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Language Reference

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Constants

ZERO

return 0.0

ONE

return 1.0

  1. 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 Model Builder's Guide Chapter 9#Continuous Functions (Arithmetic Functions)

(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 Model Builder's Guide Chapter 9#Continuous Functions (Arithmetic Functions)

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) Model Builder's Guide Chapter 9#Continuous Functions (Arithmetic Functions)

ROUND(Expr) expression value rounded to the nearest integerModel Builder's Guide Chapter 9#Continuous Functions (Arithmetic Functions) FLOOR(Expr) largest integer smaller than the expression valueModel Builder's Guide Chapter 9#Continuous Functions (Arithmetic Functions) CEILING(Expr) smallest integer larger than the expression valueModel Builder's Guide Chapter 9#Continuous Functions (Arithmetic Functions)

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)

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) Model Builder's Guide Chapter 9#Continuous Functions (Trigonometric Functions) SIN(Expr) interpret the value of the expression as an angle theta in degrees, and return sin(theta) Model Builder's Guide Chapter 9#Continuous Functions (Trigonometric Functions) 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) TAN(Expr) interpret the value of the expression as an angle theta in degrees, and return tan(theta) 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) ARCCOS(Expr) inverse cos 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)

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 Model Builder's Guide Chapter 9#Continuous Functions (Miscellaneous)

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)

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

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 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)
  :

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

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 Model Builder's Guide Chapter 9#Classified and Discrete Functions

INTERPOLATE(X): ( Number+) same as above, except the classes are implicitly 0, …. k-1 Model Builder's Guide Chapter 9#Classified and Discrete Functions INTERPOLATE(X) same as above, except the values in the CLASS Number: Expr table are obtained by evaluating expressions  : ENDFN Model Builder's Guide Chapter 9#Classified and Discrete Functions

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

  :

ENDFN Model Builder's Guide Chapter 9#Classified and Discrete Functions

INTERPOLATE(X): Filename uses the table in the named file, which is assumed to consist of class:value pairs Model Builder's Guide Chapter 9#Classified and Discrete Functions 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. Model Builder's Guide Chapter 9#Classified and Discrete Functions 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. Model Builder's Guide Chapter 9#Classified and Discrete Functions LOOKUP(X): ( Number+) same as above, except the classes are implicitly 0, …. k-1 Model Builder's Guide Chapter 9#Classified and Discrete Functions LOOKUP(X) same as above, except the values in the CLASS Number: Expr table are obtained by evaluating expressions  : ENDFN Model Builder's Guide Chapter 9#Classified and Discrete Functions LOOKUP(X) same as above, except the classes are Expr implicitly 0, …, k-1 

  :

ENDFN Model Builder's Guide Chapter 9#Classified and Discrete Functions LOOKUP(X): Filename uses the table in the named file, which is assumed to consist of class:value pairs Model Builder's Guide Chapter 9#Classified and Discrete Functions 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 Model Builder's Guide Chapter 9#Classified and Discrete Functions

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

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