Lagrange formula

Lagrange's interpolation formula

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let lagrange (x:float list) (y:float list) (v:float) =
    [for i in 0..x.Length - 1 ->
         [for j in [0..i-1]@[i+1..x.Length - 1] ->
            (v - x.[j]) / (x.[i] - x.[j])]
         |> List.fold (*) y.[i]]
    |> List.sum

//Usage

//x values
let x = [111.0;112.0;113.0;114.0;115.0]
//y values
let y = [13.0;24.0;35.0;46.0;57.0]
//interpolating value
let v = 117.0

lagrange x y v

val lagrange : x:float list -> y:float list -> v:float -> float

Full name: Script.lagrange

val x : float list

Multiple items
val float : value:'T -> float (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.float

--------------------
type float = System.Double

Full name: Microsoft.FSharp.Core.float

--------------------
type float<'Measure> = float

Full name: Microsoft.FSharp.Core.float<_>

type 'T list = List<'T>

Full name: Microsoft.FSharp.Collections.list<_>

val y : float list

val v : float

val i : int

property List.Length: int

val j : int

Multiple items
module List

from Microsoft.FSharp.Collections

--------------------
type List<'T> =
  | ( [] )
  | ( :: ) of Head: 'T * Tail: 'T list
  interface IEnumerable
  interface IEnumerable<'T>
  member GetSlice : startIndex:int option * endIndex:int option -> 'T list
  member Head : 'T
  member IsEmpty : bool
  member Item : index:int -> 'T with get
  member Length : int
  member Tail : 'T list
  static member Cons : head:'T * tail:'T list -> 'T list
  static member Empty : 'T list

Full name: Microsoft.FSharp.Collections.List<_>

val fold : folder:('State -> 'T -> 'State) -> state:'State -> list:'T list -> 'State

Full name: Microsoft.FSharp.Collections.List.fold

val sum : list:'T list -> 'T (requires member ( + ) and member get_Zero)

Full name: Microsoft.FSharp.Collections.List.sum

val x : float list

Full name: Script.x

val y : float list

Full name: Script.y

val v : float

Full name: Script.v

Raw view Test code New version

More information

Link:	http://fssnip.net/7RV
Posted:	7 years ago
Author:	Ivan Padron
Tags:	math , mathematic