Working with equations : Built-in functions

Built-in functions

Alphabetical list of most commonly used functions,  Trigonometric functions are listed separately. Please see the other categories at the bottom of the page for less common or recently added functions.

 Template  Effect

Input(s)

Return

value

abs(X)

Returns the absolute value of X

   

all([X])

all{X})

Result is true if all the elements of the array [X] or the list {X} are true

boolean array/list

 Boolean

any([X])

any({X})

Result is true if any of the elements of the array [X] or the list {X} are true.

boolean array or list

 Boolean
at_init(X) Returns X's value when last initialized or reset Any Same as input

at_posn(C)

at_posn(C, X, Y)

Causes component to get value from instance of C in a grid submodel Any, two optional integers Scalar as 1st argument
binome(P, N) Returns a value from the binomial distribution with probability P and number of trials N

Real value from 0 to 1,                  Integer value

Integer value

ceil(X)

Rounds up X to the next whole number

   

channel_is(X)

X is an immigration, reproduction or creation channel. Returns true if this individual appeared through that channel.

   
colin([X]) Returns an index to the given array, with probabilities proportional to the array's values Array of numeric values Integer or enumerated type member
const_delay(X, T) Returns the value of X as it was T time units earlier in the run, or 0 or "false" if the component did not exist at that time Any non-array type, numeric constant As 1st argument

count([X])

Number of values in the array [X] or the list {X}

scalar array/list

 

delay1(x,t), delay3(x,t), delayn(x,t,n)

Insert a material delay of order 1, 3 or n

numerical

numerical, numerical, integer (delayn only)
dies_of(X) X is a loss channel. True if channel specifies the removal of the individual this time step. from loss channel Boolean

dt(I)

Returns the duration of the time step level I

   

element([X],I)

Picks the I'th value form the array [X]

array of any type,integer or enumerated type member

 

exp(X)

Returns e to the power X

   

exprnd(mean [, seed])

Samples an exponential distribution

numerical[, integer] numerical
first(T) Returns "true" if argument is the first member of its enumerated type Enumerated type member Boolean
firsttrue([B]) Takes an array of booleans and returns the index of the first with value "true" Array of booleans Integer or enumerated type member

floor(X)

Rounds X down to a whole number

   

fmod(X,Y)

Returns remainder after dividing X by Y

numeric, numeric

 
following(T) Returns next member of argument's enumerated type Enumerated type member Enumerated type member
forcst(input, time, horizon [, initial]) New in v6.6: Performs simple trend extrapolation Real, real, real [,real] Real
gaussian_var(X,Y) Returns a sample from a Gauusian distribution with mean X and SD Y Real, real real

greatest([X])

greatest({X})

Returns the largest value from an array [X] or the list {X}

numeric array/list

 
howmanytrue([B]) Takes an array of booleans and returns the number that are true List or array of booleans Integer
hypergeom(P, M, S) Returns a deviate from a hypergeometric distribution for population, P, number of marks M, and sample size S. integer, integer, integer integer

hypot(X,Y)

Returns length of hypotenuse of triangle with base X and height Y

numeric, numeric

 

index(I)

Returns the index (instance number) of a member of a fixed membership or population submodel, for the level I of submodel nesting.

 Integer Integer or enumerated type member

inf()

New in v6.6: Returns the value of positive infinity.

 Real None

init_time(1)

Returns the time at which this instance appeared -- argument is dummy

   
in_preceding(X) New in Simile v5.7: Returns value of X in preceding submodel instance Any scalar or array type As argument
in_progenitor(X) New in Simile v5.8: Returns value of X in submodel instance that reproduced to make current one Any scalar or array type As argument

int(X)

Returns integer part of X

   
interpolate(X, [Xarray], [Yarray]) Returns interpolated value from [Yarray] corresponding to X's place in Xarray

Numeric, Array of numeric, Array of numeric

Numeric
iterations(B) Counts executions of iterative submodel Boolean Integer

last(X)

Recalls value of X from previous time step

   

least([X])

least({X})

Returns the smallest value from an array [X] or the list {X}

numeric array/list

 

log(X)

Returns natural logarithm of X

   

log10(X)

Returns base-10 logarithm of X

   

makearray(X,N)

Makes an array consisting of N lots of X

any type, integer

array of same type

max(X,Y)

Returns greater of X and Y

numeric, numeric

 

min(X,Y)

Returns lesser of X and Y

numeric, numeric

 
order([X]) Returns an array holding the indices of the argument array in ascending order of their values array of numeric array of integer

parent(I)

Returns the id of the individual whose reproduction gave rise to this one, or 0 if it immigrated or was created

   

place_in(I)

When making an array with makearray, this gives each term's position in the array -- argument is nesting depth

   
poidev(X) Returns a value from the Poisson distribution with the given mean numeric integer
posgreatest([X]) Returns the index of the highest value in the argument array Array of numeric values Integer or enumerated type member
posleast([X]) Returns the index of the lowest value in the argument array Array of numeric values Integer or enumerated type member

pow(X,Y)

Returns X raised to the power Y

numeric, numeric

 numeric
preceding(T) Returns previous member of argument's enumerated type Enumerated type member Enumerated type member

prev(N)

Returns the value of this component N time steps ago

   

product([X])

product({X})

Result is the product of all elements of the array [X] or the list {X}

numeric array/list

numeric

pulse(H, T [, I])

Generates a single time step pulse of magnitude M at time T, and before or after at intervals of I if I present

numeric, numeric, numeric

numeric

ramp(T,S)

Generate a linearly increasing or decreasing value over time with the given slope

numeric, numeric

numeric

rand_const(X,Y)

(Deprecated) Returns a random number between X and Y, which stays the same until the simulation is reset.

numeric, numeric

 

rand_var(X,Y)

Returns a random number between X and Y, with a new value every time step.

numeric, numeric

 
rankings([X]) Returns ranking of each element in order of size Array of numerics Array of integers

round(X)

Rounds X up or down to the nearest whole number

   
sgn(X) Returns the size of X; -1 if negative, 1 otherwise    

size(S)

Takes the name of a fixed-membership submodel and returns the number of instances that it has.

   

size(S,I)

Takes the name of a fixed-membership submodel and returns the size of one of its dimensions

submodel, numeric

 

smth1(x,a), smth3(x,a), smthn(x,a,n)

Insert a material smoothing of order 1, 3 or n

numerical

numerical, numerical, integer (smthn only)

sqrt(X)

Returns the square root of X

   

step(H, T)

Generate a step increase (or decrease) at the given time

numeric, numeric numeric

stop(X)

Stops the simulation, displaying value of X in a popup message

   
subtotals([X])

Returns running totals from summing the elements in the supplied array

Numeric array Numeric array

sum([X])

Result is the sum of all elements of the argument

numeric array/list

 

time()

Returns the current simulation time (the argument is ignored)

   
trigger_magnitude() Returns value of triggering event    As triggering event
var_delay(X,T) Returns value of X as it was T time units earlier in run, or 0 or "false" if this is before component existed Any non-array type, numeric expression As first argument

with_colin({N},{X})

Returns a value from the list {X} with probabilities proportional to the corresponding values in the list {N}

numeric list,       any list

member of second arg

with_greatest([N],[X])

with_greatest({N},{X})

Returns the value from an array [X] or the list {X} whose position in the array or list corresponds to the largest value in the array [N] or list {N}

numeric array/list, any array/list

 

with_least([N],[X])

with_least({N},{X})

Returns the value from an array [X] or the list {X} whose position in the array or list corresponds to the smallest value in the array [N] or list {N}

numeric array/list, any array/list

 

In addition, a full range of trigonometric functions are provided.

