SELESwiki - User contributions [en]

SELES101l02

2006-10-25T18:25:30Z

128.100.72.168:

STEPS:

->Click on the Seles program, a window will open up as shown below

[[Image:Seles1.gif]]

->Click on "New"

[[Image:Seles2.gif]]

->A black window will open up within the Seles window

[[Image:Seles3.gif]]

->Go to "StaticModels"

[[Image:Seles4.gif]]

->Select "Value Model" under "StaticModels", a window will pop up as below

[[Image:Seles5.gif]]

->Make sure to select "Single Evaluation" to run value models that evaluate to a single value

[[Image:Seles6.gif]]

Language Reference

2006-10-10T17:26:03Z

128.100.72.168:

:''Click on a term below for more information.''

{| style="background-color: transparent; width: {{{width|100%}}}"

| width="20%" align="{{{align|left}}}" valign="{{{valign|top}}}" |
*SYMBOLS
**[[Language Reference 1# + | + ]]
**[[Language Reference 1#-|-]]
**[[Language Reference 1#*|*]]
**[[Language Reference 1#/|/]]
**[[Language Reference 1#^|^]]
**[[Language Reference 1#ABS(Expr)|ABS(Expr)]]
**[[Language Reference 1#CEILING(Expr)|CEILING(Expr)]]
**[[Language Reference 1#EXP(Expr)|EXP(Expr)]]
**[[Language Reference 1#FLOOR(Expr)|FLOOR(Expr)]]
**[[Language Reference 1#LOG(Expr)|LOG(Expr)]]
**[[Language Reference 1#ROUND(Expr)|ROUND(Expr)]]
* A|Aa
**[[Language Reference 1#ABS|ABS]]
**[[Language Reference 1#ABSOLUTE|ABSOLUTE]]
**[[Language Reference 1#AND|AND]]
**[[Language Reference 1#ARCSIN|ARCSIN]]
**[[Language Reference 1#ARCTAN|ARCTAN]]
**[[Language Reference 1#ARCTAN|ARCTAN]]
* B|Bb
**[[Language Reference 1#BITWISE AND|BITWISE AND]]
**[[Language Reference 1#BITWISE NOT|BITWISE NOT]]
**[[Language Reference 1#BITWISE OR|BITWISE OR]]
**[[Language Reference 1#BITWISE XOR|BITWISE XOR]]
* C|Cc
**[[Language Reference 1#CEILING|CEILING]]
**[[Language Reference 1#CLAMP|CLAMP]]
**[[Language Reference 1#CLASSIFIED_DIST|CLASSIFIED_DIST]]
**[[Language Reference 1#CLASSIFIED_DIST_M|CLASSIFIED_DIST_M]]
**[[Language Reference 1#CLASSIFY|CLASSIFY]]
**[[Language Reference 1#CONTAINS|CONTAINS]]
**[[Language Reference 1#CONTAINS LINK|CONTAINS LINK]]
**[[Language Reference 1#COS|COS]]
**[[Language Reference 1#CRITICAL SECTION|CRITICAL SECTION]]
* D|Dd
**[[Language Reference 1#DEBUG|DEBUG]]
**[[Language Reference 1#DECISION|DECISION]]
**[[Language Reference 1#DIRECTION|DIRECTION]]
**[[Language Reference 1#DISTANCE|DISTANCE]]

| width="20%" align="{{{align|left}}}" valign="{{{valign|top}}}" |
* E|Ee
**[[Language Reference 1#ELSE|ELSE]]
**[[Language Reference 1#EQUAL TRUE|EQUAL TRUE]]
**[[Language Reference 1#EXP(Expr)|EXP(Expr)]]
**[[Language Reference 1#Expr % Expr|Expr % Expr]]
* F|Ff
**[[Language Reference 1#FIND|FIND]]
**[[Language Reference 1#FIND LINK|FIND LINK]]
**[[Language Reference 1#FIND NEXT|FIND NEXT]]
**[[Language Reference 1#FIND NEXT LINK|FIND NEXT LINK]]
**[[Language Reference 1#FIRST|FIRST]]
**[[Language Reference 1#FIRST LINK|FIRST LINK]]
**[[Language Reference 1#FLOOR|FLOOR]]
* G|Gg
**[[Language Reference 1#GEOMETRIC MEAN|GEOMETRIC MEAN]]
**[[Language Reference 1#GREATER OR EQUAL|GREATER OR EQUAL]]
**[[Language Reference 1#GREATER THAN|GREATER THAN]]
* H|Hh
**[[Language Reference 1#HEAD|HEAD]]
* I|Ii
**[[Language Reference 2#IF Expr|IF Expr]]
**[[Language Reference 2#IF Expr THEN Expr ELSE|IF Expr THEN Expr ELSE]]
**[[Language Reference 2#INSERT|INSERT]]
**[[Language Reference 2#INSERT HEAD|INSERT HEAD]]
**[[Language Reference 2#INSERT TAIL|INSERT TAIL]]
**[[Language Reference 2#INTERPOLATE|INTERPOLATE]]
**[[Language Reference 2#INTERPOLATE|INTERPOLATE]]
**[[Language Reference 2#IS EMPTY|IS EMPTY]]
**[[Language Reference 2#IS EMPTY LINKS|IS EMPTY LINKS]]

| width="20%" align="{{{align|left}}}" valign="{{{valign|top}}}" |
* J|Jj
* K|Kk
* L|Ll
**[[Language Reference 2#LESS OR EQUAL|LESS OR EQUAL]]
**[[Language Reference 2#LESS THAN|LESS THAN]]
**[[Language Reference 2#LINKED|LINKED]]
**[[Language Reference 2#LOG|LOG]]
**[[Language Reference 2#LOG NORMAL CDF|LOG NORMAL CDF]]
**[[Language Reference 2#LOG NORMAL PDF|LOG NORMAL PDF]]
**[[Language Reference 2#LOG NORMAL TEMPORAL PDF|LOG NORMAL TEMPORAL PDF]]
**[[Language Reference 2#LOOKUP|LOOKUP]]
* M|Mm
**[[Language Reference 2#MAX|MAX]]
**[[Language Reference 2#MAX POSITION|MAX POSITION]]
**[[Language Reference 2#MEAN|MEAN]]
**[[Language Reference 2#MIN|MIN]]
**[[Language Reference 2#MIN POSITION|MIN POSITION]]
* N|Nn
**[[Language Reference 2#NEGEXP|NEGEXP]]
**[[Language Reference 2#NEXT|NEXT]]
**[[Language Reference 2#NEXT LINK|NEXT LINK]]
**[[Language Reference 2#NORMAL CDF|NORMAL CDF]]
**[[Language Reference 2#NORMAL PDF|NORMAL PDF]]
**[[Language Reference 2#NORMAL TEMPORAL PDF|NORMAL TEMPORAL PDF]]
**[[Language Reference 2#NOT EQUAL|NOT EQUAL]]

| width="20%" align="{{{align|left}}}" valign="{{{valign|top}}}" |
* O|Oo
**[[Language Reference 3#ONE|ONE]]
**[[Language Reference 3#OR|OR]]
**[[Language Reference 3#OVER INDEX SEQUENCE|OVER INDEX SEQUENCE]]
* P|Pp
**[[Language Reference 3#PAUSE|PAUSE]]
**[[Language Reference 3#PAUSE (#Value)IF|PAUSE (#Value)IF]]
**[[Language Reference 3#PAUSE IF|PAUSE IF]]
**[[Language Reference 3#PREV|PREV]]
**[[Language Reference 3#PREV LINK|PREV LINK]]
* Q|Qq
* R|Rr
**[[Language Reference 3#RECOMPUTE|RECOMPUTE]]
**[[Language Reference 3#REGION CENTRED|REGION CENTRED]]
**[[Language Reference 3#REGION COST SURFACE|REGION COST SURFACE]]
**[[Language Reference 3#REGION LEAST COST PATH|REGION LEAST COST PATH]]
**[[Language Reference 3#REGION LOCATION|REGION LOCATION]]
**[[Language Reference 3#REGION LOCATION LIST|REGION LOCATION LIST]]
**[[Language Reference 3#REGION RECT|REGION RECT]]
**[[Language Reference 3#REGION WHOLE MAP|REGION WHOLE MAP]]
**[[Language Reference 3#REMOVE|REMOVE]]
**[[Language Reference 3#REMOVE ALL LINKS|REMOVE ALL LINKS]]
**[[Language Reference 3#REMOVE LINK|REMOVE LINK]]
**[[Language Reference 3#RESIZE|RESIZE]]
**[[Language Reference 3#RESPONSE|RESPONSE]]
**[[Language Reference 3#ROUND|ROUND]]
* S|Ss

| width="20%" align="{{{align|left}}}" valign="{{{valign|top}}}" |
**[[Language Reference 3#SEED()|SEED()]]
**[[Language Reference 3#SELECTAT|SELECTAT]]
**[[Language Reference 3#SET|SET]]
**[[Language Reference 3#SET LINK|SET LINK]]
**[[Language Reference 3#SETAT|SETAT]]
**[[Language Reference 3#SHIFT LEFT|SHIFT LEFT]]
**[[Language Reference 3#SHIFT RIGHT|SHIFT RIGHT]]
**[[Language Reference 3#SIN|SIN]]
**[[Language Reference 3#SIZE LINKS|SIZE LINKS]]
**[[Language Reference 3#SKEWED NORMAL CDF|SKEWED NORMAL CDF]]
**[[Language Reference 3#SKEWED NORMAL PDF|SKEWED NORMAL PDF]]
**[[Language Reference 3#SKEWED NORMAL TEMPORAL PDF|SKEWED NORMAL TEMPORAL PDF]]
**[[Language Reference 3#SORT|SORT]]
**[[Language Reference 3#SORT LINKS|SORT LINKS]]
**[[Language Reference 3#STRICT ORDERED|STRICT ORDERED]]
**[[Language Reference 3#SUM|SUM]]
* T|Tt
**[[Language Reference 3#TAIL|TAIL]]
**[[Language Reference 3#TAN|TAN]]
* U|Uu
**[[Language Reference 3#UNIFORM|UNIFORM]]
**[[Language Reference 3#UNIFORM TEMPORAL PDF|UNIFORM TEMPORAL PDF]]
* V|Vv
* W|Ww
**[[Language Reference 3#WAIT UNTIL|WAIT UNTIL]]
**[[Language Reference 3#WHILE|WHILE]]
* X|Xx
* Y|Yy
* Z|Zz
**[[Language Reference 3#ZERO|ZERO]]

|}

Language Reference 1

2006-10-10T17:24:18Z

128.100.72.168:

Language Reference 1

2006-10-10T17:22:26Z

128.100.72.168:

Language Reference 1

2006-10-10T17:20:42Z

128.100.72.168:

Language Reference 1

2006-10-10T17:19:17Z

128.100.72.168:

==+==
DESCRIPTION:
The addition operator

USAGE:
x=Expr+Expr

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
Value of the expression is the sum of two expressions

SEE ALSO:
[[Model Builder's Guide Chapter 9#Expressions:]]

Example 1:
x=1+2
=3
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

==-==
DESCRIPTION:
The subtraction operator

USAGE:
x=Expr-Expr

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
Value of the first expression minus the value of the second expression

SEE ALSO:
[[Model Builder's Guide Chapter 9#Expressions:]]

Example 1:
x=15-2
=13
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

==*==
DESCRIPTION:
The multiplication operator

USAGE:
x=Expr*Expr

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
Value is the product of two expressions

SEE ALSO:
[[Model Builder's Guide Chapter 9#Expressions:]]

Example 1:
x=5*4
=20
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

==/==
DESCRIPTION:
The division operator

USAGE:
x=Expr/Expr

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
Value of the first expression divided by value of the second expression

SEE ALSO:
[[Model Builder's Guide Chapter 9#Expressions:]]

Example 1:
x=60/6
=10
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

==^==
DESCRIPTION:
The power operator

USAGE:
x=Expr^Expr

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
The first expression to the power of the value of the second expression

SEE ALSO:
[[Model Builder's Guide Chapter 9#Expressions:]]

Example 1:
x=7^3
=343
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

==ABS==
(Expr) absolute value of the expression
[[Model Builder's Guide Chapter 9#Continuous Functions (Arithmetic Functions)]]

==ABSOLUTE==
(Expr) absolute value of the expression

==ABS(Expr)==
DESCRIPTION:
The absolute value operator

USAGE:
x=ABS(Expr)=|Expr|=Absolute(Expr)

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
Absolute value of the expression

SEE ALSO:
[[Model Builder's Guide Chapter 9#Expressions:]]

Example 1:
x=ABS(-9)=|-9|=Absolute(-9)
=9
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

==AND==
TRUE (1) if all sub-expressions evaluate to
TRUE and FALSE (0) otherwise
[[Model Builder's Guide Chapter 9#Composite Functions]]

==ARCCOS==(Expr) inverse cos of the value of the expression [[Model Builder's Guide Chapter 9#Continuous Functions (Trigonometric Functions)]]

==ARCSIN==
(Expr) inverse sine of the value of the expression [[Model Builder's Guide Chapter 9#Continuous Functions (Trigonometric Functions)]]

==ARCTAN==
(Expr) inverse tan of the value of the expression [[Model Builder's Guide Chapter 9#Continuous Functions (Trigonometric Functions)]]

==ARCTAN==
(Expr, Expr) inverse tan where first expression is x offset
and second is y offset. Providing two
expressions gives more information about the
quadrant.
[[Model Builder's Guide Chapter 9#Continuous Functions (Trigonometric Functions)]]

==BITWISE OR==
(Expr, Expr) Bitwise OR of two values[[Model Builder's Guide Chapter 9#Bit-Vector Functions]]
==BITWISE AND==
(Expr, Expr) Bitwise AND of two values[[Model Builder's Guide Chapter 9#Bit-Vector Functions]]
==BITWISE XOR==
(Expr, Expr) Bitwise exclusive-OR of two values[[Model Builder's Guide Chapter 9#Bit-Vector Functions]]
==BITWISE NOT==
Expr Bitwise NOT of a value[[Model Builder's Guide Chapter 9#Bit-Vector Functions]]

==CEILING(Expr)==
DESCRIPTION:
The ceiling operator

USAGE:
x=CEILING(Expr)

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
Smallest integer larger than the expression value

SEE ALSO:
[[Model Builder's Guide Chapter 9#Expressions:]]

Example 1:
x=CEILING(0.01)
=1
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

==CEILING==
(Expr) smallest integer larger than the expression value[[Model Builder's Guide Chapter 9#Ceiling]]

==CLAMP==
(Expr, MinExpr, MaxExpr) clamp the value X of the expression to the range
[Min, Max]: if X < Min then return Min; if X < Max return Max. Otherwise return X.
[[Model Builder's Guide Chapter 9#Continuous Functions (Arithmetic Functions)]]

==CLASSIFY==
(X) if the value of the variable X is equal to one of
CLASS Number: Expr the classes listed, then return the result of the.
: associated expression. Otherwise return 0.
[[Model Builder's Guide Chapter 9#Classified and Discrete Functions]]
ENDFN
[[Model Builder's Guide Chapter 9#Classified and Discrete Functions]]

==CLASSIFY==
(X) return the result of the kth expression in the list,
Expr where k = X – minimum value of the variables
: (this may be non-0 only for layers)
:
[[Model Builder's Guide Chapter 9#Classified and Discrete Functions]]
ENDFN
[[Model Builder's Guide Chapter 9#Classified and Discrete Functions]]

==CLASSIFY==
(X): ( Number+) return the kth number in the list, where
k = X – minimum value of the variable (this
may be non-0 only for layers)[[Model Builder's Guide Chapter 9#Classified and Discrete Functions]]

==CLASSIFY==
(X): Filename uses the table in the named file, which is
assumed to consist of class:value pairs. Rarely
used.
[[Model Builder's Guide Chapter 9#Classified and Discrete Functions]]

==CLASSIFY==
(X): Filename Key uses the table in the named file, which is
assumed to consist of class:value pairs. The key
is used to specify a sub-table in a multi-table
file. Rarely used.

Classified functions use the variable as an index into the list of numbers or expressions that follow. The “CLASS” keyword is optional. This variable must be non-negative. If “CLASS # :” is used, then the number refers to the value of the indexing variable. If a class is not specified for a given value, its expression is implicitly ZERO. Interpolation tables are very similar except that the variable is assumed to be continuous instead of classified. An interpolated value between classes is returned. Lookup tables are also similar, except that both the variable and classes are assumed to be continuous values. An interpolated value between classes is also returned. Rarely used.
[[Model Builder's Guide Chapter 9#Classified and Discrete Functions]]

==CLASSIFIED_DIST==
draw a value from a discrete distribution, where CLASS Number: Expr each expression determines the relative : probability of its associated class being drawn. ENDFN The CLASS keyword is optional.

==CLASSIFIED_DIST==
( Number+) in this form, the classes are assumed to start at zero. Only constant probabilities can be given.
==CLASSIFIED_DIST==
in this form, the classes are assumed to start at Expr zero :
ENDFN

==CLASSIFIED_DIST[M]==
In this form, the classes in a one-dimensional
array M, and so start at zero.
==COS==
(Expr) interpret the value of the expression as an angle
theta in degrees, and return cos(theta) [[Model Builder's Guide Chapter 9#Continuous Functions (Trigonometric Functions)]]

==CRITICAL SECTION==
(Flag) Enter (if Flag is TRUE) or exit (if Flag is FALSE) a critical section. A critical section gives priority to this application, and is used for
synchronizing access to shared variables
(i.e. shared with another application).[[Model Builder's Guide Chapter 9#Control Expressions]]

==DEBUG==
Update the simulation probe, if it is loaded and
The event is selected. Used to debug/verify
event behaviour.[[Model Builder's Guide Chapter 9#Control Expressions]]

==DECISION==
Expr approximation of line between end cells
Cost surface and least-cost path regions are advanced features that are best understood with an example model.
[[Model Builder's Guide Chapter 9#Region Functions]]

==DECISION==
Expr known location indices. If there is a decision expression, then only those cells for which this
expression returns TRUE will be included.
[[Model Builder's Guide Chapter 9#Region Functions]]

==DECISION== Expr location indices stored in one-dimensional X.
[[Model Builder's Guide Chapter 9#Region Functions]]

==DECISION== Expr location index. If there is a decision expression,
then only those cells for which this expression
returns TRUE will be included.
[[Model Builder's Guide Chapter 9#Region Functions]]

==DECISION==
Expr defines a region centred on the current cell.
If there is a decision expression, then only
those cells for which this expression returns
TRUE will be included.

