Copyright | (C) 2012-2013 Edward Kmett, |
---|---|

License | BSD-style (see the file LICENSE) |

Maintainer | Edward Kmett <ekmett@gmail.com> |

Stability | experimental |

Portability | non-portable |

Safe Haskell | Trustworthy |

Language | Haskell98 |

Simple matrix operation for low-dimensional primitives.

- (!*!) :: (Functor m, Foldable t, Additive t, Additive n, Num a) => m (t a) -> t (n a) -> m (n a)
- (!+!) :: (Additive m, Additive n, Num a) => m (n a) -> m (n a) -> m (n a)
- (!-!) :: (Additive m, Additive n, Num a) => m (n a) -> m (n a) -> m (n a)
- (!*) :: (Functor m, Foldable r, Additive r, Num a) => m (r a) -> r a -> m a
- (*!) :: (Num a, Foldable t, Additive f, Additive t) => t a -> t (f a) -> f a
- (!!*) :: (Functor m, Functor r, Num a) => m (r a) -> a -> m (r a)
- (*!!) :: (Functor m, Functor r, Num a) => a -> m (r a) -> m (r a)
- column :: Representable f => LensLike (Context a b) s t a b -> Lens (f s) (f t) (f a) (f b)
- adjoint :: (Functor m, Distributive n, Conjugate a) => m (n a) -> n (m a)
- type M22 a = V2 (V2 a)
- type M23 a = V2 (V3 a)
- type M24 a = V2 (V4 a)
- type M32 a = V3 (V2 a)
- type M33 a = V3 (V3 a)
- type M34 a = V3 (V4 a)
- type M42 a = V4 (V2 a)
- type M43 a = V4 (V3 a)
- type M44 a = V4 (V4 a)
- m33_to_m44 :: Num a => M33 a -> M44 a
- m43_to_m44 :: Num a => M43 a -> M44 a
- det22 :: Num a => M22 a -> a
- det33 :: Num a => M33 a -> a
- inv22 :: (Epsilon a, Floating a) => M22 a -> Maybe (M22 a)
- inv33 :: (Epsilon a, Floating a) => M33 a -> Maybe (M33 a)
- eye2 :: Num a => M22 a
- eye3 :: Num a => M33 a
- eye4 :: Num a => M44 a
- class Functor m => Trace m where
- translation :: (Representable t, R3 t, R4 v) => Lens' (t (v a)) (V3 a)
- transpose :: (Distributive g, Functor f) => f (g a) -> g (f a)
- fromQuaternion :: Num a => Quaternion a -> M33 a
- mkTransformation :: Num a => Quaternion a -> V3 a -> M44 a
- mkTransformationMat :: Num a => M33 a -> V3 a -> M44 a

# Documentation

(!*!) :: (Functor m, Foldable t, Additive t, Additive n, Num a) => m (t a) -> t (n a) -> m (n a) infixl 7 Source

Matrix product. This can compute any combination of sparse and dense multiplication.

`>>>`

V2 (V2 19 25) (V2 43 58)`V2 (V3 1 2 3) (V3 4 5 6) !*! V3 (V2 1 2) (V2 3 4) (V2 4 5)`

`>>>`

V2 (V3 0 0 2) (V3 0 0 15)`V2 (fromList [(1,2)]) (fromList [(2,3)]) !*! fromList [(1,V3 0 0 1), (2, V3 0 0 5)]`

(!+!) :: (Additive m, Additive n, Num a) => m (n a) -> m (n a) -> m (n a) infixl 6 Source

Entry-wise matrix addition.

`>>>`

V2 (V3 8 10 12) (V3 5 7 9)`V2 (V3 1 2 3) (V3 4 5 6) !+! V2 (V3 7 8 9) (V3 1 2 3)`

(!-!) :: (Additive m, Additive n, Num a) => m (n a) -> m (n a) -> m (n a) infixl 6 Source

Entry-wise matrix subtraction.

