Aggregators

Aggregation is the process of reducing a series of values to a single value that represents some property of the series. An aggregate function or aggregator is a function that performs this operation. This section describes predefined aggregators and a simple mechanism to create your own. Examples of aggregators are: count, largest value, mean...

A property like the number of elements or the number of elements that are not missing in a series is meaningful for all series regardless of their element type. The result is always an integer. A property like the first element is also universally relevant, but the type of the result depends on the element type. More than that, the type of the result is equal to the element type. These two examples illustrate the two main kinds of aggregators: those where the result is of a specific type, and those where the result type is the same as the element type.

The most common aggregators are defined as static properties or methods of the Aggregators class, and are listed below.

The above properties and methods return an aggregator group. An aggregator group represents an aggregation operation in a way that is independent of the element type of the series to which it is applied. When the aggregator group is applied to a series, an aggregator function for the element type of the series is selected to perform the actual operation.

AggregatorGroup is an abstract class that represents an aggregator group. It has two descendant classes corresponding to the two kinds of aggregators mentioned above: AggregatorGroup<TResult> represents an aggregator group where the generic type argument is the return type, and TypePreservingAggregatorGroup represents an aggregator group where the return type is the same as the element type.

By default, aggregators that compute numerical descriptive statistics, like Mean and Variance return a Double value regardless of the element type of the input. In fact, the input is first converted to Double and the aggregation is computed for the converted values.

This is useful in situations in many situations, for example, when computing descriptive statistics for sets of integers. In other situations, we may want a different intermediate type. For example, converting decimals to double in general results in a small round-off error. We may want to maintain the full accuracy and precision of decimal values.

There are two ways to achieve this. Some aggregators, like Sum, have a variant prefixed with Exact. These aggregators produce a result of the same type as the input.

Aggregator groups and aggregators have an [M:Numerics.NET.DataAnalysis.AggregatorGroup`1.As``()] method that returns an aggregator that uses a different type (supplied as the type argument to the method) for the intermediate values and the result.

For example, to compute the mean of a set of integers to quadruple precision, you can use:

int[] n = { 1, 4, 9 };
var avg = Aggregators.Mean.As<Quad>().Aggregate(n);
// avg = 4.666666666666666666666666666666667

Dim n As Integer() = { 1, 4, 9 }
Dim avg = Aggregators.Mean.As(Of Quad).Aggregate(n)
' avg = 4.666666666666666666666666666666667

No code example is currently available or this language may not be supported.

let n = [| 1; 4; 9 |];
let avg = Aggregators.Mean.As<Quad>().Aggregate(n)
// avg = 4.666666666666666666666666666666667
//

Some aggregations, such as the correlation between two variables, involve more than one series. The Aggregators class defines a number of aggregators that operate on more than one series:

The simplest way to define an aggregator that is not available from the Aggregators class is to use the Aggregators.Create``2(String, Func<Vector<UMP>, UMP>) method. This method takes two arguments: a name for the aggregator, and a delegate that maps a vector to the aggregated value. The following creates an aggregator that computes the geometric mean:

var agg = Aggregators.Create(
    (Vector<double> x) => Stats.GeometricMean(x));

Dim agg = Aggregators.Create(
    Function(x As Vector(Of Double)) Stats.GeometricMean(x))

No code example is currently available or this language may not be supported.

let agg = Aggregators.Create(fun (x : Vector<float>) -> Stats.GeometricMean(x))
//