data	B-Language
manipulation	I-Language
languages	I-Language
like	O
SQL	B-Language
.	O
</s>
<s>
Some	O
years	O
after	O
,	O
the	O
data	B-Algorithm
cube	I-Algorithm
concept	O
was	O
applied	O
to	O
describe	O
time-varying	O
business	O
data	O
as	O
data	B-Algorithm
cubes	I-Algorithm
by	O
Jim	O
Gray	O
,	O
et	O
al.	O
,	O
and	O
by	O
Venky	O
Harinarayan	O
,	O
Anand	O
Rajaraman	O
and	O
Jeff	O
Ullman	O
which	O
rank	O
among	O
the	O
top	O
500	O
most	O
cited	O
computer	O
science	O
articles	O
over	O
a	O
25-year	O
period	O
.	O
</s>
<s>
Datacube	B-Algorithm
Inc	O
.	O
was	O
an	O
image	B-Algorithm
processing	I-Algorithm
company	O
selling	O
hardware	B-Architecture
and	O
software	O
applications	O
for	O
the	O
PC	B-Device
market	I-Device
in	O
1996	O
,	O
however	O
without	O
addressing	O
data	B-Algorithm
cubes	I-Algorithm
as	O
such	O
.	O
</s>
<s>
The	O
EarthServer	O
initiative	O
has	O
established	O
geo	O
data	B-Algorithm
cube	I-Algorithm
service	O
requirements	O
.	O
</s>
<s>
In	O
2018	O
,	O
the	O
ISO	B-General_Concept
SQL	B-Language
database	I-Language
language	O
was	O
extended	O
with	O
data	B-Algorithm
cube	I-Algorithm
functionality	O
as	O
"	O
SQL	B-Language
--	O
Part	O
15	O
:	O
Multi-dimensional	O
arrays	O
(	O
SQL/MDA	O
)	O
"	O
.	O
</s>
<s>
Web	B-Application
Coverage	I-Application
Processing	I-Application
Service	I-Application
is	O
a	O
geo	O
data	B-Algorithm
cube	I-Algorithm
analytics	O
language	O
issued	O
by	O
the	O
Open	O
Geospatial	O
Consortium	O
in	O
2008	O
.	O
</s>
<s>
In	O
addition	O
to	O
the	O
common	O
data	B-Algorithm
cube	I-Algorithm
operations	O
,	O
the	O
language	O
knows	O
about	O
the	O
semantics	O
of	O
space	O
and	O
time	O
and	O
supports	O
both	O
regular	O
and	O
irregular	O
grid	O
data	B-Algorithm
cubes	I-Algorithm
,	O
based	O
on	O
the	O
concept	O
of	O
coverage	B-General_Concept
data	I-General_Concept
.	O
</s>
<s>
An	O
industry	O
standard	O
for	O
querying	O
business	O
data	B-Algorithm
cubes	I-Algorithm
,	O
originally	O
developed	O
by	O
Microsoft	O
,	O
is	O
MultiDimensional	B-Language
eXpressions	I-Language
.	O
</s>
<s>
Many	O
high-level	O
computer	O
languages	O
treat	O
data	B-Algorithm
cubes	I-Algorithm
and	O
other	O
large	O
arrays	O
as	O
single	O
entities	O
distinct	O
from	O
their	O
contents	O
.	O
</s>
<s>
These	O
languages	O
,	O
of	O
which	O
Fortran	B-Application
,	O
APL	B-Language
,	O
IDL	B-Language
,	O
NumPy	B-Application
,	O
PDL	B-Language
,	O
and	O
S-Lang	B-Device
are	O
examples	O
,	O
allow	O
the	O
programmer	O
to	O
manipulate	O
complete	O
film	O
clips	O
and	O
other	O
data	O
en	O
masse	O
with	O
simple	O
expressions	O
derived	O
from	O
linear	B-Language
algebra	I-Language
and	O