DistanceType is either CARDINAL or EUCLIDEAN (the default). Cardinal distance between two cells is the minimum number of cardinal steps (up, down, left, right) to reach one cell from the other. Euclidean distance is the straight-line distance between two points. The WRAPPED flag, if present indicates that the region wraps around the sides (vertically and horizontally) of the landscape (e.g. a location x positions beyond the right-hand side of a raster will be mapped to x positions in from the left-hand side of the raster). If not present, the landscape does not wrap.
[[Model Builder's Guide Chapter 9#Region Functions]]

==DIRECTION==
(Expr, Expr) angle in degrees between two location indices
[[Model Builder's Guide Chapter 9#Continuous Functions (Miscellaneous)]]

==DISPLAY== Display on the screen the labelled Label: Expr values computed with the expressions listed.
…. If no label is given, the expression must
ENDFN be a variable, and this is used for the label.
[[Model Builder's Guide Chapter 9#Output Expressions]]
==DISPLAY== Same as above, but only display if the DECISION Expr decision expression evaluates to TRUE
Label: Expr The keyword DECISION can be replaced by
…. a “?”
ENDFN
[[Model Builder's Guide Chapter 9#Output Expressions]]
OUTPUT RECORD(OutputVar) Output to the record file of output variable the labelled values computed with the Label: Expr expressions listed. If no label is given, the
…. Expression must be a variable and this is
ENDFN used as label.
[[Model Builder's Guide Chapter 9#Output Expressions]]
OUTPUT RECORD(OutputVar) Same as above, but only output if the DECISION Expr decision expression evaluates to TRUE
Label: Expr
….
ENDFN

==DISTANCE==
(Expr, Expr) distance between two location indices (normally
obtained using the Location variable). Thus,
DISTANCE(loc1, loc2) is
sqrt(sqr(loc1.x – loc2.x) + sqr(loc1.y – loc2.y))
[[Model Builder's Guide Chapter 9#Continuous Functions (Miscellaneous)]]

==ELSE==
expression evaluates to TRUE and the set of
… sub-expressions after the ELSE otherwise. Note
ENDFN that “ELSE IF expr” forms can be strung
together[[Model Builder's Guide Chapter 9#Control Expressions]]

==EQUAL TRUE==
(1) if the sub-expressions all evaluate to
the same value and FALSE (0) otherwise
[[Model Builder's Guide Chapter 9#Composite Functions]]

==FLOOR==
(Expr) largest integer smaller than the expression value[[Model Builder's Guide Chapter 9#Continuous Functions (Arithmetic Functions)]]

==GEOMETRIC MEAN==
geometric mean of the sub-expressions (nth
root of the product for n expressions)

[[Model Builder's Guide Chapter 9#Composite Functions]]

==GREATER OR EQUAL==
TRUE (1) if the sub-expression evaluations are
all ordered according to the relation >=, and
FALSE (0) otherwise
[[Model Builder's Guide Chapter 9#Composite Functions]]

==GREATER THAN==
TRUE (1) if the sub-expression evaluations are
all ordered according to the relation >, and
FALSE (0) otherwise

[[Model Builder's Guide Chapter 9#Composite Functions]]

==Expr % Expr==
DESCRIPTION:
The percentage operator

USAGE:
x=Expr % Expr

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
Value of the first expression modulo the value of the second expression(assumes that the values of the expression are integers

SEE ALSO:
<a link to the composite functions section of seles modellers guide>

Example 1:
x=19 % 12
=7

Example 2:
x=10 % 20
=10

Example 3:
x=10 % 10
=0
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>
[[Model Builder's Guide Chapter 9#Expressions:]]

==EXP(Expr)==
DESCRIPTION:
(Expr) base of the natural logarithm (e) to the power of
the expression
USAGE:
x=EXP(Expr)

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
Base of the natural logarithm (e) to the power of the expression

SEE ALSO:
<a link to the composite functions section of seles modellers guide>

Example 1:
x=EXP(3)
=20.08553692
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>
[[Model Builder's Guide Chapter 9#Expressions:]]

==FLOOR(Expr)==
DESCRIPTION:
The flooring operator

USAGE:
x=FLOOR(Expr)

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
Largest integer smaller than the expression value

SEE ALSO:
[[Model Builder's Guide Chapter 9#Expressions:]]

Example 1:
x=FLOOR(0.99)
=0
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

==LOG(Expr)==
DESCRIPTION:
The logarithm operator

USAGE:
x=LOG(Expr)

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
Natural logarithm of the value of the expression

SEE ALSO:
[[Model Builder's Guide Chapter 9#Expressions:]]

Example 1:
x=LOG(0.773)
=-0.111820506
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

==ROUND(Expr)==
DESCRIPTION:
The rounding operator

USAGE:
x=ROUND(Expr)

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
Expression value rounded to the nearest integer

SEE ALSO:
[[Model Builder's Guide Chapter 9#Expressions:]]

Example 1:
x=ROUND(0.773)
=1
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

==CEILING==
(Expr) smallest integer larger than the expression value[[Model Builder's Guide Chapter 9#Ceiling]]

==CLAMP==
(Expr, MinExpr, MaxExpr) clamp the value X of the expression to the range
[Min, Max]: if X < Min then return Min; if X < Max return Max. Otherwise return X.
[[Model Builder's Guide Chapter 9#Continuous Functions (Arithmetic Functions)]]

==CLASSIFY==
(X) if the value of the variable X is equal to one of
CLASS Number: Expr the classes listed, then return the result of the.
: associated expression. Otherwise return 0.
[[Model Builder's Guide Chapter 9#Classified and Discrete Functions]]
ENDFN
[[Model Builder's Guide Chapter 9#Classified and Discrete Functions]]

==CLASSIFY==
(X) return the result of the kth expression in the list,
Expr where k = X – minimum value of the variables
: (this may be non-0 only for layers)
:
[[Model Builder's Guide Chapter 9#Classified and Discrete Functions]]
ENDFN
[[Model Builder's Guide Chapter 9#Classified and Discrete Functions]]

==CLASSIFY==
(X): ( Number+) return the kth number in the list, where
k = X – minimum value of the variable (this
may be non-0 only for layers)[[Model Builder's Guide Chapter 9#Classified and Discrete Functions]]

==CLASSIFY==
(X): Filename uses the table in the named file, which is
assumed to consist of class:value pairs. Rarely
used.
[[Model Builder's Guide Chapter 9#Classified and Discrete Functions]]

==CLASSIFY==
(X): Filename Key uses the table in the named file, which is
assumed to consist of class:value pairs. The key
is used to specify a sub-table in a multi-table
file. Rarely used.

Classified functions use the variable as an index into the list of numbers or expressions that follow. The “CLASS” keyword is optional. This variable must be non-negative. If “CLASS # :” is used, then the number refers to the value of the indexing variable. If a class is not specified for a given value, its expression is implicitly ZERO. Interpolation tables are very similar except that the variable is assumed to be continuous instead of classified. An interpolated value between classes is returned. Lookup tables are also similar, except that both the variable and classes are assumed to be continuous values. An interpolated value between classes is also returned. Rarely used.
[[Model Builder's Guide Chapter 9#Classified and Discrete Functions]]

==CLASSIFIED_DIST==
draw a value from a discrete distribution, where CLASS Number: Expr each expression determines the relative : probability of its associated class being drawn. ENDFN The CLASS keyword is optional.

==CLASSIFIED_DIST==
( Number+) in this form, the classes are assumed to start at zero. Only constant probabilities can be given.
==CLASSIFIED_DIST==
in this form, the classes are assumed to start at Expr zero :
ENDFN

==CLASSIFIED_DIST[M]==
In this form, the classes in a one-dimensional
array M, and so start at zero.
==COS==
(Expr) interpret the value of the expression as an angle
theta in degrees, and return cos(theta) [[Model Builder's Guide Chapter 9#Continuous Functions (Trigonometric Functions)]]

==CRITICAL SECTION==
(Flag) Enter (if Flag is TRUE) or exit (if Flag is FALSE) a critical section. A critical section gives priority to this application, and is used for
synchronizing access to shared variables
(i.e. shared with another application).[[Model Builder's Guide Chapter 9#Control Expressions]]

==DEBUG==
Update the simulation probe, if it is loaded and
The event is selected. Used to debug/verify
event behaviour.[[Model Builder's Guide Chapter 9#Control Expressions]]

==DECISION==
Expr approximation of line between end cells
Cost surface and least-cost path regions are advanced features that are best understood with an example model.
[[Model Builder's Guide Chapter 9#Region Functions]]

==DECISION==
Expr known location indices. If there is a decision expression, then only those cells for which this
expression returns TRUE will be included.
[[Model Builder's Guide Chapter 9#Region Functions]]

==DECISION== Expr location indices stored in one-dimensional X.
[[Model Builder's Guide Chapter 9#Region Functions]]

==DECISION== Expr location index. If there is a decision expression,
then only those cells for which this expression
returns TRUE will be included.
[[Model Builder's Guide Chapter 9#Region Functions]]

==DECISION==
Expr defines a region centred on the current cell.
If there is a decision expression, then only
those cells for which this expression returns
TRUE will be included.

DistanceType is either CARDINAL or EUCLIDEAN (the default). Cardinal distance between two cells is the minimum number of cardinal steps (up, down, left, right) to reach one cell from the other. Euclidean distance is the straight-line distance between two points. The WRAPPED flag, if present indicates that the region wraps around the sides (vertically and horizontally) of the landscape (e.g. a location x positions beyond the right-hand side of a raster will be mapped to x positions in from the left-hand side of the raster). If not present, the landscape does not wrap.
[[Model Builder's Guide Chapter 9#Region Functions]]

==DIRECTION==
(Expr, Expr) angle in degrees between two location indices
[[Model Builder's Guide Chapter 9#Continuous Functions (Miscellaneous)]]

==DISPLAY== Display on the screen the labelled Label: Expr values computed with the expressions listed.
…. If no label is given, the expression must
ENDFN be a variable, and this is used for the label.
[[Model Builder's Guide Chapter 9#Output Expressions]]
==DISPLAY== Same as above, but only display if the DECISION Expr decision expression evaluates to TRUE
Label: Expr The keyword DECISION can be replaced by
…. a “?”
ENDFN
[[Model Builder's Guide Chapter 9#Output Expressions]]
OUTPUT RECORD(OutputVar) Output to the record file of output variable the labelled values computed with the Label: Expr expressions listed. If no label is given, the
…. Expression must be a variable and this is
ENDFN used as label.
[[Model Builder's Guide Chapter 9#Output Expressions]]
OUTPUT RECORD(OutputVar) Same as above, but only output if the DECISION Expr decision expression evaluates to TRUE
Label: Expr
….
ENDFN

==DISTANCE==
(Expr, Expr) distance between two location indices (normally
obtained using the Location variable). Thus,
DISTANCE(loc1, loc2) is
sqrt(sqr(loc1.x – loc2.x) + sqr(loc1.y – loc2.y))
[[Model Builder's Guide Chapter 9#Continuous Functions (Miscellaneous)]]

==ELSE==
expression evaluates to TRUE and the set of
… sub-expressions after the ELSE otherwise. Note
ENDFN that “ELSE IF expr” forms can be strung
together[[Model Builder's Guide Chapter 9#Control Expressions]]

==EQUAL TRUE==
(1) if the sub-expressions all evaluate to
the same value and FALSE (0) otherwise
[[Model Builder's Guide Chapter 9#Composite Functions]]

==FLOOR==
(Expr) largest integer smaller than the expression value[[Model Builder's Guide Chapter 9#Continuous Functions (Arithmetic Functions)]]

==GEOMETRIC MEAN==
geometric mean of the sub-expressions (nth
root of the product for n expressions)

[[Model Builder's Guide Chapter 9#Composite Functions]]

==GREATER OR EQUAL==
TRUE (1) if the sub-expression evaluations are
all ordered according to the relation >=, and
FALSE (0) otherwise
[[Model Builder's Guide Chapter 9#Composite Functions]]

==GREATER THAN==
TRUE (1) if the sub-expression evaluations are
all ordered according to the relation >, and
FALSE (0) otherwise

[[Model Builder's Guide Chapter 9#Composite Functions]]

Language Reference 1

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Language Reference 1

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==ABS==
(Expr) absolute value of the expression
[[Model Builder's Guide Chapter 9#Continuous Functions (Arithmetic Functions)]]

==ABSOLUTE==
(Expr) absolute value of the expression

==ABS(Expr)==
DESCRIPTION:
The absolute value operator

USAGE:
x=ABS(Expr)=|Expr|=Absolute(Expr)

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
Absolute value of the expression

SEE ALSO:
[[Model Builder's Guide Chapter 9#Expressions:]]

Example 1:
x=ABS(-9)=|-9|=Absolute(-9)
=9
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

==AND==
TRUE (1) if all sub-expressions evaluate to
TRUE and FALSE (0) otherwise
[[Model Builder's Guide Chapter 9#Composite Functions]]

==ARCCOS==(Expr) inverse cos of the value of the expression [[Model Builder's Guide Chapter 9#Continuous Functions (Trigonometric Functions)]]

==ARCSIN==
(Expr) inverse sine of the value of the expression [[Model Builder's Guide Chapter 9#Continuous Functions (Trigonometric Functions)]]

==ARCTAN==
(Expr) inverse tan of the value of the expression [[Model Builder's Guide Chapter 9#Continuous Functions (Trigonometric Functions)]]

==ARCTAN==
(Expr, Expr) inverse tan where first expression is x offset
and second is y offset. Providing two
expressions gives more information about the
quadrant.
[[Model Builder's Guide Chapter 9#Continuous Functions (Trigonometric Functions)]]

==BITWISE OR==
(Expr, Expr) Bitwise OR of two values[[Model Builder's Guide Chapter 9#Bit-Vector Functions]]
==BITWISE AND==
(Expr, Expr) Bitwise AND of two values[[Model Builder's Guide Chapter 9#Bit-Vector Functions]]
==BITWISE XOR==
(Expr, Expr) Bitwise exclusive-OR of two values[[Model Builder's Guide Chapter 9#Bit-Vector Functions]]
==BITWISE NOT==
Expr Bitwise NOT of a value[[Model Builder's Guide Chapter 9#Bit-Vector Functions]]

==+==
DESCRIPTION:
The addition operator

USAGE:
x=Expr+Expr

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
Value of the expression is the sum of two expressions

SEE ALSO:
[[Model Builder's Guide Chapter 9#Expressions:]]

Example 1:
x=1+2
=3
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

==-==
DESCRIPTION:
The subtraction operator

USAGE:
x=Expr-Expr

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
Value of the first expression minus the value of the second expression

SEE ALSO:
[[Model Builder's Guide Chapter 9#Expressions:]]

Example 1:
x=15-2
=13
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

==*==
DESCRIPTION:
The multiplication operator

USAGE:
x=Expr*Expr

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
Value is the product of two expressions

SEE ALSO:
[[Model Builder's Guide Chapter 9#Expressions:]]

Example 1:
x=5*4
=20
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

==/==
DESCRIPTION:
The division operator

USAGE:
x=Expr/Expr

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
Value of the first expression divided by value of the second expression

SEE ALSO:
[[Model Builder's Guide Chapter 9#Expressions:]]

Example 1:
x=60/6
=10
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

==^==
DESCRIPTION:
The power operator

USAGE:
x=Expr^Expr

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
The first expression to the power of the value of the second expression

SEE ALSO:
[[Model Builder's Guide Chapter 9#Expressions:]]

Example 1:
x=7^3
=343
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

==ABS(Expr)==
DESCRIPTION:
The absolute value operator

USAGE:
x=ABS(Expr)=|Expr|=Absolute(Expr)

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
Absolute value of the expression

SEE ALSO:
[[Model Builder's Guide Chapter 9#Expressions:]]

Example 1:
x=ABS(-9)=|-9|=Absolute(-9)
=9
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

==Expr % Expr==
value of the first expression modulo the value of
the second expression (assumes that the values
of the expressions are integers)

==EXP(Expr)==
DESCRIPTION:
(Expr) base of the natural logarithm (e) to the power of
the expression
USAGE:
x=EXP(Expr)

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
Base of the natural logarithm (e) to the power of the expression

SEE ALSO:
<a link to the composite functions section of seles modellers guide>

Example 1:
x=EXP(3)
=20.08553692
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>
[[Model Builder's Guide Chapter 9#Expressions:]]

==LOG(Expr)==
DESCRIPTION:
The logarithm operator

USAGE:
x=LOG(Expr)

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
Natural logarithm of the value of the expression

SEE ALSO:
[[Model Builder's Guide Chapter 9#Expressions:]]

Example 1:
x=LOG(0.773)
=-0.111820506
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

==ROUND(Expr)==
DESCRIPTION:
The rounding operator

USAGE:
x=ROUND(Expr)

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
Expression value rounded to the nearest integer

SEE ALSO:
[[Model Builder's Guide Chapter 9#Expressions:]]

Example 1:
x=ROUND(0.773)
=1
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

==FLOOR(Expr)==
DESCRIPTION:
The flooring operator

USAGE:
x=FLOOR(Expr)

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
Largest integer smaller than the expression value

SEE ALSO:
[[Model Builder's Guide Chapter 9#Expressions:]]

Example 1:
x=FLOOR(0.99)
=0
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

==CEILING(Expr)==
DESCRIPTION:
The ceiling operator

USAGE:
x=CEILING(Expr)

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value

VALUE:
Smallest integer larger than the expression value

SEE ALSO:
[[Model Builder's Guide Chapter 9#Expressions:]]

Example 1:
x=CEILING(0.01)
=1
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

==CEILING==
(Expr) smallest integer larger than the expression value[[Model Builder's Guide Chapter 9#Ceiling]]

==CLAMP==
(Expr, MinExpr, MaxExpr) clamp the value X of the expression to the range
[Min, Max]: if X < Min then return Min; if X < Max return Max. Otherwise return X.
[[Model Builder's Guide Chapter 9#Continuous Functions (Arithmetic Functions)]]

==CLASSIFY==
(X) if the value of the variable X is equal to one of
CLASS Number: Expr the classes listed, then return the result of the.
: associated expression. Otherwise return 0.
[[Model Builder's Guide Chapter 9#Classified and Discrete Functions]]
ENDFN
[[Model Builder's Guide Chapter 9#Classified and Discrete Functions]]

==CLASSIFY==
(X) return the result of the kth expression in the list,
Expr where k = X – minimum value of the variables
: (this may be non-0 only for layers)
:
[[Model Builder's Guide Chapter 9#Classified and Discrete Functions]]
ENDFN
[[Model Builder's Guide Chapter 9#Classified and Discrete Functions]]

==CLASSIFY==
(X): ( Number+) return the kth number in the list, where
k = X – minimum value of the variable (this
may be non-0 only for layers)[[Model Builder's Guide Chapter 9#Classified and Discrete Functions]]

==CLASSIFY==
(X): Filename uses the table in the named file, which is
assumed to consist of class:value pairs. Rarely
used.
[[Model Builder's Guide Chapter 9#Classified and Discrete Functions]]

==CLASSIFY==
(X): Filename Key uses the table in the named file, which is
assumed to consist of class:value pairs. The key
is used to specify a sub-table in a multi-table
file. Rarely used.

Classified functions use the variable as an index into the list of numbers or expressions that follow. The “CLASS” keyword is optional. This variable must be non-negative. If “CLASS # :” is used, then the number refers to the value of the indexing variable. If a class is not specified for a given value, its expression is implicitly ZERO. Interpolation tables are very similar except that the variable is assumed to be continuous instead of classified. An interpolated value between classes is returned. Lookup tables are also similar, except that both the variable and classes are assumed to be continuous values. An interpolated value between classes is also returned. Rarely used.
[[Model Builder's Guide Chapter 9#Classified and Discrete Functions]]

==CLASSIFIED_DIST==
draw a value from a discrete distribution, where CLASS Number: Expr each expression determines the relative : probability of its associated class being drawn. ENDFN The CLASS keyword is optional.

==CLASSIFIED_DIST==
( Number+) in this form, the classes are assumed to start at zero. Only constant probabilities can be given.
==CLASSIFIED_DIST==
in this form, the classes are assumed to start at Expr zero :
ENDFN

==CLASSIFIED_DIST[M]==
In this form, the classes in a one-dimensional
array M, and so start at zero.
==COS==
(Expr) interpret the value of the expression as an angle
theta in degrees, and return cos(theta) [[Model Builder's Guide Chapter 9#Continuous Functions (Trigonometric Functions)]]

==CRITICAL SECTION==
(Flag) Enter (if Flag is TRUE) or exit (if Flag is FALSE) a critical section. A critical section gives priority to this application, and is used for
synchronizing access to shared variables
(i.e. shared with another application).[[Model Builder's Guide Chapter 9#Control Expressions]]

==DEBUG==
Update the simulation probe, if it is loaded and
The event is selected. Used to debug/verify
event behaviour.[[Model Builder's Guide Chapter 9#Control Expressions]]

==DECISION==
Expr approximation of line between end cells
Cost surface and least-cost path regions are advanced features that are best understood with an example model.
[[Model Builder's Guide Chapter 9#Region Functions]]

==DECISION==
Expr known location indices. If there is a decision expression, then only those cells for which this
expression returns TRUE will be included.
[[Model Builder's Guide Chapter 9#Region Functions]]

==DECISION== Expr location indices stored in one-dimensional X.
[[Model Builder's Guide Chapter 9#Region Functions]]

==DECISION== Expr location index. If there is a decision expression,
then only those cells for which this expression
returns TRUE will be included.
[[Model Builder's Guide Chapter 9#Region Functions]]

==DECISION==
Expr defines a region centred on the current cell.
If there is a decision expression, then only
those cells for which this expression returns
TRUE will be included.