In: Contents >> Working with equations >> Functions

Built-in functions : Arithmetic functions

Arithmetic functions

Built-in functions : abs function



abs function

abs(X)

Returns the absolute value of X - i.e. ignores its sign

Input: numeric scalar or numeric array

Result: numeric scalar or array

Examples:

abs(3) --> 3

abs(-3) --> 3

abs([2,-3,4,-5]) --> [2,3,4,5]

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : pow function



pow function

pow(X,Y)

Returns X raised to the power Y

Input: numeric, numeric

Result: numeric

Comment:

This is equivalent to the use of the ^ operator: i.e.

pow(5,2)

is the same as

5^2

The latter should be used of preference, as it is the more familiar notation.

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : min function



min function

min(X,Y)

Returns lesser of X and Y; i.e. it returns X if X<=Y, otherwise it returns Y.

Inputs: numeric, numeric

Result: numeric

Comments:

The min function is a useful way of ensuring that some value does not go above some threshold. For example, if b increase as a increases, but does not exceed 20, then the equation for b could be:

b = min(20, 0.2*a)

This avoids the use of a cumbersome if…then… else… construction

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : max function



max function

max(X,Y)

Returns greater of X and Y; i.e. it returns X if X>=Y, otherwise it returns Y.

Inputs: numeric, numeric

Result: numeric

Comments:

The max function is a useful way of ensuring that some value does not go below some threshold. For example, if b declines as a increases, but does not go below zero, then the equation for b could be:

b = max(0,10-0.2*a)

This avoids the use of a cumbersome if...then...else... construction.

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : inf function

inf function

New in v6.6

inf()

Returns the value of positive infinity

Input: none

Result: numeric

Built-in functions : sgn function

sgn function

sgn(X)

Returns -1 if X is negative, or 1 if X is zero or positive

Input: numeric, or array of numeric values

Result: integer, or array of integer values

Examples:

sgn(1.9) --> 1

sgn(-1.1) --> -1

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : sqrt function



sqrt function

sqrt(X)

Returns the square root of X

Input: numeric

Result: numeric

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : round function



round function

round(X)

Rounds X up or down to the nearest whole number

Input: numeric, or array of numeric values

Result: numeric, or array of numeric value

Examples:

round(1.9) --> 2

round(1.1) --> 1

round([1,2.1,3.9]) --> [1,2,4]

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : log10 function



log10 function

log10(X)

Returns base-10 logarithm of X

Input: numeric

Result: numeric

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : log function



log function

log(X)

Returns natural logarithm of X

Input: numeric; or an array of numeric values

Result: numeric; or an array of numeric values

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : ceil function



ceil function

ceil(X)

Rounds up X to the next whole number (stands for 'ceiling')

Input: numeric, or array of numeric values

Result: numeric, or array of numeric value

Examples:

ceil(1.9) --> 2

ceil(1.1) --> 2

ceil([1,2.1,3.9]) --> [1,3,4]

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : exp function



exp function

exp(X)

Returns e (the base of natural logarithms) to the power X

Input: numeric, or an array of numeric values

Result: numeric, or an array of numeric values

Example:

The exponential growth of a population is given by the formula

Nt = N0er.t

where:

Nt is the population size at time t,

N0 is the initial population size,

e is the base of natural logarithms,

r is the intrinsic growth rate, and

t is current time
 

We can represent this in Simile using a single variable (called N), with its equation being

N = 10*exp(0.1*time(1))

assuming that the initial population size = 10 and the value of r is 0.1.
 

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : floor function

floor function

floor(X)

Rounds X down to a whole number.

Input: numeric, or an array of numeric values

Result: numeric, or an array of numeric values

Examples:

floor(3.1) --> 3

floor(3.99) --> 3

floor([1.1,2.4,3.7,4.9]) --> [1,2,3,4]

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : int function



int function

int(X)

Returns integer part of X

Input: numeric

Result: numeric

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : hypot function



hypot function

hypot(X,Y)

Returns length of hypotenuse of right-angle triangle with base X and height Y

Inputs: numeric, numeric

Result: numeric

Examples:

hypot(3,4) --> 5 (a 3:4:5 triangle)

hypot(x1-x2,y1-y2) --> the distance between two points with co-ordinates (x1,y1) and (x2,y2) respectively.

hypot(x-[xs],y-[ys]) --> [distances] I.e. an array containing the distance from one point with co-ordinates (x,y) to a set of points, with co-ordinates held in the arrays [xs] and [ys]. See comments.

Spatial modelling frequently requires that one object knows the distance to another. This requires that each has x,y co-ordinates. It is then simple to use the hypot function to work out the straight-line distance between them, as shown in the second example above.

The same principle applies when you use a multiple-instance submodel to represent a set of spatially-located objects. In this case, each object may want to know how far it is to all the other objects - for example, in working out the competition between trees in an individual-based tree model. The following model diagram fragment shows a typical model configuration for doing this:

Each tree has x,y co-ordinates. These are exported to two array variables, xs and ys, whose equations are simply:

xs = [x]

and

ys = [ys]

These arrays are then brought back into the submodel, and used to generate an array containing the distance for each tree to all the other trees, using the equation given in the third example above.

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : fmod function



fmod(X,Y)

Returns remainder after dividing X by Y

Inputs: numeric, numeric

Result: numeric

Examples:

fmod(7,3) --> 0.333 (7/2 = 2.333, i.e. the remainder is 0.333)

fmod(time(1),1) --> a result that climbs from 0 to 1 repeatedly (i.e. a sawtooth pattern) as the simulation proceeds. See comments below.

fmod((index(1)-1),5)+1 --> 1,2,3,4,5,1,2,3,4,5,1,2,3... for successive values of index(1). See comments below.

This apparently obscure function in fact has (at least) two very valuable uses.

First, it can be used to generate regular cycles, in particular annual or daily cycles. Consider the case or a model with the time unit being one year, and a time step of less than a year. You want various exogenous variables (such as temperature or rainfall) to vary in a prescribed fashion during the course of each year, with the annual pattern repeating itself from one year to the next. The following diagram is typical of the model fragment you could use for representing this:

The variable time is simply set equal to current simulation time, using the function time(1). The variable season is set to rise from 0 to 1 every year. If your model used a time unit of one week, then the equation would be changed to

season = fmod(time,52)

and the value for season would then correspond to week number. The equations for rainfall and temperature are for illustration purposes only: you would need to replace them by something appropriate.

Second, the fmod function can be used to generate a regular spatial arrangement (rows and columns) for a 2D grid. Let's say that you are modelling an area of 10x10 grid squares. In Simile, you would set up a submodel, called perhaps Patch, with 25 instances. In order to give each patch location on a grid, each one needs to have a row and column attributes, with each patch having a unique combination of the numbers 1..5 for row and column. The only thing we know about each patch is that it has an index number (given by the built-in function index(1)), a value ranging between 1 and 25. The trick is to get row number to be, in sequence,

1,1,1,1,1,2,2,2,2,2,3,3,3...

and column number to be, in sequence,

1,2,3,4,5,1,2,3,4,5,1,2,3...

thus giving each of the 25 instances a unique row-and-column pair.

This is readily done using the following two equations:

row = floor((index(1)-1)/5)+1

column = fmod((index(1)-1),5)+1

See the floor function to understand why the row numbers should be in the first sequence above. For column, we divide the index number for each instance by 5, taking the remainder: the '-1' and +1' are there to ensure that we get the results in the blocks of five that we require. See a grid-based spatial model example to see this in action.

