Safe Haskell	Safe
Language	Haskell2010

Math.Matrix.Vector4

Contents

Orphan instances

Synopsis

data Vector4 s = Vector4 {
- tcoord4 :: !s
- xcoord4 :: !s
- ycoord4 :: !s
- zcoord4 :: !s
}
x4 :: Num a => Vector4 a
y4 :: Num a => Vector4 a
z4 :: Num a => Vector4 a
t4 :: Num a => Vector4 a
dx4 :: forall {str :: Type -> Type} {a}. (Infinitesimal str a, Num (Closure str a)) => Vector4 (Closure str a)
dy4 :: forall {str :: Type -> Type} {a}. (Infinitesimal str a, Num (Closure str a)) => Vector4 (Closure str a)
dz4 :: forall {str :: Type -> Type} {a}. (Infinitesimal str a, Num (Closure str a)) => Vector4 (Closure str a)
dt4 :: forall {str :: Type -> Type} {a}. (Infinitesimal str a, Num (Closure str a)) => Vector4 (Closure str a)
setx4 :: s -> Vector4 s -> Vector4 s
sety4 :: s -> Vector4 s -> Vector4 s
setz4 :: s -> Vector4 s -> Vector4 s
sett4 :: s -> Vector4 s -> Vector4 s
updateRow4 :: g a -> Vector4 ((Vector4 :*: g) a -> (Vector4 :*: g) a)
updateColumn4 :: Applicative f => f a -> Vector4 ((f :*: Vector4) a -> (f :*: Vector4) a)
type Matrix4 a = (Vector4 :*: Vector4) a
codiag4 :: (Vector4 :*: Vector4) a -> Codiagonal Vector4 a
matrix4 :: Vector4 a -> Codiagonal Vector4 a -> (Vector4 :*: Vector4) a
diagonalProjections4 :: Vector4 (Index Vector4 a)
cycle4 :: Vector4 a -> Stream a
vector4 :: [a] -> Vector4 a
unzipV4 :: Vector4 (a, b) -> (Vector4 a, Vector4 b)
constant4 :: a -> Vector4 a
dim4 :: Vector4 Integer
sumCoordinates4 :: Num a => Vector4 a -> a
leftMultiply4Gen :: (Functor f, Num a, ConjugateSymmetric a) => Vector4 a -> (f :*: Vector4) a -> f a
rightMultiply4Gen :: (VectorSpace (f a), ConjugateSymmetric a, Scalar (f a) ~ a) => (Vector4 :*: f) a -> Vector4 a -> f a
matrixMultiply4 :: (Num a, ConjugateSymmetric a) => Matrix4 a -> Matrix4 a -> Matrix4 a
dot4 :: (Num a, ConjugateSymmetric a) => Vector4 a -> Vector4 a -> a
versor :: (Ord a, Floating a, ConjugateSymmetric a) => Vector4 a -> Vector4 a
index4 :: Int -> Vector4 a -> a
diagonal4 :: (Vector4 :*: Vector4) a -> Vector4 a
dt_4 :: Num s => s -> Vector4 s -> Vector4 s
dx_4 :: Num s => s -> Vector4 s -> Vector4 s
dy_4 :: Num s => s -> Vector4 s -> Vector4 s
dz_4 :: Num s => s -> Vector4 s -> Vector4 s
transpose4 :: Num a => Matrix4 a -> Matrix4 a
transpose4Impl :: Matrix4 a -> Matrix4 a
identity4 :: Num a => Matrix4 a
diagonal4x :: Matrix4 a -> Vector4 a
zero_codiagonal4 :: Num a => Codiagonal Vector4 a
diagonal_matrix4 :: Vector4 a -> (Vector4 :*: Vector4) a -> (Vector4 :*: Vector4) a
mat4 :: Vector4 a -> Codiagonal Vector4 a -> (Vector4 :*: Vector4) a
trace4 :: Num a => Matrix4 a -> a
removet4 :: Vector4 a -> Vector3 a
removex4 :: Vector4 a -> Vector3 a
removey4 :: Vector4 a -> Vector3 a
removez4 :: Vector4 a -> Vector3 a
removes4 :: Vector4 (Vector4 a -> Vector3 a)
project4 :: Vector4 (Vector4 a -> a)
removeIndex4 :: Matrix4 a -> Matrix4 (Matrix3 a)
cofactor4 :: Num a => Matrix4 a -> Matrix4 a
adjucate4 :: Num a => Matrix4 a -> Matrix4 a
signs4 :: Integral a => Matrix4 a
vectorIndices4 :: Integral a => Vector4 a
matrixIndices4 :: Integral a => (Vector4 :*: Vector4) (a, a)
inverse4 :: Fractional a => Matrix4 a -> Matrix4 a
cross4 :: Num a => Vector4 a -> Vector4 a -> Vector4 a -> Vector4 a
cross_product4 :: Num a => (Vector3 :*: Vector4) a -> Vector4 a
determinant4 :: Num a => Matrix4 a -> a
determinancett4 :: Num a => Determinance Vector4 Vector4 Vector3 Vector3 Vector3 a a a
coordDeterminance4 :: Num a => (forall c. Vector4 c -> c) -> (forall d. Vector4 d -> d) -> Determinance Vector4 Vector4 Vector3 Vector3 Vector3 a a a

