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Changes between Version 24 and Version 25 of Grass7/TemporalGISAlgebra

Timestamp:: 10/20/14 12:22:50 (10 years ago)
Author:: mastho
Comment:: --

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Grass7/TemporalGISAlgebra

-              v24
+              v25
 means: select all parts of space time time dataset A that are not equal to B and store it in space time dataset (STDS) C.
 We have defined the operator {"topological relations", "temporal selection operator"} to perform selection with
+We have defined the operator {"selection operator", "topological relations", "temporal operator"} to perform selection with
 different temporal topology relations. Examples:
 {{{
 C = A {equals,:} B is exactly the same as C = A : B
 C = A {equals,!:} B is exactly the same as C = A !: B
+C = A {:,equals} B is exactly the same as C = A : B
+C = A {!:,equals} B is exactly the same as C = A !: B
 }}}
 We can now define arbitrary topological relations using logical OR operator to connect them:
 {{{
 C = A {equals||during||overlaps,:} B
+C = A {:,equals|during|overlaps} B
 }}}
 Select all parts of A that are equal B, during B or overlaps B.
 …
 }}}
+==== The hash operator ====
+It is of important interest how many maps are located in the time interval of a single map when processing two space time datasets.
+For this reason the hash operator '''#''' was introduced. In addition to the hash operator the temporal relation can be specified
+that should be analysed.
+Example:
+{{{
+C = if(equal, A{contains,#}B > 2, A{contains,:}B)
+}}}
+This expression selects all maps from A that temporally contains at least 2 maps from B and stores them in space time dataset C.
+The leading '''equal''' statement in the '''if''' condition specifies the temporal relation between the if and then part of the if expression.
+This is very important, so we do not need to specify a global time reference (a space time dataset) for temporal processing.
+==== Temporal Operators ====
+The temporal algebra defines temporal operators that can be combined later with spatial operators to perform spatio-temporal operations.
+The temporal operators process the time instances and intervals of temporal related maps.
+{{{
+AND             &       Intersection
+OR              |       Union
+DISJOINT OR     +       Disjoint union
+LEFT REFERENCE  =       Use the time stamp of the left space time dataset
+}}}
+For example we can compute the intersection, union or disjoint union from time stamps of maps
+that temporally overlap, or we can just keep the time stamp of the left STDS.
+All supported operators and functions are documented below.
+== Temporal Vector Algebra ==
+The temporal vector algebra includes all functions from the temporal algebra
+and adds spatial Boolean and buffer operations that can be performed on temporal related vector maps that are registered in
+space time vector datasets.
+=== Spatio-Temporal Operators ===
+These are the spatial operators that are supported:
+{{{
+AND             &       Intersection            (v.overlay operator=and)
+OR              |       Union                   (v.overlay operator=or)
+DISJOINT OR     +       Disjoint union          (v.patch)
+XOR             ^       Symmetric difference    (v.overlay operator=xor)
+NOT             ~       Complement              (v.overlay operator=not)
+}}}
+We combine the temporal topology relations, the temporal operators and the spatial operators to create spatio-temporal operators:
+{{{
+{"list of temporal relations", "temporal operator" "spatial operator"}
+}}}
+The spatial operator can be used stand-alone. In this case the temporal topology relation "equal" and the temporal operator "left reference =" is assumed and used as default. This allows the convenient use of the spatial operators in case of space time vector datasets with equal time stamps.
+Example:
+Compute the spatial intersection between maps of STVDS A and B that are temporally equal,
+resulting spatial intersection maps are stored in C with time stamps from A:
+{{{
+C = A & B
+}}}
+Compute the spatio-temporal intersection between maps of STVDS A and B that temporally overlap,
+resulting spatial intersection maps are stored in C with new time stamps resulting from temporal intersection:
+{{{
+C = A {overlap,&&} B
+}}}
+Perform a spatial union and a temporal disjoint union between all maps of STVDS A
+and B that are temporally equal or overlap and are later than 1990,
+resulting spatial union maps are stored in C with new time stamps resulting from temporal disjoint union:
+{{{
+C = if(start_year() > 1990, A {equal,overlap,+|} B)
+}}}
+The temporal vector algebra provides point, line and area buffer functions in addition to the operators.
+All supported operators and functions are documented below.
+== Temporal Raster Algebra ==
+The temporal raster algebra uses all operators and functions of the temporal
+algebra and adds a subset of the arithmetic operators and functions from r.mapcalc.