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : Trigonometric functions

Trigonometric functions

   

Input(s)

 

acos(X)

Returns the arccos (inverse cosine) of X. Result is in radians.

   

asin(X)

Returns the arcsine of X. Result is in radians.

   

atan(X)

Returns a value in radians (range -pi/2 to pi/2), being the arctangent of X (the ratio of two sides of a right triangle). Same as arctan(X).

   

atan2(X,Y)

Returns the arctangent of X. Result is in radians.

numeric,numeric

 

cos(X)

Returns the cosine of X (an angle in radians)

   

cosh(X)

Hyperbolic cosine of X.

   

hypot(X,Y)

Returns length of hypotenuse of triangle with base X and height Y

numeric, numeric

 

sin(X)

Returns the sine of the argument (an angle in radians)

   

sinh(X)

Hyperbolic sine of X.

   

tan(X)

Returns the tan of the argument (an angle in radians)

   

tanh(X)

Hyperbolic tangent of X.

   

In: Contents >> Working with equations >> Functions

 

Built-in functions : List handling

List handling

Built-in functions : product function



product function

product([X])

product({X})

Result is the product of all elements of the array [X] or the list {X}

Input: numeric array or list

Result: numeric

Example:

product([2,3,4]) --> 24

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : place_in function



place_in function

place_in(I)

When making an array with the makearray function, place_in() returns the current position in the array. If makearray() functions are nested one inside another, the argument to the place_in() function will determine which position is returned. An argument of 1 refers to the innermost makearray().

Input: integer

Result: integer

Examples:

makearray(if place_in(1)==1 then 10 else 5, 4) --> [10, 5, 5, 5]

makearray(if place_in(1)==2 then 10 else 5, 4) --> [5, 10, 5, 5]

makearray(makearray(if place_in(2)==1 then 10 else 5, 4), 2) --> [[10, 10, 10, 10], [5, 5, 5, 5]]

makearray(makearray(if place_in(1)==1 then 10 else 5, 4), 2) --> [[10, 5, 5, 5], [10, 5, 5, 5]]

makearray(4*place_in(1),12) --> [4 8 12 16 20 24 28 32 36 40 44 48]

makearray(makearray(place_in(1)*place_in(2),12),12) -->

[[1 2 3 4 5 6 7 8 9 10 11 12],

[2 4 6 8 10 12 14 16 18 20 22 24],

[3 6 9 12 15 18 21 24 27 30 33 36],

[4 8 12 16 20 24 28 32 36 40 44 48],

[5 10 15 20 25 30 35 40 45 50 55 60],

[6 12 18 24 30 36 42 48 54 60 66 72],

[7 14 21 28 35 42 49 56 63 70 77 84],

[8 16 24 32 40 48 56 64 72 80 88 96],

[9 18 27 36 45 54 63 72 81 90 99 108],

[10 20 30 40 50 60 70 80 90 100 110 120,

[11 22 33 44 55 66 77 88 99 110 121 132],

[12 24 36 48 60 72 84 96 108 120 132 144]]

Comments:

This function is only meaningful inside makearray() function. If used elsewhere, the equation parser will signal an error.

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : makearray function

makearray function

makearray(X,N)

Makes an array consisting of N lots of X

Input: any type, numeric

Result: array of same type

Examples:

makearray(7, 3) --> [7, 7, 7]

makearray([rand_var(0, 1), rand_var(0, 5)], 5) --> [[0.62352, 2.43459], [0.11933, 0.423529], [0.94208, 4.43623], [0.40088, 1.63023], [0.11769, 4.97782]]

Comments:

This is an array constructor. The first argument can be any expression, and the second is an integer. The result is an array, each of whose elements is generated by evaluating the first argument. The size of the array is the value of the second argument, which must be a constant. If the first argument is an array, the result will be an array of arrays. See also the place_in function, which is used in complex constructions with makearray.

Use of makearray() is called explicit replication. It differs from implicit replication in that the expression being replicated is evaluated separately for each member of the generated array, including any implicit (but not explicit) intermediate results. This means that no attempt is made to combine the dimensions of the two arguments. The second argument must be a scalar integer, and the result will be an array whose outermost dimension is that value, and whose inner dimensions are the dimensions of the first argument.

makearray() could have been designed to work differently on an array first argument, replicating each element rather than the whole array. As in the case of implicit replication, the actual behaviour was chosen to be that which would be hardest to achieve by combining other functions. If you need to replicate the elements of an array, you can first split it up with the element() function then rejoin the results with makearray, e.g., makearray(makearray(element([3,6,9],place_in(2)),2),3) -> [[3,3],[6,6],[9,9]], whereas if makearray itself worked like this, it would be very hard to get its actual behaviour.

See also: place_in  function

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : with_greatest function


with_greatest function

with_greatest([N], [X])

with_greatest({N}, {X})

Returns the value from an array [X] or the list {X} whose position in the array or list corresponds to the largest value in the array [N] or list {N}.

Inputs: numeric array or list, same dimensioned array or list with members of any type

Result: single value from second input

Example:

with_greatest([2,5,7,3], ["red", "blue", "green", "yellow"]) --> "green"

This example would require the definition of an enumerated type with the members "red", "blue", "green" and "yellow".

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : sum function

sum function

sum([X])

sum({X})

Result is the sum of all elements of the array [X] or the list {X}

Input: numeric array/list

Result: numeric

Example:

sum([2,3,4]) --> 9

sum([[1,2],[3,4]]) --> [4,6]

Comment:

Note the behaviour with nested arrays. A new array results, consisting of the sum of the first value of each array, the sum of the second value of each array, etc.

sum function

sum([X])

sum({X})

Result is the sum of all elements of the array [X] or the list {X}

Input: numeric array/list

Result: numeric

Example:

sum([2,3,4]) --> 9

sum([[1,2],[3,4]]) --> [4,6]

Comment:

Note the behaviour with nested arrays. A new array results, consisting of the sum of the first value of each array, the sum of the second value of each array, etc. The reason it is implemented this way is that the converse (generating an array of the sums of each sub-array in the original, i.e., [3,7] in the above example) is easier to generate explicitly if required. In the case where the 2-D array is a value coming out of nested 1-D submodels, it can be produced by putting the sum() function inside the outer submodel. If the array is only available as a 2-D value, the same effect can be produced using the element() and makearray() functions as follows:

makearray(sum(element([[1,2],[3,4]], place_in(1))),2) --> [3,7]

All other cumulative functions behave the same way regarding selection of elements from multidimensional arrays.

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : order function

order function (new in v6.9)

Takes an array of numeric values and returns an array containing the indices of those values in ascending order.

Example:

order([1,9,2,10,3,8,5]) -> [1,3,5,7,6,2,4]

Note that the result of order() can be used to get the original values in ascending order by using it in the element function. e.g.,

mixed = [1,9,2,10,3,8,5]

sort = order(mixed)

element([mixed],[sort]) -> [1,2,3,5,8,9,10]

 

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions: interpolate function

interpolate(X, [Xarray], [Yarray])

X is an input value.   The arrays Xarray and Yarray define a series of coordinates.   They must contain the same number of elements, and the values in Xarray must be in ascending order.   If the value of X is less than the first element of Xarray, then the result is the first element of Yarray.     If the value of X is greater than the last element of Xarray, then the result is the last element of Yarray.   Otherwise, the result is the value obtained by linear interpolation between the two points which bracket the value of X.

