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## Variable Arrays in F#

Variable Arrays can be difficult to create and assign values to when dealing with large sets of complex data. This is especially true when 2-Dimensional and Jagged Arrays of data are involved. Therefore the module Variable provides various methods to make creation and assignment of such arrays both simpler and provide a more intuitive functional style of using such methods.

### Creating Arrays using a generator function

The `Variable.ArrayInit<'a>` function provides an easy way of creating and assigning the values of a VariableArray given a generator function to provide the values for assignment. The type signature for this method is : `Range -> (Range -> Variable<'a>) -> VariableArray<'a>.` The following example shows how it can be used to create and initialise the mean and precision variableArrays used in the Mixture of Gaussians tutorial.

``````let means = Variable.ArrayInit
k (fun k -> Variable.VectorGaussianFromMeanAndPrecision(
new Vector(2,0.0),
PositiveDefiniteMatrix.IdentityScaledBy(2,0.01)))
let precs = Variable.ArrayInit
k (fun k -> Variable.WishartFromShapeAndScale(
100.0, PositiveDefiniteMatrix.IdentityScaledBy(2,0.01)))
``````

### Assigning arrays from a generator function

The `Variable.AssignVariableArray` function provides an easy way of assigning the values of a VariableArray given a generator function to provide the values for assignment. The type signature for this method is : `VariableArray<'a> -> Range -> (Range -> Variable<'a>) -> VariableArray<'a>`. The following example shows how it can be used to assign values to the variableArrays used in the Clinical trial tutorial using a generator function. Similarly, methods to assign values to 2-Dimensional and jagged `VariableArrays` are also provided in the form of Variable.AssignVariableArray2D with type signature : `VariableArray2D<'a> -> Range -> (Range -> Variable<'a>) -> VariableArray2D<'a>` and

``````let controlGroup = Variable.Observed<bool>([|false; false; true; false; false|])
let treatedGroup = Variable.Observed<bool>([|true; false; true; true; true |])
let i = controlGroup.Range
let j = treatedGroup.Range
// Prior on being an effective treatment
let isEffective = Variable.Bernoulli(0.5).Named("isEffective");
let probIfTreated = ref (Variable.New<float>())
let probIfControl = ref (Variable.New<float>()) //rewrite If Block
let f1 (vb1: Variable<bool>) =
probIfControl := Variable.Beta(1.0, 1.0).Named("probIfControl")
let controlGroup = Variable.AssignVariableArray controlGroup i (fun i ->Variable.Bernoulli(!probIfControl))
let treatedGroup = Variable.AssignVariableArray treatedGroup j (fun j ->Variable.Bernoulli(!probIfTreated))
()
``````