+New spatio-temporal operators are defined that include temporal topology relations,
+temporal operators and arithmetic operators.
+Examples:
+Create the sum of all maps from STRDS A and B that have equal time stamps and store the new maps in STRDS C:
+{{{
+C = A + B
+}}}
+Same expression with explicit definition of the temporal topology relation and temporal operators:
+{{{
+C = A {equal,=+} B
+}}}
+Select all cells from STRDS B with equal temporal relations to STRDS A, if the cells
+of A are in the range of [100.0, 1600] of time intervals that have more then 30 days (Jan, Mar, Mai, Jul, Aug, Oct, Dec):
+{{{
+C = if(A > 100 && A < 1600 && td(A) > 30, B)
+}}}
+Same expression with explicit definition of the temporal topology relation and temporal operators:
+{{{
+C = if(equal, A > 100 && A < 1600 {equal,&&} td(A) > 30, B)
+}}}
+Compute the recharge in meter per second for all cells of precipitation STRDS "Prec"
+if the mean temperature specified in STRDS "Temp" is higher than 10 degrees. Computation is performed if STRDS "Prec" and "Temp" have equal time stamps. The number of days or fraction of days per interval is computed using the td() function that has as argument the STRDS "Prec":
+{{{
+C = if(Temp > 10.0, Prec / 3600.0 /24.0 / td(Prec))
+}}}
+Same expression with explicit definition of the temporal topology relation and temporal operators:
+{{{
+C = if(equal, Temp > 10.0, Prec / 3600.0 / 24.0 {equal,=/} td(Prec))
+}}}
+Compute the mean value of all maps from STRDS A that are located during time intervals of STRDS B if more than one map of A is contained in an interval of B, use A otherwise, the resulting time intervals are either from B or A:
+{{{
+C = if(B {contain,#} A > 1, (B {contain, =+} A - B) / (B {contain,#} A), A)
+}}}
+Same expression with explicit definition of the temporal topology relation and temporal operators:
+{{{
+C = if(equal, B {contain,#} A > 1, (B {contain, =+} A {equal, =-} B) {equal,=/} (B {contain,#} A), A)
+}}}
+All supported operators and functions are documented below.
+= Overview of all supported spatio-temporal operators and functions =
+== Temporal topology relations ==
+{{{
+equals            A ------
+                  B ------
+during            A  ----
+                  B ------
+contains          A ------
+                  B  ----
+starts            A ----
+                  B ------
+started           A ------
+                  B ----
+finishs           A   ----
+                  B ------
+finished          A ------
+                  B   ----
+precedes          A ----
+                  B     ----
+follows           A     ----
+                  B ----
+overlapped        A   ------
+                  B ------
+overlaps          A ------
+                  B   ------
+over              booth overlaps and overlapped
+}}}
+The relations must be read A is related to B, like
+- A equals B
+- A is during B
+- A contains B
+Topological relations must be specified in {} parentheses
+{{{
+A {equals} B
+}}}
+Topological relations are always combined with other
+temporal operators in the {} parentheses
+== Temporal operators ==
+Temporal operators that work on time intervals
+and instances of maps in space time datasets:
+'''Intersection &  '''
+ Examples with time intervals a and b:
+{{{
+ c <- a & b
+  a ------
+  b  ----
+  c  ----
+  a ----
+  b   ----
+  c   --
+  a ---
+  b    ---
+  c
+}}}
+'''Union |'''
+ Examples with time intervals a and b:
+{{{
+c <- a | b
+  a ------
+  b  ----
+  c ------
+  a ----
+  b   ----
+  c ------
+  a ---
+  b    ---
+  c ------
+  a ---
+  b     ---
+  c
+}}}
+'''Disjoint Union +'''
+ Examples with time intervals a and b:
+{{{
+ c <- a + b
+  a ------
+  b  ----
+  c ------
+  a ----
+  b   ----
+  c ------
+  a ---
+  b    ---
+  c ------
+  a ---
+  b     ---
+  c -------
+}}}
+'''Left Reference ='''
+ Examples with time intervals a and b:
+{{{
+ c <- a = b
+  a ------
+  b  ----
+  c ------
+  a ----
+  b   ----
+  c ----
+  a ---
+  b    ---
+  c ---
+  a ---
+  b     ---
+  c ---
+}}}
+ The = operator ignores indexing operators for space
+ time datasets: A[i]
+Temporal selection operators to select parts of
+space time datasets:
+'''  Selection           :'''[[BR]]
+'''  Inverse selection  !:'''
+Temporal operators have no precedence.