DistanceType is either CARDINAL or EUCLIDEAN (the default). Cardinal distance between two cells is the minimum number of cardinal steps (up, down, left, right) to reach one cell from the other. Euclidean distance is the straight-line distance between two points. The WRAPPED flag, if present indicates that the region wraps around the sides (vertically and horizontally) of the landscape (e.g. a location x positions beyond the right-hand side of a raster will be mapped to x positions in from the left-hand side of the raster). If not present, the landscape does not wrap.
[[Model Builder's Guide Chapter 9#Region Functions]]

==DIRECTION==
(Expr, Expr) angle in degrees between two location indices
[[Model Builder's Guide Chapter 9#Continuous Functions (Miscellaneous)]]

==DISPLAY== Display on the screen the labelled Label: Expr values computed with the expressions listed.
…. If no label is given, the expression must
ENDFN be a variable, and this is used for the label.
[[Model Builder's Guide Chapter 9#Output Expressions]]
==DISPLAY== Same as above, but only display if the DECISION Expr decision expression evaluates to TRUE
Label: Expr The keyword DECISION can be replaced by
…. a “?”
ENDFN
[[Model Builder's Guide Chapter 9#Output Expressions]]
OUTPUT RECORD(OutputVar) Output to the record file of output variable the labelled values computed with the Label: Expr expressions listed. If no label is given, the
…. Expression must be a variable and this is
ENDFN used as label.
[[Model Builder's Guide Chapter 9#Output Expressions]]
OUTPUT RECORD(OutputVar) Same as above, but only output if the DECISION Expr decision expression evaluates to TRUE
Label: Expr
….
ENDFN

==DISTANCE==
(Expr, Expr) distance between two location indices (normally
obtained using the Location variable). Thus,
DISTANCE(loc1, loc2) is
sqrt(sqr(loc1.x – loc2.x) + sqr(loc1.y – loc2.y))
[[Model Builder's Guide Chapter 9#Continuous Functions (Miscellaneous)]]

==ELSE==
expression evaluates to TRUE and the set of
… sub-expressions after the ELSE otherwise. Note
ENDFN that “ELSE IF expr” forms can be strung
together[[Model Builder's Guide Chapter 9#Control Expressions]]

==EQUAL TRUE==
(1) if the sub-expressions all evaluate to
the same value and FALSE (0) otherwise
[[Model Builder's Guide Chapter 9#Composite Functions]]

==FLOOR==
(Expr) largest integer smaller than the expression value[[Model Builder's Guide Chapter 9#Continuous Functions (Arithmetic Functions)]]

==GEOMETRIC MEAN==
geometric mean of the sub-expressions (nth
root of the product for n expressions)

[[Model Builder's Guide Chapter 9#Composite Functions]]

==GREATER OR EQUAL==
TRUE (1) if the sub-expression evaluations are
all ordered according to the relation >=, and
FALSE (0) otherwise
[[Model Builder's Guide Chapter 9#Composite Functions]]

==GREATER THAN==
TRUE (1) if the sub-expression evaluations are
all ordered according to the relation >, and
FALSE (0) otherwise

[[Model Builder's Guide Chapter 9#Composite Functions]]

Language Reference

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128.100.72.168:

==Constants==
==ZERO==
return 0.0
==ONE==
return 1.0
#Number return value of the number specified
<Constant> return value of a named constant
<Constant>[Expr] return value of a named vector constant
<Constant>[Expr, Expr] return value of a named array constant
<Macro>[Expr] return value of expression at specified index
in macro

==Probability Distributions==
==NORMAL==
(Expr, Expr) draw a value from a normal distribution, where
the first expression specifies the mean and
the second specifies the standard deviation

==SKEWED NORMAL==
(Expr, Expr, Expr) draw a value from a skewed normal distribution, where the first expression specifies the mode
and the second and third specify the standard
deviations to the left and right of the mode
==LOG NORMAL==
(Expr, Expr) draw a value from a log normal distribution,
where the first expression specifies the mean
and the second specifies the standard deviation
of the underlying normal distribution

==WEIBULL==
(Expr, Expr) draw a value from a Weibull distribution, where
the first expression specifies the beta and the
second specifies alpha (Note:terminology varies
between sources. The version here is equivalent
to that in Excel, with reversal of parameters).

NEGEXP(Expr) draw a value from a negative exponential distribution, where the expression specifies the
mean
POISSION(Expr) draw a value from a Poisson distribution

UNIFORM(Expr, Expr) draw a value from a uniform distribution, where the first expression determines the minimum value and the second determines the maximum
CLASSIFIED_DIST draw a value from a discrete distribution, where CLASS Number: Expr each expression determines the relative : probability of its associated class being drawn. ENDFN The CLASS keyword is optional.

CLASSIFIED_DIST( Number+) in this form, the classes are assumed to start at zero. Only constant probabilities can be given.

CLASSIFIED_DIST in this form, the classes are assumed to start at Expr zero :
ENDFN

CLASSIFIED_DIST[M] In this form, the classes in a one-dimensional
array M, and so start at zero.

===Probability Density and Cumulative Density Functions===
The following are a set of probability and cumulative density expressions. The results from probability density expressions should be multiplied by a width factor to obtain a probability of value X (i.e. the estimated area under the PDF curve). Without a width factor, the assumed class size is 1. A temporal PDF makes a PDF conditional, where the variable X is assumed to be a time or other increasing value. Essentially, a PDF will give the probability of value X occurring, while a TEMPORAL PDF will give the probability of X occurring given that if hasn’t occurred yet (i.e. given that that actual value of this variable will be >= X).

NORMAL PDF(Expr, Expr, Expr) normal probability density function, where the first expression is the value, the second is the mean and the third is the standard deviation
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

NORMAL CDF(Expr, Expr, Expr) normal cumulative density function, where the first expression is the value, the second is the mean and the third is the standard deviation
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

SKEWED NORMAL PDF(Expr, Expr, Expr, Expr) skewed normal probability density function,
where the first expression specifies the value,
the second is the mode and the third and fourth are the standard deviations to the left and right
of the mode.
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

SKEWED NORMAL CDF(Expr, Expr, Expr, Expr) skewed normal cumulative density function, where the first expression specifies the value,
the second is the mode, and the third and fourth are the left and right standard deviations
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

LOG NORMAL PDF(Expr, Expr, Expr) log normal probability density function, where
the first expression specifies the value, the
second is the mean and the third is the standard
deviation
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

LOG NORMAL CDF(Expr, Expr, Expr) log normal cumulative density function, where
the first expression specifies the value, the
second is the mean and the third is the standard
deviation
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

NORMAL TEMPORAL PDF(Expr, Expr, Expr) temporal normal probability density function
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

SKEWED NORMAL TEMPORAL PDF(Expr, Expr, Expr, Expr)
temporal skewed normal probability density
function
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

LOG NORMAL TEMPORAL PDF(Expr, Expr, Expr) temporal log normal probability density
function
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

UNIFORM TEMPORAL PDF(Expr, Expr, Expr) temporal uniform probability density expression
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

===Continuous Functions (Arithmetic Functions)===
<Variable> value of an independent variable <Variable>[Expr] value of a vector global variable
<Variable>[Expr, Expr] value of an array global variable

(Expr) value of the expression Expr + Expr sum of two expressions Expr - Expr value of the first expression minus the value
of the second expression Expr * Expr product of two expressions Expr / Expr value of the first expression divided by value
of the second expression Expr ^ Expr value of the first expression to the power of
the value of the second expression. An nth
root can be computed with1/n as the power.
| Expr | absolute value of the expression
ABS(Expr) absolute value of the expression
ABSOLUTE(Expr) absolute value of the expression

Expr % Expr value of the first expression modulo the value of
the second expression (assumes that the values
of the expressions are integers)
EXP(Expr) base of the natural logarithm (e) to the power of
the expression
LOG(Expr) natural logarithm of the value of the expression.
Logarithms in other bases can be computed as
logb(x) = ln(x) / ln(b)

ROUND(Expr) expression value rounded to the nearest integer
FLOOR(Expr) largest integer smaller than the expression value
CEILING(Expr) smallest integer larger than the expression value

CLAMP(Expr, MinExpr, MaxExpr) clamp the value X of the expression to the range
[Min, Max]: if X < Min then return Min; if X < Max return Max. Otherwise return X.

===Continuous Functions (Trigonometric Functions)===
Angles are all assumed to be in degrees (not radians). In SELES, angles in compass directions (i.e. zero is north, increasing clockwise, in contrast to geometry where zero is each increasing counter-clockwise).
SIN(Expr) interpret the value of the expression as an angle
theta in degrees, and return sin(theta)
COS(Expr) interpret the value of the expression as an angle
theta in degrees, and return cos(theta)
TAN(Expr) interpret the value of the expression as an angle
theta in degrees, and return tan(theta).
ARCSIN(Expr) inverse sine of the value of the expression
ARCCOS(Expr) inverse cos of the value of the expression
ARCTAN(Expr) inverse tan of the value of the expression
ARCTAN(Expr, Expr) inverse tan where first expression is x offset
and second is y offset. Providing two
expressions gives more information about the
quadrant.

===Continuous Functions (Miscellaneous)===
RESPONSE(Expr, #A, #B, #C) two-sided version of a standard response
function for the value X of the first expression:
if (X < A) return e^(-(X-A)^2/(2*(C^2))
else if (X > B) return e^(-(X-B)^2/(2*(C^2))
else return 1

DISTANCE(Expr, Expr) distance between two location indices (normally
obtained using the Location variable). Thus,
DISTANCE(loc1, loc2) is
sqrt(sqr(loc1.x – loc2.x) + sqr(loc1.y – loc2.y))

DIRECTION(Expr, Expr) angle in degrees between two location indices

===Classified and Discrete Functions===
CLASSIFY(X) if the value of the variable X is equal to one of
CLASS Number: Expr the classes listed, then return the result of the.
: associated expression. Otherwise return 0.
ENDFN

CLASSIFY(X) return the result of the kth expression in the list,
Expr where k = X – minimum value of the variables
: (this may be non-0 only for layers)
:
ENDFN

CLASSIFY(X): ( Number+) return the kth number in the list, where
k = X – minimum value of the variable (this
may be non-0 only for layers)

CLASSIFY(X): Filename uses the table in the named file, which is
assumed to consist of class:value pairs. Rarely
used.

CLASSIFY(X): Filename Key uses the table in the named file, which is
assumed to consist of class:value pairs. The key
is used to specify a sub-table in a multi-table
file. Rarely used.

Classified functions use the variable as an index into the list of numbers or expressions that follow. The “CLASS” keyword is optional. This variable must be non-negative. If “CLASS # :” is used, then the number refers to the value of the indexing variable. If a class is not specified for a given value, its expression is implicitly ZERO. Interpolation tables are very similar except that the variable is assumed to be continuous instead of classified. An interpolated value between classes is returned. Lookup tables are also similar, except that both the variable and classes are assumed to be continuous values. An interpolated value between classes is also returned. Rarely used.

INTERPOLATE(X) return an interpolated value where the value of
CLASS Number: Number variable X is placed between two classes or at
: either end of the table.
ENDFN

INTERPOLATE(X): ( Number+) same as above, except the classes are
implicitly 0, …. k-1

INTERPOLATE(X) same as above, except the values in the
CLASS Number: Expr table are obtained by evaluating expressions
:
ENDFN

INTERPOLATE(X) same as above, except the classes are
Expr implicitly 0, …, k-1
:
ENDFN

INTERPOLATE(X): Filename uses the table in the named file, which is
assumed to consist of class:value pairs

INTERPOLATE(X): Filename Key uses the table in the named file, which is
assumed to consist of class:value pairs. The key
is used to specify a sub-table in a multi-table
file.

LOOKUP(X) return the interpolated value where the value of
CLASS Number: Number variable X is placed between two classes or at
: either end of the table, and classes can be any.
ENDFN real values.

LOOKUP(X): ( Number+) same as above, except the classes are
implicitly 0, …. k-1

LOOKUP(X) same as above, except the values in the
CLASS Number: Expr table are obtained by evaluating expressions
:
ENDFN

LOOKUP(X) same as above, except the classes are
Expr implicitly 0, …, k-1
:
ENDFN

LOOKUP(X): Filename uses the table in the named file, which is
assumed to consist of class:value pairs

LOOKUP(X): Filename Key uses the table in the named file, which is
assumed to consist of class:value pairs. The key
is used to specify a sub-table in a multi-table
file

===Boolean Functions===
Expr EQ Expr TRUE if the values of the two expressions are
equal; otherwise FALSE
Expr == Expr alternate form of EQ comparison (Note: two equal signs distinguish this from an assignment)

Expr NEQ Expr TRUE if the values are not equal; otherwise
FALSE
Expr != Expr alternate form of NOT EQUAL comparison

Expr < Expr TRUE if the value of the first expression is less
than the value of the second expression;
otherwise FALSE
Expr <= Expr TRUE if the value of the first expression is less
than or equal to the value of the second
expression; otherwise FALSE

Expr > Expr TRUE if the value of the first expression is
greater than the value of the second
expression; otherwise FALSE
Expr >= Expr TRUE if the value of the first expression is
greater than or equal to the value of the
second expression; otherwise FALSE

!Expr Negates the expression Boolean value

Expr AND Expr TRUE if values of both expressions are
TRUE and FALSE otherwise

Expr OR Expr TRUE if value of at least one expression is
TRUE and FALSE otherwise

Note that relations can be cascaded, with the interpretation that each operator applies independently to its surrounding pair of expressions. Thus, the expression: Expression <= Expression <= Expression (e.g. 5 <= age <= 50) specifies a “between” relation, which is TRUE only if the value of the centre expression falls in the specified range.

===Bit-Vector Functions===
Bit-vector functions treat an integer value (the independent variable) as a sequence of bits, each of which can be independently set and accessed. This can allow use of a single layer to hold lots of Boolean information, since each cell as an integer has 8, 16 or 32 bits. For example, bits 0, 1, 2 and 3 can be used to store four different Boolean states (a, b, c and d), and the sequence 0110 means that states a and d are FALSE and states b and c are TRUE. PositionList is a semi-colon separated sequence of integer or ranges (lower-upper) indicating positions in the integer (0-31). For example, the PositionList 1;4-6;27 indicates bits at positions 1, 4, 5, 6 and 27.

SETAT(Expr, PositionList, #Type) Set the value specified by the expression, at
the positions in PositionList to: FALSE (0)
if Type is 0, TRUE (1) if Type is 1,
and flip the bits if Type = 2

SETAT(Expr, PositionList,#Type,#Prob) Same as above, except each position is set
with probability #Prob

SELECTAT(Expr, PositionList) FALSE(0) if none of the bits in PositionList are
set in the specified expression value and
TRUE(1) otherwise

MAX POSITION(Expr) Return the maximum 0-based bit position that is
set to one in the expression value (interpreted
as a bit-vector), or –1 if no bits are set

MIN POSITION(Expr) Return the minimum 0-based bit position that is
set to one in the expression value (interpreted
as a bit-vector), or –1 if no bits are set

BITWISE OR(Expr, Expr) Bitwise OR of two values
BITWISE AND(Expr, Expr) Bitwise AND of two values
BITWISE XOR(Expr, Expr) Bitwise exclusive-OR of two values
BITWISE NOT Expr Bitwise NOT of a value

SHIFT LEFT(Expr, Expr) Shifts value of first expression to the left by
number of bits specified by second expression
SHIFT RIGHT(Expr, Expr) Shifts value of first expression to the right by
number of bits specified by second expression

===Control Expressions===
Note the difference between the first two “functional if’s” (i.e. a value is returned) and the latter “procedural if’s” (that don’t return a value, but control flow).

IF Expr THEN Expr ELSE Expr if value of the IF expression is TRUE (>= 1), then return the value of the THEN expression,
otherwise return value of the ELSE expression

(Expr ? Expr : Expr) Same as above, but this form can be used as an
embedded sub-expression.

IF Expr Procedural IF statement to process
… sub-expressions denoted by “…” only if the
ENDFN expression evaluates to TRUE

IF Expr Procedural IF statement to process the first set
… of sub-expressions denoted by “…”if the
ELSE expression evaluates to TRUE and the set of
… sub-expressions after the ELSE otherwise. Note
ENDFN that “ELSE IF expr” forms can be strung
together

WHILE Expr While loop: process sub-expressions denoted by
… “…” while the expression evaluates to TRUE
ENDFN

PAUSE Halts the simulation and displays a dialog
box to which the user must respond to continue

PAUSE IF Expr If the expression evaluates to TRUE, halts the
simulation and displays a dialog box to which
the user must respond to continue

PAUSE(#Value) Pauses the simulation for the specified number
of milliseconds and then continues

PAUSE(#Value) IF Expr If the expression evaluates to TRUE, Pauses the
simulation for the specified number of
milliseconds and then continues

WAIT UNTIL Expr Suspend execution until the expression returns TRUE (1). This is intended for controlling
communication and synchronization with
an external application.
CRITICAL SECTION (Flag) Enter (if Flag is TRUE) or exit (if Flag is FALSE) a critical section. A critical section gives priority to this application, and is used for
synchronizing access to shared variables
(i.e. shared with another application).

DEBUG Update the simulation probe, if it is loaded and
The event is selected. Used to debug/verify
event behaviour.

SEED() Gets the random number seed
SEED(Expr) Sets the random number seed. Value returned is
next seed.

RESIZE(Variable, Expr) Changes size (number of entries) in a global
variable. Values are not maintained. Useful for
when size is not known prior to simulation.

RECOMPUTE Only valid in consequent expressions of
ProbInit and also when ProbInit recompute flag
has been set. Causes prob. surface to be
recomputed before next selection
===Output Expressions===
DISPLAY Display on the screen the labelled Label: Expr values computed with the expressions listed.
…. If no label is given, the expression must
ENDFN be a variable, and this is used for the label.

DISPLAY Same as above, but only display if the DECISION Expr decision expression evaluates to TRUE
Label: Expr The keyword DECISION can be replaced by
…. a “?”
ENDFN

OUTPUT RECORD(OutputVar) Output to the record file of output variable the labelled values computed with the Label: Expr expressions listed. If no label is given, the
…. Expression must be a variable and this is
ENDFN used as label.

OUTPUT RECORD(OutputVar) Same as above, but only output if the DECISION Expr decision expression evaluates to TRUE
Label: Expr
….
ENDFN

Note: a label/expression pair can be “expanded” by using the form: Label#n1:n2: Expr, where n1 and n2 are integers or constant names. This will create n2-n1+1 columns rather than a single column. The system variable Index can be used in the expression, and will take on values n1, n1+1,…,n2 for each column, respectively.

===Composite Functions===
Compound expressions all have the same form of an expression name followed by a list of sub-expressions. If the first expression is a region function, then the subsequent expressions are all evaluated over the defined region, instead of only at the current cell (however, it is usually simpler to use an OVER REGION expression). When arithmetic expression become complex, sometimes composite expressions can be written more clearly. The general format is as follows:

CompositeExpressionName
Expr
:
ENDFN

The following composite expressions are supported:

===SUM===
DESCRIPTION:
Returns the number that is the sum of all the expressions.

USAGE:
x=SUM
Expr
...
ENDFN

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value.

VALUE:
the sum of all the arguments.

