Safe Haskell	Safe
Language	Haskell2010

Math.Matrix.Vector2

Contents

Orphan instances

Synopsis

data Vector2 s = Vector2 {
- xcoord2 :: !s
- ycoord2 :: !s
}
setx2 :: s -> Vector2 s -> Vector2 s
sety2 :: s -> Vector2 s -> Vector2 s
updateRow2 :: g a -> Vector2 ((Vector2 :*: g) a -> (Vector2 :*: g) a)
updateColumn2 :: Applicative f => f a -> Vector2 ((f :*: Vector2) a -> (f :*: Vector2) a)
type ComplexVector2 a = (Vector2 :*: Complex) a
i2 :: Num a => Vector2 a
j2 :: Num a => Vector2 a
vector2Iso :: Vector2 a :==: Complex a
matrixRoot :: (Diagonalizable m a, ProjectionSpace m Vector1) => (m :*: m) a -> a
type Matrix2 a = (Vector2 :*: Vector2) a
zero_codiagonal2 :: Num a => Codiagonal Vector2 a
constant2 :: a -> Vector2 a
complexMatrix :: Num a => Complex a -> (Vector2 :*: Vector2) a
codiagonal2 :: Matrix2 a -> Codiagonal Vector2 a
delPartial2 :: DifferentiallyClosed a => (Vector2 a -> a) -> Vector2 a -> Vector2 a
diagonalMatrix2 :: Num a => Vector2 a -> (Vector2 :*: Vector2) a
sumCoordinates2 :: Num a => Vector2 a -> a
productCoordinates2 :: Num a => Vector2 a -> a
mat2 :: Vector2 a -> Codiagonal Vector2 a -> (Vector2 :*: Vector2) a
matrix2 :: Vector2 a -> Codiagonal Vector2 a -> (Vector2 :*: Vector2) a
vec2 :: (a, a) -> Vector2 a
su2_matrix :: (Eq a, RealFloat a) => Complex a -> Complex a -> Matrix2 (Complex a)
splitMatrix :: (Functor f, SplittableVector f f, SplittableVector m m) => ((f :+: f) :*: (m :+: m)) a -> (Vector2 :*: Vector2) ((f :*: m) a)
removex2 :: Vector2 a -> Vector1 a
removey2 :: Vector2 a -> Vector1 a
remove2 :: Vector2 (Vector2 a -> Vector1 a)
remove_index2 :: Matrix2 a -> Matrix2 (Matrix1 a)
cofactor2 :: Num a => Matrix2 a -> Matrix2 a
adjucate2 :: Num a => Matrix2 a -> Matrix2 a
inverse2 :: Fractional a => Matrix2 a -> Matrix2 a
vector_indices2 :: Vector2 Integer
matrix_indices2 :: (Vector2 :*: Vector2) (Integer, Integer)
signs2 :: (Vector2 :*: Vector2) Integer
vector_vector2 :: [a] -> Vector2 a
diagonal2 :: Num a => Matrix2 a -> Vector2 a
composeIndex :: (m (n a) :==: I (n a)) -> (n a :==: I a) -> (m :*: n) a :==: (I :*: I) a
diagonalProjections2 :: Num a => Vector2 (Index Vector2 a)
transpose2 :: Num a => Matrix2 a -> Matrix2 a
transpose2Impl :: Matrix2 a -> Matrix2 a
rotate2 :: Vector2 a -> Vector2 a
bindDiagonal2 :: Vector2 a -> (a -> Vector2 b) -> Vector2 b
bindCodiagonal2 :: Vector2 a -> (a -> Vector2 b) -> Vector2 b
crossProductScalar2 :: Num a => Vector2 a -> Vector2 a -> a
orthogonalVector2 :: Num a => Vector2 a -> Vector2 a
crossProduct2 :: Num a => (Vector1 :*: Vector2) a -> Vector2 a
leftMultiply2Gen :: (Functor f, Num a, ConjugateSymmetric a) => Vector2 a -> (f :*: Vector2) a -> f a
rightMultiply2Gen :: (VectorSpace (f a), ConjugateSymmetric a, Scalar (f a) ~ a) => (Vector2 :*: f) a -> Vector2 a -> f a
leftMultiply1_2 :: (Num a, ConjugateSymmetric a) => Vector2 a -> (Vector1 :*: Vector2) a -> Vector1 a
leftMultiply2_1 :: (Num a, ConjugateSymmetric a) => Vector1 a -> (Vector2 :*: Vector1) a -> Vector2 a
leftMultiply2 :: (Num a, ConjugateSymmetric a) => Vector2 a -> Matrix2 a -> Vector2 a
rightMultiply2 :: (Num a, ConjugateSymmetric a) => Matrix2 a -> Vector2 a -> Vector2 a
rightMultiply2_1 :: (ConjugateSymmetric a, Num a) => (Vector2 :*: Vector1) a -> Vector2 a -> Vector1 a
rightMultiply1_2 :: (ConjugateSymmetric a, Num a) => (Vector1 :*: Vector2) a -> Vector1 a -> Vector2 a
trace2 :: Num a => Matrix2 a -> a
diagonal2x :: Num a => Matrix2 a -> Vector2 a
diagonal2y :: Num a => Matrix2 a -> Vector2 a
identity2 :: Num a => Matrix2 a
determinant2 :: Num a => Matrix2 a -> a
index_vector2 :: Int -> Vector2 a -> a
rotateMatrix2 :: Floating a => a -> Matrix2 a
eigenvalue2 :: Floating a => (Vector2 :*: Vector2) a -> Vector2 a
leviCivita2 :: Num a => (Vector2 :*: Vector2) a

Documentation

data Vector2 s Source #

Constructors

Vector2
Fields xcoord2 :: !s ycoord2 :: !s

Instances

Instances details

MonadZip Vector2 Source #
Instance details Defined in Math.Matrix.Vector2 Methods mzip :: Vector2 a -> Vector2 b -> Vector2 (a, b) # mzipWith :: (a -> b -> c) -> Vector2 a -> Vector2 b -> Vector2 c # munzip :: Vector2 (a, b) -> (Vector2 a, Vector2 b) #
Foldable Vector2 Source #
Instance details Defined in Math.Matrix.Vector2 Methods fold :: Monoid m => Vector2 m -> m # foldMap :: Monoid m => (a -> m) -> Vector2 a -> m # foldMap' :: Monoid m => (a -> m) -> Vector2 a -> m # foldr :: (a -> b -> b) -> b -> Vector2 a -> b # foldr' :: (a -> b -> b) -> b -> Vector2 a -> b # foldl :: (b -> a -> b) -> b -> Vector2 a -> b # foldl' :: (b -> a -> b) -> b -> Vector2 a -> b # foldr1 :: (a -> a -> a) -> Vector2 a -> a # foldl1 :: (a -> a -> a) -> Vector2 a -> a # toList :: Vector2 a -> [a] # null :: Vector2 a -> Bool # length :: Vector2 a -> Int # elem :: Eq a => a -> Vector2 a -> Bool # maximum :: Ord a => Vector2 a -> a # minimum :: Ord a => Vector2 a -> a # sum :: Num a => Vector2 a -> a # product :: Num a => Vector2 a -> a #
Traversable Vector2 Source #
Instance details Defined in Math.Matrix.Vector2 Methods traverse :: Applicative f => (a -> f b) -> Vector2 a -> f (Vector2 b) # sequenceA :: Applicative f => Vector2 (f a) -> f (Vector2 a) # mapM :: Monad m => (a -> m b) -> Vector2 a -> m (Vector2 b) # sequence :: Monad m => Vector2 (m a) -> m (Vector2 a) #
Applicative Vector2 Source #