+ Examples:
+ * Select all maps from space time dataset A that
+   have equal time intervals with space time dataset B
+   and store them in space time datasets C.
+{{{
+   C = A : B
+   C = A {:} B
+   C = A {equals,:} B
+}}}
+ * Select all maps from space time dataset A that
+   have unequal time intervals with space time dataset B
+   and store them in space time datasets C.
+{{{
+   C = A !: B
+   C = A {!:} B
+   C = A {equals,!:} B
+}}}
+ * Select all maps from space time dataset A that
+   are during time intervals of space time dataset B
+   and store them in space time datasets C.
+{{{
+   C = A {during,:} B
+}}}
+ * Select all maps from space time dataset A
+   that are during B and during C and during D.
+{{{
+   E = A {during,:} B {during,:} C {during,:} D
+}}}
+Operator number of maps in interval  [[BR]]
+'''Number of maps #'''
+Compute the number of maps from space time dataset B that are
+during the time intervals of maps from space time dataset A.
+{{{
+A{contains,#}B
+}}}
+This will return a list of integers (scalars) corresponding to the maps of
+A that contain maps from B.
+== Logical operators ==
+Logical operators:
+{{{
+Symbol  description             precedence
+  ==    equal                   3
+  !=    not equal               3
+  >     greater than            3
+  >=    greater than or equal   3
+  <     less than               3
+  <=    less than or equal      3
+  &&    and                     4
+  ||    or                      4
+}}}
+Combination of temporal and logical operators:
+{{{
+ -------------------------------------------------
+|   |  && |  || |  == |  != |  <= |  >= |  < |  > |
+|---|-----|-----|-----|-----|-----|-----|----|----|
+| & | &&& | &|| | &== | &!= | &<= | &>= | &< | &> |
+| | | |&& | ||| | |== | |!= | |<= | |>= | |< | |> |
+| + | +&& | +|| | +== | +!= | +<= | +>= | +< | +> |
+| = | =&& | =|| | === | =!= | =<= | =>= | =< | => |
+ -------------------------------------------- ----
+}}}
+== Temporal functions ==
+Note a and b can either be space time datasets or expressions.
+{{{
+if                      decision option
+==== Conditional statements ====
+Spatiotemporal operations can be evaluated within conditional statements.
+Note A and B can either be space time datasets or expressions.
+The temporal relationship between the conditions and the conclusions can be defined at the beginning of the if statement.
+The relationship between then and else conclusion must be always equal.
+{{{
+if conditions                         conclusion option                        temporal relations
   if(if, then, else)
+  if(x, a)              a if x not 0; temporal topological relation between if and then is equal
+  if(x, a, b)           a if x not 0, b otherwise; temporal topological relation between if, then and else is equal
+  if(topo, x, a)        a if x not 0; temporal topological relation between if and then is explicit specified by topo
+  if(topo, x, a, b)     a if x not 0, b otherwise; temporal topological relation between if, then and else is explicit specified by topo
+buff_t(a, size)         Buffer stds a with granule ("1 month" or 5)
+tshift(a, size)         Shift stds a with granule ("1 month" or 5)
+tsnap(a)                Snap time instances and intervals of stds a
+td(a)                   Returns a list of time intervals of stds a
+  if(conditions, A)                    A if conditions are True;              Topological relation between conditions(if) and conclusion(then) is equal.
+  if(conditions, A, B)                 A if conditions are True, B otherwise; Topological relation between conditions(if) and conclusions(then + else) is equal.
+  if(topologies, conditions, A)        A if conditions are True;              Topological relation between conditions(if) and conclusions(then) is explicit specified by topologies.
+  if(topologies, conditions, A, B)     A if conditions are True, B otherwise; Topological relation between conditions(if) and conclusions(then + else) is explicit specified by topologies.
+}}}
+The conditions are comparison expressions that are used to evaluate
+space time datasets. Specific values of temporal variables are
+compared by logical operators and evaluated for each map of the STDS.