SEE ALSO:
<a link to the composite functions section of seles modellers guide>

EXAMPLES: <add carriage return here>
Example 1:
y = 3
x = SUM
y
y+2
5
ENDFN
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

===PRODUCT===
product of the sub-expressions

DIVIDE successive division of the sub-expressions

MEAN average of the sub-expressions

GEOMETRIC MEAN geometric mean of the sub-expressions (nth
root of the product for n expressions)

MIN minimum of the sub-expressions

MAX maximum of the sub-expressions

EQUAL TRUE (1) if the sub-expressions all evaluate to
the same value and FALSE (0) otherwise
NOT EQUAL FALSE (0) if the sub-expressions all evaluate to
the same value and TRUE (1) otherwise

OR TRUE (1) if at least one sub-expression
evaluates to TRUE and FALSE (0) otherwise

AND TRUE (1) if all sub-expressions evaluate to
TRUE and FALSE (0) otherwise

LESS OR EQUAL TRUE (1) if the sub-expression evaluations are
all ordered according to the relation <=, and
FALSE (0) otherwise

ORDERED same as LESS OR EQUAL

LESS THAN TRUE (1) if the sub-expression evaluations are
all ordered according to the relation <, and
FALSE (0) otherwise

STRICT ORDERED same as LESS THAN

GREATER OR EQUAL TRUE (1) if the sub-expression evaluations are
all ordered according to the relation >=, and
FALSE (0) otherwise

GREATER THAN TRUE (1) if the sub-expression evaluations are
all ordered according to the relation >, and
FALSE (0) otherwise

===Region Functions===
A region function returns the set of locations, one on each call. Their use is limited to the main expression of EventLocation, SpreadLocation, AgentLocation and MoveLocation properties, as the first expression of composite expressions and in OVER REGION functions.

REGION WHOLE MAP defines the region consisting of the entire
DECISION Expr landscape. If there is a decision expression,
then only those cells for which this expression
returns TRUE will be included.

REGION RECT (Expr, Expr, Expr, Expr) defines a rectangular region. If there is a
DECISION Expr decision expression defined, then only those
cells for which this expression returns
TRUE will be included

REGION CENTRED (Expr, Expr [, DistanceType][, WRAPPED])
DECISION Expr defines a region centred on the current cell.
If there is a decision expression, then only
those cells for which this expression returns
TRUE will be included.

DistanceType is either CARDINAL or EUCLIDEAN (the default). Cardinal distance between two cells is the minimum number of cardinal steps (up, down, left, right) to reach one cell from the other. Euclidean distance is the straight-line distance between two points. The WRAPPED flag, if present indicates that the region wraps around the sides (vertically and horizontally) of the landscape (e.g. a location x positions beyond the right-hand side of a raster will be mapped to x positions in from the left-hand side of the raster). If not present, the landscape does not wrap.

REGION LOCATION LIST(Number+) defines the region consisting of a set of
DECISION Expr known location indices. If there is a decision expression, then only those cells for which this
expression returns TRUE will be included.

REGION LOCATION LIST(X,n) defines the region consisting of a set of n
DECISION Expr location indices stored in one-dimensional X.

REGION LOCATION (Expr) defines the region consisting of a of a single
DECISION Expr location index. If there is a decision expression,
then only those cells for which this expression
returns TRUE will be included.

REGION VECTOR (StartLocation, EndLocation) defines region consisting of cells along an
DECISION Expr approximation of line between end cells

Cost surface and least-cost path regions are advanced features that are best understood with an example model.

REGION COST SURFACE(EndLocation, MaxCost, CostSurface)
DECISION Expr
COST Expr
REGION COST SURFACE(EndLocation, MaxCost, CostSurface, LeastCostNeighbs, AnchorLoc)
DECISION Expr
COST Expr
Defines a region surrounding a cell with
cumulative costs less than MaxCost. Stops
growing when EndLocation is reached or all
costs are greater than MaxCost. Second form
also records gradient and anchor location
layers. The CostSurface layer records the
cumulative cost from the cost function

REGION LEAST COST PATH(StartLocation, EndLocation)
DECISION Expr
COST Expr
REGION LEAST COST PATH(StartLocation, EndLocation, LeastCostNeighbs)
DECISION Expr
REGION LEAST COST PATH(StartLocation, EndLocation, LeastCostNeighbs, AnchorLoc)
DECISION Expr
Defines a region with cells that approximate
the least-cost path between two cells. The
first generates the cost function internally.
The latter two use input information from a
pre-computed cost surface region. Providing
both the gradient and anchor location layers
provides the most accurate approximation.

Iteration is a common aspect of models (even if it is very procedural). Most programming languages offer a “for-loop” of some kind. SELES presently provides “over index sequence” expressions as a slightly more declarative (although also more cumbersome) expression for iterating. While-loops can also be used.

OVER INDEX SEQUENCE(Expr, Expr) defines linear sequence of location indices.
DECISION Expr If there is a decision expression, then only
those cells for which this expression returns
TRUE will be included. The system variable
Index holds the value of the index at each value
in the sequence

Over region expressions are very frequently used to visit all cells in a landscape that meet some condition (e.g. to compute the size of the forest at initiation).

OVER RegionFunction Apply a set of sub-expressions at all spatial
Expression locations specified by a region function
:
ENDFN

AT LOCATION #Expr Apply a set of state-changes at a specified
Expression location
:
ENDFN

===Matrix Functions===
Matrix assignment is indicated using “[=]” instead of “=”. The proper dimensions of the component arrays must be met.

Variable [=] Variable assign variable of same dimension, or a
single value to all entries
Variable [=] Variable + Variable sum variables of same dimension (or with a
constant)
Variable [=] Variable - Variable subtract variables of same dimension (or
with a constant)
Variable [=] Variable * Variable matrix or scalar multiplication.

Variable [=] TRANSPOSE(Variable) matrix transposition
Variable [=] Variable^-1 invert a matrix
Variable = SUM(Variable) sum all entries in a matrix
Variable [=] SUM ROWS (Variable) sum all rows of a matrix (result has one
value per column)
Variable [=] SUM COLS(Variable) sum all columns of a matrix

Variables [=] SORT(Variable, Expr) sort rows of an input matrix where rank is
given by Expr. The system variable “Index”
can appear in the expression and will take on
the range of indices in the input array. The
resulting sorted matrix will be assigned.

Variable [=] MPM_MULT(Variable, Variable) Performs a “matrix population model”
(MPM) integer-based multiplication.
Assumes that first matrix is two-dimensional
and that second is a vector. The result is
two-dimensional, where entries above
diagonal represent "offspring", entries on the
diagonal represent "survivors" and entries
below the diagonal represent "succeeders"

Variable [=] CONTAG(Variable, Variable) Creates a “temporal contagion” matrix.
Given probabilities (first parameter) for a set
of states and a two-dimensional contagion
array (values –1 to 1 indicating affinity),
generates a matrix where each row is a prob.
dist. For transitions given the row value, and
the overall target dist. will be met.

===General Set, List and Graph Functions===
REMOVE ALL(LinkedVariable) clears variable. No return value
SIZE(LinkedVariable) number of elements, entries or nodes
IS EMPTY(LinkedVariable) TRUE if and only if variable has 0 elements

FIRST(LinkedVariable) returns position of first element, entry or
node
NEXT(LinkedVariable, PosVariable) returns position of element, entry or node
following position provided
PREV(LinkedVariable, PosVariable) returns position of element, entry or node
preceding position provided
REMOVE(LinkedVariable, PosVariable) remove and deletes element, entry or node
at position

Variable [=] GET(LinkedVariable, PosVariable) get element, entry or node at position
X [=] GET(LinkedVariable, PosVariable, Index) get single value in a given index
SET(LinkedVariable, PosVariable, Variable) set element, entry or node at position
SET(LinkedVariable, PosVariable, entryIndex, Value)
set value at specified index of element,
entry or node at position
FIND(LinkedVariable, , TmpVariable Condition) return first position of an element, entry or
node that satisfies the condition
FIND NEXT(LinkedVariable, PosVariable, TmpVariable, Condition)
return next position of an element, entry or
node that satisfies the condition
SORT(LinkedVariable, TmpVariable1, TmpVariable2, Condition)
sort elements, entries or nodes according to
condition

===Set Functions===
CONTAINS(SetVariable, ElementVariable) TRUE if and only if set variable “contains”
variable provided, where two elements are
identical if they have identical values
INSERT(SetVariable, ElementVariable) add element to set. Only changes set if it
doesn’t already contain the element
SetVariable = UNION(Set1, Set2) take union of two set variables
SetVariable = INTERSECTION(Sete1, Set2) take intersection of two set variables
SetVariable = SUBTRACT(Sete1, Set2) subtract second set variable from first

===List Functions===
HEAD(ListVariable) returns position of first entry
TAIL(ListVariable) returns position of last entry
INSERT HEAD(ListVariable, EntryElement) add an entry to front of list
INSERT TAIL(ListVariable, EntryElement) add an entry to end of list
INSERT BEFORE(ListVariable, Index, EntryElement)
add an entry before given index
INSERT AFTER(ListVariable, Index, EntryElement)
add an entry after given index
INSERT AT(ListVariable, Index, EntryElement) add an entry at given index

REMOVE HEAD(ListVariable) removes and deletes first entry
REMOVE TAIL (ListVariable) removes and deletes last entry
REMOVE AT INDEX(ListVariable, Index) removes and deletes entry at given index

Variable [=] GET HEAD(ListVariable) returns first entry
Variable [=] GET TAIL(ListVariable) returns first entry
Variable [=] GET AT INDEX(ListVariable, Index) returns entry at given index
Pos = POS AT INDEX(ListVariable, Index) returns position at given index

===Tree Functions===
ADD ROOT(TreeVariable, EntryElement) add root element of a tree
INSERT LEFT CHILD(TreeVariable, PosVariable, EntryElement)
add child to a node on the left of current
children
INSERT RIGHT CHILD(TreeVariable, PosVariable, EntryElement)
add child to a node on the right of current
children
INSERT CHILD(TreeVariable, PosVariable, EntryElement, Index)
add child to a node at given index (from
left)

n = CHILDREN(TreeVariable, PosVariable) number of children at a given position
Pos = PARENT(TreeVariable, PosVariable) Position of parent of a node
Pos = LEFT CHILD(TreeVariable, PosVariable) Position of leftmost child of a node
Pos = RIGHT CHILD(TreeVariable, PosVariable) Position of rightmost child of a node
Pos = CHILD(TreeVariable, PosVariable, Index) Position of indexed (from left) child of a
node
Pos = NEXT SIBLING(TreeVariable, PosVariable) Position of next sibling to right of a node
Pos = PREV SIBLING(TreeVariable, PosVariable) Position of previous sibling to right of a
node

Pos = NEXT DFS(TreeVariable, PosVariable) Position of next node in depth-first
pre-order traversal of a tree. If the position
variable is NULL, then the root is returned
Pos = NEXT POSTORDER DFS(TreeVariable, PosVariable)
Position of next node in depth-first
post-order traversal of a tree. If the position
variable is NULL, then the root is returned
Variable [=] GET LEFT CHILD(TreeVariable, PosVariable)
returns entry of leftmost child for a given
node
Variable [=] GET RIGHT CHILD(TreeVariable, PosVariable)
returns entry of rightmost child for a given
node
Variable [=] GET CHILD(TreeVariable, PosVariable, Index)
returns entry of child with given index
(from left) for a given node

===Graph Functions===
REMOVE ALL LINKS(GraphVariable) clears links of a graph variable
SIZE LINKS(GraphVariable) number of links in graph
IS EMPTY LINKS(GraphVariable) TRUE if and only if graph has 0 links

FIRST LINK(GraphVariable) returns position of first link
NEXT LINK (GraphVariable, PosVariable) returns position of link following position
provided
PREV LINK (GraphVariable, PosVariable) returns position of link preceding position
provided
Variable [=] GET LINK(GraphVariable, PosVariable)
get link at position
CONTAINS LINK(GraphVariable, LinkVariable) TRUE if and only if graph variable contains
variable provided
REMOVE LINK(GraphVariable, PosVariable) remove and deletes link at position
SET LINK(GraphVariable, PosVariable, LinkVariable)
Set link at position
SET LINK(GraphVariable, PosVariable, entryIndex, Value)
Set value at specified index of link at
position
FIND LINK(GraphVariable, TmpVariable, Condition)
Return first position of link that satisfies the
condition
FIND NEXT LINK(GraphVariable, PosVariable, TmpVariable, Condition)
Return next position of a link that satisfies
the condition
SORT LINKS(GraphVariable, TmpVariable1, TmpVariable2, Condition)
Sort links according to condition
LINKED(GraphVariable, NodeVariable1, NodeVariable2, LinkType)
TRUE if the nodes are linked. Set LinkType
to 0 for direct links and 1 for indirect

Language Reference

2006-10-03T14:35:02Z

128.100.72.168:

==Constants==
===ZERO===
return 0.0
===ONE===
return 1.0
#Number return value of the number specified
<Constant> return value of a named constant
<Constant>[Expr] return value of a named vector constant
<Constant>[Expr, Expr] return value of a named array constant
<Macro>[Expr] return value of expression at specified index
in macro

==Probability Distributions==
===NORMAL===
(Expr, Expr) draw a value from a normal distribution, where
the first expression specifies the mean and
the second specifies the standard deviation

===SKEWED NORMAL===
(Expr, Expr, Expr) draw a value from a skewed normal distribution, where the first expression specifies the mode
and the second and third specify the standard
deviations to the left and right of the mode
===LOG NORMAL===
(Expr, Expr) draw a value from a log normal distribution,
where the first expression specifies the mean
and the second specifies the standard deviation
of the underlying normal distribution

===WEIBULL===
(Expr, Expr) draw a value from a Weibull distribution, where
the first expression specifies the beta and the
second specifies alpha (Note:terminology varies
between sources. The version here is equivalent
to that in Excel, with reversal of parameters).

NEGEXP(Expr) draw a value from a negative exponential distribution, where the expression specifies the
mean
POISSION(Expr) draw a value from a Poisson distribution

UNIFORM(Expr, Expr) draw a value from a uniform distribution, where the first expression determines the minimum value and the second determines the maximum
CLASSIFIED_DIST draw a value from a discrete distribution, where CLASS Number: Expr each expression determines the relative : probability of its associated class being drawn. ENDFN The CLASS keyword is optional.

CLASSIFIED_DIST( Number+) in this form, the classes are assumed to start at zero. Only constant probabilities can be given.

CLASSIFIED_DIST in this form, the classes are assumed to start at Expr zero :
ENDFN

CLASSIFIED_DIST[M] In this form, the classes in a one-dimensional
array M, and so start at zero.

===Probability Density and Cumulative Density Functions===
The following are a set of probability and cumulative density expressions. The results from probability density expressions should be multiplied by a width factor to obtain a probability of value X (i.e. the estimated area under the PDF curve). Without a width factor, the assumed class size is 1. A temporal PDF makes a PDF conditional, where the variable X is assumed to be a time or other increasing value. Essentially, a PDF will give the probability of value X occurring, while a TEMPORAL PDF will give the probability of X occurring given that if hasn’t occurred yet (i.e. given that that actual value of this variable will be >= X).

NORMAL PDF(Expr, Expr, Expr) normal probability density function, where the first expression is the value, the second is the mean and the third is the standard deviation
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

NORMAL CDF(Expr, Expr, Expr) normal cumulative density function, where the first expression is the value, the second is the mean and the third is the standard deviation
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

SKEWED NORMAL PDF(Expr, Expr, Expr, Expr) skewed normal probability density function,
where the first expression specifies the value,
the second is the mode and the third and fourth are the standard deviations to the left and right
of the mode.
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

SKEWED NORMAL CDF(Expr, Expr, Expr, Expr) skewed normal cumulative density function, where the first expression specifies the value,
the second is the mode, and the third and fourth are the left and right standard deviations
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

LOG NORMAL PDF(Expr, Expr, Expr) log normal probability density function, where
the first expression specifies the value, the
second is the mean and the third is the standard
deviation
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

LOG NORMAL CDF(Expr, Expr, Expr) log normal cumulative density function, where
the first expression specifies the value, the
second is the mean and the third is the standard
deviation
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

NORMAL TEMPORAL PDF(Expr, Expr, Expr) temporal normal probability density function
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

SKEWED NORMAL TEMPORAL PDF(Expr, Expr, Expr, Expr)
temporal skewed normal probability density
function
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

LOG NORMAL TEMPORAL PDF(Expr, Expr, Expr) temporal log normal probability density
function
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

UNIFORM TEMPORAL PDF(Expr, Expr, Expr) temporal uniform probability density expression
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

===Continuous Functions (Arithmetic Functions)===
<Variable> value of an independent variable <Variable>[Expr] value of a vector global variable
<Variable>[Expr, Expr] value of an array global variable

(Expr) value of the expression Expr + Expr sum of two expressions Expr - Expr value of the first expression minus the value
of the second expression Expr * Expr product of two expressions Expr / Expr value of the first expression divided by value
of the second expression Expr ^ Expr value of the first expression to the power of
the value of the second expression. An nth
root can be computed with1/n as the power.
| Expr | absolute value of the expression
ABS(Expr) absolute value of the expression
ABSOLUTE(Expr) absolute value of the expression

Expr % Expr value of the first expression modulo the value of
the second expression (assumes that the values
of the expressions are integers)
EXP(Expr) base of the natural logarithm (e) to the power of
the expression
LOG(Expr) natural logarithm of the value of the expression.
Logarithms in other bases can be computed as
logb(x) = ln(x) / ln(b)

ROUND(Expr) expression value rounded to the nearest integer
FLOOR(Expr) largest integer smaller than the expression value
CEILING(Expr) smallest integer larger than the expression value

CLAMP(Expr, MinExpr, MaxExpr) clamp the value X of the expression to the range
[Min, Max]: if X < Min then return Min; if X < Max return Max. Otherwise return X.

===Continuous Functions (Trigonometric Functions)===
Angles are all assumed to be in degrees (not radians). In SELES, angles in compass directions (i.e. zero is north, increasing clockwise, in contrast to geometry where zero is each increasing counter-clockwise).
SIN(Expr) interpret the value of the expression as an angle
theta in degrees, and return sin(theta)
COS(Expr) interpret the value of the expression as an angle
theta in degrees, and return cos(theta)
TAN(Expr) interpret the value of the expression as an angle
theta in degrees, and return tan(theta).
ARCSIN(Expr) inverse sine of the value of the expression
ARCCOS(Expr) inverse cos of the value of the expression
ARCTAN(Expr) inverse tan of the value of the expression
ARCTAN(Expr, Expr) inverse tan where first expression is x offset
and second is y offset. Providing two
expressions gives more information about the
quadrant.

===Continuous Functions (Miscellaneous)===
RESPONSE(Expr, #A, #B, #C) two-sided version of a standard response
function for the value X of the first expression:
if (X < A) return e^(-(X-A)^2/(2*(C^2))
else if (X > B) return e^(-(X-B)^2/(2*(C^2))
else return 1

DISTANCE(Expr, Expr) distance between two location indices (normally
obtained using the Location variable). Thus,
DISTANCE(loc1, loc2) is
sqrt(sqr(loc1.x – loc2.x) + sqr(loc1.y – loc2.y))

DIRECTION(Expr, Expr) angle in degrees between two location indices

===Classified and Discrete Functions===
CLASSIFY(X) if the value of the variable X is equal to one of
CLASS Number: Expr the classes listed, then return the result of the.
: associated expression. Otherwise return 0.
ENDFN

CLASSIFY(X) return the result of the kth expression in the list,
Expr where k = X – minimum value of the variables
: (this may be non-0 only for layers)
:
ENDFN

CLASSIFY(X): ( Number+) return the kth number in the list, where
k = X – minimum value of the variable (this
may be non-0 only for layers)

CLASSIFY(X): Filename uses the table in the named file, which is
assumed to consist of class:value pairs. Rarely
used.

CLASSIFY(X): Filename Key uses the table in the named file, which is
assumed to consist of class:value pairs. The key
is used to specify a sub-table in a multi-table
file. Rarely used.

