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Monad instance for Vector and Matrix #607

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merged 3 commits into from
Sep 22, 2024
Merged

Monad instance for Vector and Matrix #607

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29f98d6
Add join operator to vector and matrix
cannorin Sep 19, 2024
6644a01
Add bind operator to vector and matrix using join
cannorin Sep 19, 2024
c9af144
Create a separate test file for vectors and matrices
cannorin Sep 22, 2024
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33 changes: 31 additions & 2 deletions src/FSharpPlus.TypeLevel/Data/Matrix.fs
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Original file line number Diff line number Diff line change
Expand Up @@ -251,6 +251,17 @@ module Vector =

let inline apply (f: Vector<'a -> 'b, 'n>) (v: Vector<'a, 'n>) : Vector<'b, 'n> = map2 id f v

/// <description>
/// Converts the vector of vectors to a square matrix and returns its diagonal.
/// </description>
/// <seealso href="https://stackoverflow.com/questions/5802628/monad-instance-of-a-number-parameterised-vector" />
[<MethodImpl(MethodImplOptions.AggressiveInlining)>]
let join (vv: Vector<Vector<'a, 'n>, 'n>): Vector<'a, 'n> =
{ Items = Array.init (Array.length vv.Items) (fun i -> vv.Items.[i].Items.[i]) }

let inline bind (f: 'a -> Vector<'b, 'n>) (v: Vector<'a, 'n>) : Vector<'b, 'n> =
v |> map f |> join

let inline norm (v: Vector< ^a, ^n >) : ^a =
v |> toArray |> Array.sumBy (fun x -> x * x) |> sqrt
let inline maximumNorm (v: Vector< ^a, ^n >) : ^a =
Expand Down Expand Up @@ -327,6 +338,20 @@ module Matrix =
for j = 0 to Array2D.length2 m1.Items - 1 do
f i j m1.Items.[i, j] m2.Items.[i, j]

let inline apply (f: Matrix<'a -> 'b, 'm, 'n>) (m: Matrix<'a, 'm, 'n>) : Matrix<'b, 'm, 'n> = map2 id f m

/// <description>
/// Converts the matrix of matrices to a 3D cube matrix and returns its diagonal.
/// </description>
/// <seealso href="https://stackoverflow.com/questions/5802628/monad-instance-of-a-number-parameterised-vector" />
[<MethodImpl(MethodImplOptions.AggressiveInlining)>]
let join (m: Matrix<Matrix<'a, 'm, 'n>, 'm, 'n>) : Matrix<'a, 'm, 'n> =
{ Items =
Array2D.init (Array2D.length1 m.Items) (Array2D.length2 m.Items)
(fun i j -> m.Items.[i, j].Items.[i, j] ) }

let inline bind (f: 'a -> Matrix<'b, 'm, 'n>) (m: Matrix<'a, 'm, 'n>) : Matrix<'b, 'm, 'n> = m |> map f |> join

let inline rowLength (_: Matrix<'a, 'm, 'n>) : 'm = Singleton<'m>
let inline colLength (_: Matrix<'a, 'm, 'n>) : 'n = Singleton<'n>
let inline rowLength' (_: Matrix<'a, ^m, 'n>) : int = RuntimeValue (Singleton< ^m >)
Expand Down Expand Up @@ -571,8 +596,10 @@ type Matrix<'Item, 'Row, 'Column> with

static member inline Return (x: 'x) : Matrix<'x, 'm, 'n> = Matrix.replicate Singleton Singleton x
static member inline Pure (x: 'x) : Matrix<'x, 'm, 'n> = Matrix.replicate Singleton Singleton x
static member inline ( <*> ) (f: Matrix<'x -> 'y, 'm, 'n>, x: Matrix<'x, 'm, 'n>) = Matrix.map2 id f x
static member inline ( <.> ) (f: Matrix<'x -> 'y, 'm, 'n>, x: Matrix<'x, 'm, 'n>) = Matrix.map2 id f x
static member inline ( <*> ) (f: Matrix<'x -> 'y, 'm, 'n>, x: Matrix<'x, 'm, 'n>) = Matrix.apply f x
static member inline ( <.> ) (f: Matrix<'x -> 'y, 'm, 'n>, x: Matrix<'x, 'm, 'n>) = Matrix.apply f x
static member inline Join (x: Matrix<Matrix<'x, 'm, 'n>, 'm, 'n>) = Matrix.join x
static member inline ( >>= ) (x: Matrix<'x, 'm, 'n>, f: 'x -> Matrix<'y, 'm, 'n>) = Matrix.bind f x
static member inline get_Zero () : Matrix<'a, 'm, 'n> = Matrix.zero
static member inline ( + ) (m1, m2) = Matrix.map2 (+) m1 m2
static member inline ( - ) (m1, m2) = Matrix.map2 (-) m1 m2
Expand Down Expand Up @@ -607,6 +634,8 @@ type Vector<'Item, 'Length> with
static member inline Pure (x: 'x) : Vector<'x, 'n> = Vector.replicate Singleton x
static member inline ( <*> ) (f: Vector<'x -> 'y, 'n>, x: Vector<'x, 'n>) : Vector<'y, 'n> = Vector.apply f x
static member inline ( <.> ) (f: Vector<'x -> 'y, 'n>, x: Vector<'x, 'n>) : Vector<'y, 'n> = Vector.apply f x
static member inline Join (x: Vector<Vector<'x, 'n>, 'n>) : Vector<'x, 'n> = Vector.join x
static member inline ( >>= ) (x: Vector<'x, 'n>, f: 'x -> Vector<'y, 'n>) = Vector.bind f x

[<EditorBrowsable(EditorBrowsableState.Never)>]
static member inline Zip (x, y) = Vector.zip x y
Expand Down
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