vector	O
mathematics	O
.	O
</s>
<s>
Some	O
languages	O
(	O
such	O
as	O
PDL	B-Language
)	O
distinguish	O
between	O
a	O
list	O
of	O
images	O
and	O
a	O
data	B-Algorithm
cube	I-Algorithm
,	O
while	O
many	O
(	O
such	O
as	O
IDL	B-Language
)	O
do	O
not	O
.	O
</s>
<s>
Array	O
DBMSs	O
(	O
Database	O
Management	O
Systems	O
)	O
offer	O
a	O
data	O
model	O
which	O
generically	O
supports	O
definition	O
,	O
management	O
,	O
retrieval	O
,	O
and	O
manipulation	O
of	O
n-dimensional	O
data	B-Algorithm
cubes	I-Algorithm
.	O
</s>
<s>
This	O
database	O
category	O
has	O
been	O
pioneered	O
by	O
the	O
rasdaman	B-Application
system	O
since	O
1994	O
.	O
</s>
<s>
Generally	O
,	O
any	O
kind	O
of	O
axis	O
can	O
be	O
combined	O
with	O
any	O
other	O
into	O
a	O
data	B-Algorithm
cube	I-Algorithm
.	O
</s>
<s>
In	O
mathematics	O
,	O
a	O
one-dimensional	O
array	O
corresponds	O
to	O
a	O
vector	O
,	O
a	O
two-dimensional	O
array	O
resembles	O
a	O
matrix	B-Architecture
;	O
more	O
generally	O
,	O
a	O
tensor	B-Device
may	O
be	O
represented	O
as	O
an	O
n-dimensional	O
data	B-Algorithm
cube	I-Algorithm
.	O
</s>
<s>
For	O
a	O
time	O
sequence	O
of	O
color	O
images	O
,	O
the	O
array	O
is	O
generally	O
four-dimensional	O
,	O
with	O
the	O
dimensions	O
representing	O
image	O
X	O
and	O
Y	O
coordinates	O
,	O
time	O
,	O
and	O
RGB	O
(	O
or	O
other	O
color	B-Algorithm
space	I-Algorithm
)	O
color	O
plane	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
EarthServer	O
initiative	O
unites	O
data	O
centers	O
from	O
different	O
continents	O
offering	O
3-D	O
x/y/t	O
satellite	O
image	O
timeseries	O
and	O
4-D	O
x/y/z/t	O
weather	O
data	O
for	O
retrieval	O
and	O
server-side	O
processing	O
through	O
the	O
Open	O
Geospatial	O
Consortium	O
WCPS	O
geo	O
data	B-Algorithm
cube	I-Algorithm
query	O
language	O
standard	O
.	O
</s>
<s>
A	O
data	B-Algorithm
cube	I-Algorithm
is	O
also	O
used	O
in	O
the	O
field	O
of	O
imaging	O
spectroscopy	O
,	O
since	O
a	O
spectrally-resolved	O
image	O
is	O
represented	O
as	O
a	O
three-dimensional	O
volume	O
.	O
</s>
<s>
Earth	O
observation	O
data	B-Algorithm
cubes	I-Algorithm
combine	O
satellite	O
imagery	O
such	O
as	O
Landsat	O
8	O
and	O
Sentinel-2	O
with	O
Geographic	B-Application
information	I-Application
system	I-Application
analytics	O
.	O
</s>
<s>
In	O
online	B-Application
analytical	I-Application
processing	I-Application
(	O
OLAP	B-Application
)	O
,	O
data	B-Algorithm
cubes	I-Algorithm
are	O
a	O
common	O
arrangement	O
of	O
business	O
data	O
suitable	O
for	O
analysis	O
from	O
different	O
perspectives	O
through	O
operations	O
like	O
slicing	O
,	O
dicing	O
,	O
pivoting	O
,	O
and	O
aggregation	O
.	O
</s>