Classified functions use the variable as an index into the list of numbers or expressions that follow. The “CLASS” keyword is optional. This variable must be non-negative. If “CLASS # :” is used, then the number refers to the value of the indexing variable. If a class is not specified for a given value, its expression is implicitly ZERO. Interpolation tables are very similar except that the variable is assumed to be continuous instead of classified. An interpolated value between classes is returned. Lookup tables are also similar, except that both the variable and classes are assumed to be continuous values. An interpolated value between classes is also returned. Rarely used.

INTERPOLATE(X) return an interpolated value where the value of
CLASS Number: Number variable X is placed between two classes or at
: either end of the table.
ENDFN

INTERPOLATE(X): ( Number+) same as above, except the classes are
implicitly 0, …. k-1

INTERPOLATE(X) same as above, except the values in the
CLASS Number: Expr table are obtained by evaluating expressions
:
ENDFN

INTERPOLATE(X) same as above, except the classes are
Expr implicitly 0, …, k-1
:
ENDFN

INTERPOLATE(X): Filename uses the table in the named file, which is
assumed to consist of class:value pairs

INTERPOLATE(X): Filename Key uses the table in the named file, which is
assumed to consist of class:value pairs. The key
is used to specify a sub-table in a multi-table
file.

LOOKUP(X) return the interpolated value where the value of
CLASS Number: Number variable X is placed between two classes or at
: either end of the table, and classes can be any.
ENDFN real values.

LOOKUP(X): ( Number+) same as above, except the classes are
implicitly 0, …. k-1

LOOKUP(X) same as above, except the values in the
CLASS Number: Expr table are obtained by evaluating expressions
:
ENDFN

LOOKUP(X) same as above, except the classes are
Expr implicitly 0, …, k-1
:
ENDFN

LOOKUP(X): Filename uses the table in the named file, which is
assumed to consist of class:value pairs

LOOKUP(X): Filename Key uses the table in the named file, which is
assumed to consist of class:value pairs. The key
is used to specify a sub-table in a multi-table
file

===Boolean Functions===
Expr EQ Expr TRUE if the values of the two expressions are
equal; otherwise FALSE
Expr == Expr alternate form of EQ comparison (Note: two equal signs distinguish this from an assignment)

Expr NEQ Expr TRUE if the values are not equal; otherwise
FALSE
Expr != Expr alternate form of NOT EQUAL comparison

Expr < Expr TRUE if the value of the first expression is less
than the value of the second expression;
otherwise FALSE
Expr <= Expr TRUE if the value of the first expression is less
than or equal to the value of the second
expression; otherwise FALSE

Expr > Expr TRUE if the value of the first expression is
greater than the value of the second
expression; otherwise FALSE
Expr >= Expr TRUE if the value of the first expression is
greater than or equal to the value of the
second expression; otherwise FALSE

!Expr Negates the expression Boolean value

Expr AND Expr TRUE if values of both expressions are
TRUE and FALSE otherwise

Expr OR Expr TRUE if value of at least one expression is
TRUE and FALSE otherwise

Note that relations can be cascaded, with the interpretation that each operator applies independently to its surrounding pair of expressions. Thus, the expression: Expression <= Expression <= Expression (e.g. 5 <= age <= 50) specifies a “between” relation, which is TRUE only if the value of the centre expression falls in the specified range.

===Bit-Vector Functions===
Bit-vector functions treat an integer value (the independent variable) as a sequence of bits, each of which can be independently set and accessed. This can allow use of a single layer to hold lots of Boolean information, since each cell as an integer has 8, 16 or 32 bits. For example, bits 0, 1, 2 and 3 can be used to store four different Boolean states (a, b, c and d), and the sequence 0110 means that states a and d are FALSE and states b and c are TRUE. PositionList is a semi-colon separated sequence of integer or ranges (lower-upper) indicating positions in the integer (0-31). For example, the PositionList 1;4-6;27 indicates bits at positions 1, 4, 5, 6 and 27.

SETAT(Expr, PositionList, #Type) Set the value specified by the expression, at
the positions in PositionList to: FALSE (0)
if Type is 0, TRUE (1) if Type is 1,
and flip the bits if Type = 2

SETAT(Expr, PositionList,#Type,#Prob) Same as above, except each position is set
with probability #Prob

SELECTAT(Expr, PositionList) FALSE(0) if none of the bits in PositionList are
set in the specified expression value and
TRUE(1) otherwise

MAX POSITION(Expr) Return the maximum 0-based bit position that is
set to one in the expression value (interpreted
as a bit-vector), or –1 if no bits are set

MIN POSITION(Expr) Return the minimum 0-based bit position that is
set to one in the expression value (interpreted
as a bit-vector), or –1 if no bits are set

BITWISE OR(Expr, Expr) Bitwise OR of two values
BITWISE AND(Expr, Expr) Bitwise AND of two values
BITWISE XOR(Expr, Expr) Bitwise exclusive-OR of two values
BITWISE NOT Expr Bitwise NOT of a value

SHIFT LEFT(Expr, Expr) Shifts value of first expression to the left by
number of bits specified by second expression
SHIFT RIGHT(Expr, Expr) Shifts value of first expression to the right by
number of bits specified by second expression

===Control Expressions===
Note the difference between the first two “functional if’s” (i.e. a value is returned) and the latter “procedural if’s” (that don’t return a value, but control flow).

IF Expr THEN Expr ELSE Expr if value of the IF expression is TRUE (>= 1), then return the value of the THEN expression,
otherwise return value of the ELSE expression

(Expr ? Expr : Expr) Same as above, but this form can be used as an
embedded sub-expression.

IF Expr Procedural IF statement to process
… sub-expressions denoted by “…” only if the
ENDFN expression evaluates to TRUE

IF Expr Procedural IF statement to process the first set
… of sub-expressions denoted by “…”if the
ELSE expression evaluates to TRUE and the set of
… sub-expressions after the ELSE otherwise. Note
ENDFN that “ELSE IF expr” forms can be strung
together

WHILE Expr While loop: process sub-expressions denoted by
… “…” while the expression evaluates to TRUE
ENDFN

PAUSE Halts the simulation and displays a dialog
box to which the user must respond to continue

PAUSE IF Expr If the expression evaluates to TRUE, halts the
simulation and displays a dialog box to which
the user must respond to continue

PAUSE(#Value) Pauses the simulation for the specified number
of milliseconds and then continues

PAUSE(#Value) IF Expr If the expression evaluates to TRUE, Pauses the
simulation for the specified number of
milliseconds and then continues

WAIT UNTIL Expr Suspend execution until the expression returns TRUE (1). This is intended for controlling
communication and synchronization with
an external application.
CRITICAL SECTION (Flag) Enter (if Flag is TRUE) or exit (if Flag is FALSE) a critical section. A critical section gives priority to this application, and is used for
synchronizing access to shared variables
(i.e. shared with another application).

DEBUG Update the simulation probe, if it is loaded and
The event is selected. Used to debug/verify
event behaviour.

SEED() Gets the random number seed
SEED(Expr) Sets the random number seed. Value returned is
next seed.

RESIZE(Variable, Expr) Changes size (number of entries) in a global
variable. Values are not maintained. Useful for
when size is not known prior to simulation.

RECOMPUTE Only valid in consequent expressions of
ProbInit and also when ProbInit recompute flag
has been set. Causes prob. surface to be
recomputed before next selection
===Output Expressions===
DISPLAY Display on the screen the labelled Label: Expr values computed with the expressions listed.
…. If no label is given, the expression must
ENDFN be a variable, and this is used for the label.

DISPLAY Same as above, but only display if the DECISION Expr decision expression evaluates to TRUE
Label: Expr The keyword DECISION can be replaced by
…. a “?”
ENDFN

OUTPUT RECORD(OutputVar) Output to the record file of output variable the labelled values computed with the Label: Expr expressions listed. If no label is given, the
…. Expression must be a variable and this is
ENDFN used as label.

OUTPUT RECORD(OutputVar) Same as above, but only output if the DECISION Expr decision expression evaluates to TRUE
Label: Expr
….
ENDFN

Note: a label/expression pair can be “expanded” by using the form: Label#n1:n2: Expr, where n1 and n2 are integers or constant names. This will create n2-n1+1 columns rather than a single column. The system variable Index can be used in the expression, and will take on values n1, n1+1,…,n2 for each column, respectively.

===Composite Functions===
Compound expressions all have the same form of an expression name followed by a list of sub-expressions. If the first expression is a region function, then the subsequent expressions are all evaluated over the defined region, instead of only at the current cell (however, it is usually simpler to use an OVER REGION expression). When arithmetic expression become complex, sometimes composite expressions can be written more clearly. The general format is as follows:

CompositeExpressionName
Expr
:
ENDFN

The following composite expressions are supported:

===SUM===
DESCRIPTION:
Returns the number that is the sum of all the expressions.

USAGE:
x=SUM
Expr
...
ENDFN

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value.

VALUE:
the sum of all the arguments.

SEE ALSO:
<a link to the composite functions section of seles modellers guide>

EXAMPLES: <add carriage return here>
Example 1:
y = 3
x = SUM
y
y+2
5
ENDFN
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

===PRODUCT===
product of the sub-expressions

DIVIDE successive division of the sub-expressions

MEAN average of the sub-expressions

GEOMETRIC MEAN geometric mean of the sub-expressions (nth
root of the product for n expressions)

MIN minimum of the sub-expressions

MAX maximum of the sub-expressions

EQUAL TRUE (1) if the sub-expressions all evaluate to
the same value and FALSE (0) otherwise
NOT EQUAL FALSE (0) if the sub-expressions all evaluate to
the same value and TRUE (1) otherwise

OR TRUE (1) if at least one sub-expression
evaluates to TRUE and FALSE (0) otherwise

AND TRUE (1) if all sub-expressions evaluate to
TRUE and FALSE (0) otherwise

LESS OR EQUAL TRUE (1) if the sub-expression evaluations are
all ordered according to the relation <=, and
FALSE (0) otherwise

ORDERED same as LESS OR EQUAL

LESS THAN TRUE (1) if the sub-expression evaluations are
all ordered according to the relation <, and
FALSE (0) otherwise

STRICT ORDERED same as LESS THAN

GREATER OR EQUAL TRUE (1) if the sub-expression evaluations are
all ordered according to the relation >=, and
FALSE (0) otherwise

GREATER THAN TRUE (1) if the sub-expression evaluations are
all ordered according to the relation >, and
FALSE (0) otherwise

===Region Functions===
A region function returns the set of locations, one on each call. Their use is limited to the main expression of EventLocation, SpreadLocation, AgentLocation and MoveLocation properties, as the first expression of composite expressions and in OVER REGION functions.

REGION WHOLE MAP defines the region consisting of the entire
DECISION Expr landscape. If there is a decision expression,
then only those cells for which this expression
returns TRUE will be included.

REGION RECT (Expr, Expr, Expr, Expr) defines a rectangular region. If there is a
DECISION Expr decision expression defined, then only those
cells for which this expression returns
TRUE will be included

REGION CENTRED (Expr, Expr [, DistanceType][, WRAPPED])
DECISION Expr defines a region centred on the current cell.
If there is a decision expression, then only
those cells for which this expression returns
TRUE will be included.

DistanceType is either CARDINAL or EUCLIDEAN (the default). Cardinal distance between two cells is the minimum number of cardinal steps (up, down, left, right) to reach one cell from the other. Euclidean distance is the straight-line distance between two points. The WRAPPED flag, if present indicates that the region wraps around the sides (vertically and horizontally) of the landscape (e.g. a location x positions beyond the right-hand side of a raster will be mapped to x positions in from the left-hand side of the raster). If not present, the landscape does not wrap.

REGION LOCATION LIST(Number+) defines the region consisting of a set of
DECISION Expr known location indices. If there is a decision expression, then only those cells for which this
expression returns TRUE will be included.

REGION LOCATION LIST(X,n) defines the region consisting of a set of n
DECISION Expr location indices stored in one-dimensional X.

REGION LOCATION (Expr) defines the region consisting of a of a single
DECISION Expr location index. If there is a decision expression,
then only those cells for which this expression
returns TRUE will be included.

REGION VECTOR (StartLocation, EndLocation) defines region consisting of cells along an
DECISION Expr approximation of line between end cells

Cost surface and least-cost path regions are advanced features that are best understood with an example model.

REGION COST SURFACE(EndLocation, MaxCost, CostSurface)
DECISION Expr
COST Expr
REGION COST SURFACE(EndLocation, MaxCost, CostSurface, LeastCostNeighbs, AnchorLoc)
DECISION Expr
COST Expr
Defines a region surrounding a cell with
cumulative costs less than MaxCost. Stops
growing when EndLocation is reached or all
costs are greater than MaxCost. Second form
also records gradient and anchor location
layers. The CostSurface layer records the
cumulative cost from the cost function

REGION LEAST COST PATH(StartLocation, EndLocation)
DECISION Expr
COST Expr
REGION LEAST COST PATH(StartLocation, EndLocation, LeastCostNeighbs)
DECISION Expr
REGION LEAST COST PATH(StartLocation, EndLocation, LeastCostNeighbs, AnchorLoc)
DECISION Expr
Defines a region with cells that approximate
the least-cost path between two cells. The
first generates the cost function internally.
The latter two use input information from a
pre-computed cost surface region. Providing
both the gradient and anchor location layers
provides the most accurate approximation.

Iteration is a common aspect of models (even if it is very procedural). Most programming languages offer a “for-loop” of some kind. SELES presently provides “over index sequence” expressions as a slightly more declarative (although also more cumbersome) expression for iterating. While-loops can also be used.

OVER INDEX SEQUENCE(Expr, Expr) defines linear sequence of location indices.
DECISION Expr If there is a decision expression, then only
those cells for which this expression returns
TRUE will be included. The system variable
Index holds the value of the index at each value
in the sequence

Over region expressions are very frequently used to visit all cells in a landscape that meet some condition (e.g. to compute the size of the forest at initiation).

OVER RegionFunction Apply a set of sub-expressions at all spatial
Expression locations specified by a region function
:
ENDFN

AT LOCATION #Expr Apply a set of state-changes at a specified
Expression location
:
ENDFN

===Matrix Functions===
Matrix assignment is indicated using “[=]” instead of “=”. The proper dimensions of the component arrays must be met.

Variable [=] Variable assign variable of same dimension, or a
single value to all entries
Variable [=] Variable + Variable sum variables of same dimension (or with a
constant)
Variable [=] Variable - Variable subtract variables of same dimension (or
with a constant)
Variable [=] Variable * Variable matrix or scalar multiplication.

Variable [=] TRANSPOSE(Variable) matrix transposition
Variable [=] Variable^-1 invert a matrix
Variable = SUM(Variable) sum all entries in a matrix
Variable [=] SUM ROWS (Variable) sum all rows of a matrix (result has one
value per column)
Variable [=] SUM COLS(Variable) sum all columns of a matrix

Variables [=] SORT(Variable, Expr) sort rows of an input matrix where rank is
given by Expr. The system variable “Index”
can appear in the expression and will take on
the range of indices in the input array. The
resulting sorted matrix will be assigned.

Variable [=] MPM_MULT(Variable, Variable) Performs a “matrix population model”
(MPM) integer-based multiplication.
Assumes that first matrix is two-dimensional
and that second is a vector. The result is
two-dimensional, where entries above
diagonal represent "offspring", entries on the
diagonal represent "survivors" and entries
below the diagonal represent "succeeders"

Variable [=] CONTAG(Variable, Variable) Creates a “temporal contagion” matrix.
Given probabilities (first parameter) for a set
of states and a two-dimensional contagion
array (values –1 to 1 indicating affinity),
generates a matrix where each row is a prob.
dist. For transitions given the row value, and
the overall target dist. will be met.

===General Set, List and Graph Functions===
REMOVE ALL(LinkedVariable) clears variable. No return value
SIZE(LinkedVariable) number of elements, entries or nodes
IS EMPTY(LinkedVariable) TRUE if and only if variable has 0 elements

FIRST(LinkedVariable) returns position of first element, entry or
node
NEXT(LinkedVariable, PosVariable) returns position of element, entry or node
following position provided
PREV(LinkedVariable, PosVariable) returns position of element, entry or node
preceding position provided
REMOVE(LinkedVariable, PosVariable) remove and deletes element, entry or node
at position

Variable [=] GET(LinkedVariable, PosVariable) get element, entry or node at position
X [=] GET(LinkedVariable, PosVariable, Index) get single value in a given index
SET(LinkedVariable, PosVariable, Variable) set element, entry or node at position
SET(LinkedVariable, PosVariable, entryIndex, Value)
set value at specified index of element,
entry or node at position
FIND(LinkedVariable, , TmpVariable Condition) return first position of an element, entry or
node that satisfies the condition
FIND NEXT(LinkedVariable, PosVariable, TmpVariable, Condition)
return next position of an element, entry or
node that satisfies the condition
SORT(LinkedVariable, TmpVariable1, TmpVariable2, Condition)
sort elements, entries or nodes according to
condition

===Set Functions===
CONTAINS(SetVariable, ElementVariable) TRUE if and only if set variable “contains”
variable provided, where two elements are
identical if they have identical values
INSERT(SetVariable, ElementVariable) add element to set. Only changes set if it
doesn’t already contain the element
SetVariable = UNION(Set1, Set2) take union of two set variables
SetVariable = INTERSECTION(Sete1, Set2) take intersection of two set variables
SetVariable = SUBTRACT(Sete1, Set2) subtract second set variable from first

===List Functions===
HEAD(ListVariable) returns position of first entry
TAIL(ListVariable) returns position of last entry
INSERT HEAD(ListVariable, EntryElement) add an entry to front of list
INSERT TAIL(ListVariable, EntryElement) add an entry to end of list
INSERT BEFORE(ListVariable, Index, EntryElement)
add an entry before given index
INSERT AFTER(ListVariable, Index, EntryElement)
add an entry after given index
INSERT AT(ListVariable, Index, EntryElement) add an entry at given index

REMOVE HEAD(ListVariable) removes and deletes first entry
REMOVE TAIL (ListVariable) removes and deletes last entry
REMOVE AT INDEX(ListVariable, Index) removes and deletes entry at given index

Variable [=] GET HEAD(ListVariable) returns first entry
Variable [=] GET TAIL(ListVariable) returns first entry
Variable [=] GET AT INDEX(ListVariable, Index) returns entry at given index
Pos = POS AT INDEX(ListVariable, Index) returns position at given index

===Tree Functions===
ADD ROOT(TreeVariable, EntryElement) add root element of a tree
INSERT LEFT CHILD(TreeVariable, PosVariable, EntryElement)
add child to a node on the left of current
children
INSERT RIGHT CHILD(TreeVariable, PosVariable, EntryElement)
add child to a node on the right of current
children
INSERT CHILD(TreeVariable, PosVariable, EntryElement, Index)
add child to a node at given index (from
left)

n = CHILDREN(TreeVariable, PosVariable) number of children at a given position
Pos = PARENT(TreeVariable, PosVariable) Position of parent of a node
Pos = LEFT CHILD(TreeVariable, PosVariable) Position of leftmost child of a node
Pos = RIGHT CHILD(TreeVariable, PosVariable) Position of rightmost child of a node
Pos = CHILD(TreeVariable, PosVariable, Index) Position of indexed (from left) child of a
node
Pos = NEXT SIBLING(TreeVariable, PosVariable) Position of next sibling to right of a node
Pos = PREV SIBLING(TreeVariable, PosVariable) Position of previous sibling to right of a
node

Pos = NEXT DFS(TreeVariable, PosVariable) Position of next node in depth-first
pre-order traversal of a tree. If the position
variable is NULL, then the root is returned
Pos = NEXT POSTORDER DFS(TreeVariable, PosVariable)
Position of next node in depth-first
post-order traversal of a tree. If the position
variable is NULL, then the root is returned
Variable [=] GET LEFT CHILD(TreeVariable, PosVariable)
returns entry of leftmost child for a given
node
Variable [=] GET RIGHT CHILD(TreeVariable, PosVariable)
returns entry of rightmost child for a given
node
Variable [=] GET CHILD(TreeVariable, PosVariable, Index)
returns entry of child with given index
(from left) for a given node

===Graph Functions===
REMOVE ALL LINKS(GraphVariable) clears links of a graph variable
SIZE LINKS(GraphVariable) number of links in graph
IS EMPTY LINKS(GraphVariable) TRUE if and only if graph has 0 links

FIRST LINK(GraphVariable) returns position of first link
NEXT LINK (GraphVariable, PosVariable) returns position of link following position
provided
PREV LINK (GraphVariable, PosVariable) returns position of link preceding position
provided
Variable [=] GET LINK(GraphVariable, PosVariable)
get link at position
CONTAINS LINK(GraphVariable, LinkVariable) TRUE if and only if graph variable contains
variable provided
REMOVE LINK(GraphVariable, PosVariable) remove and deletes link at position
SET LINK(GraphVariable, PosVariable, LinkVariable)
Set link at position
SET LINK(GraphVariable, PosVariable, entryIndex, Value)
Set value at specified index of link at
position
FIND LINK(GraphVariable, TmpVariable, Condition)
Return first position of link that satisfies the
condition
FIND NEXT LINK(GraphVariable, PosVariable, TmpVariable, Condition)
Return next position of a link that satisfies
the condition
SORT LINKS(GraphVariable, TmpVariable1, TmpVariable2, Condition)
Sort links according to condition
LINKED(GraphVariable, NodeVariable1, NodeVariable2, LinkType)
TRUE if the nodes are linked. Set LinkType
to 0 for direct links and 1 for indirect

Language Reference

2006-10-03T14:29:50Z

128.100.72.168: /* Probability Density and Cumulative Density Functions */

==Constants==
===ZERO===
return 0.0
===ONE===
return 1.0
#Number return value of the number specified
<Constant> return value of a named constant
<Constant>[Expr] return value of a named vector constant
<Constant>[Expr, Expr] return value of a named array constant
<Macro>[Expr] return value of expression at specified index
in macro

==Probability Distributions==
===NORMAL===
(Expr, Expr) draw a value from a normal distribution, where
the first expression specifies the mean and
the second specifies the standard deviation

===SKEWED NORMAL===
(Expr, Expr, Expr) draw a value from a skewed normal distribution, where the first expression specifies the mode
and the second and third specify the standard
deviations to the left and right of the mode
LOG NORMAL(Expr, Expr) draw a value from a log normal distribution,
where the first expression specifies the mean
and the second specifies the standard deviation
of the underlying normal distribution

WEIBULL(Expr, Expr) draw a value from a Weibull distribution, where
the first expression specifies the beta and the
second specifies alpha (Note:terminology varies
between sources. The version here is equivalent
to that in Excel, with reversal of parameters).