Instance details Defined in Math.Matrix.Vector2 Methods pure :: a -> Vector2 a # (<>) :: Vector2 (a -> b) -> Vector2 a -> Vector2 b # liftA2 :: (a -> b -> c) -> Vector2 a -> Vector2 b -> Vector2 c # (>) :: Vector2 a -> Vector2 b -> Vector2 b # (<*) :: Vector2 a -> Vector2 b -> Vector2 a #
Functor Vector2 Source #
Instance details Defined in Math.Matrix.Vector2 Methods fmap :: (a -> b) -> Vector2 a -> Vector2 b # (<$) :: a -> Vector2 b -> Vector2 a #
Monad Vector2 Source #
Instance details Defined in Math.Matrix.Vector2 Methods (>>=) :: Vector2 a -> (a -> Vector2 b) -> Vector2 b # (>>) :: Vector2 a -> Vector2 b -> Vector2 b # return :: a -> Vector2 a #
UpdateableMatrixDimension Vector2 Source #
Instance details Defined in Math.Matrix.Vector2 Methods writeRow :: Applicative h => h a -> Vector2 ((Vector2 :: h) a -> (Vector2 :: h) a) Source # writeColumn :: Applicative h => h a -> Vector2 ((h :: Vector2) a -> (h :: Vector2) a) Source #
DifferentialOperator Vector2 Source #
Instance details Defined in Math.Matrix.Vector2 Methods partial :: DifferentiallyClosed a => (Vector2 a -> a) -> Vector2 a -> Vector2 a Source #
CircularComonad Vector2 Source #
Instance details Defined in Math.Matrix.Vector2 Methods rotate :: Vector2 a -> Vector2 a Source #
Comonad Vector2 Source #
Instance details Defined in Math.Matrix.Vector2 Methods extract :: Vector2 a -> a Source # duplicate :: Vector2 a -> Vector2 (Vector2 a) Source # extend :: (Vector2 a -> b) -> Vector2 a -> Vector2 b Source # (=>>) :: Vector2 a -> (Vector2 a -> b) -> Vector2 b Source # (.>>) :: Vector2 a -> b -> Vector2 b Source #
PpShowF Vector2 Source #
Instance details Defined in Math.Matrix.Vector2 Methods ppf :: PpShow a => Vector2 a -> Doc Source #
PpShowVerticalF Vector2 Source #
Instance details Defined in Math.Matrix.Vector2 Methods ppfVertical :: PpShow a => Vector2 a -> Doc Source #
AppendableVector Vector1 Vector2 Source #
Instance details Defined in Math.Matrix.Vector3 Associated Types type Vector1 :+: Vector2 :: Type -> Type Source # Methods (\|\|>>) :: Vector1 a -> Vector2 a -> (Vector1 :+: Vector2) a Source #
AppendableVector Vector2 Vector1 Source #
Instance details Defined in Math.Matrix.Vector3 Associated Types type Vector2 :+: Vector1 :: Type -> Type Source # Methods (\|\|>>) :: Vector2 a -> Vector1 a -> (Vector2 :+: Vector1) a Source #
AppendableVector Vector2 Vector2 Source #
Instance details Defined in Math.Matrix.Vector4 Associated Types type Vector2 :+: Vector2 :: Type -> Type Source # Methods (\|\|>>) :: Vector2 a -> Vector2 a -> (Vector2 :+: Vector2) a Source #
AppendableVector Vector2 Stream Source #
Instance details Defined in Math.Matrix.VectorConversions Associated Types type Vector2 :+: Stream :: Type -> Type Source # Methods (\|\|>>) :: Vector2 a -> Stream a -> (Vector2 :+: Stream) a Source #
CodiagonalMatrix Vector2 a Source #
Instance details Defined in Math.Matrix.Vector2 Associated Types data Codiagonal Vector2 a Source # type Vector2 \\ a Source # Methods codiagonalImpl :: (Vector2 :: Vector2) a -> Codiagonal Vector2 a Source # (\|\\|) :: Vector2 a -> Codiagonal Vector2 a -> (Vector2 :: Vector2) a Source # downProject :: Codiagonal Vector2 a -> Vector2 \\ a Source # rightProject :: Codiagonal Vector2 a -> Vector2 \\ a Source #
Num a => Diagonalizable Vector2 a Source #
Instance details Defined in Math.Matrix.Vector2 Methods identityImpl :: Vector2 Integer -> (Vector2 :: Vector2) a Source # identity :: (Vector2 :: Vector2) a Source # diagonalImpl :: (Vector2 :: Vector2) a -> Vector2 a Source # diagonalMatrixImpl :: Vector2 a -> (Vector2 :: Vector2) a Source #
Floating a => EigenDecomposable Vector2 a Source #
Instance details Defined in Math.Matrix.Vector2 Methods eigenvalues :: (Vector2 :*: Vector2) a -> Vector2 a Source #
Num a => Indexable Vector2 a Source #
Instance details Defined in Math.Matrix.Vector2 Methods diagonalProjections :: Vector2 (Index Vector2 a) Source # basisVector :: Index Vector2 a -> Vector2 a Source # indexProject :: Index Vector2 a -> Vector2 a -> a Source # indexableIndices :: Vector2 a Source #
Fractional a => Invertible Vector2 a Source #
Instance details Defined in Math.Matrix.Vector2 Methods cofactorImpl :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a Source # adjucateImpl :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a Source # inverseImpl :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a Source #
ProjectionSpace Vector2 Vector1 Source #
Instance details Defined in Math.Matrix.Vector2 Associated Types data (Vector2 \\\ Vector1) a Source # Methods projectFirst :: Vector2 a -> Vector1 a Source # projectSecond :: Vector2 a -> (Vector2 \\\ Vector1) a Source # joinVector :: Vector1 a -> (Vector2 \\\ Vector1) a -> Vector2 a Source #
ProjectionSpace Vector3 Vector2 Source #
Instance details Defined in Math.Matrix.Vector3 Associated Types data (Vector3 \\\ Vector2) a Source # Methods projectFirst :: Vector3 a -> Vector2 a Source # projectSecond :: Vector3 a -> (Vector3 \\\ Vector2) a Source # joinVector :: Vector2 a -> (Vector3 \\\ Vector2) a -> Vector3 a Source #
SplittableVector Vector1 Vector2 Source #
Instance details Defined in Math.Matrix.Vector3 Methods vsplit :: (Vector1 :+: Vector2) a -> (Vector1 a, Vector2 a) Source #
SplittableVector Vector2 Vector1 Source #
Instance details Defined in Math.Matrix.Vector3 Methods vsplit :: (Vector2 :+: Vector1) a -> (Vector2 a, Vector1 a) Source #
SplittableVector Vector2 Vector2 Source #
Instance details Defined in Math.Matrix.Vector4 Methods vsplit :: (Vector2 :+: Vector2) a -> (Vector2 a, Vector2 a) Source #