`>>>`

V2 (V3 (-6) (-6) (-6)) (V3 3 3 3)`V2 (V3 1 2 3) (V3 4 5 6) !-! V2 (V3 7 8 9) (V3 1 2 3)`

(!*) :: (Functor m, Foldable r, Additive r, Num a) => m (r a) -> r a -> m a infixl 7 Source

Matrix * column vector

`>>>`

V2 50 122`V2 (V3 1 2 3) (V3 4 5 6) !* V3 7 8 9`

(*!) :: (Num a, Foldable t, Additive f, Additive t) => t a -> t (f a) -> f a infixl 7 Source

Row vector * matrix

`>>>`

V3 15 18 21`V2 1 2 *! V2 (V3 3 4 5) (V3 6 7 8)`

(!!*) :: (Functor m, Functor r, Num a) => m (r a) -> a -> m (r a) infixl 7 Source

Matrix-scalar product

`>>>`

V2 (V2 5 10) (V2 15 20)`V2 (V2 1 2) (V2 3 4) !!* 5`

(*!!) :: (Functor m, Functor r, Num a) => a -> m (r a) -> m (r a) infixl 7 Source

Scalar-matrix product

`>>>`

V2 (V2 5 10) (V2 15 20)`5 *!! V2 (V2 1 2) (V2 3 4)`

adjoint :: (Functor m, Distributive n, Conjugate a) => m (n a) -> n (m a) Source

Hermitian conjugate or conjugate transpose

`>>>`

V2 (V2 (1.0 :+ (-2.0)) (5.0 :+ (-6.0))) (V2 (3.0 :+ (-4.0)) (7.0 :+ (-8.0)))`adjoint (V2 (V2 (1 :+ 2) (3 :+ 4)) (V2 (5 :+ 6) (7 :+ 8)))`

m33_to_m44 :: Num a => M33 a -> M44 a Source

Convert a 3x3 matrix to a 4x4 matrix extending it with 0's in the new row and column.

m43_to_m44 :: Num a => M43 a -> M44 a Source

Convert from a 4x3 matrix to a 4x4 matrix, extending it with the `[ 0 0 0 1 ]`

column vector

det22 :: Num a => M22 a -> a Source

2x2 matrix determinant.

`>>>`

a * d - b * c`det22 (V2 (V2 a b) (V2 c d))`

det33 :: Num a => M33 a -> a Source

3x3 matrix determinant.

`>>>`

a * (e * i - f * h) - d * (b * i - c * h) + g * (b * f - c * e)`det33 (V3 (V3 a b c) (V3 d e f) (V3 g h i))`

inv22 :: (Epsilon a, Floating a) => M22 a -> Maybe (M22 a) Source

2x2 matrix inverse.

`>>>`

Just (V2 (V2 (-2.0) 1.0) (V2 1.5 (-0.5)))`inv22 $ V2 (V2 1 2) (V2 3 4)`

inv33 :: (Epsilon a, Floating a) => M33 a -> Maybe (M33 a) Source

3x3 matrix inverse.

`>>>`

Just (V3 (V3 0.0 0.5 (-1.0)) (V3 (-0.5) (-0.75) 3.5) (V3 0.5 0.25 (-1.5)))`inv33 $ V3 (V3 1 2 4) (V3 4 2 2) (V3 1 1 1)`

4x4 identity matrix.

`>>>`

V4 (V4 1 0 0 0) (V4 0 1 0 0) (V4 0 0 1 0) (V4 0 0 0 1)`eye4`

class Functor m => Trace m where Source

Nothing

translation :: (Representable t, R3 t, R4 v) => Lens' (t (v a)) (V3 a) Source

Extract the translation vector (first three entries of the last column) from a 3x4 or 4x4 matrix.

transpose :: (Distributive g, Functor f) => f (g a) -> g (f a) Source

`transpose`

is just an alias for `distribute`

transpose (V3 (V2 1 2) (V2 3 4) (V2 5 6))

V2 (V3 1 3 5) (V3 2 4 6)

fromQuaternion :: Num a => Quaternion a -> M33 a Source

Build a rotation matrix from a unit `Quaternion`

.

mkTransformation :: Num a => Quaternion a -> V3 a -> M44 a Source

Build a transformation matrix from a rotation expressed as a
`Quaternion`

and a translation vector.