Examples:
   interpolate(3, [2,4,7], [10,20,30])  --> 15  (linear interpolation between the points (2,10) and (4,20))
   interpolate(1, [2,4,7], [10,20,30])  --> 10  (X value is less than first element of Xarray, so use first element of Yarray)
   interpolate(9, [2,4,7], [10,20,30])  --> 30  (X value is greater than first element of Xarray, so use last element of Yarray)

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions: rankings function

rankings function

Takes an array of numeric values, and returns an array with the ranks of the corresponding elements in the argument. This is 1 for the largest element, and equal to the size of the array for the smallest.

Example:

rankings([1,9,2,10,3,8,5]) -> [7,2,6,1,5,3,4]

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions: subtotals function

subtotals function

Takes an array of numeric values, and returns an array containing the running totals from summing the elements in the original array.

Example:

subtotals([1,9,2,10,3,8,5]) -> [1,10,12,22,25,33,38]

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : element function

element function

element([X],I)

Picks the Ith value from the array [X]

Inputs: an array [X] of any type

integer I

Result: type

Examples:

element([10,20,30,40],3) --> 30 (since 30 is the value of the 3rd element of the array.

element([[1,2], [3,4], [5,6]],2) --> [3,4] (since the array [3,4] is the 2nd element of the input array)

element([10,20,30,40],index(1)) --> 10 for the first instance of a four-instance submodel, 20 for the second instance, etc, since index(1) has the value 1 for the first instance, 2 for the second instance, etc.

Comments:

This is an essential function for use with multiple-instance submodels, in which case it is almost always used in combination with the function index(1) in the second argument. One common use is to provide each instance of a multiple-instance submodel with a unique value for some parameter or other value. The third example (above) illustrates this: that could, for example, be the expression in a compartment element inside a four-instance submodel, initialising the compartment for each of the four instances to 10, 20, 30 and 40 respectively.

For advanced users:

The element function has rather more power than suggested above. The second argument can act as a sort of template to say how values (or sub-arrays) from the first argument are to be picked up. This is illustrated by the following example:

element([3,2,7,4,9,34,1,5], [[5,2], [1,5]]) --> [[9,2], [3,9]]

If the first argument is multidimensional and the second argument is a one-dimensional array, the elements of the second argument will be used to pick elements from the innermost arrays of the first argument from whuch to build the result, e.g.,

element([[3,5,11], [1,2,8]], [2,1,2]) --> [1,5,8].

The reason it works this way is that the converse behaviour, i.e., each element of the second argument selecting a value from the corresponding element of the first argument, is easy to get in the case where the first argument is a value from a nested submodel by putting the element() function inside the outer submodel, and can be obtained in general by building up from simple cases, e.g.,

makearray(element(element([[3,5,11], [1,2,8]],place_in(1)), element([3,1], place_in(1))), 2) --> [11,1].

makearray(element([[5,7],[1,4],[8,5]], element([3,3,2,2], place_in(1))), 4) --> [[8,5], [8,5], [1,4], [1,4]]

Use of element() on lists

Starting with Simile version 6.1, it is possible to have a list-valued expression as the first argument of element(), in which case the result is a sublist of that list, i.e., a list containing some, all or none of the members of the original list in the same order. The second argument can be a single value, in which case the resulting list has one element if the list includes a value with that index, and none otherwise. So applying sum() to it gives either a value from the original list or zero.

If the second argument is an array or list, the result is a sublist of the first argument containing all the values whose indices appear as values in the second argument. There are a few points to note about all these uses:

  • It is not computationally efficient. The values from the list are found by searching through it sequentially rather than by lookup as can be done on arrays.
  • If the second argument is an array or list, its values must be in ascending order, or in the order in which they appear in the definition if they are of an enumerated type. If a value occurs more than once in the second argument, the value with that index will still only appear once in the result. This is because rather than searching the list from the start for each value, the generated code merely starts from where the last one was found, since the indices in the original list should always be in ascending order. (This does not apply when selecting a sublist from a list of neighbour values in a special-purpose submodel; the direction identifiers can be in any order, and if one occurs more than once, its value from the original list will also be repeated).
  • The resulting list cannot itself be used as the first argument of element(), or arithmetically combined with other list-valued expressions.

element() with multiple indices

Starting with Simile version 6.1, if you have a 2-D (or higher) array, you can look up a single member by using element() with 3 (or more) arguments, e.g.,

element([[arr]], x, y)

Formerly you would have had to do this by nesting element() calls, but the new format is neater and allows the indices to be matching arrays or lists themselves to get multiple values.

Examples:


element([[6,1,8],[7,5,3],[2,9,4]], 2, 2) --> 5
element([[6,1,8],[7,5,3],[2,9,4]], [2,1,3], [3,1,2]) --> [3,6,9]

 

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : any function



any function

any(([X])

any({X})

Result is true if any of the elements of the array [X] or the list {X} are true.

Input: boolean array or list

Result: boolean

Examples:

any([false,false,false,true,false]) --> true

any([false,false,false]) --> false

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : all function



all function

all([X])

all({X})

Result is true if all the elements of the array [X] or the list {X} are true

Input: boolean array/list

Result: boolean

Examples:

all([true,true,true,false]) --> false

all([true,true,true,true]) --> true

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : least function


least function

least([X])

least({X})

Returns the smallest value from an array [X] or the list {X}

Inputs: numeric array/list

Result: numeric

Example:

least([2,5,7,3]) --> 2

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : greatest function



greatest function

greatest([X])

greatest({X})

Returns the largest value from an array [X] or the list {X}

Inputs: numeric array or list

Result: numeric

Example:

greatest([2,5,7,3]) --> 7

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : with_least function


with_least function

with_least([N], [X])

with_least({N}, {X})

Returns the value from an array [X] or the list {X} whose position in the array or list corresponds to the smallest value in the array [N] or list {N}.

Inputs: numeric array or list, same dimensioned array or list with members of any type

Result: single value from second input

Example:

with_least([2,5,7,3], ["red", "blue", "green", "yellow"]) --> "red"

This example would require the definition of an enumerated type with the members "red", "blue", "green" and "yellow".

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : Model properties

Model properties

Built-in functions : after function

after function

after(T, M)

Use only as whole equation of derived event. Instead of firing immediately when triggered, event is delayed by value of 1st argument, then fires with magnitude the 2nd argument had when triggered.

Inputs: Real, Any data type

Result: Same type as 2nd arg

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : last function

last function

last(X)

Recalls value of X, another element, from previous time step. X must influence this element in order to be used in the equation. See prev, for a function that returns a previous value from this element itself.

This function has been replaced with the const_delay( ) and var_delay( ) functions, which are more general in allowing the value of a variable to be returned from an arbitrary number of time steps before.

Input: numeric

Result: numeric

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : as_number function

as_number function

as_number(N)

Converts integral types to integer

Input: Boolean, enumerated type or integer (for flexibility)

Result: Value of argument as integer

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : prev function



prev function

prev(N)

Returns the value of this element itself, N time steps ago. See last, for a function that returns a previous value of any element other than this one itself.

Input: numeric

Result: numeric

Example:

Consider a variable that flips from state 1 to state 2 when some triggering condition is satisfied (the Boolean variable, trigger, is true, for example) then stays in state 2. The equation for the variable could make use of prev, as follows:

if time()==0 then 1 elseif trigger then 2 else prev(1)

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : parent function



parent function

parent(1)

Returns the id (instance number) of the individual whose reproduction gave rise to this one, or 0 if the individual being considered was created at the start of the simulation or by immigration.

