In Math.Net Linear Algebra, you can write extension that allows you to use very nice slice notation:
// Open Math.NET namespaces (you need MathNet.Numerics package)
open MathNet.Numerics
open MathNet.Numerics.FSharp
open MathNet.Numerics.LinearAlgebra.Double
// Define type extension for the generic vector type
// (Here we need to repeat all constraints, so it is a bit ugly)
type MathNet.Numerics.LinearAlgebra.Generic.
Vector<'T when 'T : struct and 'T : (new : unit -> 'T)
and 'T :> System.IEquatable<'T> and 'T :> System.IFormattable
and 'T :> System.ValueType> with
/// Implements slicing of vector - both arguments are option types
member x.GetSlice(start, finish) =
let start = defaultArg start 0
let finish = defaultArg finish (x.Count - 1)
x.SubVector(start, finish - start + 1)
// Define type extension for the generic matrix type
type MathNet.Numerics.LinearAlgebra.Generic.
Matrix<'T when 'T : struct and 'T : (new : unit -> 'T)
and 'T :> System.IEquatable<'T> and 'T :> System.IFormattable
and 'T :> System.ValueType> with
// Implement slicing for matrices (using rows & columns)
member x.GetSlice(rstart, rfinish, cstart, cfinish) =
let cstart = defaultArg cstart 0
let rstart = defaultArg rstart 0
let cfinish = defaultArg cfinish (x.ColumnCount - 1)
let rfinish = defaultArg rfinish (x.RowCount - 1)
x.SubMatrix(rstart, rfinish - rstart + 1, cstart, cfinish - cstart + 1)
Then taking slices is very easy
// Get some slices from a vector
let v = vector [ 1.0; 2.0; 3.0 ]
v.[0 .. 1] // elements [1.0; 2.0]
v.[1 ..] // elements [2.0; 3.0]
v.[.. 1] // elements [1.0; 2.0]
// Example: Get some slices from a matrix
let m = matrix [ [ 1.0; 2.0; 3.0 ]
[ 4.0; 5.0; 6.0 ] ]
m.[0 .. 1, 0 .. 1] // get first square 2x2
m.[0 .. 1, 2 ..] // get the last column
m.[1 .., 0 .. 2] // get the last row
I need to build a matrix from a vector, and slicing it in this manner is probably the most efficient way. Let me explain:
You are given a column vector of say q length observations with the latest observation is the top value x(t) and the qth observation is the bottom value, x(t - q). So the first column of the matrix goes from x(t) to x(t-q). You are also given a number n such that the first row in the matrix is x(t), x(t-1),...,x(t-n), the second row becomes x(t-1), x(t-2), ..., x(t-n-1), and so on until the row whose last element is x(t-q-n).
So you are left with a triangular matrix q rows by n columns.
What is the equivalent version of the above F# functions in C# for slicing Math.Net Linear Algebra vectors?
