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# matrix-inv.fsx

calcula la matriz inversa

 ``` 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25: 26: 27: 28: 29: 30: 31: 32: 33: 34: 35: 36: 37: 38: 39: 40: 41: 42: 43: 44: 45: 46: 47: 48: 49: 50: 51: 52: 53: 54: 55: 56: 57: 58: 59: 60: 61: 62: 63: 64: 65: ``` ``````open System type matrix(m:float list list) = ///Numero de filas de la matriz member this.rows = m.Length ///Numero de columnas de la matriz member this.cols = m.Head.Length //Elementos de la matriz member this.items = m //Obtiene el valor de un elemento de la matriz member this.item i j = m.[i].[j] //Convierte a string la matriz override this.ToString() = "\ " + (this.items |> List.fold (fun r s -> r + "[ " + (s |> List.fold (fun x y -> x + (sprintf "%*.01f "4 y)) "") + "]\ ") "") (******Metodos para poder realizar operaciones de suma, resta y productos de matrices******) ///Operador para suma de matrices donde x y son del mismo tamaño static member (+) (x:matrix, y:matrix) = matrix (List.map2 (fun x y-> List.map2(fun x y-> x + y) x y) x.items y.items) ///Operador para resta de matrices donde x y son del mismo tamaño static member (-) (x:matrix, y:matrix) = matrix (List.map2 (fun x y -> List.map2(fun x y-> x - y) x y) x.items y.items) ///Operador para multiplicacion de una matriz por un numero n static member (*) (n:_, x:matrix) = matrix ( x.items |> List.map (fun x-> x |> List.map(fun x -> x * (float)n))) ///Operador para multiplicacion de matrices static member (*) (x:matrix, y:matrix) = matrix([for k in 0..x.rows - 1 do yield [for i in 0..y.cols - 1 do yield List.sum [for j in 0..x.cols - 1 do yield (x.item k j) * (y.item j i)]]]) ///Obtiene la inversa de una matriz cuadrada member this.inv() = //Generamos la matriz identidad let id = matrix [for i = 0 to this.rows - 1 do yield [for j = 0 to this.cols - 1 do yield if j = i then 1.0 else 0.0]] //Agregamos la matriz identidad a la derecha de nuestra matriz let mi = ref (matrix (List.map2 (fun x y -> List.append x y) this.items id.items)) //Hacemos los calculos necesarios para pasar la matriz identidad a la izquierda for i = 0 to mi.Value.rows - 1 do //Se hace 1 los elementos que estan en diagonal mi := matrix (mi.Value.items |> List.mapi (fun ix x -> x |> List.map (fun y -> if ix = i then y / mi.Value.item i i else y))) //Hacer 0 las columna i de los otros renglones mi := matrix (mi.Value.items |> List.mapi (fun ix x -> x |> List.mapi (fun j y -> if ix <> i then (mi.Value.item i j * - mi.Value.item ix i) + y else y ))) matrix [for i = 0 to this.rows - 1 do yield [for j = this.rows to mi.Value.cols - 1 do yield mi.Value.item i j]] //Ejemplo //Generamos una matriz let a = matrix [[ 7.0; 1.0; 0.0] [ 6.0; 4.0; 2.0] [ 1.0; 1.0; 5.0]] //Obtenemos la inversa de la matriz let i = a.inv() //Validamos que la matriz inversa sea correcta // Multiplicamos la matriz inversa por la matriz original y el resultado // debe ser la matriz identidad let x = a * i ``````
namespace System
Multiple items
type matrix =
new : m:float list list -> matrix
override ToString : unit -> string
member cols : int
member items : float list list
member rows : int
member inv : unit -> matrix
member item : i:int -> j:int -> float
static member ( + ) : x:matrix * y:matrix -> matrix
static member ( * ) : n:int * x:matrix -> matrix
static member ( * ) : x:matrix * y:matrix -> matrix
...

Full name: Script.matrix

--------------------
new : m:float list list -> matrix
val m : float list list
Multiple items
val float : value:'T -> float (requires member op_Explicit)

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

--------------------
type float = 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 this : matrix
member matrix.rows : int

Full name: Script.matrix.rows

Numero de filas de la matriz
property List.Length: int
member matrix.cols : int

Full name: Script.matrix.cols

Numero de columnas de la matriz
member matrix.items : float list list

Full name: Script.matrix.items
member matrix.item : i:int -> j:int -> float

Full name: Script.matrix.item
val i : int
val j : int
override matrix.ToString : unit -> string

Full name: Script.matrix.ToString
property matrix.items: float list list
Multiple items
module List

from Microsoft.FSharp.Collections

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type List<'T> =
| ( [] )
| ( :: ) of Head: 'T * Tail: 'T list
interface IEnumerable
interface IEnumerable<'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 sprintf : format:Printf.StringFormat<'T> -> 'T

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.sprintf
val x : matrix
val y : matrix
val map2 : mapping:('T1 -> 'T2 -> 'U) -> list1:'T1 list -> list2:'T2 list -> 'U list

Full name: Microsoft.FSharp.Collections.List.map2
val x : float list
val y : float list
val x : float
val y : float
val n : int
val map : mapping:('T -> 'U) -> list:'T list -> 'U list

Full name: Microsoft.FSharp.Collections.List.map
val k : int
property matrix.rows: int

Numero de filas de la matriz
property matrix.cols: int

Numero de columnas de la matriz
val sum : list:'T list -> 'T (requires member ( + ) and member get_Zero)

Full name: Microsoft.FSharp.Collections.List.sum
member matrix.item : i:int -> j:int -> float
member matrix.inv : unit -> matrix

Full name: Script.matrix.inv

val id : matrix
val mi : matrix ref
Multiple items
val ref : value:'T -> 'T ref

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

--------------------
type 'T ref = Ref<'T>

Full name: Microsoft.FSharp.Core.ref<_>
val append : list1:'T list -> list2:'T list -> 'T list

Full name: Microsoft.FSharp.Collections.List.append
property Ref.Value: matrix
val mapi : mapping:(int -> 'T -> 'U) -> list:'T list -> 'U list

Full name: Microsoft.FSharp.Collections.List.mapi
val ix : int
val a : matrix

Full name: Script.a
val i : matrix

Full name: Script.i
member matrix.inv : unit -> matrix