Input: numeric (but a dummy value: use the value 1).

Result: integer (in fact, a negative integer number, being the instance number of a member of a population submodel. These are all numbered from -1 downwards.)

Comment:

This function is vital for the simulation of any form of biological inheritance from one generation to the next. You have to know who the parent is before you can allow the newly-created individual to inherit (possibly with modification) one or more of the characteristics of the parent.

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : time function

time function

time()

Returns the current simulation time.

Input: none

Result: numeric (units = day)

Comment:

Any model which has exogenous variables (variables that change as a function of time, independently of the behaviour of the model, such as air temperature or rainfall) needs some way of knowing what the current clock time is: i.e. how far the simulation has proceeded. This function provides that information.

This function is not strictly-speaking necessary: you could get exactly the same behaviour by having a single compartment, initialised to zero, with a single flow in, with a constant value of 1. So, after 1 time unit the value of the compartment would be 1, after 12.5 it would be 12.5, and so on. However, the function is provided to avoid cluttering up the model with an extra compartment and flow.

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : delay1, delay3, delayn functions

delay1, delay3, delayn functions

delay1(input, duration [, initial])

delay3(input, duration [, initial])

delayn(input, duration, n [, initial])

Arguments:

input: the value to be delayed

duration: time by which to delay the input value

n (delayn only): order of the material delay (delayn only)

initial (optional): the value of the result when the function first applies

Result:

The delayed value of input.

The delay1, delay3 ​and delayn function calculates a first, third or nth-order material delay of input, using an exponential delay time of delay duration, and an optional initial value initial for the delay. delay3 does this by setting up a cascade of three first-order material delays, each with a delay duration of delay duration/3. Other versions of the function behave analogously. delay3 returns the value of the final delay in the cascade. If you do not specify an initial value initial, all functions assume the value to be the initial value of input.

The delay3 function will return the value of delay 3 in the structure and equations shown in the following figure:

Compartment   comp1 : 
    Initial value = start_fill (real)
Compartment   comp2 : 
    Initial value = start_fill (real)
Compartment   comp3 : 
    Initial value = start_fill (real)
Flow   delay 1 : 
    delay 1 =         comp1*3/duration (1/day) 
Flow   delay 2 : 
    delay 2 =         comp2*3/duration (1/day) 
Flow   delay 3 : 
    delay 3 =         comp3*3/duration (1/day) 
Flow   inflow : 
    inflow =         input (1/day) 
Variable   start fill : 

    start fill =         initial*duration/3 (real) 

Example:

Delay 3 = delay3(input, 5) where input = 5 + step(10,3) produces the pattern shown below:

 

Built-in functions : first function

first function

first(T)

Takes an argument T that is a member of an enumerated type, and returns "true" if it is the first member of its type, and "false" otherwise.

Input: enumerated type member, or array of enumerated type members

Result: boolean, or array of boolean values

Examples:

If enumerated type "fruit" is defined as "apple", "grape", "banana":

first("apple") --> "true"

 

first(["banana", "apple", "banana"]) --> ["false", "true", "false"]

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : following function

 

following function

following(T)

Takes an argument T that is a member of an enumerated type, and returns the next member of the enumerated type.

Input: enumerated type member, or array of enumerated type members

Result: enumerated type member, or array of enumerated type members

Examples:

If enumerated type "fruit" is defined as "apple", "grape", "banana":

following("apple") --> "grape"

following(["grape", "apple", "grape"]) --> ["banana", "grape", "banana"]

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : forcst function

forcst(<input>,<time>,<horizon>[,<initial>])

New in v6.6

The forcst function performs simple trend extrapolation. Here's how it works. First, forcst calculates the trend in input, based upon the value of input, the first order exponential average of input, and the averaging time. (Think of the averaging time as the time over which you wish to calculate a trend.) Then forcst extrapolates the trend into the future - you specify the distance into the future by providing a value for horizon. If you do not specify initial, forcst substitutes 0 for the initial value of the trend in input.

The forcst function is equivalent to the structural diagram and equations shown in this figure:

Put diagram here

Compartment   Average input : 

    Initial value = input-(averaging*initial) (real)
Flow   change in average : 
    change in average =         (input-Average_input)/averaging (1/day) 
 Variable   averaging : 
    averaging =         Variable parameter (day) 
 Variable   forecast : 
    forecast =         input*(1+trend*horizon) (real) 
Variable   horizon : 
    horizon =         Variable parameter (day) 
 Variable   initial : 
    initial =         Variable parameter (real) 
Variable   input : 
    input =         Variable parameter (real) 
Variable   trend : 
    trend =         (input-Average_input)/(Average_input*averaging) (1/day) 

Example:

Sales_Forecast = FORCST(Sales,10,15,0) produces a forecast of sales 15 time units into the future. The forecast is based on current sales, and the trend in sales over the last 10 time units. The initial growth trend in sales is set to 0.

Built-in functions : in_preceding function

in_preceding function -- new in Simile v5.7

Usage: in_preceding(expression of any type) returns that type

Definition: Used in a multi-instance submodel, returns the value of the argument expression  as it would be in the preceding instance of that submodel, or 0 or "false" in the first instance. The argument can include the function prev(0) to refer to the value in the previous submodel instance of the component in whose equation the in_preceding() function appears.

Note that a model that contains a circular set of influences can build and run properly if the input parameter associated with one of the influences is only used in the argument of an in_preceding() function. This is because since the value of the argument is calculated for one submodel instance and then used in the next, there is no actual circular dependency.

Example 1:

A 5-instance submodel contains a variable with the equation

index(1)+in_preceding(prev(0)).

The values will be:

1 3 6 10 15

Example 2:

An 8-instance submodel contains two variables, "received" and "forwarded". These are connected to one another by influences in each direction. The equation for "forwarded" is received/2. The equation for "received" is

if index(1)==1 then 200 else in_preceding(forwarded)

The values of "received" for the 8 instances will be:

200 100 50 25 12.5 6.25 3.125 1.5625
In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : ramp function

ramp(time,slope)

Generates a ramp of slope slope, starting at time time and zero before that time.

Result: the ramp function.

Arguments: time at which to start ramping, slope (positive or negative) of ramp

Example:

the function ramp(20,-7) will have a return value of 0 at time 20 and -70 at time 30

 

Built-in functions : smth1, smth3, smthn functions

smth1, smth3, smthn functions

smth1(input, averaging [, initial])

smth3(input, averaging [, initial])

​smthn(input, averaging, n [, initial])

Arguments:

input: the value to be smoothed

averaging: time over which to smooth the input value

n (smthn only): order of the material smoothing

initial (optional): the value of the result when the function first applies

Result:

The smoothed value of input.

The smth1, smth3 and smthn functions perform a first-, third- and nth-order respectively exponential smooth of input, using an exponential averaging time of averaging, and an optional initial value initial for the smooth. smth3 does this by setting up a cascade of three first-order exponential smooths, each with an averaging time of averaging/3. The other functions behave analogously. They return the value of the final smooth in the cascade. If you do not specify an initial value initial, they assume the value to be the initial value of input.

The smth3 function will return the value of comp3 in the structure and equations shown below.