NEGEXP(Expr) draw a value from a negative exponential distribution, where the expression specifies the
mean
POISSION(Expr) draw a value from a Poisson distribution

UNIFORM(Expr, Expr) draw a value from a uniform distribution, where the first expression determines the minimum value and the second determines the maximum
CLASSIFIED_DIST draw a value from a discrete distribution, where CLASS Number: Expr each expression determines the relative : probability of its associated class being drawn. ENDFN The CLASS keyword is optional.

CLASSIFIED_DIST( Number+) in this form, the classes are assumed to start at zero. Only constant probabilities can be given.

CLASSIFIED_DIST in this form, the classes are assumed to start at Expr zero :
ENDFN

CLASSIFIED_DIST[M] In this form, the classes in a one-dimensional
array M, and so start at zero.

===Probability Density and Cumulative Density Functions===
The following are a set of probability and cumulative density expressions. The results from probability density expressions should be multiplied by a width factor to obtain a probability of value X (i.e. the estimated area under the PDF curve). Without a width factor, the assumed class size is 1. A temporal PDF makes a PDF conditional, where the variable X is assumed to be a time or other increasing value. Essentially, a PDF will give the probability of value X occurring, while a TEMPORAL PDF will give the probability of X occurring given that if hasn’t occurred yet (i.e. given that that actual value of this variable will be >= X).

NORMAL PDF(Expr, Expr, Expr) normal probability density function, where the first expression is the value, the second is the mean and the third is the standard deviation
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

NORMAL CDF(Expr, Expr, Expr) normal cumulative density function, where the first expression is the value, the second is the mean and the third is the standard deviation
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

SKEWED NORMAL PDF(Expr, Expr, Expr, Expr) skewed normal probability density function,
where the first expression specifies the value,
the second is the mode and the third and fourth are the standard deviations to the left and right
of the mode.
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

SKEWED NORMAL CDF(Expr, Expr, Expr, Expr) skewed normal cumulative density function, where the first expression specifies the value,
the second is the mode, and the third and fourth are the left and right standard deviations
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

LOG NORMAL PDF(Expr, Expr, Expr) log normal probability density function, where
the first expression specifies the value, the
second is the mean and the third is the standard
deviation
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

LOG NORMAL CDF(Expr, Expr, Expr) log normal cumulative density function, where
the first expression specifies the value, the
second is the mean and the third is the standard
deviation
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

NORMAL TEMPORAL PDF(Expr, Expr, Expr) temporal normal probability density function
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

SKEWED NORMAL TEMPORAL PDF(Expr, Expr, Expr, Expr)
temporal skewed normal probability density
function
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

LOG NORMAL TEMPORAL PDF(Expr, Expr, Expr) temporal log normal probability density
function
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

UNIFORM TEMPORAL PDF(Expr, Expr, Expr) temporal uniform probability density expression
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

===Continuous Functions (Arithmetic Functions)===
<Variable> value of an independent variable <Variable>[Expr] value of a vector global variable
<Variable>[Expr, Expr] value of an array global variable

(Expr) value of the expression Expr + Expr sum of two expressions Expr - Expr value of the first expression minus the value
of the second expression Expr * Expr product of two expressions Expr / Expr value of the first expression divided by value
of the second expression Expr ^ Expr value of the first expression to the power of
the value of the second expression. An nth
root can be computed with1/n as the power.
| Expr | absolute value of the expression
ABS(Expr) absolute value of the expression
ABSOLUTE(Expr) absolute value of the expression

Expr % Expr value of the first expression modulo the value of
the second expression (assumes that the values
of the expressions are integers)
EXP(Expr) base of the natural logarithm (e) to the power of
the expression
LOG(Expr) natural logarithm of the value of the expression.
Logarithms in other bases can be computed as
logb(x) = ln(x) / ln(b)

ROUND(Expr) expression value rounded to the nearest integer
FLOOR(Expr) largest integer smaller than the expression value
CEILING(Expr) smallest integer larger than the expression value

CLAMP(Expr, MinExpr, MaxExpr) clamp the value X of the expression to the range
[Min, Max]: if X < Min then return Min; if X < Max return Max. Otherwise return X.

===Continuous Functions (Trigonometric Functions)===
Angles are all assumed to be in degrees (not radians). In SELES, angles in compass directions (i.e. zero is north, increasing clockwise, in contrast to geometry where zero is each increasing counter-clockwise).
SIN(Expr) interpret the value of the expression as an angle
theta in degrees, and return sin(theta)
COS(Expr) interpret the value of the expression as an angle
theta in degrees, and return cos(theta)
TAN(Expr) interpret the value of the expression as an angle
theta in degrees, and return tan(theta).
ARCSIN(Expr) inverse sine of the value of the expression
ARCCOS(Expr) inverse cos of the value of the expression
ARCTAN(Expr) inverse tan of the value of the expression
ARCTAN(Expr, Expr) inverse tan where first expression is x offset
and second is y offset. Providing two
expressions gives more information about the
quadrant.

===Continuous Functions (Miscellaneous)===
RESPONSE(Expr, #A, #B, #C) two-sided version of a standard response
function for the value X of the first expression:
if (X < A) return e^(-(X-A)^2/(2*(C^2))
else if (X > B) return e^(-(X-B)^2/(2*(C^2))
else return 1

DISTANCE(Expr, Expr) distance between two location indices (normally
obtained using the Location variable). Thus,
DISTANCE(loc1, loc2) is
sqrt(sqr(loc1.x – loc2.x) + sqr(loc1.y – loc2.y))

DIRECTION(Expr, Expr) angle in degrees between two location indices

===Classified and Discrete Functions===
CLASSIFY(X) if the value of the variable X is equal to one of
CLASS Number: Expr the classes listed, then return the result of the.
: associated expression. Otherwise return 0.
ENDFN

CLASSIFY(X) return the result of the kth expression in the list,
Expr where k = X – minimum value of the variables
: (this may be non-0 only for layers)
:
ENDFN

CLASSIFY(X): ( Number+) return the kth number in the list, where
k = X – minimum value of the variable (this
may be non-0 only for layers)

CLASSIFY(X): Filename uses the table in the named file, which is
assumed to consist of class:value pairs. Rarely
used.

CLASSIFY(X): Filename Key uses the table in the named file, which is
assumed to consist of class:value pairs. The key
is used to specify a sub-table in a multi-table
file. Rarely used.

Classified functions use the variable as an index into the list of numbers or expressions that follow. The “CLASS” keyword is optional. This variable must be non-negative. If “CLASS # :” is used, then the number refers to the value of the indexing variable. If a class is not specified for a given value, its expression is implicitly ZERO. Interpolation tables are very similar except that the variable is assumed to be continuous instead of classified. An interpolated value between classes is returned. Lookup tables are also similar, except that both the variable and classes are assumed to be continuous values. An interpolated value between classes is also returned. Rarely used.

INTERPOLATE(X) return an interpolated value where the value of
CLASS Number: Number variable X is placed between two classes or at
: either end of the table.
ENDFN

INTERPOLATE(X): ( Number+) same as above, except the classes are
implicitly 0, …. k-1

INTERPOLATE(X) same as above, except the values in the
CLASS Number: Expr table are obtained by evaluating expressions
:
ENDFN

INTERPOLATE(X) same as above, except the classes are
Expr implicitly 0, …, k-1
:
ENDFN

INTERPOLATE(X): Filename uses the table in the named file, which is
assumed to consist of class:value pairs

INTERPOLATE(X): Filename Key uses the table in the named file, which is
assumed to consist of class:value pairs. The key
is used to specify a sub-table in a multi-table
file.

LOOKUP(X) return the interpolated value where the value of
CLASS Number: Number variable X is placed between two classes or at
: either end of the table, and classes can be any.
ENDFN real values.

LOOKUP(X): ( Number+) same as above, except the classes are
implicitly 0, …. k-1

LOOKUP(X) same as above, except the values in the
CLASS Number: Expr table are obtained by evaluating expressions
:
ENDFN

LOOKUP(X) same as above, except the classes are
Expr implicitly 0, …, k-1
:
ENDFN

LOOKUP(X): Filename uses the table in the named file, which is
assumed to consist of class:value pairs

LOOKUP(X): Filename Key uses the table in the named file, which is
assumed to consist of class:value pairs. The key
is used to specify a sub-table in a multi-table
file

===Boolean Functions===
Expr EQ Expr TRUE if the values of the two expressions are
equal; otherwise FALSE
Expr == Expr alternate form of EQ comparison (Note: two equal signs distinguish this from an assignment)

Expr NEQ Expr TRUE if the values are not equal; otherwise
FALSE
Expr != Expr alternate form of NOT EQUAL comparison

Expr < Expr TRUE if the value of the first expression is less
than the value of the second expression;
otherwise FALSE
Expr <= Expr TRUE if the value of the first expression is less
than or equal to the value of the second
expression; otherwise FALSE

Expr > Expr TRUE if the value of the first expression is
greater than the value of the second
expression; otherwise FALSE
Expr >= Expr TRUE if the value of the first expression is
greater than or equal to the value of the
second expression; otherwise FALSE

!Expr Negates the expression Boolean value

Expr AND Expr TRUE if values of both expressions are
TRUE and FALSE otherwise

Expr OR Expr TRUE if value of at least one expression is
TRUE and FALSE otherwise

Note that relations can be cascaded, with the interpretation that each operator applies independently to its surrounding pair of expressions. Thus, the expression: Expression <= Expression <= Expression (e.g. 5 <= age <= 50) specifies a “between” relation, which is TRUE only if the value of the centre expression falls in the specified range.

===Bit-Vector Functions===
Bit-vector functions treat an integer value (the independent variable) as a sequence of bits, each of which can be independently set and accessed. This can allow use of a single layer to hold lots of Boolean information, since each cell as an integer has 8, 16 or 32 bits. For example, bits 0, 1, 2 and 3 can be used to store four different Boolean states (a, b, c and d), and the sequence 0110 means that states a and d are FALSE and states b and c are TRUE. PositionList is a semi-colon separated sequence of integer or ranges (lower-upper) indicating positions in the integer (0-31). For example, the PositionList 1;4-6;27 indicates bits at positions 1, 4, 5, 6 and 27.

SETAT(Expr, PositionList, #Type) Set the value specified by the expression, at
the positions in PositionList to: FALSE (0)
if Type is 0, TRUE (1) if Type is 1,
and flip the bits if Type = 2

SETAT(Expr, PositionList,#Type,#Prob) Same as above, except each position is set
with probability #Prob

SELECTAT(Expr, PositionList) FALSE(0) if none of the bits in PositionList are
set in the specified expression value and
TRUE(1) otherwise

MAX POSITION(Expr) Return the maximum 0-based bit position that is
set to one in the expression value (interpreted
as a bit-vector), or –1 if no bits are set

MIN POSITION(Expr) Return the minimum 0-based bit position that is
set to one in the expression value (interpreted
as a bit-vector), or –1 if no bits are set

BITWISE OR(Expr, Expr) Bitwise OR of two values
BITWISE AND(Expr, Expr) Bitwise AND of two values
BITWISE XOR(Expr, Expr) Bitwise exclusive-OR of two values
BITWISE NOT Expr Bitwise NOT of a value

SHIFT LEFT(Expr, Expr) Shifts value of first expression to the left by
number of bits specified by second expression
SHIFT RIGHT(Expr, Expr) Shifts value of first expression to the right by
number of bits specified by second expression

===Control Expressions===
Note the difference between the first two “functional if’s” (i.e. a value is returned) and the latter “procedural if’s” (that don’t return a value, but control flow).

IF Expr THEN Expr ELSE Expr if value of the IF expression is TRUE (>= 1), then return the value of the THEN expression,
otherwise return value of the ELSE expression

(Expr ? Expr : Expr) Same as above, but this form can be used as an
embedded sub-expression.

IF Expr Procedural IF statement to process
… sub-expressions denoted by “…” only if the
ENDFN expression evaluates to TRUE

IF Expr Procedural IF statement to process the first set
… of sub-expressions denoted by “…”if the
ELSE expression evaluates to TRUE and the set of
… sub-expressions after the ELSE otherwise. Note
ENDFN that “ELSE IF expr” forms can be strung
together

WHILE Expr While loop: process sub-expressions denoted by
… “…” while the expression evaluates to TRUE
ENDFN

PAUSE Halts the simulation and displays a dialog
box to which the user must respond to continue

PAUSE IF Expr If the expression evaluates to TRUE, halts the
simulation and displays a dialog box to which
the user must respond to continue

PAUSE(#Value) Pauses the simulation for the specified number
of milliseconds and then continues

PAUSE(#Value) IF Expr If the expression evaluates to TRUE, Pauses the
simulation for the specified number of
milliseconds and then continues

WAIT UNTIL Expr Suspend execution until the expression returns TRUE (1). This is intended for controlling
communication and synchronization with
an external application.
CRITICAL SECTION (Flag) Enter (if Flag is TRUE) or exit (if Flag is FALSE) a critical section. A critical section gives priority to this application, and is used for
synchronizing access to shared variables
(i.e. shared with another application).

DEBUG Update the simulation probe, if it is loaded and
The event is selected. Used to debug/verify
event behaviour.

SEED() Gets the random number seed
SEED(Expr) Sets the random number seed. Value returned is
next seed.

RESIZE(Variable, Expr) Changes size (number of entries) in a global
variable. Values are not maintained. Useful for
when size is not known prior to simulation.

RECOMPUTE Only valid in consequent expressions of
ProbInit and also when ProbInit recompute flag
has been set. Causes prob. surface to be
recomputed before next selection
===Output Expressions===
DISPLAY Display on the screen the labelled Label: Expr values computed with the expressions listed.
…. If no label is given, the expression must
ENDFN be a variable, and this is used for the label.

DISPLAY Same as above, but only display if the DECISION Expr decision expression evaluates to TRUE
Label: Expr The keyword DECISION can be replaced by
…. a “?”
ENDFN

OUTPUT RECORD(OutputVar) Output to the record file of output variable the labelled values computed with the Label: Expr expressions listed. If no label is given, the
…. Expression must be a variable and this is
ENDFN used as label.

OUTPUT RECORD(OutputVar) Same as above, but only output if the DECISION Expr decision expression evaluates to TRUE
Label: Expr
….
ENDFN

Note: a label/expression pair can be “expanded” by using the form: Label#n1:n2: Expr, where n1 and n2 are integers or constant names. This will create n2-n1+1 columns rather than a single column. The system variable Index can be used in the expression, and will take on values n1, n1+1,…,n2 for each column, respectively.

===Composite Functions===
Compound expressions all have the same form of an expression name followed by a list of sub-expressions. If the first expression is a region function, then the subsequent expressions are all evaluated over the defined region, instead of only at the current cell (however, it is usually simpler to use an OVER REGION expression). When arithmetic expression become complex, sometimes composite expressions can be written more clearly. The general format is as follows:

CompositeExpressionName
Expr
:
ENDFN

The following composite expressions are supported:

===SUM===
DESCRIPTION:
Returns the number that is the sum of all the expressions.

USAGE:
x=SUM
Expr
...
ENDFN

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value.

VALUE:
the sum of all the arguments.

SEE ALSO:
<a link to the composite functions section of seles modellers guide>

EXAMPLES: <add carriage return here>
Example 1:
y = 3
x = SUM
y
y+2
5
ENDFN
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

===PRODUCT===
product of the sub-expressions

DIVIDE successive division of the sub-expressions

MEAN average of the sub-expressions

GEOMETRIC MEAN geometric mean of the sub-expressions (nth
root of the product for n expressions)

MIN minimum of the sub-expressions

MAX maximum of the sub-expressions

EQUAL TRUE (1) if the sub-expressions all evaluate to
the same value and FALSE (0) otherwise
NOT EQUAL FALSE (0) if the sub-expressions all evaluate to
the same value and TRUE (1) otherwise

OR TRUE (1) if at least one sub-expression
evaluates to TRUE and FALSE (0) otherwise

AND TRUE (1) if all sub-expressions evaluate to
TRUE and FALSE (0) otherwise

LESS OR EQUAL TRUE (1) if the sub-expression evaluations are
all ordered according to the relation <=, and
FALSE (0) otherwise

ORDERED same as LESS OR EQUAL

LESS THAN TRUE (1) if the sub-expression evaluations are
all ordered according to the relation <, and
FALSE (0) otherwise

STRICT ORDERED same as LESS THAN

GREATER OR EQUAL TRUE (1) if the sub-expression evaluations are
all ordered according to the relation >=, and
FALSE (0) otherwise

GREATER THAN TRUE (1) if the sub-expression evaluations are
all ordered according to the relation >, and
FALSE (0) otherwise

===Region Functions===
A region function returns the set of locations, one on each call. Their use is limited to the main expression of EventLocation, SpreadLocation, AgentLocation and MoveLocation properties, as the first expression of composite expressions and in OVER REGION functions.

REGION WHOLE MAP defines the region consisting of the entire
DECISION Expr landscape. If there is a decision expression,
then only those cells for which this expression
returns TRUE will be included.

REGION RECT (Expr, Expr, Expr, Expr) defines a rectangular region. If there is a
DECISION Expr decision expression defined, then only those
cells for which this expression returns
TRUE will be included

REGION CENTRED (Expr, Expr [, DistanceType][, WRAPPED])
DECISION Expr defines a region centred on the current cell.
If there is a decision expression, then only
those cells for which this expression returns
TRUE will be included.

