```{-# LANGUAGE DataKinds             #-}
{-# LANGUAGE FlexibleContexts      #-}
{-# LANGUAGE KindSignatures        #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE TypeFamilies          #-}
module Numeric.Matrix.Class
( MatrixCalculus (..)
, SquareMatrixCalculus (..)
, MatrixInverse (..)
, Matrix
, HomTransform4 (..)
, Mat22f, Mat23f, Mat24f
, Mat32f, Mat33f, Mat34f
, Mat42f, Mat43f, Mat44f
, Mat22d, Mat23d, Mat24d
, Mat32d, Mat33d, Mat34d
, Mat42d, Mat43d, Mat44d
) where

import           Numeric.Commons
import           Numeric.DataFrame.Type
import           Numeric.Dimensions     (Nat)
import           Numeric.Scalar
import           Numeric.Vector

-- | Alias for DataFrames of rank 2
type Matrix t (n :: Nat) (m :: Nat) = DataFrame t '[n,m]

class MatrixCalculus t (n :: Nat) (m :: Nat) where
-- | Transpose Mat
transpose :: (MatrixCalculus t m n, PrimBytes (Matrix t m n)) => Matrix t n m -> Matrix t m n

class SquareMatrixCalculus t (n :: Nat) where
-- | Mat with 1 on diagonal and 0 elsewhere
eye :: Matrix t n n
-- | Put the same value on the Mat diagonal, 0 otherwise
diag :: Scalar t -> Matrix t n n
-- | Determinant of  Mat
det :: Matrix t n n -> Scalar t
-- | Sum of diagonal elements
trace :: Matrix t n n -> Scalar t

class MatrixInverse t (n :: Nat) where
-- | Matrix inverse
inverse :: DataFrame t '[n,n] -> DataFrame t '[n,n]

-- | Operations on 4x4 transformation matrices and vectors in homogeneous coordinates.
--   All angles are specified in radians.
class HomTransform4 t where
-- | Create a translation matrix from a vector
translate4  :: Vector t 4 -> Matrix t 4 4
-- | Create a translation matrix from a vector
translate3  :: Vector t 3 -> Matrix t 4 4
-- | Rotation matrix for a rotation around the X axis, angle is given in radians.
rotateX     :: t -> Matrix t 4 4
-- | Rotation matrix for a rotation around the Y axis, angle is given in radians.
rotateY     :: t -> Matrix t 4 4
-- | Rotation matrix for a rotation around the Z axis, angle is given in radians.
rotateZ     :: t -> Matrix t 4 4
-- | Rotation matrix for a rotation around an arbitrary normalized vector
rotate      :: Vector t 3 -> t -> Matrix t 4 4
-- | Rotation matrix from the Euler angles yaw pitch and roll
rotateEuler :: t -> t -> t -> Matrix t 4 4
-- | Create a transform matrix using up direction, camera position and a point to look at.
--   Just the same as GluLookAt.
lookAt      :: Vector t 3 -- ^ The up direction, not necessary unit length or perpendicular to the view vector
-> Vector t 3 -- ^ The viewers position
-> Vector t 3 -- ^ The point to look at
-> Matrix t 4 4
-- | A perspective symmetric projection matrix. Right-handed coordinate system. (@x@ - right, @y@ - top)
--   http://en.wikibooks.org/wiki/GLSL_Programming/Vertex_Transformations
perspective :: t -- ^ Near plane clipping distance (always positive)
-> t -- ^ Far plane clipping distance (always positive)
-> t -- ^ Field of view of the y axis, in radians
-> t -- ^ Aspect ratio, i.e. screen's width\/height
-> Matrix t 4 4
-- | An orthogonal symmetric projection matrix. Right-handed coordinate system. (@x@ - right, @y@ - top)
--   http://en.wikibooks.org/wiki/GLSL_Programming/Vertex_Transformations
orthogonal  :: t -- ^ Near plane clipping distance
-> t -- ^ Far plane clipping distance
-> t -- ^ width
-> t -- ^ height
-> Matrix t 4 4
-- | Add one more dimension and set it to 1.
toHomPoint  :: Vector t 3 -> Vector t 4
-- | Add one more dimension and set it to 0.
toHomVector :: Vector t 3 -> Vector t 4
-- | Transform a homogenous vector or point into a normal 3D vector.
--   If the last coordinate is not zero, divide the rest by it.
fromHom     :: Vector t 4 -> Vector t 3

-- Type abbreviations

type Mat22f = Matrix Float 2 2
type Mat32f = Matrix Float 3 2
type Mat42f = Matrix Float 4 2
type Mat23f = Matrix Float 2 3
type Mat33f = Matrix Float 3 3
type Mat43f = Matrix Float 4 3
type Mat24f = Matrix Float 2 4
type Mat34f = Matrix Float 3 4
type Mat44f = Matrix Float 4 4

type Mat22d = Matrix Double 2 2
type Mat32d = Matrix Double 3 2
type Mat42d = Matrix Double 4 2
type Mat23d = Matrix Double 2 3
type Mat33d = Matrix Double 3 3
type Mat43d = Matrix Double 4 3
type Mat24d = Matrix Double 2 4
type Mat34d = Matrix Double 3 4
type Mat44d = Matrix Double 4 4
```