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This commit is contained in:
Kiana Sheibani 2022-09-14 13:39:12 -04:00
parent d610874abc
commit 98223b180f
Signed by: toki
GPG key ID: 6CB106C25E86A9F7
6 changed files with 170 additions and 28 deletions
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23
src/Data/NumIdr/Interfaces.idr
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@ -8,19 +8,27 @@ module Data.NumIdr.Interfaces
--------------------------------------------------------------------------------
||| An interface synonym for types which form a field, such as `Double`.
public export
Field : Type -> Type
Field a = (Eq a, Neg a, Fractional a)
||| An interface for number types which allow for LUP decomposition to be performed.
|||
||| The function `abslt` is required for the internal decomposition algorithm.
||| An instance of this interface must satisfy:
||| * The relation `abslt` is a preorder.
||| * `0` is a minimum of `abslt`.
public export
interface (Eq a, Neg a, Fractional a) => FieldCmp a where
abscmp : a -> a -> Ordering
||| Compare the absolute values of two inputs.
abslt : a -> a -> Bool
export
(Ord a, Abs a, Neg a, Fractional a) => FieldCmp a where
abscmp x y = compare (abs x) (abs y)
abslt x y = abs x < abs y
--------------------------------------------------------------------------------
@ -38,8 +46,11 @@ infixr 10 ^
||| * If `x *. (y *. z)` is defined, then `(x *. y) *. z` is defined and equal.
public export
interface Mult a b c | a,b where
||| A generalized multiplication/application operator for matrices and
||| vector transformations.
(*.) : a -> b -> c
||| A synonym for `Mult a a a`, or homogenous multiplication.
public export
Mult' : Type -> Type
Mult' a = Mult a a a
@ -52,6 +63,10 @@ Mult' a = Mult a a a
||| * `identity *. x == x`
public export
interface Mult' a => MultMonoid a where
||| Construct an identity matrix or transformation.
|||
||| NOTE: Creating an identity element for an `n`-dimensional transformation
||| usually requires `n` to be available at runtime.
identity : a
||| An interface for groups using the `*.` operator.
@ -61,6 +76,10 @@ interface Mult' a => MultMonoid a where
||| * `inverse x *. x == identity`
public export
interface MultMonoid a => MultGroup a where
||| Calculate the inverse of the matrix or transformation.
||| WARNING: This function will not check if an inverse exists for the given
||| input, and will happily return results containing NaN values. To avoid
||| this, use `tryInverse` instead.
inverse : a -> a