Documentation

data Vector4 s Source #

Constructors

Vector4
Fields tcoord4 :: !s xcoord4 :: !s ycoord4 :: !s zcoord4 :: !s

Instances

Instances details

MonadZip Vector4 Source #
Instance details Defined in Math.Matrix.Vector4 Methods mzip :: Vector4 a -> Vector4 b -> Vector4 (a, b) # mzipWith :: (a -> b -> c) -> Vector4 a -> Vector4 b -> Vector4 c # munzip :: Vector4 (a, b) -> (Vector4 a, Vector4 b) #
Foldable Vector4 Source #
Instance details Defined in Math.Matrix.Vector4 Methods fold :: Monoid m => Vector4 m -> m # foldMap :: Monoid m => (a -> m) -> Vector4 a -> m # foldMap' :: Monoid m => (a -> m) -> Vector4 a -> m # foldr :: (a -> b -> b) -> b -> Vector4 a -> b # foldr' :: (a -> b -> b) -> b -> Vector4 a -> b # foldl :: (b -> a -> b) -> b -> Vector4 a -> b # foldl' :: (b -> a -> b) -> b -> Vector4 a -> b # foldr1 :: (a -> a -> a) -> Vector4 a -> a # foldl1 :: (a -> a -> a) -> Vector4 a -> a # toList :: Vector4 a -> [a] # null :: Vector4 a -> Bool # length :: Vector4 a -> Int # elem :: Eq a => a -> Vector4 a -> Bool # maximum :: Ord a => Vector4 a -> a # minimum :: Ord a => Vector4 a -> a # sum :: Num a => Vector4 a -> a # product :: Num a => Vector4 a -> a #
Traversable Vector4 Source #
Instance details Defined in Math.Matrix.Vector4 Methods traverse :: Applicative f => (a -> f b) -> Vector4 a -> f (Vector4 b) # sequenceA :: Applicative f => Vector4 (f a) -> f (Vector4 a) # mapM :: Monad m => (a -> m b) -> Vector4 a -> m (Vector4 b) # sequence :: Monad m => Vector4 (m a) -> m (Vector4 a) #
Applicative Vector4 Source #
Instance details Defined in Math.Matrix.Vector4 Methods pure :: a -> Vector4 a # (<>) :: Vector4 (a -> b) -> Vector4 a -> Vector4 b # liftA2 :: (a -> b -> c) -> Vector4 a -> Vector4 b -> Vector4 c # (>) :: Vector4 a -> Vector4 b -> Vector4 b # (<*) :: Vector4 a -> Vector4 b -> Vector4 a #
Functor Vector4 Source #
Instance details Defined in Math.Matrix.Vector4 Methods fmap :: (a -> b) -> Vector4 a -> Vector4 b # (<$) :: a -> Vector4 b -> Vector4 a #
Monad Vector4 Source #
Instance details Defined in Math.Matrix.Vector4 Methods (>>=) :: Vector4 a -> (a -> Vector4 b) -> Vector4 b # (>>) :: Vector4 a -> Vector4 b -> Vector4 b # return :: a -> Vector4 a #
UpdateableMatrixDimension Vector4 Source #
Instance details Defined in Math.Matrix.Vector4 Methods writeRow :: Applicative h => h a -> Vector4 ((Vector4 :: h) a -> (Vector4 :: h) a) Source # writeColumn :: Applicative h => h a -> Vector4 ((h :: Vector4) a -> (h :: Vector4) a) Source #
DifferentialOperator Vector4 Source #
Instance details Defined in Math.Matrix.LinearOperations Methods partial :: DifferentiallyClosed a => (Vector4 a -> a) -> Vector4 a -> Vector4 a Source #
Comonad Vector4 Source #
Instance details Defined in Math.Matrix.Vector4 Methods extract :: Vector4 a -> a Source # duplicate :: Vector4 a -> Vector4 (Vector4 a) Source # extend :: (Vector4 a -> b) -> Vector4 a -> Vector4 b Source # (=>>) :: Vector4 a -> (Vector4 a -> b) -> Vector4 b Source # (.>>) :: Vector4 a -> b -> Vector4 b Source #
PpShowF Vector4 Source #
Instance details Defined in Math.Matrix.Vector4 Methods ppf :: PpShow a => Vector4 a -> Doc Source #
PpShowVerticalF Vector4 Source #
Instance details Defined in Math.Matrix.Vector4 Methods ppfVertical :: PpShow a => Vector4 a -> Doc Source #
Unfoldable Vector4 Source #
Instance details Defined in Math.Matrix.Vector4 Methods unfoldF :: forall (m :: Type -> Type) s a. Monad m => StateT s m a -> StateT s m (Vector4 a) Source #
StreamBuilder str => AppendableVector Vector4 str Source #
Instance details Defined in Math.Matrix.Vector4 Associated Types type Vector4 :+: str :: Type -> Type Source # Methods (\|\|>>) :: Vector4 a -> str a -> (Vector4 :+: str) a Source #
CodiagonalMatrix Vector4 a Source #
Instance details Defined in Math.Matrix.Vector4 Associated Types data Codiagonal Vector4 a Source # type Vector4 \\ a Source # Methods codiagonalImpl :: (Vector4 :: Vector4) a -> Codiagonal Vector4 a Source # (\|\\|) :: Vector4 a -> Codiagonal Vector4 a -> (Vector4 :: Vector4) a Source # downProject :: Codiagonal Vector4 a -> Vector4 \\ a Source # rightProject :: Codiagonal Vector4 a -> Vector4 \\ a Source #
Diagonalizable Vector4 a Source #
Instance details Defined in Math.Matrix.Vector4 Methods identity :: (Vector4 :: Vector4) a Source # diagonalImpl :: (Vector4 :: Vector4) a -> Vector4 a Source # diagonalMatrixImpl :: Vector4 a -> (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a Source #
Indexable Vector4 a Source #
Instance details Defined in Math.Matrix.Vector4 Methods diagonalProjections :: Vector4 (Index Vector4 a) Source # basisVector :: Index Vector4 a -> a -> Vector4 a -> Vector4 a Source # indexProject :: Index Vector4 a -> Vector4 a -> a Source # indexableIndices :: Vector4 a Source #
(ConjugateSymmetric a, Num a) => InnerProductSpaceFunctor Vector4 a Source #
Instance details Defined in Math.Matrix.Vector4 Methods innerProductF :: Vector4 a -> Vector4 a -> a Source #
Fractional a => Invertible Vector4 a Source #
Instance details Defined in Math.Matrix.Vector4 Methods cofactorImpl :: (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a Source # adjucateImpl :: (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a Source # inverseImpl :: (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a Source #
Num a => Traceable Vector4 a Source #
Instance details Defined in Math.Matrix.Vector4 Methods traceImpl :: (Vector4 :: Vector4) a -> a Source # determinantImpl :: (Vector4 :: Vector4) a -> a Source # vectorDimension :: Vector4 a -> a Source #
HasIdentityLinear Vector4 LinearMap Source #
Instance details Defined in Math.Matrix.Linear Methods matIdentity :: (Ord a, Num a, ConjugateSymmetric a) => LinearMap (Vector4 a) (Vector4 a) Source #
(ConjugateSymmetric a, Fractional a, Ord a) => LinearInvertible LinearMap Vector4 a Source #
Instance details Defined in Math.Matrix.Linear Methods cofactor :: LinearMap (Vector4 a) (Vector4 a) -> LinearMap (Vector4 a) (Vector4 a) Source # adjucate :: LinearMap (Vector4 a) (Vector4 a) -> LinearMap (Vector4 a) (Vector4 a) Source # inverse :: LinearMap (Vector4 a) (Vector4 a) -> LinearMap (Vector4 a) (Vector4 a) Source #
(ConjugateSymmetric a, Num a, Ord a) => LinearTraceable LinearMap Vector4 a Source #
Instance details Defined in Math.Matrix.Linear Methods determinant :: LinearMap (Vector4 a) (Vector4 a) -> a Source # trace :: LinearMap (Vector4 a) (Vector4 a) -> a Source #
(Ord a, Num a, ConjugateSymmetric a) => LinearTransform Vector1 Vector4 a Source #
Instance details Defined in Math.Matrix.Vector4 Methods (<>>) :: Vector4 a -> (Vector1 :: Vector4) a -> Vector1 a Source # (<<>) :: (Vector1 :: Vector4) a -> Vector1 a -> Vector4 a Source #