Num a => Traceable Vector2 a Source #
Instance details Defined in Math.Matrix.Vector2 Methods traceImpl :: (Vector2 :: Vector2) a -> a Source # determinantImpl :: (Vector2 :: Vector2) a -> a Source # vectorDimension :: Vector2 a -> a Source #
HasIdentityLinear Vector2 LinearMap Source #
Instance details Defined in Math.Matrix.Linear Methods matIdentity :: (Num a, ConjugateSymmetric a) => LinearMap (Vector2 a) (Vector2 a) Source #
(ConjugateSymmetric a, Fractional a) => LinearInvertible LinearMap Vector2 a Source #
Instance details Defined in Math.Matrix.Linear Methods cofactor :: LinearMap (Vector2 a) (Vector2 a) -> LinearMap (Vector2 a) (Vector2 a) Source # adjucate :: LinearMap (Vector2 a) (Vector2 a) -> LinearMap (Vector2 a) (Vector2 a) Source # inverse :: LinearMap (Vector2 a) (Vector2 a) -> LinearMap (Vector2 a) (Vector2 a) Source #
(ConjugateSymmetric a, Num a) => LinearTraceable LinearMap Vector2 a Source #
Instance details Defined in Math.Matrix.Linear Methods determinant :: LinearMap (Vector2 a) (Vector2 a) -> a Source # trace :: LinearMap (Vector2 a) (Vector2 a) -> a Source #
(ConjugateSymmetric a, Num a) => LinearTransform Vector1 Vector2 a Source #
Instance details Defined in Math.Matrix.Vector2 Methods (<>>) :: Vector2 a -> (Vector1 :: Vector2) a -> Vector1 a Source # (<<>) :: (Vector1 :: Vector2) a -> Vector1 a -> Vector2 a Source #
(ConjugateSymmetric a, Num a) => LinearTransform Vector2 Vector1 a Source #
Instance details Defined in Math.Matrix.Vector2 Methods (<>>) :: Vector1 a -> (Vector2 :: Vector1) a -> Vector2 a Source # (<<>) :: (Vector2 :: Vector1) a -> Vector2 a -> Vector1 a Source #
Scalar (SIMDVec 2 Double) ~ Double => LinearTransform Vector2 Vector2 Double Source #
Instance details Defined in Math.Matrix.SIMD Methods (<>>) :: Vector2 Double -> (Vector2 :: Vector2) Double -> Vector2 Double Source # (<<>) :: (Vector2 :: Vector2) Double -> Vector2 Double -> Vector2 Double Source #
(ConjugateSymmetric a, Num a) => LinearTransform Vector2 Vector2 a Source #
Instance details Defined in Math.Matrix.Vector2 Methods (<>>) :: Vector2 a -> (Vector2 :: Vector2) a -> Vector2 a Source # (<<>) :: (Vector2 :: Vector2) a -> Vector2 a -> Vector2 a Source #
(Num a, ConjugateSymmetric a) => LinearTransform Vector2 Vector3 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods (<>>) :: Vector3 a -> (Vector2 :: Vector3) a -> Vector2 a Source # (<<>) :: (Vector2 :: Vector3) a -> Vector2 a -> Vector3 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 Vector2 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods (<>>) :: Vector2 a -> (Vector3 :: Vector2) a -> Vector3 a Source # (<<>) :: (Vector3 :: Vector2) a -> Vector3 a -> Vector2 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 #
(ConjugateSymmetric a, Num a) => ProjectionDual Vector2 Dual a Source #
Instance details Defined in Math.Matrix.Linear Methods projectionDual :: Vector2 (Dual (Vector2 a)) Source #
Transposable Vector1 Vector2 a Source #
Instance details Defined in Math.Matrix.Vector2 Methods transposeImpl :: (Vector1 :: Vector2) a -> (Vector2 :: Vector1) a Source #
Transposable Vector2 Vector1 a Source #
Instance details Defined in Math.Matrix.Vector2 Methods transposeImpl :: (Vector2 :: Vector1) a -> (Vector1 :: Vector2) a Source #
Transposable Vector2 Vector2 a Source #
Instance details Defined in Math.Matrix.Vector2 Methods transposeImpl :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a Source #
Transposable Vector2 Vector3 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods transposeImpl :: (Vector2 :: Vector3) a -> (Vector3 :: Vector2) 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 Vector2 a Source #
Instance details Defined in Math.Matrix.Vector3 Methods transposeImpl :: (Vector3 :: Vector2) a -> (Vector2 :: Vector3) 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 Stream Vector2 a Source #
Instance details Defined in Math.Matrix.Vector2 Methods transposeImpl :: (Stream :: Vector2) a -> (Vector2 :: Stream) a Source #
FunctorArrow Vector2 (:==:) (:==:) Source #
Instance details Defined in Math.Matrix.Vector2 Methods amap :: forall (c :: k) (d :: k). (c :==: d) -> Vector2 c :==: Vector2 d Source #
(Scalar a ~ a, Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Dual Vector2 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Dual a) (Vector2 a) -> (Dual :: Vector2) a Source # linear :: (Dual :: Vector2) a -> LinearMap (Dual a) (Vector2 a) Source #
(Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector1 Vector2 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector1 a) (Vector2 a) -> (Vector1 :: Vector2) a Source # linear :: (Vector1 :: Vector2) a -> LinearMap (Vector1 a) (Vector2 a) Source #
(Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector2 Vector1 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector2 a) (Vector1 a) -> (Vector2 :: Vector1) a Source # linear :: (Vector2 :: Vector1) a -> LinearMap (Vector2 a) (Vector1 a) Source #
(Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector2 Vector2 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector2 a) (Vector2 a) -> (Vector2 :: Vector2) a Source # linear :: (Vector2 :: Vector2) a -> LinearMap (Vector2 a) (Vector2 a) Source #
(Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector2 Vector3 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector2 a) (Vector3 a) -> (Vector2 :: Vector3) a Source # linear :: (Vector2 :: Vector3) a -> LinearMap (Vector2 a) (Vector3 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, InnerProductSpace (Stream a)) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector2 Stream (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector2 a) (Stream a) -> (Vector2 :: Stream) a Source # linear :: (Vector2 :: Stream) a -> LinearMap (Vector2 a) (Stream a) Source #
(Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector3 Vector2 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector3 a) (Vector2 a) -> (Vector3 :: Vector2) a Source # linear :: (Vector3 :: Vector2) a -> LinearMap (Vector3 a) (Vector2 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, InnerProductSpace (Stream a)) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Stream Vector2 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Stream a) (Vector2 a) -> (Stream :: Vector2) a Source # linear :: (Stream :: Vector2) a -> LinearMap (Stream a) (Vector2 a) Source #
(Num a, ConjugateSymmetric a) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector2 Dual (f a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector2 (f a)) (Dual (f a)) -> (Vector2 :: Dual) (f a) Source # linear :: (Vector2 :: Dual) (f a) -> LinearMap (Vector2 (f a)) (Dual (f a)) Source #
(Num a, ConjugateSymmetric a, Universe col) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Vector2 ((->) col :: Type -> Type) (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (Vector2 a) (col -> a) -> (Vector2 :: (->) col) a Source # linear :: (Vector2 :: (->) col) a -> LinearMap (Vector2 a) (col -> a) Source #
(Num a, ConjugateSymmetric a, Universe row) => Linearizable LinearMap ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) ((->) row :: Type -> Type) Vector2 (a :: Type) Source #
Instance details Defined in Math.Matrix.Linear Methods fromLinear :: LinearMap (row -> a) (Vector2 a) -> ((->) row :: Vector2) a Source # linear :: ((->) row :: Vector2) a -> LinearMap (row -> a) (Vector2 a) Source #
(Limiting str a, Monad str) => Limiting str (Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 Associated Types data Closure str (Vector2 a) Source # Methods limit :: str (Vector2 a) -> Closure str (Vector2 a) Source # approximations :: Closure str (Vector2 a) -> str (Vector2 a) Source #
Lift a => Lift (Vector2 a :: Type) Source #
Instance details Defined in Math.Matrix.QuasiQuoter Methods lift :: Quote m => Vector2 a -> m Exp # liftTyped :: forall (m :: Type -> Type). Quote m => Vector2 a -> Code m (Vector2 a) #
(ConjugateSymmetric a, Infinitesimal Stream a, VectorSpace a, Closed a) => VectorCrossProduct (Vector2 a :: Type) LinearMap Source #
Instance details Defined in Math.Matrix.Linear Methods curl :: LinearMap (Vector2 a) (Vector2 a) -> LinearMap (Vector2 a) (Vector2 a) Source #
(Infinitesimal Stream a, Closed a) => VectorLaplacian (Vector2 a :: Type) LinearMap Source #
Instance details Defined in Math.Matrix.Linear Methods vectorLaplace :: LinearMap (Vector2 a) (Vector2 a) -> LinearMap (Vector2 a) (Vector2 a) Source #
(Num a, Universe col) => LinearTransform Vector2 ((->) col) a Source #
Instance details Defined in Math.Matrix.Simple Methods (<>>) :: (col -> a) -> (Vector2 :: (->) col) a -> Vector2 a Source # (<<>) :: (Vector2 :: (->) col) a -> Vector2 a -> col -> a Source #
Transposable Vector2 ((->) row) a Source #
Instance details Defined in Math.Matrix.Vector2 Methods transposeImpl :: (Vector2 :: (->) row) a -> ((->) row :: Vector2) a Source #
Data a => Data (Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Vector2 a -> c (Vector2 a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Vector2 a) # toConstr :: Vector2 a -> Constr # dataTypeOf :: Vector2 a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Vector2 a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Vector2 a)) # gmapT :: (forall b. Data b => b -> b) -> Vector2 a -> Vector2 a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Vector2 a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Vector2 a -> r # gmapQ :: (forall d. Data d => d -> u) -> Vector2 a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Vector2 a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Vector2 a -> m (Vector2 a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Vector2 a -> m (Vector2 a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Vector2 a -> m (Vector2 a) #
Applicative (Codiagonal Vector2) Source #
Instance details Defined in Math.Matrix.Vector2 Methods pure :: a -> Codiagonal Vector2 a # (<>) :: Codiagonal Vector2 (a -> b) -> Codiagonal Vector2 a -> Codiagonal Vector2 b # liftA2 :: (a -> b -> c) -> Codiagonal Vector2 a -> Codiagonal Vector2 b -> Codiagonal Vector2 c # (>) :: Codiagonal Vector2 a -> Codiagonal Vector2 b -> Codiagonal Vector2 b # (<*) :: Codiagonal Vector2 a -> Codiagonal Vector2 b -> Codiagonal Vector2 a #
Functor (Codiagonal Vector2) Source #
Instance details Defined in Math.Matrix.Vector2 Methods fmap :: (a -> b) -> Codiagonal Vector2 a -> Codiagonal Vector2 b # (<$) :: a -> Codiagonal Vector2 b -> Codiagonal Vector2 a #
Num s => Monoid (Vector2 s) Source #
Instance details Defined in Math.Matrix.Vector2 Methods mempty :: Vector2 s # mappend :: Vector2 s -> Vector2 s -> Vector2 s # mconcat :: [Vector2 s] -> Vector2 s #
Num s => Semigroup (Vector2 s) Source #
Instance details Defined in Math.Matrix.Vector2 Methods (<>) :: Vector2 s -> Vector2 s -> Vector2 s # sconcat :: NonEmpty (Vector2 s) -> Vector2 s # stimes :: Integral b => b -> Vector2 s -> Vector2 s #