DistanceType is either CARDINAL or EUCLIDEAN (the default). Cardinal distance between two cells is the minimum number of cardinal steps (up, down, left, right) to reach one cell from the other. Euclidean distance is the straight-line distance between two points. The WRAPPED flag, if present indicates that the region wraps around the sides (vertically and horizontally) of the landscape (e.g. a location x positions beyond the right-hand side of a raster will be mapped to x positions in from the left-hand side of the raster). If not present, the landscape does not wrap.

REGION LOCATION LIST(Number+) defines the region consisting of a set of
DECISION Expr known location indices. If there is a decision expression, then only those cells for which this
expression returns TRUE will be included.

REGION LOCATION LIST(X,n) defines the region consisting of a set of n
DECISION Expr location indices stored in one-dimensional X.

REGION LOCATION (Expr) defines the region consisting of a of a single
DECISION Expr location index. If there is a decision expression,
then only those cells for which this expression
returns TRUE will be included.

REGION VECTOR (StartLocation, EndLocation) defines region consisting of cells along an
DECISION Expr approximation of line between end cells

Cost surface and least-cost path regions are advanced features that are best understood with an example model.

REGION COST SURFACE(EndLocation, MaxCost, CostSurface)
DECISION Expr
COST Expr
REGION COST SURFACE(EndLocation, MaxCost, CostSurface, LeastCostNeighbs, AnchorLoc)
DECISION Expr
COST Expr
Defines a region surrounding a cell with
cumulative costs less than MaxCost. Stops
growing when EndLocation is reached or all
costs are greater than MaxCost. Second form
also records gradient and anchor location
layers. The CostSurface layer records the
cumulative cost from the cost function

REGION LEAST COST PATH(StartLocation, EndLocation)
DECISION Expr
COST Expr
REGION LEAST COST PATH(StartLocation, EndLocation, LeastCostNeighbs)
DECISION Expr
REGION LEAST COST PATH(StartLocation, EndLocation, LeastCostNeighbs, AnchorLoc)
DECISION Expr
Defines a region with cells that approximate
the least-cost path between two cells. The
first generates the cost function internally.
The latter two use input information from a
pre-computed cost surface region. Providing
both the gradient and anchor location layers
provides the most accurate approximation.

Iteration is a common aspect of models (even if it is very procedural). Most programming languages offer a “for-loop” of some kind. SELES presently provides “over index sequence” expressions as a slightly more declarative (although also more cumbersome) expression for iterating. While-loops can also be used.

OVER INDEX SEQUENCE(Expr, Expr) defines linear sequence of location indices.
DECISION Expr If there is a decision expression, then only
those cells for which this expression returns
TRUE will be included. The system variable
Index holds the value of the index at each value
in the sequence

Over region expressions are very frequently used to visit all cells in a landscape that meet some condition (e.g. to compute the size of the forest at initiation).

OVER RegionFunction Apply a set of sub-expressions at all spatial
Expression locations specified by a region function
:
ENDFN

AT LOCATION #Expr Apply a set of state-changes at a specified
Expression location
:
ENDFN

===Matrix Functions===
Matrix assignment is indicated using “[=]” instead of “=”. The proper dimensions of the component arrays must be met.

Variable [=] Variable assign variable of same dimension, or a
single value to all entries
Variable [=] Variable + Variable sum variables of same dimension (or with a
constant)
Variable [=] Variable - Variable subtract variables of same dimension (or
with a constant)
Variable [=] Variable * Variable matrix or scalar multiplication.

Variable [=] TRANSPOSE(Variable) matrix transposition
Variable [=] Variable^-1 invert a matrix
Variable = SUM(Variable) sum all entries in a matrix
Variable [=] SUM ROWS (Variable) sum all rows of a matrix (result has one
value per column)
Variable [=] SUM COLS(Variable) sum all columns of a matrix

Variables [=] SORT(Variable, Expr) sort rows of an input matrix where rank is
given by Expr. The system variable “Index”
can appear in the expression and will take on
the range of indices in the input array. The
resulting sorted matrix will be assigned.

Variable [=] MPM_MULT(Variable, Variable) Performs a “matrix population model”
(MPM) integer-based multiplication.
Assumes that first matrix is two-dimensional
and that second is a vector. The result is
two-dimensional, where entries above
diagonal represent "offspring", entries on the
diagonal represent "survivors" and entries
below the diagonal represent "succeeders"

Variable [=] CONTAG(Variable, Variable) Creates a “temporal contagion” matrix.
Given probabilities (first parameter) for a set
of states and a two-dimensional contagion
array (values –1 to 1 indicating affinity),
generates a matrix where each row is a prob.
dist. For transitions given the row value, and
the overall target dist. will be met.

===General Set, List and Graph Functions===
REMOVE ALL(LinkedVariable) clears variable. No return value
SIZE(LinkedVariable) number of elements, entries or nodes
IS EMPTY(LinkedVariable) TRUE if and only if variable has 0 elements

FIRST(LinkedVariable) returns position of first element, entry or
node
NEXT(LinkedVariable, PosVariable) returns position of element, entry or node
following position provided
PREV(LinkedVariable, PosVariable) returns position of element, entry or node
preceding position provided
REMOVE(LinkedVariable, PosVariable) remove and deletes element, entry or node
at position

Variable [=] GET(LinkedVariable, PosVariable) get element, entry or node at position
X [=] GET(LinkedVariable, PosVariable, Index) get single value in a given index
SET(LinkedVariable, PosVariable, Variable) set element, entry or node at position
SET(LinkedVariable, PosVariable, entryIndex, Value)
set value at specified index of element,
entry or node at position
FIND(LinkedVariable, , TmpVariable Condition) return first position of an element, entry or
node that satisfies the condition
FIND NEXT(LinkedVariable, PosVariable, TmpVariable, Condition)
return next position of an element, entry or
node that satisfies the condition
SORT(LinkedVariable, TmpVariable1, TmpVariable2, Condition)
sort elements, entries or nodes according to
condition

===Set Functions===
CONTAINS(SetVariable, ElementVariable) TRUE if and only if set variable “contains”
variable provided, where two elements are
identical if they have identical values
INSERT(SetVariable, ElementVariable) add element to set. Only changes set if it
doesn’t already contain the element
SetVariable = UNION(Set1, Set2) take union of two set variables
SetVariable = INTERSECTION(Sete1, Set2) take intersection of two set variables
SetVariable = SUBTRACT(Sete1, Set2) subtract second set variable from first

===List Functions===
HEAD(ListVariable) returns position of first entry
TAIL(ListVariable) returns position of last entry
INSERT HEAD(ListVariable, EntryElement) add an entry to front of list
INSERT TAIL(ListVariable, EntryElement) add an entry to end of list
INSERT BEFORE(ListVariable, Index, EntryElement)
add an entry before given index
INSERT AFTER(ListVariable, Index, EntryElement)
add an entry after given index
INSERT AT(ListVariable, Index, EntryElement) add an entry at given index

REMOVE HEAD(ListVariable) removes and deletes first entry
REMOVE TAIL (ListVariable) removes and deletes last entry
REMOVE AT INDEX(ListVariable, Index) removes and deletes entry at given index

Variable [=] GET HEAD(ListVariable) returns first entry
Variable [=] GET TAIL(ListVariable) returns first entry
Variable [=] GET AT INDEX(ListVariable, Index) returns entry at given index
Pos = POS AT INDEX(ListVariable, Index) returns position at given index

===Tree Functions===
ADD ROOT(TreeVariable, EntryElement) add root element of a tree
INSERT LEFT CHILD(TreeVariable, PosVariable, EntryElement)
add child to a node on the left of current
children
INSERT RIGHT CHILD(TreeVariable, PosVariable, EntryElement)
add child to a node on the right of current
children
INSERT CHILD(TreeVariable, PosVariable, EntryElement, Index)
add child to a node at given index (from
left)

n = CHILDREN(TreeVariable, PosVariable) number of children at a given position
Pos = PARENT(TreeVariable, PosVariable) Position of parent of a node
Pos = LEFT CHILD(TreeVariable, PosVariable) Position of leftmost child of a node
Pos = RIGHT CHILD(TreeVariable, PosVariable) Position of rightmost child of a node
Pos = CHILD(TreeVariable, PosVariable, Index) Position of indexed (from left) child of a
node
Pos = NEXT SIBLING(TreeVariable, PosVariable) Position of next sibling to right of a node
Pos = PREV SIBLING(TreeVariable, PosVariable) Position of previous sibling to right of a
node

Pos = NEXT DFS(TreeVariable, PosVariable) Position of next node in depth-first
pre-order traversal of a tree. If the position
variable is NULL, then the root is returned
Pos = NEXT POSTORDER DFS(TreeVariable, PosVariable)
Position of next node in depth-first
post-order traversal of a tree. If the position
variable is NULL, then the root is returned
Variable [=] GET LEFT CHILD(TreeVariable, PosVariable)
returns entry of leftmost child for a given
node
Variable [=] GET RIGHT CHILD(TreeVariable, PosVariable)
returns entry of rightmost child for a given
node
Variable [=] GET CHILD(TreeVariable, PosVariable, Index)
returns entry of child with given index
(from left) for a given node

===Graph Functions===
REMOVE ALL LINKS(GraphVariable) clears links of a graph variable
SIZE LINKS(GraphVariable) number of links in graph
IS EMPTY LINKS(GraphVariable) TRUE if and only if graph has 0 links

FIRST LINK(GraphVariable) returns position of first link
NEXT LINK (GraphVariable, PosVariable) returns position of link following position
provided
PREV LINK (GraphVariable, PosVariable) returns position of link preceding position
provided
Variable [=] GET LINK(GraphVariable, PosVariable)
get link at position
CONTAINS LINK(GraphVariable, LinkVariable) TRUE if and only if graph variable contains
variable provided
REMOVE LINK(GraphVariable, PosVariable) remove and deletes link at position
SET LINK(GraphVariable, PosVariable, LinkVariable)
Set link at position
SET LINK(GraphVariable, PosVariable, entryIndex, Value)
Set value at specified index of link at
position
FIND LINK(GraphVariable, TmpVariable, Condition)
Return first position of link that satisfies the
condition
FIND NEXT LINK(GraphVariable, PosVariable, TmpVariable, Condition)
Return next position of a link that satisfies
the condition
SORT LINKS(GraphVariable, TmpVariable1, TmpVariable2, Condition)
Sort links according to condition
LINKED(GraphVariable, NodeVariable1, NodeVariable2, LinkType)
TRUE if the nodes are linked. Set LinkType
to 0 for direct links and 1 for indirect

Language Reference

2006-10-03T14:28:41Z

128.100.72.168: /* Probability Density and Cumulative Density Functions */

==Constants==
===ZERO===
return 0.0
===ONE===
return 1.0
#Number return value of the number specified
<Constant> return value of a named constant
<Constant>[Expr] return value of a named vector constant
<Constant>[Expr, Expr] return value of a named array constant
<Macro>[Expr] return value of expression at specified index
in macro

==Probability Distributions==
===NORMAL===
(Expr, Expr) draw a value from a normal distribution, where
the first expression specifies the mean and
the second specifies the standard deviation

===SKEWED NORMAL===
(Expr, Expr, Expr) draw a value from a skewed normal distribution, where the first expression specifies the mode
and the second and third specify the standard
deviations to the left and right of the mode
LOG NORMAL(Expr, Expr) draw a value from a log normal distribution,
where the first expression specifies the mean
and the second specifies the standard deviation
of the underlying normal distribution

WEIBULL(Expr, Expr) draw a value from a Weibull distribution, where
the first expression specifies the beta and the
second specifies alpha (Note:terminology varies
between sources. The version here is equivalent
to that in Excel, with reversal of parameters).

NEGEXP(Expr) draw a value from a negative exponential distribution, where the expression specifies the
mean
POISSION(Expr) draw a value from a Poisson distribution

UNIFORM(Expr, Expr) draw a value from a uniform distribution, where the first expression determines the minimum value and the second determines the maximum
CLASSIFIED_DIST draw a value from a discrete distribution, where CLASS Number: Expr each expression determines the relative : probability of its associated class being drawn. ENDFN The CLASS keyword is optional.

CLASSIFIED_DIST( Number+) in this form, the classes are assumed to start at zero. Only constant probabilities can be given.

CLASSIFIED_DIST in this form, the classes are assumed to start at Expr zero :
ENDFN

CLASSIFIED_DIST[M] In this form, the classes in a one-dimensional
array M, and so start at zero.

===Probability Density and Cumulative Density Functions===
The following are a set of probability and cumulative density expressions. The results from probability density expressions should be multiplied by a width factor to obtain a probability of value X (i.e. the estimated area under the PDF curve). Without a width factor, the assumed class size is 1. A temporal PDF makes a PDF conditional, where the variable X is assumed to be a time or other increasing value. Essentially, a PDF will give the probability of value X occurring, while a TEMPORAL PDF will give the probability of X occurring given that if hasn’t occurred yet (i.e. given that that actual value of this variable will be >= X).

NORMAL PDF(Expr, Expr, Expr) normal probability density function, where the first expression is the value, the second is the mean and the third is the standard deviation
[[Model Builder's Guide Chapter 9#Probability Density and Cumulative Density Functions]]

NORMAL CDF(Expr, Expr, Expr) normal cumulative density function, where the first expression is the value, the second is the mean and the third is the standard deviation
Probability Density and Cumulative Density Functions

SKEWED NORMAL PDF(Expr, Expr, Expr, Expr) skewed normal probability density function,
where the first expression specifies the value,
the second is the mode and the third and fourth are the standard deviations to the left and right
of the mode.
Probability Density and Cumulative Density Functions

SKEWED NORMAL CDF(Expr, Expr, Expr, Expr) skewed normal cumulative density function, where the first expression specifies the value,
the second is the mode, and the third and fourth are the left and right standard deviations
Probability Density and Cumulative Density Functions

LOG NORMAL PDF(Expr, Expr, Expr) log normal probability density function, where
the first expression specifies the value, the
second is the mean and the third is the standard
deviation
Probability Density and Cumulative Density Functions

LOG NORMAL CDF(Expr, Expr, Expr) log normal cumulative density function, where
the first expression specifies the value, the
second is the mean and the third is the standard
deviation
NORMAL TEMPORAL PDF(Expr, Expr, Expr) temporal normal probability density function
SKEWED NORMAL TEMPORAL PDF(Expr, Expr, Expr, Expr)
temporal skewed normal probability density
function

LOG NORMAL TEMPORAL PDF(Expr, Expr, Expr) temporal log normal probability density
function
UNIFORM TEMPORAL PDF(Expr, Expr, Expr) temporal uniform probability density expression

===Continuous Functions (Arithmetic Functions)===
<Variable> value of an independent variable <Variable>[Expr] value of a vector global variable
<Variable>[Expr, Expr] value of an array global variable

(Expr) value of the expression Expr + Expr sum of two expressions Expr - Expr value of the first expression minus the value
of the second expression Expr * Expr product of two expressions Expr / Expr value of the first expression divided by value
of the second expression Expr ^ Expr value of the first expression to the power of
the value of the second expression. An nth
root can be computed with1/n as the power.
| Expr | absolute value of the expression
ABS(Expr) absolute value of the expression
ABSOLUTE(Expr) absolute value of the expression

Expr % Expr value of the first expression modulo the value of
the second expression (assumes that the values
of the expressions are integers)
EXP(Expr) base of the natural logarithm (e) to the power of
the expression
LOG(Expr) natural logarithm of the value of the expression.
Logarithms in other bases can be computed as
logb(x) = ln(x) / ln(b)

ROUND(Expr) expression value rounded to the nearest integer
FLOOR(Expr) largest integer smaller than the expression value
CEILING(Expr) smallest integer larger than the expression value

CLAMP(Expr, MinExpr, MaxExpr) clamp the value X of the expression to the range
[Min, Max]: if X < Min then return Min; if X < Max return Max. Otherwise return X.

===Continuous Functions (Trigonometric Functions)===
Angles are all assumed to be in degrees (not radians). In SELES, angles in compass directions (i.e. zero is north, increasing clockwise, in contrast to geometry where zero is each increasing counter-clockwise).
SIN(Expr) interpret the value of the expression as an angle
theta in degrees, and return sin(theta)
COS(Expr) interpret the value of the expression as an angle
theta in degrees, and return cos(theta)
TAN(Expr) interpret the value of the expression as an angle
theta in degrees, and return tan(theta).
ARCSIN(Expr) inverse sine of the value of the expression
ARCCOS(Expr) inverse cos of the value of the expression
ARCTAN(Expr) inverse tan of the value of the expression
ARCTAN(Expr, Expr) inverse tan where first expression is x offset
and second is y offset. Providing two
expressions gives more information about the
quadrant.

===Continuous Functions (Miscellaneous)===
RESPONSE(Expr, #A, #B, #C) two-sided version of a standard response
function for the value X of the first expression:
if (X < A) return e^(-(X-A)^2/(2*(C^2))
else if (X > B) return e^(-(X-B)^2/(2*(C^2))
else return 1

DISTANCE(Expr, Expr) distance between two location indices (normally
obtained using the Location variable). Thus,
DISTANCE(loc1, loc2) is
sqrt(sqr(loc1.x – loc2.x) + sqr(loc1.y – loc2.y))

DIRECTION(Expr, Expr) angle in degrees between two location indices

===Classified and Discrete Functions===
CLASSIFY(X) if the value of the variable X is equal to one of
CLASS Number: Expr the classes listed, then return the result of the.
: associated expression. Otherwise return 0.
ENDFN

CLASSIFY(X) return the result of the kth expression in the list,
Expr where k = X – minimum value of the variables
: (this may be non-0 only for layers)
:
ENDFN

CLASSIFY(X): ( Number+) return the kth number in the list, where
k = X – minimum value of the variable (this
may be non-0 only for layers)

CLASSIFY(X): Filename uses the table in the named file, which is
assumed to consist of class:value pairs. Rarely
used.

CLASSIFY(X): Filename Key uses the table in the named file, which is
assumed to consist of class:value pairs. The key
is used to specify a sub-table in a multi-table
file. Rarely used.

Classified functions use the variable as an index into the list of numbers or expressions that follow. The “CLASS” keyword is optional. This variable must be non-negative. If “CLASS # :” is used, then the number refers to the value of the indexing variable. If a class is not specified for a given value, its expression is implicitly ZERO. Interpolation tables are very similar except that the variable is assumed to be continuous instead of classified. An interpolated value between classes is returned. Lookup tables are also similar, except that both the variable and classes are assumed to be continuous values. An interpolated value between classes is also returned. Rarely used.

INTERPOLATE(X) return an interpolated value where the value of
CLASS Number: Number variable X is placed between two classes or at
: either end of the table.
ENDFN

INTERPOLATE(X): ( Number+) same as above, except the classes are
implicitly 0, …. k-1

INTERPOLATE(X) same as above, except the values in the
CLASS Number: Expr table are obtained by evaluating expressions
:
ENDFN

INTERPOLATE(X) same as above, except the classes are
Expr implicitly 0, …, k-1
:
ENDFN

INTERPOLATE(X): Filename uses the table in the named file, which is
assumed to consist of class:value pairs

INTERPOLATE(X): Filename Key uses the table in the named file, which is
assumed to consist of class:value pairs. The key
is used to specify a sub-table in a multi-table
file.

LOOKUP(X) return the interpolated value where the value of
CLASS Number: Number variable X is placed between two classes or at
: either end of the table, and classes can be any.
ENDFN real values.

