Analytica User FAQs/Expressions - How to

(In progress -- two things need to occur. Common questions need to be collected here and organized, and then answers need to be added. Feel free to contribute to either aspect)

Array Abstraction

How do I access a single row of an array?

See Subscript/Slice Operator. The syntax is A[I=x], where A is the array, I is the index that identifies the row dimension, and x identifies the row using the value or label from I.

How do I represent a square matrix?

The rule in Analytica is that every dimension must correspond to a different index. So when you have two dimensions, you need two separate indexes. In the case of a square matrix, the second index is often a copy of the first.

Try this. Create an index node, name it State, and define it as 1..5. How create a second index, name it State2, and define it as CopyIndex(State). Now you have two indexes with identical value. You have what you need to represent a square matrix. Finally, create a variable, name it State_Identity, define it as State=State2, and show the result table. You just created a square identity matrix.

How do I re-index an array, exchanging one index, I, for another of the same length, J?

Again, this is accomplished using the Subscript/Slice Operator. Two methods:

• A[I=J]
• A[@I=@J]

The first re-indexes associatively, the second re-indexes by position. You can use the first when I and J have the same labels or values with no duplicates (in general, it is bad practice to have duplicate values in indexes). The second can be used if they are the same length, but have different values.

How do I aggregate an array from a fine grain index (e.g., days) to a coarser index (e.g., months)?

Generally, to aggregate, you will need a mapping (many-to-one) from the fine grain to the coarse grain. This mapping will take the form of an array, indexed by the fine grain (e.g., days), where each value in the array is an element in the coarser index (e.g., months). For illustration, let's call this Day2Month.

There are many different ways to aggregate data. The most common is to sum all fine grain values that belong to the same coarse grain category. For clarity and flexibility, I like to always create a User-Defined Function (UDF) to actually perform the aggregation, so that the intended operation is clear in the definition that uses it, hiding "implementation details". In this case, the aggregation function could look like this:

Function SumAggregate( x : Array[I] ; map : Array[I] ; I,J : Index )

Description: Aggregates x from a fine-grained index I to a coarser index J, but summing all values that aggregate to the same coarse category. Map contains the mapping from I to J.

Definition: Frequency(w:x, X:map, I:I, A:J )

Once you've introduced this function, then all you need to do to aggregate daily revenue to a monthly level is:

SumAggregate( revenue, day2Month, Day, Month )

Distributions

• How do I generate independent distributions across an index, for example, so that Noise := Normal(0,1) is independent for each time point t?

• How do I define a chance variable so that its uncertainty is correlated with an existing chance variable?

• How do a fit a distribution to historical data?

User-Defined Functions

• How do I create my own User-Defined function?

• How do I create a custom distribution function?

How do I model XXX?

How do I model Depreciation (offset in time)?

To model depreciation, two inputs are required: 1) a schedule of spend to be depreciated 2) a depreciation schedule

For this example, the index time is 10 year series with a constant startYear=2008 time:=sequence (startYear,startYear+9,1)

Example depreciation schedule is a 5yr MACRS depreciation schedule entered as a variable: Table(time)(.2,.32,.192,.1152,.1152,.0576,0,0,0,0)

SpendOverTime is a variable indexed by time with the capital spend amounts as desired: table(time)(0,0,111,0,0,0,0,0,0,0)

Create a user defined function: Function_Depreciation, Parameters: (SpendOverTime,DepreciationSchedule), Definition: index depr_years = copyindex(time); var deprStartyr:=time; sum(if time-depr_years+1<1 then 0 else slice(SpendOverTime,time,Depr_years-startYear+1)*slice(depreciationSchedule,time,time-depr_years+1),depr_years)

Then create a depreciation test variable to check the result Variable: DepreciationTest definition: function_Depreciation(spendOverTime,DepreciationSchedule)

What does Analytica use to represent missing values?

Analytica has no special MissingValue constant. The constant Null typically serves that purpose.

Several common functions that operate over arrays, but not all functions, will ignore Null values. For example, Sum, Product, Max, Min, Average, etc. This treatment of Null by these functions is relatively recent -- starting with 4.0 -- and we've been enhancing the remaining functions with successive releases. Currently there still remain several built-in functions that do not ignore Null, such as many statistical functions, and your own UDFs may not ignore nulls. You may also desire a different treatment of missing values than just ignoring the values. To deal with these cases, you will need to insert appropriate conditional logic to deal with the missing values in the appropriate fashion. For example:

Variance( MaybeMissing(x), I )

Cumulate( MaybeMissing(x,1), I )

where

Function MaybeMissing( x ; defX : optional )

Definition: if x=Null then if IsNotSpecified(defX) then 0 else defX else X