Generic a => Generic (Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 Associated Types type Rep (Vector2 a) :: Type -> Type # Methods from :: Vector2 a -> Rep (Vector2 a) x # to :: Rep (Vector2 a) x -> Vector2 a #
Num a => Num (Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 Methods (+) :: Vector2 a -> Vector2 a -> Vector2 a # (-) :: Vector2 a -> Vector2 a -> Vector2 a # (*) :: Vector2 a -> Vector2 a -> Vector2 a # negate :: Vector2 a -> Vector2 a # abs :: Vector2 a -> Vector2 a # signum :: Vector2 a -> Vector2 a # fromInteger :: Integer -> Vector2 a #
Read a => Read (Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 Methods readsPrec :: Int -> ReadS (Vector2 a) # readList :: ReadS [Vector2 a] # readPrec :: ReadPrec (Vector2 a) # readListPrec :: ReadPrec [Vector2 a] #
Show a => Show (Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 Methods showsPrec :: Int -> Vector2 a -> ShowS # show :: Vector2 a -> String # showList :: [Vector2 a] -> ShowS #
Binary s => Binary (Vector2 s) Source #
Instance details Defined in Math.Matrix.Vector2 Methods put :: Vector2 s -> Put # get :: Get (Vector2 s) # putList :: [Vector2 s] -> Put #
ConjugateSymmetric a => ConjugateSymmetric (Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 Methods conj :: Vector2 a -> Vector2 a Source #
Num a => CoordinateSpace (Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 Associated Types type Coordinate (Vector2 a) Source # Methods index :: Coordinate (Vector2 a) -> Vector2 a -> Scalar (Vector2 a) Source # listVector :: [Scalar (Vector2 a)] -> Vector2 a Source # dimensionSize :: Vector2 a -> Int Source # coordinates :: Vector2 a -> [Coordinate (Vector2 a)] Source #
Scalar (SIMDVec 2 Double) ~ Double => InnerProductSpace (Vector2 Double) Source #
Instance details Defined in Math.Matrix.SIMD Methods (%.) :: Vector2 Double -> Vector2 Double -> Scalar (Vector2 Double) Source #
(Num a, ConjugateSymmetric a) => InnerProductSpace (Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 Methods (%.) :: Vector2 a -> Vector2 a -> Scalar (Vector2 a) Source #
NormedSpace (Vector2 (Complex Float)) Source #
Instance details Defined in Math.Matrix.SIMD Methods norm :: Vector2 (Complex Float) -> Scalar (Vector2 (Complex Float)) Source # normSquared :: Vector2 (Complex Float) -> Scalar (Vector2 (Complex Float)) Source #
(Floating a, ConjugateSymmetric a) => NormedSpace (Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 Methods norm :: Vector2 a -> Scalar (Vector2 a) Source # normSquared :: Vector2 a -> Scalar (Vector2 a) Source #
StandardBasis (Vector2 (Vector2 Int)) Source #
Instance details Defined in Math.Matrix.Vector2 Methods unitVectors :: [Vector2 (Vector2 Int)] Source #
StandardBasis (Vector2 Int) Source #
Instance details Defined in Math.Matrix.Vector2 Methods unitVectors :: [Vector2 Int] Source #
Num a => StandardBasis (Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 Methods unitVectors :: [Vector2 a] Source #
Num a => VectorSpace (Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 Associated Types type Scalar (Vector2 a) Source # Methods vzero :: Vector2 a Source # vnegate :: Vector2 a -> Vector2 a Source # (%+) :: Vector2 a -> Vector2 a -> Vector2 a Source # (%*) :: Scalar (Vector2 a) -> Vector2 a -> Vector2 a Source #
Optimal (Vector2 (Complex Float)) Source #
Instance details Defined in Math.Matrix.SIMD Associated Types type Optimized (Vector2 (Complex Float)) Source # Methods toO :: Vector2 (Complex Float) -> Optimized (Vector2 (Complex Float)) Source # fromO :: Optimized (Vector2 (Complex Float)) -> Vector2 (Complex Float) Source # zipO :: (Scalar (Vector2 (Complex Float)) -> Scalar (Vector2 (Complex Float)) -> Scalar (Vector2 (Complex Float))) -> Optimized (Vector2 (Complex Float)) -> Optimized (Vector2 (Complex Float)) -> Optimized (Vector2 (Complex Float)) Source # mapO :: (Scalar (Vector2 (Complex Float)) -> Scalar (Vector2 (Complex Float))) -> Optimized (Vector2 (Complex Float)) -> Optimized (Vector2 (Complex Float)) Source # sumCoordinatesO :: Optimized (Vector2 (Complex Float)) -> Scalar (Vector2 (Complex Float)) Source # constantO :: Scalar (Vector2 (Complex Float)) -> Optimized (Vector2 (Complex Float)) Source #
Optimal (Vector2 Int64) Source #
Instance details Defined in Math.Matrix.SIMD Associated Types type Optimized (Vector2 Int64) Source # Methods toO :: Vector2 Int64 -> Optimized (Vector2 Int64) Source # fromO :: Optimized (Vector2 Int64) -> Vector2 Int64 Source # zipO :: (Scalar (Vector2 Int64) -> Scalar (Vector2 Int64) -> Scalar (Vector2 Int64)) -> Optimized (Vector2 Int64) -> Optimized (Vector2 Int64) -> Optimized (Vector2 Int64) Source # mapO :: (Scalar (Vector2 Int64) -> Scalar (Vector2 Int64)) -> Optimized (Vector2 Int64) -> Optimized (Vector2 Int64) Source # sumCoordinatesO :: Optimized (Vector2 Int64) -> Scalar (Vector2 Int64) Source # constantO :: Scalar (Vector2 Int64) -> Optimized (Vector2 Int64) Source #
Optimal (Vector2 Double) Source #
Instance details Defined in Math.Matrix.SIMD Associated Types type Optimized (Vector2 Double) Source # Methods toO :: Vector2 Double -> Optimized (Vector2 Double) Source # fromO :: Optimized (Vector2 Double) -> Vector2 Double Source # zipO :: (Scalar (Vector2 Double) -> Scalar (Vector2 Double) -> Scalar (Vector2 Double)) -> Optimized (Vector2 Double) -> Optimized (Vector2 Double) -> Optimized (Vector2 Double) Source # mapO :: (Scalar (Vector2 Double) -> Scalar (Vector2 Double)) -> Optimized (Vector2 Double) -> Optimized (Vector2 Double) Source # sumCoordinatesO :: Optimized (Vector2 Double) -> Scalar (Vector2 Double) Source # constantO :: Scalar (Vector2 Double) -> Optimized (Vector2 Double) Source #