(Num a, ConjugateSymmetric a) => LinearTransform Vector2 Vector4 a Source #
Instance details Defined in Math.Matrix.Vector4 Methods (<>>) :: Vector4 a -> (Vector2 :: Vector4) a -> Vector2 a Source # (<<>) :: (Vector2 :: Vector4) a -> Vector2 a -> Vector4 a Source #
(Num a, ConjugateSymmetric a) => LinearTransform Vector3 Vector4 a Source #
Instance details Defined in Math.Matrix.Vector4 Methods (<>>) :: Vector4 a -> (Vector3 :: Vector4) a -> Vector3 a Source # (<<>) :: (Vector3 :: Vector4) a -> Vector3 a -> Vector4 a Source #
(Num a, ConjugateSymmetric a) => LinearTransform Vector4 Vector1 a Source #
Instance details Defined in Math.Matrix.Vector4 Methods (<>>) :: Vector1 a -> (Vector4 :: Vector1) a -> Vector4 a Source # (<<>) :: (Vector4 :: Vector1) a -> Vector4 a -> Vector1 a Source #
(Num a, ConjugateSymmetric a) => LinearTransform Vector4 Vector2 a Source #
Instance details Defined in Math.Matrix.Vector4 Methods (<>>) :: Vector2 a -> (Vector4 :: Vector2) a -> Vector4 a Source # (<<>) :: (Vector4 :: Vector2) a -> Vector4 a -> Vector2 a Source #
(Num a, ConjugateSymmetric a) => LinearTransform Vector4 Vector3 a Source #
Instance details Defined in Math.Matrix.Vector4 Methods (<>>) :: Vector3 a -> (Vector4 :: Vector3) a -> Vector4 a Source # (<<>) :: (Vector4 :: Vector3) a -> Vector4 a -> Vector3 a Source #
LinearTransform Vector4 Vector4 Float Source #
Instance details Defined in Math.Matrix.SIMD Methods (<>>) :: Vector4 Float -> (Vector4 :: Vector4) Float -> Vector4 Float Source # (<<>) :: (Vector4 :: Vector4) Float -> Vector4 Float -> Vector4 Float Source #
(Num a, ConjugateSymmetric a) => LinearTransform Vector4 Vector4 a Source #
Instance details Defined in Math.Matrix.Vector4 Methods (<>>) :: Vector4 a -> (Vector4 :: Vector4) a -> Vector4 a Source # (<<>) :: (Vector4 :: Vector4) a -> Vector4 a -> Vector4 a Source #
(Num a, ConjugateSymmetric a) => ProjectionDual Vector4 Dual a Source #
Instance details Defined in Math.Matrix.LinearOperations Methods projectionDual :: Vector4 (Dual (Vector4 a)) Source #
Transposable Vector1 Vector4 a Source #	1 x 4 matrices:
Instance details Defined in Math.Matrix.Vector4 Methods transposeImpl :: (Vector1 :: Vector4) a -> (Vector4 :: Vector1) a Source #
Transposable Vector2 Vector4 a Source #	2 x 4 matrices:
Instance details Defined in Math.Matrix.Vector4 Methods transposeImpl :: (Vector2 :: Vector4) a -> (Vector4 :: Vector2) a Source #
Transposable Vector3 Vector4 a Source #	3 x 4 matrices
Instance details Defined in Math.Matrix.Vector4 Methods transposeImpl :: (Vector3 :: Vector4) a -> (Vector4 :: Vector3) a Source #
Transposable Vector4 Vector1 a Source #	4 x 1 matrices:
Instance details Defined in Math.Matrix.Vector4 Methods transposeImpl :: (Vector4 :: Vector1) a -> (Vector1 :: Vector4) a Source #
Transposable Vector4 Vector2 a Source #	4 x 2 matrices
Instance details Defined in Math.Matrix.Vector4 Methods transposeImpl :: (Vector4 :: Vector2) a -> (Vector2 :: Vector4) a Source #
Transposable Vector4 Vector3 a Source #	4 x 3 matrices:
Instance details Defined in Math.Matrix.Vector4 Methods transposeImpl :: (Vector4 :: Vector3) a -> (Vector3 :: Vector4) a Source #
Transposable Vector4 Vector4 a Source #	4 x 4 matrices
Instance details Defined in Math.Matrix.Vector4 Methods transposeImpl :: (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a Source #
Transposable Stream Vector4 a Source #
Instance details Defined in Math.Matrix.Vector4 Methods transposeImpl :: (Stream :: Vector4) a -> (Vector4 :: Stream) a Source #
(Scalar a ~ a, Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Dual Vector4 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Dual a) (Vector4 a) -> (Dual :: Vector4) a Source # linear :: (Dual :: Vector4) a -> LinearMap (Dual a) (Vector4 a) Source #
(Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector1 Vector4 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector1 a) (Vector4 a) -> (Vector1 :: Vector4) a Source # linear :: (Vector1 :: Vector4) a -> LinearMap (Vector1 a) (Vector4 a) Source #
(Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector2 Vector4 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector2 a) (Vector4 a) -> (Vector2 :: Vector4) a Source # linear :: (Vector2 :: Vector4) a -> LinearMap (Vector2 a) (Vector4 a) Source #
(Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector3 Vector4 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector3 a) (Vector4 a) -> (Vector3 :: Vector4) a Source # linear :: (Vector3 :: Vector4) a -> LinearMap (Vector3 a) (Vector4 a) Source #
(Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector4 Vector1 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector4 a) (Vector1 a) -> (Vector4 :: Vector1) a Source # linear :: (Vector4 :: Vector1) a -> LinearMap (Vector4 a) (Vector1 a) Source #
(Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector4 Vector2 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector4 a) (Vector2 a) -> (Vector4 :: Vector2) a Source # linear :: (Vector4 :: Vector2) a -> LinearMap (Vector4 a) (Vector2 a) Source #
(Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector4 Vector3 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector4 a) (Vector3 a) -> (Vector4 :: Vector3) a Source # linear :: (Vector4 :: Vector3) a -> LinearMap (Vector4 a) (Vector3 a) Source #
(Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector4 Vector4 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector4 a) (Vector4 a) -> (Vector4 :: Vector4) a Source # linear :: (Vector4 :: Vector4) a -> LinearMap (Vector4 a) (Vector4 a) Source #
(Num a, ConjugateSymmetric a, InnerProductSpaceFunctor Stream a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector4 Stream (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector4 a) (Stream a) -> (Vector4 :: Stream) a Source # linear :: (Vector4 :: Stream) a -> LinearMap (Vector4 a) (Stream a) Source #
(Num a, ConjugateSymmetric a, InnerProductSpaceFunctor Stream a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Stream Vector4 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Stream a) (Vector4 a) -> (Stream :: Vector4) a Source # linear :: (Stream :: Vector4) a -> LinearMap (Stream a) (Vector4 a) Source #
(Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector4 Dual (f a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector4 (f a)) (Dual (f a)) -> (Vector4 :: Dual) (f a) Source # linear :: (Vector4 :: Dual) (f a) -> LinearMap (Vector4 (f a)) (Dual (f a)) Source #
(InnerProductSpaceFunctor ((->) col) a, ConjugateSymmetric a, Universe col) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector4 ((->) col :: Type -> Type) (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector4 a) (col -> a) -> (Vector4 :: (->) col) a Source # linear :: (Vector4 :: (->) col) a -> LinearMap (Vector4 a) (col -> a) Source #