+The supported logical operators:
+{{{
+Symbol  description
+  ==    equal
+  !=    not equal
+  >     greater than
+  >=    greater than or equal
+  <     less than
+  <=    less than or equal
+  &&    and
+  ||    or
+}}}
+Temporal functions:
+{{{
+td(A)                   Returns a list of time intervals of STDS A
 start_time()            Start time as HH::MM:SS
 …
 }}}
+Examples:
+  Select all maps from space time dataset A that have equal time stamps
+  with space time dataset B and C and are ealier that Jan. 1. 2005 and
+  store them in space time dataset D.
+{{{
+D = if(start_date() < "2005-01-01", A : B : C)
+}}}
+= Temporal Vector Algebra =
+Boolean vector operations:
+Additionally the number of maps in intervals can be computed and
+used in conditional statements with the hash (#) operator.
+==== The hash operator ====
+It is of important interest how many maps are located in the time interval of a single map when processing two space time datasets.
+For this reason the hash operator '''#''' was introduced. In addition to the hash operator the temporal relation can be specified
+that should be analysed.
+Example:
+{{{
+C = if({equal}, A{#,contains}B > 2, A{:,contains}B)
+}}}
+This expression selects all maps from A that temporally contains at least 2 maps from B and stores them in space time dataset C.
+The leading '''equal''' statement in the '''if''' condition specifies the temporal relation between the if and then part of the if expression.
+This is very important, so we do not need to specify a global time reference (a space time dataset) for temporal processing.
+== Temporal Vector Algebra ==
+The temporal vector algebra includes all functions from the temporal algebra
+and adds spatial Boolean and buffer operations that can be performed on temporal related vector maps that are registered in
+space time vector datasets.
+=== Spatio-Temporal Operators ===
+These are the spatial operators that are supported:
 {{{
 AND             &       Intersection            (v.overlay operator=and)
 …
 NOT             ~       Complement              (v.overlay operator=not)
 }}}
+Vector functions:
+{{{
+buff_p(a, size)         Buffer the points of all maps from space time vector dataset a with size
+buff_l(a, size)         Buffer the lines of all maps from space time vector dataset a with size
+buff_a(a, size)         Buffer the areas of all maps from space time vector dataset a with size
+}}}
+We combine the spatial operators, the temporal topology relations and the temporal operators to create spatio-temporal operators:
+{{{
+{"list of temporal relations", "temporal operator" "spatial operator"}
+}}}
+The spatial operator can be used stand-alone. In this case the temporal topology relation "equal" and the temporal operator "left reference =" is assumed and used as default. This allows the convenient use of the spatial operators in case of space time vector datasets with equal time stamps.
+Example:
+Compute the spatial intersection between maps of STVDS A and B that are temporally equal,
+resulting spatial intersection maps are stored in C with time stamps from A:
+{{{
+C = A & B
+}}}
+Compute the spatio-temporal intersection between maps of STVDS A and B that temporally overlap,
+resulting spatial intersection maps are stored in C with new time stamps resulting from temporal intersection:
+{{{
+C = A {&,overlap,&} B
+}}}
+Perform a spatial union and a temporal disjoint union between all maps of STVDS A
+and B that are temporally equal or overlap and are later than 1990,
+resulting spatial union maps are stored in C with new time stamps resulting from temporal disjoint union:
+{{{
+C = if(start_year(A) > 1990, A {|,equal|overlap,+} B)
+}}}
+The temporal vector algebra provides point, line and area buffer functions in addition to the operators.
+All supported operators and functions are documented below.
+== Temporal Raster Algebra ==
+The temporal raster algebra uses all operators and functions of the temporal
+algebra and adds a subset of the arithmetic operators and functions from r.mapcalc.
+New spatio-temporal operators are defined that include temporal topology relations,
+temporal operators and arithmetic operators.
 Examples:
+ * Create an intersection between all maps of space time dataset
+   A and B that have equal time stamps.
+{{{
+   C = A & B
+   C = A {&} B
+   C = A {=&} B
+   C = A {equals,=&} B
+}}}
+ * Question: Meeting of two animals that occur when the distance between two sea elephants is less than 10 meters?
+   Space time vector dataset A and B contains the measured positions and time instances/intervals of two sea elephants.
+   The granularity of the space time vector datasets is 1h. We create a new space time vector dataset C that contains the
+   spatio-temporal intersections of the positions of the sea elephants.