Compartment   comp1 : 
    Initial value = initial (real)

 

Compartment   comp2 : 
    Initial value = initial (real)

Compartment   comp3 : 
    Initial value = initial (real)

 

Flow   flow1 : 
    flow1 =         (input-comp1)*3/averaging (1/day) 

Flow   flow2 : 
    flow2 =         (comp1-comp2)*3/averaging (1/day) 

Flow   flow3 : 
    flow3 =         (comp2-comp3)*3/averaging (1/day) 

Examples:

Smooth_of_Step = smth3(Step_Input,5)

where

Step_Input = 5 + step(10,3) produces the pattern shown below.

 

 

 

 

Built-in functions : step function

step(height,time)

creates a step function. Output is 0 up until time, and equal to step thereafter.

Result: the step function.

Arguments: height of step, time at which to step.

Example:

step(30, 20) has output 0 at time 19, and 30 at time 20 and after

Built-in functions : stop function



stop function

stop(n)

Input: is a number (real or integer) of your choice

Result: None (see text)

When executed, this function halts execution of the model, and produces the following error message:

Simile ran into a problem trying to run this model.

While it was trying to calculate the value of variable

var (node x) during execution of the model at

time t, there was a user-defined interruption: n.

It is useful to define error conditions where you (the model designer) know that the model should not be used or is not applicable for some reason. Trivially, it can be used to guard against mathematical errors, for example:

if (time()-50) != 0 then 1/(time()-50) else stop(5)

This form has some merit when running in C++, but generally, to track down mathematical errors, it is easier to debug in Tcl. If execution in Tcl would take too long, then this is a useful alternative. Its primary use however, is to enable you to catch out-of-range conditions in the specific circumstances of your model.

The use of an error code in the user-defined interruption (e.g. stop(13) ) enables you to see which stop( ) function caused the model to stop running, if there is more than one in your model.

Result is undefined, because simulation stops at the point at which the function is called, but has integer type (this is important because if it is called in a conditional, the other branch of the conditional must also have a numerical type).

Examples:

if population>50 then stop(1) else 0

if (time()-50) != 0 then 1/(time()-50) else stop(5)

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : trend function

trend(<input>,<time>[,<initial>])

New in v6.6

The trend function calculates the trend in input, based upon the value of input, the first order exponential average of input, and the exponential averaging time averaging time. trend is expressed as the fractional change in input per unit time. If you do not specify initial, trend substitutes the value 0 for the initial value of the trend.

The trend function is equivalent to the structural diagram and equations shown in this figure:

Put diagram here

Compartment   Average input : 

    Initial value = input-(averaging*initial) (real)
Flow   change in average : 
    change in average =         (input-Average_input)/averaging (1/day) 
 Variable   averaging : 
    averaging =         Variable parameter (day) 
Variable   initial : 
    initial =         Variable parameter (real) 
Variable   input : 
    input =         Variable parameter (real) 
Variable   trend : 
    trend =         (input-Average_input)/(Average_input*averaging) (1/day) 

Example:

Yearly_Change_in_GNP = TREND(GNP,1,.04)

This equation calculates the annual change in the input GNP. It starts with an initial value of .04 (4% per year).

Built-in functions : var_delay function

var_delay function

var_delay(var,n)

Input: a variable name and a numerical value (real or integer) of time units

Result: the value (any type) of the named variable, n time units ago

This function returns some previous value of another variable, an arbitrary period of time before. The period of time is defined in time units (not steps). The number need not be an integer, but whatever the actual time step, delay is always rounded to the nearest multiple of 0.1 of a time unit. The variable whose previous value is required is specified by name. The variables must be linked with an influence arrow.

This is a general replacement for the last( ) function, which returns the value of the named variable from the previous time step only. The delay must be between 0 and 100 and is rounded to the nearest 0.1. The delay can vary; if the delay is constant, the function const_delay() will do the job more efficiently.

Examples:

runoff=var_delay(rain,soak_time)

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions: at_init function

at_init function

at_init(X)

Returns the value the argument had when first used, i.e., on model reset or when the submodel instance containing this equation was created.

at_init(X) creates an implicit intermediate result, which has the same dimensions as its argument. So if this result is implicitly replicated elsewhere in the equation, the same value will be used each time. See makearray for behaviour in explicit replication.

Input: Any data type

Result: Same type as input

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions: at_posn function

at_posn function

at_posn(C)

at_posn(C,Row,Col)

Must form the whole equation of a component. Sets the component's value to the value of a component in an instance of a 2-D submodel representing a grid. C is the caption of the component in the grid submodel, and Row and Col if present are the outer and inner indices of the source instance (i.e., grid square) from which to get the value. If Row and Col are not present, the grid is mapped onto the diagram of the submodel containing the target component and the source instance selected by the component's position in the submodel diagram.

Input: Any data type plus optionally two integers

Result: Same type as input

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions: const_delay function

 

const_delay function

const_delay(var,n)

Input: a variable name and a numerical constant (real or integer) of time units

Result: the value (any type) of the named variable, n time units ago

This function returns some previous value of another variable, a arbitrary period of time before. The period of time is defined in time units (not steps). The number need not be an integer, but whatever the actual time step, delay is always rounded to the nearest multiple of 0.1 of a time unit. The variable whose previous value is required is specified by name. The variables must be linked with an influence arrow.

This is a general replacement for the last( ) function, which returns the value of the named variable from the previous time step only. The delay must be a numeric constant; for variable delay see var_delay().

Examples:

runoff=const_delay(rain,10)

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions: dies_of function

 

 

dies_of function

dies_of(X)

Returns true if argument is the loss channel that will cause the individual to disappear at the end of the current time step.

Input: value from a loss channel in the local submodel

Result: boolean

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions: in_progenitor function

in_progenitor function -- new in Simile v5.8

Usage: in_progenitor(expression of any type) returns that type

Definition: Used in a population submodel, returns the value of the argument expression  as it would be in the instance of that submodel containing the reproduction channel responsible for the instance being evaluated, or 0 or "false" in an instance that arrived via a channel other than reproduction. The argument can include the function prev(0) to refer to the value in the progenitor submodel instance of the component in whose equation the in_progenitor() function appears.

Note that a model that contains a circular set of influences can build and run properly if the input parameter associated with one of the influences is only used in the argument of an in_progenitor() function. This is because since the value of the argument is calculated for the progenitor instance and then used in the offspring instance, and the progenitor always comes before the offspring in evaluation order, there is no actual circular dependency.

Important: If the progenitor instance has been removed (see Extermination) then using this function will return meaningless values, and may cause model execution to be aborted due to memory access violations. To avoid this problem, make the in_progenitor function itself the argument of an at_init() function, e.g., at_init(in_progenitor(index(1))). If this is done, the inner argument will be evaluated for the progenitor instance when the offspring instance is created -- at which time the progenitor definitiely exists -- and then retained within the offspring instance's data structure. The only reason for not doing this would be if changes in the value in the progenitor continue to affect the offspring, and offspring never outlive their progenitors, e.g., in an L-systems model of tree branching.

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions: iterations function

iterations function

iterations(X)

Returns number of iterations that have been done up to this point in an alarm submodel. Argument is the boolean balue from the alarm symbol.

Input: value from an alarm symbol in the local submodel

Result: integer

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions: preceding function

preceding function

preceding(T)

Takes an argument T that is a member of an enumerated type, and returns the previous member of the enumerated type.