(InnerProductSpaceFunctor ((->) row) a, ConjugateSymmetric a, Universe row) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) ((->) row :: Type -> Type) Vector4 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (row -> a) (Vector4 a) -> ((->) row :: Vector4) a Source # linear :: ((->) row :: Vector4) a -> LinearMap (row -> a) (Vector4 a) Source #
Limiting Stream a => Limiting Stream (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 Associated Types data Closure Stream (Vector4 a) Source # Methods limit :: Stream (Vector4 a) -> Closure Stream (Vector4 a) Source # approximations :: Closure Stream (Vector4 a) -> Stream (Vector4 a) Source #
Lift a => Lift (Vector4 a :: Type) Source #
Instance details Defined in Math.Matrix.QuasiQuoter Methods lift :: Quote m => Vector4 a -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => Vector4 a -> Code m (Vector4 a) #
(Closed a, Ord a, ConjugateSymmetric a, LinearTransform Vector4 Vector1 a) => VectorLaplacian (Vector4 a :: Type) LinearMap Source #
Instance details Defined in Math.Matrix.LinearOperations Methods vectorLaplace :: LinearMap (Vector4 a) (Vector4 a) -> LinearMap (Vector4 a) (Vector4 a) Source #
(Universe col, Num a) => LinearTransform Vector4 ((->) col) a Source #
Instance details Defined in Math.Matrix.Simple Methods (<>>) :: (col -> a) -> (Vector4 :: (->) col) a -> Vector4 a Source # (<<>) :: (Vector4 :: (->) col) a -> Vector4 a -> col -> a Source #
Transposable Vector4 ((->) row) a Source #
Instance details Defined in Math.Matrix.Vector4 Methods transposeImpl :: (Vector4 :: (->) row) a -> ((->) row :: Vector4) a Source #
Data a => Data (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Vector4 a -> c (Vector4 a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Vector4 a) # toConstr :: Vector4 a -> Constr # dataTypeOf :: Vector4 a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Vector4 a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Vector4 a)) # gmapT :: (forall b. Data b => b -> b) -> Vector4 a -> Vector4 a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Vector4 a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Vector4 a -> r # gmapQ :: (forall d. Data d => d -> u) -> Vector4 a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Vector4 a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Vector4 a -> m (Vector4 a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Vector4 a -> m (Vector4 a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Vector4 a -> m (Vector4 a) #
Applicative (Codiagonal Vector4) Source #
Instance details Defined in Math.Matrix.Vector4 Methods pure :: a -> Codiagonal Vector4 a # (<>) :: Codiagonal Vector4 (a -> b) -> Codiagonal Vector4 a -> Codiagonal Vector4 b # liftA2 :: (a -> b -> c) -> Codiagonal Vector4 a -> Codiagonal Vector4 b -> Codiagonal Vector4 c # (>) :: Codiagonal Vector4 a -> Codiagonal Vector4 b -> Codiagonal Vector4 b # (<*) :: Codiagonal Vector4 a -> Codiagonal Vector4 b -> Codiagonal Vector4 a #
Functor (Codiagonal Vector4) Source #
Instance details Defined in Math.Matrix.Vector4 Methods fmap :: (a -> b) -> Codiagonal Vector4 a -> Codiagonal Vector4 b # (<$) :: a -> Codiagonal Vector4 b -> Codiagonal Vector4 a #
Num s => Monoid (Vector4 s) Source #
Instance details Defined in Math.Matrix.Vector4 Methods mempty :: Vector4 s # mappend :: Vector4 s -> Vector4 s -> Vector4 s # mconcat :: [Vector4 s] -> Vector4 s #
Num s => Semigroup (Vector4 s) Source #
Instance details Defined in Math.Matrix.Vector4 Methods (<>) :: Vector4 s -> Vector4 s -> Vector4 s # sconcat :: NonEmpty (Vector4 s) -> Vector4 s # stimes :: Integral b => b -> Vector4 s -> Vector4 s #
Generic a => Generic (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 Associated Types type Rep (Vector4 a) :: Type -> Type # Methods from :: Vector4 a -> Rep (Vector4 a) x # to :: Rep (Vector4 a) x -> Vector4 a #
Num a => Num (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 Methods (+) :: Vector4 a -> Vector4 a -> Vector4 a # (-) :: Vector4 a -> Vector4 a -> Vector4 a # (*) :: Vector4 a -> Vector4 a -> Vector4 a # negate :: Vector4 a -> Vector4 a # abs :: Vector4 a -> Vector4 a # signum :: Vector4 a -> Vector4 a # fromInteger :: Integer -> Vector4 a #
Read a => Read (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 Methods readsPrec :: Int -> ReadS (Vector4 a) # readList :: ReadS [Vector4 a] # readPrec :: ReadPrec (Vector4 a) # readListPrec :: ReadPrec [Vector4 a] #
Show a => Show (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 Methods showsPrec :: Int -> Vector4 a -> ShowS # show :: Vector4 a -> String # showList :: [Vector4 a] -> ShowS #
Binary s => Binary (Vector4 s) Source #
Instance details Defined in Math.Matrix.Vector4 Methods put :: Vector4 s -> Put # get :: Get (Vector4 s) # putList :: [Vector4 s] -> Put #
ConjugateSymmetric a => ConjugateSymmetric (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 Methods conj :: Vector4 a -> Vector4 a Source #
Num a => CoordinateSpace (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 Associated Types type Coordinate (Vector4 a) Source # Methods index :: Coordinate (Vector4 a) -> Vector4 a -> Scalar (Vector4 a) Source # listVector :: [Scalar (Vector4 a)] -> Vector4 a Source # dimensionSize :: Vector4 a -> Int Source # coordinates :: Vector4 a -> [Coordinate (Vector4 a)] Source #
InnerProductSpace (Vector4 Float) Source #
Instance details Defined in Math.Matrix.SIMD Methods (%.) :: Vector4 Float -> Vector4 Float -> Scalar (Vector4 Float) Source # areOrthogonal :: Vector4 Float -> Vector4 Float -> Bool Source # canonicalNorm :: Vector4 Float -> Scalar (Vector4 Float) Source #
(Num a, ConjugateSymmetric a) => InnerProductSpace (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 Methods (%.) :: Vector4 a -> Vector4 a -> Scalar (Vector4 a) Source # areOrthogonal :: Vector4 a -> Vector4 a -> Bool Source # canonicalNorm :: Vector4 a -> Scalar (Vector4 a) Source #
(MetricSpace a, Floating (Distance a)) => MetricSpace (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 Associated Types type Distance (Vector4 a) Source # Methods distance :: Vector4 a -> Vector4 a -> Distance (Vector4 a) Source #
(Ord a, Floating a, ConjugateSymmetric a) => NormedSpace (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 Methods norm :: Vector4 a -> Scalar (Vector4 a) Source # normSquared :: Vector4 a -> Scalar (Vector4 a) Source #
Num a => StandardBasis (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 Methods unitVectors :: [Vector4 a] Source #