MedianAlgebra s => MedianAlgebra (Vector2 s) Source #
Instance details Defined in Math.Matrix.Vector2 Methods med :: Vector2 s -> Vector2 s -> Vector2 s -> Vector2 s Source #
PpShow a => PpShow (Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 Methods pp :: Vector2 a -> Doc Source #
Universe a => Universe (Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 Methods allElements :: [Vector2 a] Source #
Visitor (Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 Associated Types data Fold (Vector2 a) :: Type -> Type Source # Methods visit :: Fold (Vector2 a) a0 -> Vector2 a -> a0 Source #
Eq a => Eq (Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 Methods (==) :: Vector2 a -> Vector2 a -> Bool # (/=) :: Vector2 a -> Vector2 a -> Bool #
Ord a => Ord (Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 Methods compare :: Vector2 a -> Vector2 a -> Ordering # (<) :: Vector2 a -> Vector2 a -> Bool # (<=) :: Vector2 a -> Vector2 a -> Bool # (>) :: Vector2 a -> Vector2 a -> Bool # (>=) :: Vector2 a -> Vector2 a -> Bool # max :: Vector2 a -> Vector2 a -> Vector2 a # min :: Vector2 a -> Vector2 a -> Vector2 a #
(Num a, ConjugateSymmetric a) => Dualizable (Vector2 a) Dual Source #
Instance details Defined in Math.Matrix.Linear Methods covector :: (Vector2 a -> Scalar (Vector2 a)) -> Dual (Vector2 a) Source # bracket :: Dual (Vector2 a) -> Vector2 a -> Scalar (Vector2 a) Source #
(ConjugateSymmetric a, Infinitesimal Stream a, Closed a) => VectorDerivative (Vector2 a) Dual LinearMap Source #
Instance details Defined in Math.Matrix.Linear Methods divergence :: LinearMap (Vector2 a) (Vector2 a) -> Dual (Vector2 a) Source # grad :: Dual (Vector2 a) -> LinearMap (Vector2 a) (Vector2 a) Source # directionalDerivative :: Vector2 a -> Dual (Vector2 a) -> Dual (Vector2 a) Source # laplace :: Dual (Vector2 a) -> Dual (Vector2 a) Source #
Num a => DecomposableVectorSpace (Vector2 a) ((->) TwoD) Source #
Instance details Defined in Math.Matrix.Simple Methods decompose :: (Scalar (Vector2 a) -> res) -> Vector2 a -> TwoD -> res Source # project :: Vector2 a -> TwoD -> Scalar (Vector2 a) Source #
Applicative (Vector2 \\\ Vector1) Source #
Instance details Defined in Math.Matrix.Vector2 Methods pure :: a -> (Vector2 \\\ Vector1) a # (<>) :: (Vector2 \\\ Vector1) (a -> b) -> (Vector2 \\\ Vector1) a -> (Vector2 \\\ Vector1) b # liftA2 :: (a -> b -> c) -> (Vector2 \\\ Vector1) a -> (Vector2 \\\ Vector1) b -> (Vector2 \\\ Vector1) c # (>) :: (Vector2 \\\ Vector1) a -> (Vector2 \\\ Vector1) b -> (Vector2 \\\ Vector1) b # (<*) :: (Vector2 \\\ Vector1) a -> (Vector2 \\\ Vector1) b -> (Vector2 \\\ Vector1) a #
Applicative (Vector3 \\\ Vector2) Source #
Instance details Defined in Math.Matrix.Vector3 Methods pure :: a -> (Vector3 \\\ Vector2) a # (<>) :: (Vector3 \\\ Vector2) (a -> b) -> (Vector3 \\\ Vector2) a -> (Vector3 \\\ Vector2) b # liftA2 :: (a -> b -> c) -> (Vector3 \\\ Vector2) a -> (Vector3 \\\ Vector2) b -> (Vector3 \\\ Vector2) c # (>) :: (Vector3 \\\ Vector2) a -> (Vector3 \\\ Vector2) b -> (Vector3 \\\ Vector2) b # (<*) :: (Vector3 \\\ Vector2) a -> (Vector3 \\\ Vector2) b -> (Vector3 \\\ Vector2) a #
Functor (Vector2 \\\ Vector1) Source #
Instance details Defined in Math.Matrix.Vector2 Methods fmap :: (a -> b) -> (Vector2 \\\ Vector1) a -> (Vector2 \\\ Vector1) b # (<$) :: a -> (Vector2 \\\ Vector1) b -> (Vector2 \\\ Vector1) a #
Functor (Vector3 \\\ Vector2) Source #
Instance details Defined in Math.Matrix.Vector3 Methods fmap :: (a -> b) -> (Vector3 \\\ Vector2) a -> (Vector3 \\\ Vector2) b # (<$) :: a -> (Vector3 \\\ Vector2) b -> (Vector3 \\\ Vector2) a #
Show a => Show (Codiagonal Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 Methods showsPrec :: Int -> Codiagonal Vector2 a -> ShowS # show :: Codiagonal Vector2 a -> String # showList :: [Codiagonal Vector2 a] -> ShowS #
Show a => Show ((Vector3 \\\ Vector2) a) Source #
Instance details Defined in Math.Matrix.Vector3 Methods showsPrec :: Int -> (Vector3 \\\ Vector2) a -> ShowS # show :: (Vector3 \\\ Vector2) a -> String # showList :: [(Vector3 \\\ Vector2) a] -> ShowS #
(Universe row, Num a) => LinearTransform ((->) row) Vector2 a Source #
Instance details Defined in Math.Matrix.Simple Methods (<>>) :: Vector2 a -> ((->) row :: Vector2) a -> row -> a Source # (<<>) :: ((->) row :: Vector2) a -> (row -> a) -> Vector2 a Source #
Transposable ((->) row) Vector2 a Source #
Instance details Defined in Math.Matrix.Vector2 Methods transposeImpl :: ((->) row :: Vector2) a -> (Vector2 :: (->) row) a Source #
Num a => Indexable (Vector2 :*: Vector2) a Source #
Instance details Defined in Math.Matrix.Vector2 Methods diagonalProjections :: (Vector2 :: Vector2) (Index (Vector2 :: Vector2) a) Source # basisVector :: Index (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a Source # indexProject :: Index (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a -> a Source # indexableIndices :: (Vector2 :*: Vector2) a Source #
(Num a, ConjugateSymmetric a) => Monoid ((Vector2 :*: Vector2) a) Source #	see "Lawvere,Rosebrugh: Sets for mathematics", pg. 167.