Input: enumerated type member, or array of enumerated type members

Result: enumerated type member, or array of enumerated type members

Examples:

If enumerated type "fruit" is defined as "apple", "grape", "banana":

preceding("grape") --> "apple"

preceding(["banana", "grape", "banana"]) --> ["grape", "apple", "grape"]

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions: pulse function

New in v6.6. Note this function is provided purely for compatibility with continuous-only modelling tools, and new models should use squirts instead.

pulse function:

pulse(magnitude, first_time [, interval])

Generate a pulse with a duration of a single time step and a given cumulative value.

Result: the pulse waveform

Arguments:

magnitude: the cumulative value of the pulse. This will be the level change of a compartment due to a flow with this value coming into it.

first_time: The first, last or only time at which the pulse will occur

interval (optional) : If this is positive, the pulse will occur regularly with this interval after the initial time

If it is negative, the pulse will occur with this interval up until the initial time and not after

If zero or not present, the pulse will occur only once at the initial time

Example: pulse(20, 12, 5) generates a pulse value of 20/DT at time 12, 17, 22, etc.

 

Built-in functions: trigger_magnitude function

trigger_magnitude function

trigger_magnitude()

Returns a value representing the magnitude of the triggering event. Can only be used in the equations of derived events, squirts and rule-based state variables. Events influencing these components are not listed as parameters so this function is used to get their values. If the trigger is a simple event, this function gives the value of that event's equation. If it is a time series, it is the current value from the series. If it is a limit event then it is 'true' if there is only one limit, and -1/1 for lower/upper limit if both are given.

Inputs: none

Result: same units and dimensions as triggering events

 

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : sofar function



sofar function

sofar([X])

sofar({X})

Result is…

Input: numeric array/list

Result: numeric

Example:

Comment:

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : size function



size function

size(S)

size(S,I)

The first form takes the name of a fixed-membership submodel and returns the number of instances that it has. The second form takes the name of a fixed-membership submodel and returns the size of the Ith level of nesting of this submodel.

Input: submodel name

Result: integer

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : dt function



dt function

dt(I)

Returns the duration of the level I time step.

Input: numeric. This is the time step level.

Result: numeric

Examples:

dt(1) --> 0.1 (for a model whose top-level time step was set to 0.1 in the Run Control panel)

dt(2) --> 0.001 (for a model whose 2nd-level time step was set to 0.001 in the Run Control panel)

If you are starting off with Simile, it is unlikely you will need to understand the concept of "time step index". You will probably just be making models with a single time step, hence one level, so don't worry about anything except the use of dt(1).

The main use of the dt function is to engineer the addition or removal of a specified amount of a substance into or out of a compartment. The only handle we have for causing changes to the amount in a compartment are flows, and flows are expressed as a rate per unit of time (whatever time unit is used for the model, e.g. year). This creates a problem if we want to add or remove a specified amount of substance at some instant in time. For example, consider a model with a time unit of year, a time step of 0.1, and with a compartment X from which we want to remove 5 units at the instant that some condition, which only lasts for 1 time step (0.1 years), is met. If we simply had a flow out that was zero when the condition was not met, and was 5 when the condition was met, then for one time step the flow would be 5 (units per year): hence, only 0.5 units would be removed in the 1/10th of a year, not the 5 we intended. What we need to do is to artificially inflate the flow rate by a factor of 10 (in this case, with a time step of 0.1) for this one time step. We do this by dividing the flow rate (in our flow equation) by 0.1 (in this case), or by dt(1) in general. The flow rate then appears to be 50 units per year for that one time step, giving a loss of 5 units in the one time step. Bingo!

The actual flow expression for the case considered above would be:

flowout = 5/dt(1)

Special case

Using the argument zero in the function, i.e. dt(0), is equivalent to saying dt(n), where n is the time step index of the submodel in which the function is used. This is useful, because when a submodel time step index is changed, it is then not necessary to edit the dt() functions within it to preserve the meaning.

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Built-in functions : count function



count function

count([X])

count({X})

Number of values in the array [X] or the list {X}

Input: array or list of values (numeric or boolean)

Result: integer

Examples:

count([4,5,6]) --> 3

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : channel_is function

channel function

channel_is(X)

X is an immigration, reproduction or creation channel. Returns true if this individual appeared through that channel.

Input: numeric

Result: Boolean

Examples:

channel_is(cr1) --> true, for each instance of the population that was initially created through channel cr1.

Comments:

This function can only be used inside population submodels. Its argument is the name of a channel (i.e. a population control symbol, one of creation, immigration or reproduction). Note that the value of the channel itself is not used, just the name. The result can be used in calculations inside the population submodel. For example, the expression

land_owned = if channel_is(im1) then 0 elseif channel_is(cr1) then 10

would allocate 10 acres of land to each member of the original population, but none to immigrants.

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : init_time function



init_time function

init_time(1)

Returns the time at which this model component first came into existence. This really only has any use for:

  • population submodels, so that the model knows when a new member of the population was created; and
  • conditional submodels, so that the model knows when the submodel, or one instance of it, came into existence because the condition controlling it became true.

Input: numeric. In fact, the argument is not used, so simply insert the number 1. The only reason for having the brackets and an argument enclosed between them is that this is the only way that Simile can recognise that this is a function.

Result: numeric

Example:

Let's assume you have a population submodel, and some property of each individual is related to its age (e.g. its growth rate, or its probability of dying). Simply create a variable called age (inside the submodel), and insert the following equation:

age = time(1) - init_time(1)

The result is the difference between the current simulation time (given by the function time(1), and the time when the instance was created, given by init_time(1).

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Built-in functions : index function


index function

index(I)

Returns the index (instance number) of a member of a fixed membership or population submodel, for the level of submodel nesting specified by the argument.

Input: numeric

Result: numeric

Comment:

The index function is frequently used in conjunction with the element function when working with multiple-instance submodels: both fixed-membership and population submodels.

The argument specifies which index is to be returned. You can see summary information about the meanings of the different indices in the listbox headed Indices: in the equation dialogue. The argument is an integer between 1 and the maximum number of indices available. index(1) corresponds to the 'innermost' index, i.e., if you have one multiple-instance model inside another, the result of index(1) will be the index of the inner submodel instance, and the result of index(2) will be that of the outer submodel instance. Similarly, if a submodel has two dimensions, then index(1) and index(2) will be valid in that submodel, giving an instance's position along the inner and outer dimension respectively.

Relation submodels do not usually have indices of their own, but you can get the indices of their base submodel instances using the index() function. If one of the roles in a relation has been specified to 'allow base instance lookup', then the base submodel for this role will be 'innermost' and and the index of the instance in this role will be the result of calling 'index(1)' in the relation submodel.

For fixed-membership submodels, the function returns an integer value between 1 and n, where n is the number of instances for the submodel. For variable-membership submodels, it returns an integer between 1 and n, where n is the maximum possible index. For a population submodel this would be the total number of instances of the population that have ever existed during this simulation run. For a conditional submodel the maximum will be the size given in the submodel dimensions. For either of these, an instance with a particular index number may or may not exist.

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : Statistics

Statistical functions produce variates from distributions, and generally produce different values at each point in the model where they are called.

There are up to three forms of each statistical function:

  • The form with a _const suffix. This will produce a new value when the simulation is initialized or reset, or when a submodel instance containing it is created. This value stays the same until the end of the run, or until the submodel instance containing it ceases to exist.
  • The form with a _var suffix (or no suffix). This will produce a new value on each time step for each instance where it occurs. The sequence of values for all such functions can be initialized using the Initialize pseudo-random tool. If there is no _const form of a function, the _const behaviour can be produced by wrapping this form in the at_init() function.
  • The form with an extra argument. The last argument (an integer) serves as a seed for the values produced by that particular occurrence of the function. These will be the same each run, and independent of any other statistical functions in the model. For instance if it is used in a conditional submodel, it will start producing the same sequence of results each time an instance of the submodel comes into existence (assuming the seed value is the same).