LOOKUP(X): ( Number+) same as above, except the classes are
implicitly 0, …. k-1

LOOKUP(X) same as above, except the values in the
CLASS Number: Expr table are obtained by evaluating expressions
:
ENDFN

LOOKUP(X) same as above, except the classes are
Expr implicitly 0, …, k-1
:
ENDFN

LOOKUP(X): Filename uses the table in the named file, which is
assumed to consist of class:value pairs

LOOKUP(X): Filename Key uses the table in the named file, which is
assumed to consist of class:value pairs. The key
is used to specify a sub-table in a multi-table
file

===Boolean Functions===
Expr EQ Expr TRUE if the values of the two expressions are
equal; otherwise FALSE
Expr == Expr alternate form of EQ comparison (Note: two equal signs distinguish this from an assignment)

Expr NEQ Expr TRUE if the values are not equal; otherwise
FALSE
Expr != Expr alternate form of NOT EQUAL comparison

Expr < Expr TRUE if the value of the first expression is less
than the value of the second expression;
otherwise FALSE
Expr <= Expr TRUE if the value of the first expression is less
than or equal to the value of the second
expression; otherwise FALSE

Expr > Expr TRUE if the value of the first expression is
greater than the value of the second
expression; otherwise FALSE
Expr >= Expr TRUE if the value of the first expression is
greater than or equal to the value of the
second expression; otherwise FALSE

!Expr Negates the expression Boolean value

Expr AND Expr TRUE if values of both expressions are
TRUE and FALSE otherwise

Expr OR Expr TRUE if value of at least one expression is
TRUE and FALSE otherwise

Note that relations can be cascaded, with the interpretation that each operator applies independently to its surrounding pair of expressions. Thus, the expression: Expression <= Expression <= Expression (e.g. 5 <= age <= 50) specifies a “between” relation, which is TRUE only if the value of the centre expression falls in the specified range.

===Bit-Vector Functions===
Bit-vector functions treat an integer value (the independent variable) as a sequence of bits, each of which can be independently set and accessed. This can allow use of a single layer to hold lots of Boolean information, since each cell as an integer has 8, 16 or 32 bits. For example, bits 0, 1, 2 and 3 can be used to store four different Boolean states (a, b, c and d), and the sequence 0110 means that states a and d are FALSE and states b and c are TRUE. PositionList is a semi-colon separated sequence of integer or ranges (lower-upper) indicating positions in the integer (0-31). For example, the PositionList 1;4-6;27 indicates bits at positions 1, 4, 5, 6 and 27.

SETAT(Expr, PositionList, #Type) Set the value specified by the expression, at
the positions in PositionList to: FALSE (0)
if Type is 0, TRUE (1) if Type is 1,
and flip the bits if Type = 2

SETAT(Expr, PositionList,#Type,#Prob) Same as above, except each position is set
with probability #Prob

SELECTAT(Expr, PositionList) FALSE(0) if none of the bits in PositionList are
set in the specified expression value and
TRUE(1) otherwise

MAX POSITION(Expr) Return the maximum 0-based bit position that is
set to one in the expression value (interpreted
as a bit-vector), or –1 if no bits are set

MIN POSITION(Expr) Return the minimum 0-based bit position that is
set to one in the expression value (interpreted
as a bit-vector), or –1 if no bits are set

BITWISE OR(Expr, Expr) Bitwise OR of two values
BITWISE AND(Expr, Expr) Bitwise AND of two values
BITWISE XOR(Expr, Expr) Bitwise exclusive-OR of two values
BITWISE NOT Expr Bitwise NOT of a value

SHIFT LEFT(Expr, Expr) Shifts value of first expression to the left by
number of bits specified by second expression
SHIFT RIGHT(Expr, Expr) Shifts value of first expression to the right by
number of bits specified by second expression

===Control Expressions===
Note the difference between the first two “functional if’s” (i.e. a value is returned) and the latter “procedural if’s” (that don’t return a value, but control flow).

IF Expr THEN Expr ELSE Expr if value of the IF expression is TRUE (>= 1), then return the value of the THEN expression,
otherwise return value of the ELSE expression

(Expr ? Expr : Expr) Same as above, but this form can be used as an
embedded sub-expression.

IF Expr Procedural IF statement to process
… sub-expressions denoted by “…” only if the
ENDFN expression evaluates to TRUE

IF Expr Procedural IF statement to process the first set
… of sub-expressions denoted by “…”if the
ELSE expression evaluates to TRUE and the set of
… sub-expressions after the ELSE otherwise. Note
ENDFN that “ELSE IF expr” forms can be strung
together

WHILE Expr While loop: process sub-expressions denoted by
… “…” while the expression evaluates to TRUE
ENDFN

PAUSE Halts the simulation and displays a dialog
box to which the user must respond to continue

PAUSE IF Expr If the expression evaluates to TRUE, halts the
simulation and displays a dialog box to which
the user must respond to continue

PAUSE(#Value) Pauses the simulation for the specified number
of milliseconds and then continues

PAUSE(#Value) IF Expr If the expression evaluates to TRUE, Pauses the
simulation for the specified number of
milliseconds and then continues

WAIT UNTIL Expr Suspend execution until the expression returns TRUE (1). This is intended for controlling
communication and synchronization with
an external application.
CRITICAL SECTION (Flag) Enter (if Flag is TRUE) or exit (if Flag is FALSE) a critical section. A critical section gives priority to this application, and is used for
synchronizing access to shared variables
(i.e. shared with another application).

DEBUG Update the simulation probe, if it is loaded and
The event is selected. Used to debug/verify
event behaviour.

SEED() Gets the random number seed
SEED(Expr) Sets the random number seed. Value returned is
next seed.

RESIZE(Variable, Expr) Changes size (number of entries) in a global
variable. Values are not maintained. Useful for
when size is not known prior to simulation.

RECOMPUTE Only valid in consequent expressions of
ProbInit and also when ProbInit recompute flag
has been set. Causes prob. surface to be
recomputed before next selection
===Output Expressions===
DISPLAY Display on the screen the labelled Label: Expr values computed with the expressions listed.
…. If no label is given, the expression must
ENDFN be a variable, and this is used for the label.

DISPLAY Same as above, but only display if the DECISION Expr decision expression evaluates to TRUE
Label: Expr The keyword DECISION can be replaced by
…. a “?”
ENDFN

OUTPUT RECORD(OutputVar) Output to the record file of output variable the labelled values computed with the Label: Expr expressions listed. If no label is given, the
…. Expression must be a variable and this is
ENDFN used as label.

OUTPUT RECORD(OutputVar) Same as above, but only output if the DECISION Expr decision expression evaluates to TRUE
Label: Expr
….
ENDFN

Note: a label/expression pair can be “expanded” by using the form: Label#n1:n2: Expr, where n1 and n2 are integers or constant names. This will create n2-n1+1 columns rather than a single column. The system variable Index can be used in the expression, and will take on values n1, n1+1,…,n2 for each column, respectively.

===Composite Functions===
Compound expressions all have the same form of an expression name followed by a list of sub-expressions. If the first expression is a region function, then the subsequent expressions are all evaluated over the defined region, instead of only at the current cell (however, it is usually simpler to use an OVER REGION expression). When arithmetic expression become complex, sometimes composite expressions can be written more clearly. The general format is as follows:

CompositeExpressionName
Expr
:
ENDFN

The following composite expressions are supported:

===SUM===
DESCRIPTION:
Returns the number that is the sum of all the expressions.

USAGE:
x=SUM
Expr
...
ENDFN

REQUIRED ARGUMENTS:
Expr is any expression that evaluates to single numeric value.

VALUE:
the sum of all the arguments.

SEE ALSO:
<a link to the composite functions section of seles modellers guide>

EXAMPLES: <add carriage return here>
Example 1:
y = 3
x = SUM
y
y+2
5
ENDFN
<figure out an end example indicator. For example, ***>

SAMPLE MODELS:
<links to sample models where this function is used>

===PRODUCT===
product of the sub-expressions

DIVIDE successive division of the sub-expressions

MEAN average of the sub-expressions

GEOMETRIC MEAN geometric mean of the sub-expressions (nth
root of the product for n expressions)

MIN minimum of the sub-expressions

MAX maximum of the sub-expressions

EQUAL TRUE (1) if the sub-expressions all evaluate to
the same value and FALSE (0) otherwise
NOT EQUAL FALSE (0) if the sub-expressions all evaluate to
the same value and TRUE (1) otherwise

OR TRUE (1) if at least one sub-expression
evaluates to TRUE and FALSE (0) otherwise

AND TRUE (1) if all sub-expressions evaluate to
TRUE and FALSE (0) otherwise

LESS OR EQUAL TRUE (1) if the sub-expression evaluations are
all ordered according to the relation <=, and
FALSE (0) otherwise

ORDERED same as LESS OR EQUAL

LESS THAN TRUE (1) if the sub-expression evaluations are
all ordered according to the relation <, and
FALSE (0) otherwise

STRICT ORDERED same as LESS THAN

GREATER OR EQUAL TRUE (1) if the sub-expression evaluations are
all ordered according to the relation >=, and
FALSE (0) otherwise

GREATER THAN TRUE (1) if the sub-expression evaluations are
all ordered according to the relation >, and
FALSE (0) otherwise

===Region Functions===
A region function returns the set of locations, one on each call. Their use is limited to the main expression of EventLocation, SpreadLocation, AgentLocation and MoveLocation properties, as the first expression of composite expressions and in OVER REGION functions.

REGION WHOLE MAP defines the region consisting of the entire
DECISION Expr landscape. If there is a decision expression,
then only those cells for which this expression
returns TRUE will be included.

REGION RECT (Expr, Expr, Expr, Expr) defines a rectangular region. If there is a
DECISION Expr decision expression defined, then only those
cells for which this expression returns
TRUE will be included

REGION CENTRED (Expr, Expr [, DistanceType][, WRAPPED])
DECISION Expr defines a region centred on the current cell.
If there is a decision expression, then only
those cells for which this expression returns
TRUE will be included.

DistanceType is either CARDINAL or EUCLIDEAN (the default). Cardinal distance between two cells is the minimum number of cardinal steps (up, down, left, right) to reach one cell from the other. Euclidean distance is the straight-line distance between two points. The WRAPPED flag, if present indicates that the region wraps around the sides (vertically and horizontally) of the landscape (e.g. a location x positions beyond the right-hand side of a raster will be mapped to x positions in from the left-hand side of the raster). If not present, the landscape does not wrap.

REGION LOCATION LIST(Number+) defines the region consisting of a set of
DECISION Expr known location indices. If there is a decision expression, then only those cells for which this
expression returns TRUE will be included.

REGION LOCATION LIST(X,n) defines the region consisting of a set of n
DECISION Expr location indices stored in one-dimensional X.

REGION LOCATION (Expr) defines the region consisting of a of a single
DECISION Expr location index. If there is a decision expression,
then only those cells for which this expression
returns TRUE will be included.

REGION VECTOR (StartLocation, EndLocation) defines region consisting of cells along an
DECISION Expr approximation of line between end cells

Cost surface and least-cost path regions are advanced features that are best understood with an example model.

REGION COST SURFACE(EndLocation, MaxCost, CostSurface)
DECISION Expr
COST Expr
REGION COST SURFACE(EndLocation, MaxCost, CostSurface, LeastCostNeighbs, AnchorLoc)
DECISION Expr
COST Expr
Defines a region surrounding a cell with
cumulative costs less than MaxCost. Stops
growing when EndLocation is reached or all
costs are greater than MaxCost. Second form
also records gradient and anchor location
layers. The CostSurface layer records the
cumulative cost from the cost function

REGION LEAST COST PATH(StartLocation, EndLocation)
DECISION Expr
COST Expr
REGION LEAST COST PATH(StartLocation, EndLocation, LeastCostNeighbs)
DECISION Expr
REGION LEAST COST PATH(StartLocation, EndLocation, LeastCostNeighbs, AnchorLoc)
DECISION Expr
Defines a region with cells that approximate
the least-cost path between two cells. The
first generates the cost function internally.
The latter two use input information from a
pre-computed cost surface region. Providing
both the gradient and anchor location layers
provides the most accurate approximation.

Iteration is a common aspect of models (even if it is very procedural). Most programming languages offer a “for-loop” of some kind. SELES presently provides “over index sequence” expressions as a slightly more declarative (although also more cumbersome) expression for iterating. While-loops can also be used.

OVER INDEX SEQUENCE(Expr, Expr) defines linear sequence of location indices.
DECISION Expr If there is a decision expression, then only
those cells for which this expression returns
TRUE will be included. The system variable
Index holds the value of the index at each value
in the sequence

Over region expressions are very frequently used to visit all cells in a landscape that meet some condition (e.g. to compute the size of the forest at initiation).

OVER RegionFunction Apply a set of sub-expressions at all spatial
Expression locations specified by a region function
:
ENDFN

AT LOCATION #Expr Apply a set of state-changes at a specified
Expression location
:
ENDFN

===Matrix Functions===
Matrix assignment is indicated using “[=]” instead of “=”. The proper dimensions of the component arrays must be met.

Variable [=] Variable assign variable of same dimension, or a
single value to all entries
Variable [=] Variable + Variable sum variables of same dimension (or with a
constant)
Variable [=] Variable - Variable subtract variables of same dimension (or
with a constant)
Variable [=] Variable * Variable matrix or scalar multiplication.

Variable [=] TRANSPOSE(Variable) matrix transposition
Variable [=] Variable^-1 invert a matrix
Variable = SUM(Variable) sum all entries in a matrix
Variable [=] SUM ROWS (Variable) sum all rows of a matrix (result has one
value per column)
Variable [=] SUM COLS(Variable) sum all columns of a matrix

Variables [=] SORT(Variable, Expr) sort rows of an input matrix where rank is
given by Expr. The system variable “Index”
can appear in the expression and will take on
the range of indices in the input array. The
resulting sorted matrix will be assigned.

Variable [=] MPM_MULT(Variable, Variable) Performs a “matrix population model”
(MPM) integer-based multiplication.
Assumes that first matrix is two-dimensional
and that second is a vector. The result is
two-dimensional, where entries above
diagonal represent "offspring", entries on the
diagonal represent "survivors" and entries
below the diagonal represent "succeeders"

Variable [=] CONTAG(Variable, Variable) Creates a “temporal contagion” matrix.
Given probabilities (first parameter) for a set
of states and a two-dimensional contagion
array (values –1 to 1 indicating affinity),
generates a matrix where each row is a prob.
dist. For transitions given the row value, and
the overall target dist. will be met.

===General Set, List and Graph Functions===
REMOVE ALL(LinkedVariable) clears variable. No return value
SIZE(LinkedVariable) number of elements, entries or nodes
IS EMPTY(LinkedVariable) TRUE if and only if variable has 0 elements

FIRST(LinkedVariable) returns position of first element, entry or
node
NEXT(LinkedVariable, PosVariable) returns position of element, entry or node
following position provided
PREV(LinkedVariable, PosVariable) returns position of element, entry or node
preceding position provided
REMOVE(LinkedVariable, PosVariable) remove and deletes element, entry or node
at position

Variable [=] GET(LinkedVariable, PosVariable) get element, entry or node at position
X [=] GET(LinkedVariable, PosVariable, Index) get single value in a given index
SET(LinkedVariable, PosVariable, Variable) set element, entry or node at position
SET(LinkedVariable, PosVariable, entryIndex, Value)
set value at specified index of element,
entry or node at position
FIND(LinkedVariable, , TmpVariable Condition) return first position of an element, entry or
node that satisfies the condition
FIND NEXT(LinkedVariable, PosVariable, TmpVariable, Condition)
return next position of an element, entry or
node that satisfies the condition
SORT(LinkedVariable, TmpVariable1, TmpVariable2, Condition)
sort elements, entries or nodes according to
condition

===Set Functions===
CONTAINS(SetVariable, ElementVariable) TRUE if and only if set variable “contains”
variable provided, where two elements are
identical if they have identical values
INSERT(SetVariable, ElementVariable) add element to set. Only changes set if it
doesn’t already contain the element
SetVariable = UNION(Set1, Set2) take union of two set variables
SetVariable = INTERSECTION(Sete1, Set2) take intersection of two set variables
SetVariable = SUBTRACT(Sete1, Set2) subtract second set variable from first

===List Functions===
HEAD(ListVariable) returns position of first entry
TAIL(ListVariable) returns position of last entry
INSERT HEAD(ListVariable, EntryElement) add an entry to front of list
INSERT TAIL(ListVariable, EntryElement) add an entry to end of list
INSERT BEFORE(ListVariable, Index, EntryElement)
add an entry before given index
INSERT AFTER(ListVariable, Index, EntryElement)
add an entry after given index
INSERT AT(ListVariable, Index, EntryElement) add an entry at given index

REMOVE HEAD(ListVariable) removes and deletes first entry
REMOVE TAIL (ListVariable) removes and deletes last entry
REMOVE AT INDEX(ListVariable, Index) removes and deletes entry at given index

Variable [=] GET HEAD(ListVariable) returns first entry
Variable [=] GET TAIL(ListVariable) returns first entry
Variable [=] GET AT INDEX(ListVariable, Index) returns entry at given index
Pos = POS AT INDEX(ListVariable, Index) returns position at given index

===Tree Functions===
ADD ROOT(TreeVariable, EntryElement) add root element of a tree
INSERT LEFT CHILD(TreeVariable, PosVariable, EntryElement)
add child to a node on the left of current
children
INSERT RIGHT CHILD(TreeVariable, PosVariable, EntryElement)
add child to a node on the right of current
children
INSERT CHILD(TreeVariable, PosVariable, EntryElement, Index)
add child to a node at given index (from
left)

n = CHILDREN(TreeVariable, PosVariable) number of children at a given position
Pos = PARENT(TreeVariable, PosVariable) Position of parent of a node
Pos = LEFT CHILD(TreeVariable, PosVariable) Position of leftmost child of a node
Pos = RIGHT CHILD(TreeVariable, PosVariable) Position of rightmost child of a node
Pos = CHILD(TreeVariable, PosVariable, Index) Position of indexed (from left) child of a
node
Pos = NEXT SIBLING(TreeVariable, PosVariable) Position of next sibling to right of a node
Pos = PREV SIBLING(TreeVariable, PosVariable) Position of previous sibling to right of a
node

Pos = NEXT DFS(TreeVariable, PosVariable) Position of next node in depth-first
pre-order traversal of a tree. If the position
variable is NULL, then the root is returned
Pos = NEXT POSTORDER DFS(TreeVariable, PosVariable)
Position of next node in depth-first
post-order traversal of a tree. If the position
variable is NULL, then the root is returned
Variable [=] GET LEFT CHILD(TreeVariable, PosVariable)
returns entry of leftmost child for a given
node
Variable [=] GET RIGHT CHILD(TreeVariable, PosVariable)
returns entry of rightmost child for a given
node
Variable [=] GET CHILD(TreeVariable, PosVariable, Index)
returns entry of child with given index
(from left) for a given node

===Graph Functions===
REMOVE ALL LINKS(GraphVariable) clears links of a graph variable
SIZE LINKS(GraphVariable) number of links in graph
IS EMPTY LINKS(GraphVariable) TRUE if and only if graph has 0 links

FIRST LINK(GraphVariable) returns position of first link
NEXT LINK (GraphVariable, PosVariable) returns position of link following position
provided
PREV LINK (GraphVariable, PosVariable) returns position of link preceding position
provided
Variable [=] GET LINK(GraphVariable, PosVariable)
get link at position
CONTAINS LINK(GraphVariable, LinkVariable) TRUE if and only if graph variable contains
variable provided
REMOVE LINK(GraphVariable, PosVariable) remove and deletes link at position
SET LINK(GraphVariable, PosVariable, LinkVariable)
Set link at position
SET LINK(GraphVariable, PosVariable, entryIndex, Value)
Set value at specified index of link at
position
FIND LINK(GraphVariable, TmpVariable, Condition)
Return first position of link that satisfies the
condition
FIND NEXT LINK(GraphVariable, PosVariable, TmpVariable, Condition)
Return next position of a link that satisfies
the condition
SORT LINKS(GraphVariable, TmpVariable1, TmpVariable2, Condition)
Sort links according to condition
LINKED(GraphVariable, NodeVariable1, NodeVariable2, LinkType)
TRUE if the nodes are linked. Set LinkType
to 0 for direct links and 1 for indirect