Instance details Defined in Math.Matrix.Vector2 Methods mempty :: (Vector2 :: Vector2) a # mappend :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a # mconcat :: [(Vector2 :: Vector2) a] -> (Vector2 :: Vector2) a #
(Num a, ConjugateSymmetric a) => Semigroup ((Vector2 :*: Vector2) a) Source #	see "Lawvere,Rosebrugh: Sets for mathematics", pg. 167.
Instance details Defined in Math.Matrix.Vector2 Methods (<>) :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a # sconcat :: NonEmpty ((Vector2 :: Vector2) a) -> (Vector2 :: Vector2) a # stimes :: Integral b => b -> (Vector2 :: Vector2) a -> (Vector2 :*: Vector2) a #
(Num a, ConjugateSymmetric a) => Num ((Vector2 :*: Vector2) a) Source #
Instance details Defined in Math.Matrix.Vector2 Methods (+) :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a # (-) :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a # () :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a # negate :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a # abs :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a # signum :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a # fromInteger :: Integer -> (Vector2 :*: Vector2) a #
(Fractional a, ConjugateSymmetric a) => Fractional ((Vector2 :*: Vector2) a) Source #
Instance details Defined in Math.Matrix.Linear Methods (/) :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a # recip :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a # fromRational :: Rational -> (Vector2 :: Vector2) a #
Show (f a) => Show ((Vector2 :*: f) a) Source #
Instance details Defined in Math.Matrix.Vector2 Methods showsPrec :: Int -> (Vector2 :: f) a -> ShowS # show :: (Vector2 :: f) a -> String # showList :: [(Vector2 :*: f) a] -> ShowS #
(Num a, ConjugateSymmetric a) => ConjugateSymmetric ((Vector2 :*: Vector2) a) Source #	https://en.wikipedia.org/wiki/Conjugate_transpose
Instance details Defined in Math.Matrix.Vector2 Methods conj :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a Source #
(ConjugateSymmetric a, Num a) => StandardBasis ((Dual :*: Vector2) a) Source #	https://en.wikipedia.org/wiki/Dual_space
Instance details Defined in Math.Matrix.Covector Methods unitVectors :: [(Dual :*: Vector2) a] Source #
Num a => VectorSpace ((Vector1 :*: Vector2) a) Source #
Instance details Defined in Math.Matrix.Vector2 Associated Types type Scalar ((Vector1 :: Vector2) a) Source # Methods vzero :: (Vector1 :: Vector2) a Source # vnegate :: (Vector1 :: Vector2) a -> (Vector1 :: Vector2) a Source # (%+) :: (Vector1 :: Vector2) a -> (Vector1 :: Vector2) a -> (Vector1 :: Vector2) a Source # (%) :: Scalar ((Vector1 :: Vector2) a) -> (Vector1 :: Vector2) a -> (Vector1 :*: Vector2) a Source #
Num a => VectorSpace ((Vector2 :*: Vector1) a) Source #
Instance details Defined in Math.Matrix.Vector2 Associated Types type Scalar ((Vector2 :: Vector1) a) Source # Methods vzero :: (Vector2 :: Vector1) a Source # vnegate :: (Vector2 :: Vector1) a -> (Vector2 :: Vector1) a Source # (%+) :: (Vector2 :: Vector1) a -> (Vector2 :: Vector1) a -> (Vector2 :: Vector1) a Source # (%) :: Scalar ((Vector2 :: Vector1) a) -> (Vector2 :: Vector1) a -> (Vector2 :*: Vector1) a Source #
Num a => VectorSpace ((Vector2 :*: Vector2) a) Source #
Instance details Defined in Math.Matrix.Vector2 Associated Types type Scalar ((Vector2 :: Vector2) a) Source # Methods vzero :: (Vector2 :: Vector2) a Source # vnegate :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a Source # (%+) :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a Source # (%) :: Scalar ((Vector2 :: Vector2) a) -> (Vector2 :: Vector2) a -> (Vector2 :*: Vector2) a Source #
Num a => VectorSpace ((Vector2 :*: Vector3) a) Source #	2 x 3 matrices:
Instance details Defined in Math.Matrix.Vector3 Associated Types type Scalar ((Vector2 :: Vector3) a) Source # Methods vzero :: (Vector2 :: Vector3) a Source # vnegate :: (Vector2 :: Vector3) a -> (Vector2 :: Vector3) a Source # (%+) :: (Vector2 :: Vector3) a -> (Vector2 :: Vector3) a -> (Vector2 :: Vector3) a Source # (%) :: Scalar ((Vector2 :: Vector3) a) -> (Vector2 :: Vector3) a -> (Vector2 :*: Vector3) 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 ((Vector2 :*: (->) col) a) Source #
Instance details Defined in Math.Matrix.Simple Associated Types type Scalar ((Vector2 :: (->) col) a) Source # Methods vzero :: (Vector2 :: (->) col) a Source # vnegate :: (Vector2 :: (->) col) a -> (Vector2 :: (->) col) a Source # (%+) :: (Vector2 :: (->) col) a -> (Vector2 :: (->) col) a -> (Vector2 :: (->) col) a Source # (%) :: Scalar ((Vector2 :: (->) col) a) -> (Vector2 :: (->) col) a -> (Vector2 :*: (->) col) a Source #
Num a => VectorSpace ((Vector3 :*: Vector2) a) Source #	3 x 2 matrices
Instance details Defined in Math.Matrix.Vector3 Associated Types type Scalar ((Vector3 :: Vector2) a) Source # Methods vzero :: (Vector3 :: Vector2) a Source # vnegate :: (Vector3 :: Vector2) a -> (Vector3 :: Vector2) a Source # (%+) :: (Vector3 :: Vector2) a -> (Vector3 :: Vector2) a -> (Vector3 :: Vector2) a Source # (%) :: Scalar ((Vector3 :: Vector2) a) -> (Vector3 :: Vector2) a -> (Vector3 :*: Vector2) 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 (((->) row :*: Vector2) a) Source #