If a statistical function only has one form, it behaves like the 'var' form.

Built-in functions : rand_const function

rand_const function

rand_const(X,Y)

Returns a random number between X and Y at the start of the simulation or when the submodel instance is created. The random-number generator is not called again, and so the value stays the same until the simulation is reset.

Input: numeric, numeric

Result: numeric

Comment:

The main use of this function is to assign values to a set of instances of a multiple-instance submodel (fixed-membership or population). For example, to randomly assign initial sizes to a set of trees in a multiple-instance tree submodel, we could use the equation:

size = rand_const(12,20)

or to assign random locations to the trees, we could use the equations:

x = rand_const(0,50)

y = rand_const(0,100)

which would randomly place the trees in the left-hand half of a one-hectare plot, assuming that the values are in metres.

The use of rand_const() is deprecated because it cannot be made to behave in the same way as rand_var when implicitly replicating over an array. It is implemented by internal conversion to at_init(rand_var(x,y)) and this form should be used in full to make the replicatio behaviour clear.

Historical note: You may come across some models that use a rand(X,Y) function. This behaves like rand_const if Simile deduces that the model element will only be called at initialisation time, and like rand_var if the equation contains some variable that changes over time. The use of this function is now also deprecated because the semantics of the two uses are so very different. Also, there are some situations when you need to be able to over-ride this behind-the-scenes decision about how the function should behave.

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : rand_var function

rand_var function

rand_var(X,Y)

Returns a random number between X and Y, with a new value every time step.

Input: numeric, numeric

Result: numeric

Comment:

This function is used for doing stochastic modelling and Monte-Carlo simulations, i.e. one or more processes in the model (like giving birth or dying) have a random element to them.

rand_var gives a new result for every call, and if it is used in an expression that is replicated to make an array, each element's random value will be different.

rand_var uses the pseudo-random sequence generator built into the c++ compiler which Simile is using to create executable models. The sequence is initialized with a value generated from the process ID and clock time when Simile starts up, so no two runs will produce the same results. However, if it is required that a model has exactly the same behaviour each time it runs, despite including calls to rand_var, this can be achieved by means of a tool that sets the seed to a given value; see Initializing pseudo-random sequence.

Historical note: You may come across some models that use a rand(X,Y) function. This behaves like rand_const if Simile deduces that the model element will only be called at initialisation time, and like rand_var if the equation contains some variable that changes over time. The use of this function is now deprecated because the semantics of the two uses are so very different. Also, there are some situations when you need to be able to over-ride this behind-the-scenes decision about how the function should behave.

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : binome function

binome function

binome(prob, n)

Input: Real numerical value, integer value

Result: A value from the binomial distribution with the given probability and number of trials. A new random deviate is generated each time step.

The binomial distribution describes the probability of a given number of positive outcomes occurring when a number n of trials are carried out, each with a certain probability p of a positive outcome.

This function is implemented using a pseudo-random sequence generator; notes regarding its behaviour can be found in the documentation for the rand_var function.

Examples:

coins_heads_up = binome(0.5, coins_tossed)

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Built-in functions : colin function

colin function

colin([Array])

Returns a deviate from a distribution whose relative probabilities are given by the values in the argument array. A new deviate is generated each time step.

Inputs: array of probabilities (real).

Outputs: index to value in array (int).

This can be used to make a deviate from an explicit set of probabilities where the pattern does not match any other built-in statistical function.

This function is implemented using a pseudo-random sequence generator; notes regarding its behaviour can be found in the documentation for the rand_var function.

Example:

colin([1,1,1,10,1]) --> 4 (usually), 1,2,3 or 5 (occasionally).

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : exprnd function

exprnd function

exprnd(mean [, seed])

Returns: value sampled from an exponential distribution (numerical)

Arguments: mean of distribution (numerical), seed for random sequence (integer, only required if a reproducible series of values is needed)

Example: A Geiger counter pointed at a radioactive source will emit a series of clicks at random times. The durations of the intervals between the clicks are distributed exponentially.

In: Contents >> Working with equations >> Functions >> Built-in functions

 

Built-in functions : gaussian_var function

gaussian_var function

gaussian_var(mean, sd)

Input: Two real numerical values

Result: A random sample from a Gaussian (normal) distribution, with the supplied mean and standard deviation. A new random sample is generated each time step.

This function is implemented using a pseudo-random sequence generator; notes regarding its behaviour can be found in the documentation for the rand_var function.

Examples:

daily_rainfall = gaussian_var(annual_rainfall/365, 1.0)

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions : with_colin function

with_colin function

with_colin({ProbList},{ValList})

Takes two lists with equal size, and returns an element from the second argument, picked at random with the probability of each element proportional to the value of the corresponding element in the first argument. A new return value is generated each time step.

Inputs: list of probabilities (real), list of corresponding values (any).

Outputs: element picked from second list (any).

This can be used to make a deviate from an explicit set of probabilities where the pattern does not match any other built-in statistical function.

Note that it only works on lists; if you want to do something similar with fixed-size arrays, you can combine the element and colin functions to achieve the same effect as follows: element([ValList], colin([ProbList]))

This function is implemented using a pseudo-random sequence generator; notes regarding its behaviour can be found in the documentation for the rand_var function.

Example:

with_colin({1,1,1,10,1}, {"apples", "pears", "oranges", "grapes", "bananas"}) --> "grapes" (usually), "apples", "pears", "oranges" or "bananas" (occasionally)

In: Contents >> Working with equations >> Functions >> Built-in functions

Built-in functions: hypergeom function

hypergeom function

hypergeom(Pop, Mark, Sample)

Returns a deviate from a hypergeometric distribution for a given population, number of marks, and size of sample.

Inputs: Population size (int), number of marked individuals (int), size of sample from population (int)

Outputs: deviate of number of marked individuals from sample

The hypergeometric distribution tells us the range of probabilities of getting a number of "marked" individuals when taking a sample of a certain size from a population, a given number of which are "marked".

This function is implemented using a pseudo-random sequence generator; notes regarding its behaviour can be found in the documentation for the rand_var function.

Example: A research process involves ringing a certain number of seabirds from a population and releasing them, then at a later date recapturing a different number of the birds and checking how many ringed individuals are retreived. If a random group of individuals are captured each time, the probability of getting n rings back is equal to the probability of getting the result n from the equation:

rings_retrieved = hypergeom(Seabird_population, Birds_ringed, Birds_caught)

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Buit-in functions : poidev function

poidev function

poidev(mean)

Input: Real numerical values

Result: A value from the Poisson distribution with the given mean. A new random deviate is generated each time step.

The poisson distribution describes the probability of a given number of positive outcomes occurring in the limiting case of the binomial distribution, i.e., with very many trials each with a very small chance of a positive outcome.

This function is implemented using a pseudo-random sequence generator; notes regarding its behaviour can be found in the documentation for the rand_var function.

Example: A hospital serves a large community in which a certain percentage of individuals are thought to be carriers of the hospital superbug MRSA. If we admit a small number of individuals to hospital, we would expect the probability of getting a certain number of MRSA carriers in that group to be equal to the probability of getting that number as the result of this equation:

MRSA_positive_admissions = poidev(Total_admissions*MRSA_prevalence_percent/100)

In: Contents >> Working with equations >> Functions >> Built-in functions