Num a => VectorSpace (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 Associated Types type Scalar (Vector4 a) Source # Methods vzero :: Vector4 a Source # vnegate :: Vector4 a -> Vector4 a Source # (%+) :: Vector4 a -> Vector4 a -> Vector4 a Source # (%*) :: Scalar (Vector4 a) -> Vector4 a -> Vector4 a Source #
Optimal (Vector4 Int32) Source #
Instance details Defined in Math.Matrix.SIMD Associated Types type Optimized (Vector4 Int32) Source # Methods toO :: Vector4 Int32 -> Optimized (Vector4 Int32) Source # fromO :: Optimized (Vector4 Int32) -> Vector4 Int32 Source # zipO :: (Scalar (Vector4 Int32) -> Scalar (Vector4 Int32) -> Scalar (Vector4 Int32)) -> Optimized (Vector4 Int32) -> Optimized (Vector4 Int32) -> Optimized (Vector4 Int32) Source # mapO :: (Scalar (Vector4 Int32) -> Scalar (Vector4 Int32)) -> Optimized (Vector4 Int32) -> Optimized (Vector4 Int32) Source # sumCoordinatesO :: Optimized (Vector4 Int32) -> Scalar (Vector4 Int32) Source # constantO :: Scalar (Vector4 Int32) -> Optimized (Vector4 Int32) Source #
Optimal (Vector4 Float) Source #
Instance details Defined in Math.Matrix.SIMD Associated Types type Optimized (Vector4 Float) Source # Methods toO :: Vector4 Float -> Optimized (Vector4 Float) Source # fromO :: Optimized (Vector4 Float) -> Vector4 Float Source # zipO :: (Scalar (Vector4 Float) -> Scalar (Vector4 Float) -> Scalar (Vector4 Float)) -> Optimized (Vector4 Float) -> Optimized (Vector4 Float) -> Optimized (Vector4 Float) Source # mapO :: (Scalar (Vector4 Float) -> Scalar (Vector4 Float)) -> Optimized (Vector4 Float) -> Optimized (Vector4 Float) Source # sumCoordinatesO :: Optimized (Vector4 Float) -> Scalar (Vector4 Float) Source # constantO :: Scalar (Vector4 Float) -> Optimized (Vector4 Float) Source #
ShowPrecision s => ShowPrecision (Vector4 s) Source #
Instance details Defined in Math.Matrix.Vector4 Methods showAtPrecision :: Vector4 s -> Integer -> String Source #
MedianAlgebra s => MedianAlgebra (Vector4 s) Source #
Instance details Defined in Math.Matrix.Vector4 Methods med :: Vector4 s -> Vector4 s -> Vector4 s -> Vector4 s Source #
PpShow a => PpShow (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 Methods pp :: Vector4 a -> Doc Source #
Universe a => Universe (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 Methods allElements :: [Vector4 a] Source #
IdVisitor (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 Methods idFold :: Fold (Vector4 a) (Vector4 a) Source #
Visitor (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 Associated Types data Fold (Vector4 a) :: Type -> Type Source # Methods visit :: Fold (Vector4 a) a0 -> Vector4 a -> a0 Source #
Eq a => Eq (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 Methods (==) :: Vector4 a -> Vector4 a -> Bool # (/=) :: Vector4 a -> Vector4 a -> Bool #
Ord a => Ord (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 Methods compare :: Vector4 a -> Vector4 a -> Ordering # (<) :: Vector4 a -> Vector4 a -> Bool # (<=) :: Vector4 a -> Vector4 a -> Bool # (>) :: Vector4 a -> Vector4 a -> Bool # (>=) :: Vector4 a -> Vector4 a -> Bool # max :: Vector4 a -> Vector4 a -> Vector4 a # min :: Vector4 a -> Vector4 a -> Vector4 a #
(ConjugateSymmetric a, Num a) => Dualizable (Vector4 a) Dual Source #
Instance details Defined in Math.Matrix.Linear Methods covector :: (Vector4 a -> Scalar (Vector4 a)) -> Dual (Vector4 a) Source # bracket :: Dual (Vector4 a) -> Vector4 a -> Scalar (Vector4 a) Source #
(Num a, Closed a, ConjugateSymmetric a, LinearTransform Vector4 Vector1 a) => VectorDerivative (Vector4 a) Dual LinearMap Source #
Instance details Defined in Math.Matrix.LinearOperations Methods divergence :: LinearMap (Vector4 a) (Vector4 a) -> Dual (Vector4 a) Source # grad :: Dual (Vector4 a) -> LinearMap (Vector4 a) (Vector4 a) Source # directionalDerivative :: Vector4 a -> Dual (Vector4 a) -> Dual (Vector4 a) Source # laplace :: Dual (Vector4 a) -> Dual (Vector4 a) Source #
Num a => DecomposableVectorSpace (Vector4 a) ((->) FourD) Source #
Instance details Defined in Math.Matrix.Simple Methods decompose :: (Scalar (Vector4 a) -> res) -> Vector4 a -> FourD -> res Source # project :: Vector4 a -> FourD -> Scalar (Vector4 a) Source #
Show a => Show (Codiagonal Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 Methods showsPrec :: Int -> Codiagonal Vector4 a -> ShowS # show :: Codiagonal Vector4 a -> String # showList :: [Codiagonal Vector4 a] -> ShowS #
Optimal (Vector4 Int16, Vector4 Int16) Source #
Instance details Defined in Math.Matrix.SIMD Associated Types type Optimized (Vector4 Int16, Vector4 Int16) Source # Methods toO :: (Vector4 Int16, Vector4 Int16) -> Optimized (Vector4 Int16, Vector4 Int16) Source # fromO :: Optimized (Vector4 Int16, Vector4 Int16) -> (Vector4 Int16, Vector4 Int16) Source # zipO :: (Scalar (Vector4 Int16, Vector4 Int16) -> Scalar (Vector4 Int16, Vector4 Int16) -> Scalar (Vector4 Int16, Vector4 Int16)) -> Optimized (Vector4 Int16, Vector4 Int16) -> Optimized (Vector4 Int16, Vector4 Int16) -> Optimized (Vector4 Int16, Vector4 Int16) Source # mapO :: (Scalar (Vector4 Int16, Vector4 Int16) -> Scalar (Vector4 Int16, Vector4 Int16)) -> Optimized (Vector4 Int16, Vector4 Int16) -> Optimized (Vector4 Int16, Vector4 Int16) Source # sumCoordinatesO :: Optimized (Vector4 Int16, Vector4 Int16) -> Scalar (Vector4 Int16, Vector4 Int16) Source # constantO :: Scalar (Vector4 Int16, Vector4 Int16) -> Optimized (Vector4 Int16, Vector4 Int16) Source #
(Universe row, Num a) => LinearTransform ((->) row) Vector4 a Source #
Instance details Defined in Math.Matrix.Simple Methods (<>>) :: Vector4 a -> ((->) row :: Vector4) a -> row -> a Source # (<<>) :: ((->) row :: Vector4) a -> (row -> a) -> Vector4 a Source #
Transposable ((->) row) Vector4 a Source #
Instance details Defined in Math.Matrix.Vector4 Methods transposeImpl :: ((->) row :: Vector4) a -> (Vector4 :: (->) row) a Source #
SupportsMatrixMultiplication Vector4 Vector4 Vector4 a => Monoid ((Vector4 :*: Vector4) a) Source #	see "Lawvere,Rosebrugh: Sets for mathematics", pg. 167.
Instance details Defined in Math.Matrix.Vector4 Methods mempty :: (Vector4 :: Vector4) a # mappend :: (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a # mconcat :: [(Vector4 :: Vector4) a] -> (Vector4 :: Vector4) a #
SupportsMatrixMultiplication Vector4 Vector4 Vector4 a => Semigroup ((Vector4 :*: Vector4) a) Source #
Instance details Defined in Math.Matrix.Vector4 Methods (<>) :: (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a # sconcat :: NonEmpty ((Vector4 :: Vector4) a) -> (Vector4 :: Vector4) a # stimes :: Integral b => b -> (Vector4 :: Vector4) a -> (Vector4 :*: Vector4) a #
SupportsMatrixMultiplication Vector4 Vector4 Vector4 a => Num ((Vector4 :*: Vector4) a) Source #
