EMK:Formulae and Functions

Formulae can be entered as substitutes for specific values into most fields in EMarket to control the derivation of variable values at run time. A formula can contain any combination of:

• Constants
• Variables
• Operators
• Entities and Traits
• Functions

Constants

Constants can be:

• Numbers: Integers or Reals (e.g. 1, 2.5, -3), they can also be entered in scientific notation e.g. '3E+10'.
• Strings: Written inside double quotes e.g. "A Node"
• Dates: Must be enclosed in single quotes e.g '1/3/2004' or '14 April 2005'

Warning: The format for entering dates should compatible with the computer's local date (locality) setting

Variables

Variables can be regarded as user-defined Entity.Traits which can be defined in the Volatility Matrix or the Schedule. Previously defined variables can be used in formulae.

Note: EMarket provides a 'system' variable the user need not define: 'DateTime' which is of type 'Date' and gives the current simulation date as the model runs.

Operators

Operators are all pre-defined in EMarket. Their purpose is to separate a formula into parts that are then combined to give a single value.

The following operators are shown in descending order of precedence.

Operator	Meaning	Example	Parameter Type	Return Type
\	Integer Division	3\2 = 1	Real; Int	Int
%	Modulus	7%5 = 2	Real; Int	Int
/	Division	3/2 = 1.5	Real; Int	Real
*	Multiplication	5*4.2 = 21	Real; Int	Real
-	Subtraction	7-3.2 = 3.8	Real; Int	Real
+	Addition	3.5+1.5 = 5	Real; Int	Real

Functions

Functions provide a powerful mechanism for deriving field and variable data values from input parameters.

A function has the form FunctionName(Parameter1, Parameter2, ...)

An operator is used in a Function in the following form: <Parameter1>Operator<Parameter2>.

EMarket provides the following function types:

• Arithmetic functions
• Logic functions
• Run information functions
• Time functions
• Other functions

Note: Logic operators and functions evaluate to one for a result that is true (for example 6 = 6), and zero for false.

Arithmetic Functions

The following table lists EMarket's Arithmetic functions:

Function	Purpose	Parameters	Return Type	Example	Result
Sqrt	Square root of a number	Integer or Real	Real	Sqrt(546.94)	23.387
Abs	Absolute value of a number	Integer or Real	Real	Abs(-19.1)	19.1
Int	Integer portion of a number	Integer or Real	Integer	Int(45.786)	45
Sum	Total value of numbers in an array	Value Array (Exclude Value), Integer or Real	Real	Sum(Node.Price)
Max	Maximum value of numbers in an array, optionally excluding values with value over an exclude value	Value Array (Exclude Value), Integer or Real	Real	Max(Generator.Generation)
Min	Minimum value of numbers in an array	Value Array (Exclude Value), Integer or Real	Real	Min(Generator.Generation)
StdDev	Standard deviation of numbers in an array	Value Array (Exclude Value), Integer or Real	Real	StdDev(Generator.Generation)
Avg	Average value of numbers in an array	Value Array (Exclude Value), Integer or Real	Real	Avg(Generator.Generation)
WgtAvg	Average of numbers in an array, weighted by numbers in another array	Value Array (Weights Array), Integer or Real	Real	WgtAvg(Generator.Generation,Generator.Cost)
Choke	Returns a collared value (i.e. the value of the referenced variable is returned if it falls within the specified range otherwise the relevant minimum or maximum value is returned)	Integer or Real	Real	Choke(500,200,Generator.Generation)

Logic Functions

The following table lists EMarket3's Logic functions:

Operator	Purpose	Parameters	Return Value	Example	Result
=	Whether two numbers are Equal	2 numbers, Integer or Real	0 or 1	5 = 6	0
<	Whether first number is less than the second	2 numbers, Integer or Real	0 or 1	-2 < 7	1
>	Whether first number is Greater than the second	2 numbers, Integer or Real	0 or 1	9 > 7	1
AND	Whether two numbers are both non-zero	2 numbers, Integer or Real	0 or 1	And(6=6,4<3)	0
OR	Whether either of two numbers are non-zero	2 numbers, Integer or Real	0 or 1	OR(3<5, 2>3)	1
Between	Whether a number is between two limits	Number: lower limit; upper limit, Integer, real or date	0 or 1	Between(5.7,9.7)	0

Run Information Functions

The following table lists EMarket's Run information functions:

Function	Purpose	Parameters	Return Type
Date	Date of current Tick	None	Date
TP	TP number of current Tick	None	Integer
Version	The position of a Run in a Batch sequence. For first Run, Version is zero.	None	Integer

Time Functions

The following table lists EMarket's Time functions:

Function	Purpose	Parameters	Return Type	Example	Result
GetDate	Converts a date to a day number	Date	Integer	GetDate('1/4/2004')
hh	Gets the half hourly TP from a date	'DateTime'	Integer	hh(DateTime)
4h	Gets the number of the block of 4 hourly trading periods for a given date (e.g. 1 = TP 1-8)	'DateTime'	Integer	4h(DateTime)
6h	Gets the number of the block of 6 hourly trading periods for a given date (e.g. 0 = TP 1-12)	'DateTime'	Integer	6h(DateTime)
DOW	Gets the weekday for a date, 0 = Sunday	Date	Integer	Dow('14/6/2004')	1
WO	Whether a date is a week day rather than a weekend or holiday, 1 = Weekend; 0 = Weekday	Date	0 or 1	WO('13/6/2004')	1
WODN	0=Week Night(WN); 1=Week Day(WD); 2=Other Night(ON); 3=Other Day(OF)	Date (and time)	0 to 3	WODN('1/5/2004 22:00')	3
WODN6	0=Week Night(WN); 1=Week Day(WD); 2=Other Night(ON); 3=Other Day(OF). Using A night period running from Midnight to 6am (not to 8am as in WODN)	Date (and time)	0 to 3	WODN6('1/5/2004 22:00')	3
Month	Gets the month from a date, 0 = January	Date	0 to 11	Month('1/5/2004')	4
WeekOfYear	Gets the week from a date, 0 = 1st full week in April	Date	0 to 51	WeekOfYear('1/5/2004')	4
DateDiff	Calculates the number of days between two date/times	Date 1, Date2	Real	DateDiff('1/5/2004', '5/5/004')	4
DateSeq	Gets the position of a required date within a list of ordered dates	Date required, Lists of dates	Integer	DateSeq('5 / 4 / 2004', '1 / 4 / 2004', '2 / 4 / 2004', '3 / 4 / 2004', '4 / 4 / 2004', '5 / 4 / 2004')	5
TimeSeries	Given a date ordered sequence of values, finds the value for a required date. Date format is Date:TimePeriod 'dd/mm/yyy:TP' , if no TP then TP '01' is used	List of (value, first date and time period applies)	Real	TimeSeries(735 , '1/04/2004:24', 760 , ' 1/04/2005', 840)

Other Functions

The following table lists EMarket's other functions:

Function	Purpose	Parameters	Return Type	Example	Result
ArrayTable	Uses two indices to retrieve a value from an array (matrix)	Index1, Index2, Value array. May be real or Integer	Real or Integer	ArrayTable(p,q,m,n, V00, V01, V02, ...V0m, V10, V11, ... Vnm) where p,q represent the position of the array; m,n represent the numbers of columns and rows in the array; 0<= p < m and 0 <= q < n would return Vpq. E.g. ArrayTable(1, 1, 2, 3, 4, 32.1, 6.3, 1.8, 31, 5). This defines a 2 * 3 matrix, and looks for the entry indexed by 1, 1. Note that if the indices are out of bounds no error will be given, and an indeterminate value will be returned.	31
Index	Gets the number in given position (index) in a list of numbers. First number has position zero.	1 or more numbers, can be integers or real	Real	Index(p, V0, V1, V2, ... Vm) where p is the position (index) in a list of numbers. E.g. Index(3, 4.5, 7, 8.9, -23.4)	-23.4
PieceWiseLinear	Generates a value based on an extrapolation of existing data. Given a target value (p) and a set of x, y pairings defining a function, the PieceWiseLinear function will find the y value corresponding to p. This function is included primarily for use in defining Demand elasticity.	Set of x,y value pairings, can be integers or real	Real or Integer	PieceWiseLinear(p, x1, y1, x2, y2, ...xn, yn) where p is the target value. Note that you can use internal model variables as the target value, as in this example: PieceWiseLinear(HydroSystem:Waitaki.SystemMWV, 0, 1, 80, 1, 150, 0.8, 400, 0.64)

Random Functions

the following random functions create a random sequence, the results of which depend on the seed given, the start date of the sequence and the order of definition and exact formula used to define the function. The RandomSeed variable should usually be used as the seed as this will ensure a unique sequence is generated based on the "Random Seed" option chosen for the run

Function	Purpose	Parameters	Return Type	Example
RandomBinaryState	Returns values from a random sequence of values which are either 0 or 1 with the properties that proportion of the time spent in the zero state is a given proportion and the average length of time spent in the one state is a given number of days	Seed for random sequence, Date/Time, Zero state proportion, Average One state length	Real	RandomBinaryState(Seed, DateTime, 0.95, 4), will return a random 0/1 series with 0.05 time spent in the one state and an average four day span of each one state
MRJD	Returns a value that follows a mean reverting random walk on a logarithmic scale	Seed for random sequence, Date/Time, Starting Value, Mean, Reversion Rate, Volatility[,ProportionalJump, JumpVolatility, JumpFrequency]	Real	MRJD(RandomSeed, DateTime, 5, 10, 11, 5), will return a random walk starting with the value 5 where the average log value is equal to log(10), reversion rate of 10 (half reversion in 1/10 year), volatility of 5 (two times diffusion in 1/5 year). The jump parameters are optional

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