+{{{
+   C = buff_p(buff_t(A, "2 hours"), 5) {over||equals,&&} buff_p(buff_t(B, "2 hours"), 5)
+}}}
+== Combinations of temporal and vector operators ==
+{{{
+ ----------------------------
+|   |  & |  | |  ^ |  ~ |  + |
+|---|----|----|----|----|----|
+| & | && | &| | &^ | &~ | &+ |
+| | | |& | || | |^ | |~ | |+ |
+| + | +& | +| | +^ | +~ | ++ |
+| = | =& | =| | =^ | =~ | =+ |
+ ----------------------------
+}}}
+= Temporal Raster Algebra =
+Arithmetic Operators:
+{{{
+Symbol  description     precedence
+  %     modulus         1
+  /     division        1
+  *     multiplication  1
+  +     addition        2
+  -     subtraction     2
+}}}
+Raster functions:
+{{{
+abs(x)                  return absolute value of x
+foat(x)                 convert x to foating point
+if decision options:
+  if(x)                 1 if x not zero, 0 otherwise
+  if(x,a)               a if x not zero, 0 otherwise
+  if(x,a,b)             a if x not zero, b otherwise
+int(x)                  convert x to integer [ truncates ]
+log(x)                  natural log of x
+log(x,b)                log of x base b
+max(x,y[,z...])         largest value of those listed
+median(x,y[,z...])      median value of those listed
+min(x,y[,z...])         smallest value of those listed
+round(x)                round x to nearest integer
+sqrt(x)                 square root of x
+tan(x)                  tangent of x (x is in degrees)
+not(x)                  1 if x is zero, 0 otherwise
+pow(x,y)                x to the power y
+rand(a,b)               random value x : a <= x < b
+round(x)                round x to nearest integer
+sin(x)                  sine of x (x is in degrees)
+sqrt(x)                 square root of x
+tan(x)                  tangent of x (x is in degrees)
+xor(x,y)                exclusive-or (XOR) of x and y
+isnull(x)              check if x = NULL
+}}}
+Internal variables:
+{{{
+row()                   current row of moving window
+col()                   current col of moving window
+x()                     current x-coordinate of moving window
+y()                     current y-coordinate of moving window
+ewres()                 current east-west resolution
+nsres()                 current north-south resolution
+null()                  NULL value
+}}}
+Combination of temporal and arithmetical raster operators:
+{{{
+ ----------------------------
+|   |  % |  / |  * |  - |  + |
+|---|----|----|----|----|----|
+| & | &% | &/ | &* | &- | &+ |
+| | | |% | |/ | |* | |- | |+ |
+| + | +% | +/ | +* | +- | ++ |
+| = | =% | =/ | =* | =- | =+ |
+ ----------------------------
+}}}
+Create the sum of all maps from STRDS A and B that have equal time stamps and store the new maps in STRDS C:
+{{{
+C = A + B
+}}}
+Same expression with explicit definition of the temporal topology relation and temporal operators:
+{{{
+C = A {+,equal,l} B
+}}}
+Select all cells from STRDS B with equal temporal relations to STRDS A, if the cells
+of A are in the range of [100.0, 1600] of time intervals that have more then 30 days (Jan, Mar, Mai, Jul, Aug, Oct, Dec):
+{{{
+C = if(A > 100 && A < 1600 && td(A) > 30, B)
+}}}
+Same expression with explicit definition of the temporal topology relation and temporal operators:
+{{{
+C = if({equal}, A > 100 && A < 1600 {&&,equal} td(A) > 30, B)
+}}}
+Compute the recharge in meter per second for all cells of precipitation STRDS "Prec"
+if the mean temperature specified in STRDS "Temp" is higher than 10 degrees. Computation is performed if STRDS "Prec" and "Temp" have equal time stamps. The number of days or fraction of days per interval is computed using the td() function that has as argument the STRDS "Prec":
+{{{
+C = if(Temp > 10.0, Prec / 3600.0 /24.0 / td(Prec))
+}}}
+Same expression with explicit definition of the temporal topology relation and temporal operators:
+{{{
+C = if({equal}, Temp > 10.0, Prec / 3600.0 / 24.0 {/,equal,l} td(Prec))
+}}}
+Compute the mean value of all maps from STRDS A that are located during time intervals of STRDS B if more than one map of A is contained in an interval of B, use A otherwise, the resulting time intervals are either from B or A:
+{{{
+C = if(B {#,contain} A > 1, (B {+,contain,l} A - B) / (B {#,contain} A), A)
+}}}
+Same expression with explicit definition of the temporal topology relation and temporal operators:
+{{{
+C = if({equal}, B {#,contain} A > 1, (B {+,contain,l} A {-,equal,l} B) {equal,=/} (B {#,contain} A), A)
+}}}
+All supported operators and functions are documented below.