Instance details Defined in Math.Matrix.Vector4 Methods (+) :: (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a # (-) :: (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a # () :: (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a # negate :: (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a # abs :: (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a # signum :: (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a # fromInteger :: Integer -> (Vector4 :*: Vector4) a #
Show (f a) => Show ((Vector4 :*: f) a) Source #
Instance details Defined in Math.Matrix.Vector4 Methods showsPrec :: Int -> (Vector4 :: f) a -> ShowS # show :: (Vector4 :: f) a -> String # showList :: [(Vector4 :*: f) a] -> ShowS #
ConjugateSymmetric a => ConjugateSymmetric ((Vector4 :*: Vector4) a) Source #	https://en.wikipedia.org/wiki/Conjugate_transpose
Instance details Defined in Math.Matrix.Vector4 Methods conj :: (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a Source #
(Floating a, ConjugateSymmetric a) => InnerProductSpace ((Vector4 :*: Vector4) a) Source #	4 x 4 matrices
Instance details Defined in Math.Matrix.Vector4 Methods (%.) :: (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a -> Scalar ((Vector4 :: Vector4) a) Source # areOrthogonal :: (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a -> Bool Source # canonicalNorm :: (Vector4 :: Vector4) a -> Scalar ((Vector4 :*: Vector4) a) Source #
(Num a, ConjugateSymmetric a) => LieAlgebra ((Vector4 :*: Vector4) a) Source #
Instance details Defined in Math.Matrix.Matrix Methods (%<>%) :: (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a -> (Vector4 :*: Vector4) a Source #
(Floating a, ConjugateSymmetric a) => NormedSpace ((Vector4 :*: Vector4) a) Source #	4 x 4 matrices
Instance details Defined in Math.Matrix.Vector4 Methods norm :: (Vector4 :: Vector4) a -> Scalar ((Vector4 :: Vector4) a) Source # normSquared :: (Vector4 :: Vector4) a -> Scalar ((Vector4 :: Vector4) a) Source #
Num a => VectorSpace ((Vector1 :*: Vector4) a) Source #	1 x 4 matrices:
Instance details Defined in Math.Matrix.Vector4 Associated Types type Scalar ((Vector1 :: Vector4) a) Source # Methods vzero :: (Vector1 :: Vector4) a Source # vnegate :: (Vector1 :: Vector4) a -> (Vector1 :: Vector4) a Source # (%+) :: (Vector1 :: Vector4) a -> (Vector1 :: Vector4) a -> (Vector1 :: Vector4) a Source # (%) :: Scalar ((Vector1 :: Vector4) a) -> (Vector1 :: Vector4) a -> (Vector1 :*: Vector4) a Source #
Num a => VectorSpace ((Vector2 :*: Vector4) a) Source #	2 x 4 matrices
Instance details Defined in Math.Matrix.Vector4 Associated Types type Scalar ((Vector2 :: Vector4) a) Source # Methods vzero :: (Vector2 :: Vector4) a Source # vnegate :: (Vector2 :: Vector4) a -> (Vector2 :: Vector4) a Source # (%+) :: (Vector2 :: Vector4) a -> (Vector2 :: Vector4) a -> (Vector2 :: Vector4) a Source # (%) :: Scalar ((Vector2 :: Vector4) a) -> (Vector2 :: Vector4) a -> (Vector2 :*: Vector4) a Source #
Num a => VectorSpace ((Vector3 :*: Vector4) a) Source #	3 x 4 matrices
Instance details Defined in Math.Matrix.Vector4 Associated Types type Scalar ((Vector3 :: Vector4) a) Source # Methods vzero :: (Vector3 :: Vector4) a Source # vnegate :: (Vector3 :: Vector4) a -> (Vector3 :: Vector4) a Source # (%+) :: (Vector3 :: Vector4) a -> (Vector3 :: Vector4) a -> (Vector3 :: Vector4) a Source # (%) :: Scalar ((Vector3 :: Vector4) a) -> (Vector3 :: Vector4) a -> (Vector3 :*: Vector4) a Source #
Num a => VectorSpace ((Vector4 :*: Vector1) a) Source #	4 x 1 matrices:
Instance details Defined in Math.Matrix.Vector4 Associated Types type Scalar ((Vector4 :: Vector1) a) Source # Methods vzero :: (Vector4 :: Vector1) a Source # vnegate :: (Vector4 :: Vector1) a -> (Vector4 :: Vector1) a Source # (%+) :: (Vector4 :: Vector1) a -> (Vector4 :: Vector1) a -> (Vector4 :: Vector1) a Source # (%) :: Scalar ((Vector4 :: Vector1) a) -> (Vector4 :: Vector1) a -> (Vector4 :*: Vector1) a Source #
Num a => VectorSpace ((Vector4 :*: Vector2) a) Source #	4 x 2 matrices
Instance details Defined in Math.Matrix.Vector4 Associated Types type Scalar ((Vector4 :: Vector2) a) Source # Methods vzero :: (Vector4 :: Vector2) a Source # vnegate :: (Vector4 :: Vector2) a -> (Vector4 :: Vector2) a Source # (%+) :: (Vector4 :: Vector2) a -> (Vector4 :: Vector2) a -> (Vector4 :: Vector2) a Source # (%) :: Scalar ((Vector4 :: Vector2) a) -> (Vector4 :: Vector2) a -> (Vector4 :*: Vector2) a Source #
Num a => VectorSpace ((Vector4 :*: Vector3) a) Source #	4 x 3 matrices:
Instance details Defined in Math.Matrix.Vector4 Associated Types type Scalar ((Vector4 :: Vector3) a) Source # Methods vzero :: (Vector4 :: Vector3) a Source # vnegate :: (Vector4 :: Vector3) a -> (Vector4 :: Vector3) a Source # (%+) :: (Vector4 :: Vector3) a -> (Vector4 :: Vector3) a -> (Vector4 :: Vector3) a Source # (%) :: Scalar ((Vector4 :: Vector3) a) -> (Vector4 :: Vector3) a -> (Vector4 :*: Vector3) a Source #
Num a => VectorSpace ((Vector4 :*: Vector4) a) Source #	4 x 4 matrices
Instance details Defined in Math.Matrix.Vector4 Associated Types type Scalar ((Vector4 :: Vector4) a) Source # Methods vzero :: (Vector4 :: Vector4) a Source # vnegate :: (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a Source # (%+) :: (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a Source # (%) :: Scalar ((Vector4 :: Vector4) a) -> (Vector4 :: Vector4) a -> (Vector4 :*: Vector4) a Source #
Num a => VectorSpace ((Vector4 :*: (->) col) a) Source #
Instance details Defined in Math.Matrix.Simple Associated Types type Scalar ((Vector4 :: (->) col) a) Source # Methods vzero :: (Vector4 :: (->) col) a Source # vnegate :: (Vector4 :: (->) col) a -> (Vector4 :: (->) col) a Source # (%+) :: (Vector4 :: (->) col) a -> (Vector4 :: (->) col) a -> (Vector4 :: (->) col) a Source # (%) :: Scalar ((Vector4 :: (->) col) a) -> (Vector4 :: (->) col) a -> (Vector4 :*: (->) col) a Source #
Num a => VectorSpace (((->) row :*: Vector4) a) Source #
Instance details Defined in Math.Matrix.Simple Associated Types type Scalar (((->) row :: Vector4) a) Source # Methods vzero :: ((->) row :: Vector4) a Source # vnegate :: ((->) row :: Vector4) a -> ((->) row :: Vector4) a Source # (%+) :: ((->) row :: Vector4) a -> ((->) row :: Vector4) a -> ((->) row :: Vector4) a Source # (%) :: Scalar (((->) row :: Vector4) a) -> ((->) row :: Vector4) a -> ((->) row :*: Vector4) a Source #
Optimal ((Vector2 :*: Vector4) Int16) Source #
Instance details Defined in Math.Matrix.SIMD Associated Types type Optimized ((Vector2 :: Vector4) Int16) Source # Methods toO :: (Vector2 :: Vector4) Int16 -> Optimized ((Vector2 :: Vector4) Int16) Source # fromO :: Optimized ((Vector2 :: Vector4) Int16) -> (Vector2 :: Vector4) Int16 Source # zipO :: (Scalar ((Vector2 :: Vector4) Int16) -> Scalar ((Vector2 :: Vector4) Int16) -> Scalar ((Vector2 :: Vector4) Int16)) -> Optimized ((Vector2 :: Vector4) Int16) -> Optimized ((Vector2 :: Vector4) Int16) -> Optimized ((Vector2 :: Vector4) Int16) Source # mapO :: (Scalar ((Vector2 :: Vector4) Int16) -> Scalar ((Vector2 :: Vector4) Int16)) -> Optimized ((Vector2 :: Vector4) Int16) -> Optimized ((Vector2 :: Vector4) Int16) Source # sumCoordinatesO :: Optimized ((Vector2 :: Vector4) Int16) -> Scalar ((Vector2 :: Vector4) Int16) Source # constantO :: Scalar ((Vector2 :: Vector4) Int16) -> Optimized ((Vector2 :*: Vector4) Int16) Source #
Optimal ((Vector4 :*: Vector2) Int16) Source #
Instance details Defined in Math.Matrix.SIMD Associated Types type Optimized ((Vector4 :: Vector2) Int16) Source # Methods toO :: (Vector4 :: Vector2) Int16 -> Optimized ((Vector4 :: Vector2) Int16) Source # fromO :: Optimized ((Vector4 :: Vector2) Int16) -> (Vector4 :: Vector2) Int16 Source # zipO :: (Scalar ((Vector4 :: Vector2) Int16) -> Scalar ((Vector4 :: Vector2) Int16) -> Scalar ((Vector4 :: Vector2) Int16)) -> Optimized ((Vector4 :: Vector2) Int16) -> Optimized ((Vector4 :: Vector2) Int16) -> Optimized ((Vector4 :: Vector2) Int16) Source # mapO :: (Scalar ((Vector4 :: Vector2) Int16) -> Scalar ((Vector4 :: Vector2) Int16)) -> Optimized ((Vector4 :: Vector2) Int16) -> Optimized ((Vector4 :: Vector2) Int16) Source # sumCoordinatesO :: Optimized ((Vector4 :: Vector2) Int16) -> Scalar ((Vector4 :: Vector2) Int16) Source # constantO :: Scalar ((Vector4 :: Vector2) Int16) -> Optimized ((Vector4 :*: Vector2) Int16) Source #
Optimal ((Vector4 :*: Vector4) Int8) Source #
Instance details Defined in Math.Matrix.SIMD Associated Types type Optimized ((Vector4 :: Vector4) Int8) Source # Methods toO :: (Vector4 :: Vector4) Int8 -> Optimized ((Vector4 :: Vector4) Int8) Source # fromO :: Optimized ((Vector4 :: Vector4) Int8) -> (Vector4 :: Vector4) Int8 Source # zipO :: (Scalar ((Vector4 :: Vector4) Int8) -> Scalar ((Vector4 :: Vector4) Int8) -> Scalar ((Vector4 :: Vector4) Int8)) -> Optimized ((Vector4 :: Vector4) Int8) -> Optimized ((Vector4 :: Vector4) Int8) -> Optimized ((Vector4 :: Vector4) Int8) Source # mapO :: (Scalar ((Vector4 :: Vector4) Int8) -> Scalar ((Vector4 :: Vector4) Int8)) -> Optimized ((Vector4 :: Vector4) Int8) -> Optimized ((Vector4 :: Vector4) Int8) Source # sumCoordinatesO :: Optimized ((Vector4 :: Vector4) Int8) -> Scalar ((Vector4 :: Vector4) Int8) Source # constantO :: Scalar ((Vector4 :: Vector4) Int8) -> Optimized ((Vector4 :*: Vector4) Int8) Source #
(SupportsMatrixMultiplication Vector4 Vector4 Vector4 a, Fractional a) => Group ((Vector4 :*: Vector4) a) Source #
Instance details Defined in Math.Matrix.Vector4 Methods ginvert :: (Vector4 :: Vector4) a -> (Vector4 :: Vector4) a Source #
PpShow (f a) => PpShow ((Vector4 :*: f) a) Source #
Instance details Defined in Math.Matrix.Vector4 Methods pp :: (Vector4 :*: f) a -> Doc Source #
data Codiagonal Vector4 a Source #
Instance details Defined in Math.Matrix.Vector4 data Codiagonal Vector4 a = Codiagonal4 { downCodiagonal4 :: Vector3 a rightCodiagonal4 :: Vector3 a diagonalCodiagonal4 :: Codiagonal Vector3 a }
type Vector4 :+: str Source #
Instance details Defined in Math.Matrix.Vector4 type Vector4 :+: str = str
type Vector4 \\ a Source #
Instance details Defined in Math.Matrix.Vector4 type Vector4 \\ a = Vector3 a
data Closure Stream (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 data Closure Stream (Vector4 a) = Vector4Closure { runVector4Closure :: Vector4 (Closure Stream a) }
type Rep (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 type Rep (Vector4 a) = D1 ('MetaData "Vector4" "Math.Matrix.Vector4" "cifl-math-library-2.0.0.0-K3Wcv1zXOBxvFThQyThI4" 'False) (C1 ('MetaCons "Vector4" 'PrefixI 'True) ((S1 ('MetaSel ('Just "tcoord4") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :: S1 ('MetaSel ('Just "xcoord4") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a)) :: (S1 ('MetaSel ('Just "ycoord4") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Just "zcoord4") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a))))
type Coordinate (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 type Coordinate (Vector4 a) = Int
type Distance (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 type Distance (Vector4 a) = Distance a
type Scalar (Vector4 a) Source #
Instance details Defined in Math.Matrix.Vector4 type Scalar (Vector4 a) = a
type Optimized (Vector4 Int32) Source #
Instance details Defined in Math.Matrix.SIMD type Optimized (Vector4 Int32) = SIMDVec 4 Int32
type Optimized (Vector4 Float) Source #
Instance details Defined in Math.Matrix.SIMD type Optimized (Vector4 Float) = SIMDVec 4 Float
data Fold (Vector4 a) b Source #
Instance details Defined in Math.Matrix.Vector4 data Fold (Vector4 a) b = Vector4Fold (a -> a -> a -> a -> b)
type Optimized (Vector4 Int16, Vector4 Int16) Source #
Instance details Defined in Math.Matrix.SIMD type Optimized (Vector4 Int16, Vector4 Int16) = SIMDVec 8 Int16
type Scalar ((Vector1 :*: Vector4) a) Source #
Instance details Defined in Math.Matrix.Vector4 type Scalar ((Vector1 :*: Vector4) a) = a
type Scalar ((Vector2 :*: Vector4) a) Source #
Instance details Defined in Math.Matrix.Vector4 type Scalar ((Vector2 :*: Vector4) a) = a
type Scalar ((Vector3 :*: Vector4) a) Source #
Instance details Defined in Math.Matrix.Vector4 type Scalar ((Vector3 :*: Vector4) a) = a
type Scalar ((Vector4 :*: Vector1) a) Source #
Instance details Defined in Math.Matrix.Vector4 type Scalar ((Vector4 :*: Vector1) a) = a
type Scalar ((Vector4 :*: Vector2) a) Source #
Instance details Defined in Math.Matrix.Vector4 type Scalar ((Vector4 :*: Vector2) a) = a
type Scalar ((Vector4 :*: Vector3) a) Source #
Instance details Defined in Math.Matrix.Vector4 type Scalar ((Vector4 :*: Vector3) a) = a
type Scalar ((Vector4 :*: Vector4) a) Source #
Instance details Defined in Math.Matrix.Vector4 type Scalar ((Vector4 :*: Vector4) a) = a
type Scalar ((Vector4 :*: (->) col) a) Source #
Instance details Defined in Math.Matrix.Simple type Scalar ((Vector4 :*: (->) col) a) = a
type Scalar (((->) row :*: Vector4) a) Source #
Instance details Defined in Math.Matrix.Simple type Scalar (((->) row :*: Vector4) a) = a
type Optimized ((Vector2 :*: Vector4) Int16) Source #
Instance details Defined in Math.Matrix.SIMD type Optimized ((Vector2 :*: Vector4) Int16) = SIMDVec 8 Int16
type Optimized ((Vector4 :*: Vector2) Int16) Source #
Instance details Defined in Math.Matrix.SIMD type Optimized ((Vector4 :*: Vector2) Int16) = SIMDVec 8 Int16
type Optimized ((Vector4 :*: Vector4) Int8) Source #
Instance details Defined in Math.Matrix.SIMD type Optimized ((Vector4 :*: Vector4) Int8) = SIMDVec 16 Int8