+= Overview of all supported spatio-temporal operators and functions =
+== Temporal topology relations ==
+{{{
+equal             A ------
+                  B ------
+during            A  ----
+                  B ------
+contains          A ------
+                  B  ----
+starts            A ----
+                  B ------
+started           A ------
+                  B ----
+finishs           A   ----
+                  B ------
+finished          A ------
+                  B   ----
+precedes          A ----
+                  B     ----
+follows           A     ----
+                  B ----
+overlapped        A   ------
+                  B ------
+overlaps          A ------
+                  B   ------
+over              booth overlaps and overlapped
+}}}
+The relations must be read A is related to B, like
+- A equals B
+- A is during B
+- A contains B
+Topological relations must be specified in {} parentheses
+{{{
+A {equal} B
+}}}
+Topological relations are always combined with other
+temporal operators in the {} parentheses
+== Temporal operators ==
+The temporal algebra defines temporal operators that can be combined later with spatial operators to perform spatio-temporal operations.
+The temporal operators process the time instances and intervals of temporal related maps.
+{{{
+LEFT REFERENCE     l       Use the time stamp of the left space time dataset
+INTERSECTION       i       Intersection
+DISJOINT UNION     d       Disjoint union
+UNION              u       Union
+RIGHT REFERENCE    r       Use the time stamp of the right space time dataset
+}}}
+For example we can compute the intersection, union or disjoint union from time stamps of maps
+that temporally overlap, or we can just keep the time stamp of the left STDS.
+Temporal operators that work on time intervals
+and instances of maps in space time datasets:
+'''Left Reference l'''
+ Examples with time intervals a, b and left referenced c:
+{{{
+  a ------
+  b  ----
+  c ------
+  a ----
+  b   ----
+  c ----
+  a ---
+  b    ---
+  c ---
+  a ---
+  b     ---
+  c ---
+}}}
+'''Intersection i  '''
+ Examples with time intervals a, b and intersection c:
+{{{
+  a ------
+  b  ----
+  c  ----
+  a ----
+  b   ----
+  c   --
+  a ---
+  b    ---
+  c
+}}}
+'''Disjoint Union d'''
+ Examples with time intervals a, b and disjoint union c:
+{{{
+  a ------
+  b  ----
+  c ------
+  a ----
+  b   ----
+  c ------
+  a ---
+  b    ---
+  c ------
+  a ---
+  b     ---
+  c -------
+}}}
+'''Union u'''
+ Examples with time intervals a, b and union c:
+{{{
+  a ------
+  b  ----
+  c ------
+  a ----
+  b   ----
+  c ------
+  a ---
+  b    ---
+  c ------
+  a ---
+  b     ---
+  c
+}}}
+'''Right Reference r'''
+ Examples with time intervals a, b and right referenced c:
+{{{
+  a ------
+  b  ----
+  c ------
+  a ----
+  b   ----
+  c ----
+  a ---
+  b    ---
+  c ---
+  a ---
+  b     ---
+  c ---
+}}}
+ The l operator ignores indexing operators for space
+ time datasets: A[i]
+Temporal selection operators to select parts of
+space time datasets:
+'''  Selection           :'''[[BR]]
+'''  Inverse selection  !:'''
+Temporal operators have no precedence.
+ Examples:
+ * Select all maps from space time dataset A that
+   have equal time intervals with space time dataset B
+   and store them in space time datasets C.
+{{{
+   C = A : B
+   C = A {:} B
+   C = A {:,equal} B
+}}}
+ * Select all maps from space time dataset A that
+   have unequal time intervals with space time dataset B
+   and store them in space time datasets C.
+{{{
+   C = A !: B
+   C = A {!:} B
+   C = A {!:,equal} B
+}}}
+ * Select all maps from space time dataset A that
+   are during time intervals of space time dataset B
+   and store them in space time datasets C.
+{{{
+   C = A {:,during} B
+}}}
+ * Select all maps from space time dataset A
+   that are during B and during C and during D.
+{{{
+   E = A {:,during} B {:,during} C {:,during} D
+}}}
+Operator number of maps in interval  [[BR]]
+'''Number of maps #'''
+Compute the number of maps from space time dataset B that are
+during the time intervals