x4 :: Num a => Vector4 a Source #

y4 :: Num a => Vector4 a Source #

z4 :: Num a => Vector4 a Source #

t4 :: Num a => Vector4 a Source #

dx4 :: forall {str :: Type -> Type} {a}. (Infinitesimal str a, Num (Closure str a)) => Vector4 (Closure str a) Source #

dy4 :: forall {str :: Type -> Type} {a}. (Infinitesimal str a, Num (Closure str a)) => Vector4 (Closure str a) Source #

dz4 :: forall {str :: Type -> Type} {a}. (Infinitesimal str a, Num (Closure str a)) => Vector4 (Closure str a) Source #

dt4 :: forall {str :: Type -> Type} {a}. (Infinitesimal str a, Num (Closure str a)) => Vector4 (Closure str a) Source #

setx4 :: s -> Vector4 s -> Vector4 s Source #

sety4 :: s -> Vector4 s -> Vector4 s Source #

setz4 :: s -> Vector4 s -> Vector4 s Source #

sett4 :: s -> Vector4 s -> Vector4 s Source #

updateRow4 :: g a -> Vector4 ((Vector4 :*: g) a -> (Vector4 :*: g) a) Source #

updateColumn4 :: Applicative f => f a -> Vector4 ((f :*: Vector4) a -> (f :*: Vector4) a) Source #

type Matrix4 a = (Vector4 :*: Vector4) a Source #

codiag4 :: (Vector4 :*: Vector4) a -> Codiagonal Vector4 a Source #

matrix4 :: Vector4 a -> Codiagonal Vector4 a -> (Vector4 :*: Vector4) a Source #

diagonalProjections4 :: Vector4 (Index Vector4 a) Source #

cycle4 :: Vector4 a -> Stream a Source #

vector4 :: [a] -> Vector4 a Source #

unzipV4 :: Vector4 (a, b) -> (Vector4 a, Vector4 b) Source #

constant4 :: a -> Vector4 a Source #

dim4 :: Vector4 Integer Source #

sumCoordinates4 :: Num a => Vector4 a -> a Source #

leftMultiply4Gen :: (Functor f, Num a, ConjugateSymmetric a) => Vector4 a -> (f :*: Vector4) a -> f a Source #

rightMultiply4Gen :: (VectorSpace (f a), ConjugateSymmetric a, Scalar (f a) ~ a) => (Vector4 :*: f) a -> Vector4 a -> f a Source #

matrixMultiply4 :: (Num a, ConjugateSymmetric a) => Matrix4 a -> Matrix4 a -> Matrix4 a Source #

dot4 :: (Num a, ConjugateSymmetric a) => Vector4 a -> Vector4 a -> a Source #

versor :: (Ord a, Floating a, ConjugateSymmetric a) => Vector4 a -> Vector4 a Source #

index4 :: Int -> Vector4 a -> a Source #

diagonal4 :: (Vector4 :*: Vector4) a -> Vector4 a Source #

dt_4 :: Num s => s -> Vector4 s -> Vector4 s Source #

dx_4 :: Num s => s -> Vector4 s -> Vector4 s Source #

dy_4 :: Num s => s -> Vector4 s -> Vector4 s Source #

dz_4 :: Num s => s -> Vector4 s -> Vector4 s Source #

transpose4 :: Num a => Matrix4 a -> Matrix4 a Source #

transpose4Impl :: Matrix4 a -> Matrix4 a Source #

identity4 :: Num a => Matrix4 a Source #

diagonal4x :: Matrix4 a -> Vector4 a Source #

zero_codiagonal4 :: Num a => Codiagonal Vector4 a Source #

diagonal_matrix4 :: Vector4 a -> (Vector4 :*: Vector4) a -> (Vector4 :*: Vector4) a Source #

mat4 :: Vector4 a -> Codiagonal Vector4 a -> (Vector4 :*: Vector4) a Source #

trace4 :: Num a => Matrix4 a -> a Source #

removet4 :: Vector4 a -> Vector3 a Source #

removex4 :: Vector4 a -> Vector3 a Source #

removey4 :: Vector4 a -> Vector3 a Source #

removez4 :: Vector4 a -> Vector3 a Source #

removes4 :: Vector4 (Vector4 a -> Vector3 a) Source #

project4 :: Vector4 (Vector4 a -> a) Source #

removeIndex4 :: Matrix4 a -> Matrix4 (Matrix3 a) Source #

cofactor4 :: Num a => Matrix4 a -> Matrix4 a Source #

adjucate4 :: Num a => Matrix4 a -> Matrix4 a Source #

signs4 :: Integral a => Matrix4 a Source #

vectorIndices4 :: Integral a => Vector4 a Source #

matrixIndices4 :: Integral a => (Vector4 :*: Vector4) (a, a) Source #

inverse4 :: Fractional a => Matrix4 a -> Matrix4 a Source #

https://en.wikipedia.org/wiki/Invertible_matrix

cross4 :: Num a => Vector4 a -> Vector4 a -> Vector4 a -> Vector4 a Source #

Generalization of cross product to four dimensions This is computed using formal determinant representation of cross product expanded to four dimensions https://en.wikipedia.org/wiki/Cross_product This computes vector that is linearly independent of all three vectors given in four dimensional space.

cross_product4 :: Num a => (Vector3 :*: Vector4) a -> Vector4 a Source #

determinant4 :: Num a => Matrix4 a -> a Source #

determinancett4 :: Num a => Determinance Vector4 Vector4 Vector3 Vector3 Vector3 a a a Source #

coordDeterminance4 :: Num a => (forall c. Vector4 c -> c) -> (forall d. Vector4 d -> d) -> Determinance Vector4 Vector4 Vector3 Vector3 Vector3 a a a Source #

Orphan instances

AppendableVector Vector1 Vector3 Source #
Instance details Associated Types type Vector1 :+: Vector3 :: Type -> Type Source # Methods (\|\|>>) :: Vector1 a -> Vector3 a -> (Vector1 :+: Vector3) a Source #
AppendableVector Vector2 Vector2 Source #
Instance details Associated Types type Vector2 :+: Vector2 :: Type -> Type Source # Methods (\|\|>>) :: Vector2 a -> Vector2 a -> (Vector2 :+: Vector2) a Source #
AppendableVector Vector3 Vector1 Source #
Instance details Associated Types type Vector3 :+: Vector1 :: Type -> Type Source # Methods (\|\|>>) :: Vector3 a -> Vector1 a -> (Vector3 :+: Vector1) a Source #
SplittableVector Vector1 Vector3 Source #
Instance details Methods vsplit :: (Vector1 :+: Vector3) a -> (Vector1 a, Vector3 a) Source #
SplittableVector Vector2 Vector2 Source #
Instance details Methods vsplit :: (Vector2 :+: Vector2) a -> (Vector2 a, Vector2 a) Source #
SplittableVector Vector3 Vector1 Source #
Instance details Methods vsplit :: (Vector3 :+: Vector1) a -> (Vector3 a, Vector1 a) Source #