Instance details Defined in Math.Matrix.Simple Associated Types type Scalar (((->) row :: Vector2) a) Source # Methods vzero :: ((->) row :: Vector2) a Source # vnegate :: ((->) row :: Vector2) a -> ((->) row :: Vector2) a Source # (%+) :: ((->) row :: Vector2) a -> ((->) row :: Vector2) a -> ((->) row :: Vector2) a Source # (%) :: Scalar (((->) row :: Vector2) a) -> ((->) row :: Vector2) a -> ((->) row :*: Vector2) a Source #
Optimal ((Vector2 :*: Vector2) Int32) Source #
Instance details Defined in Math.Matrix.SIMD Associated Types type Optimized ((Vector2 :: Vector2) Int32) Source # Methods toO :: (Vector2 :: Vector2) Int32 -> Optimized ((Vector2 :: Vector2) Int32) Source # fromO :: Optimized ((Vector2 :: Vector2) Int32) -> (Vector2 :: Vector2) Int32 Source # zipO :: (Scalar ((Vector2 :: Vector2) Int32) -> Scalar ((Vector2 :: Vector2) Int32) -> Scalar ((Vector2 :: Vector2) Int32)) -> Optimized ((Vector2 :: Vector2) Int32) -> Optimized ((Vector2 :: Vector2) Int32) -> Optimized ((Vector2 :: Vector2) Int32) Source # mapO :: (Scalar ((Vector2 :: Vector2) Int32) -> Scalar ((Vector2 :: Vector2) Int32)) -> Optimized ((Vector2 :: Vector2) Int32) -> Optimized ((Vector2 :: Vector2) Int32) Source # sumCoordinatesO :: Optimized ((Vector2 :: Vector2) Int32) -> Scalar ((Vector2 :: Vector2) Int32) Source # constantO :: Scalar ((Vector2 :: Vector2) Int32) -> Optimized ((Vector2 :*: Vector2) Int32) Source #
Optimal ((Vector2 :*: Vector2) Float) Source #
Instance details Defined in Math.Matrix.SIMD Associated Types type Optimized ((Vector2 :: Vector2) Float) Source # Methods toO :: (Vector2 :: Vector2) Float -> Optimized ((Vector2 :: Vector2) Float) Source # fromO :: Optimized ((Vector2 :: Vector2) Float) -> (Vector2 :: Vector2) Float Source # zipO :: (Scalar ((Vector2 :: Vector2) Float) -> Scalar ((Vector2 :: Vector2) Float) -> Scalar ((Vector2 :: Vector2) Float)) -> Optimized ((Vector2 :: Vector2) Float) -> Optimized ((Vector2 :: Vector2) Float) -> Optimized ((Vector2 :: Vector2) Float) Source # mapO :: (Scalar ((Vector2 :: Vector2) Float) -> Scalar ((Vector2 :: Vector2) Float)) -> Optimized ((Vector2 :: Vector2) Float) -> Optimized ((Vector2 :: Vector2) Float) Source # sumCoordinatesO :: Optimized ((Vector2 :: Vector2) Float) -> Scalar ((Vector2 :: Vector2) Float) Source # constantO :: Scalar ((Vector2 :: Vector2) Float) -> Optimized ((Vector2 :*: Vector2) Float) 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 #
(Fractional a, ConjugateSymmetric a) => Group ((Vector2 :*: Vector2) a) Source #
Instance details Defined in Math.Matrix.Vector2 Methods ginvert :: (Vector2 :: Vector2) a -> (Vector2 :: Vector2) a Source #
PpShow (f a) => PpShow ((Vector2 :*: f) a) Source #
Instance details Defined in Math.Matrix.Vector2 Methods pp :: (Vector2 :*: f) a -> Doc Source #
data Codiagonal Vector2 a Source #
Instance details Defined in Math.Matrix.Vector2 data Codiagonal Vector2 a = Codiagonal2 { down_codiagonal2 :: Vector1 a right_codiagonal2 :: Vector1 a }
type Vector1 :+: Vector2 Source #
Instance details Defined in Math.Matrix.Vector3 type Vector1 :+: Vector2 = Vector3
type Vector2 :+: Vector1 Source #
Instance details Defined in Math.Matrix.Vector3 type Vector2 :+: Vector1 = Vector3
type Vector2 :+: Vector2 Source #
Instance details Defined in Math.Matrix.Vector4 type Vector2 :+: Vector2 = Vector4
type Vector2 :+: Stream Source #
Instance details Defined in Math.Matrix.VectorConversions type Vector2 :+: Stream = Stream
type Vector2 \\ a Source #
Instance details Defined in Math.Matrix.Vector2 type Vector2 \\ a = Vector1 a
data (Vector2 \\\ Vector1) a Source #
Instance details Defined in Math.Matrix.Vector2 data (Vector2 \\\ Vector1) a = S21Vector (Vector1 a)
data (Vector3 \\\ Vector2) a Source #
Instance details Defined in Math.Matrix.Vector3 data (Vector3 \\\ Vector2) a = S32Vector (Vector1 a)
data Closure str (Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 data Closure str (Vector2 a) = Vector2Closure (Vector2 (Closure str a))
type Rep (Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 type Rep (Vector2 a) = D1 ('MetaData "Vector2" "Math.Matrix.Vector2" "cifl-math-library-2.0.0.0-K3Wcv1zXOBxvFThQyThI4" 'False) (C1 ('MetaCons "Vector2" 'PrefixI 'True) (S1 ('MetaSel ('Just "xcoord2") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Just "ycoord2") 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a)))
type Coordinate (Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 type Coordinate (Vector2 a) = Int
type Scalar (Vector2 a) Source #
Instance details Defined in Math.Matrix.Vector2 type Scalar (Vector2 a) = a
type Optimized (Vector2 (Complex Float)) Source #
Instance details Defined in Math.Matrix.SIMD type Optimized (Vector2 (Complex Float)) = SIMDVec 2 (Complex Float)
type Optimized (Vector2 Int64) Source #
Instance details Defined in Math.Matrix.SIMD type Optimized (Vector2 Int64) = SIMDVec 2 Int64
type Optimized (Vector2 Double) Source #
Instance details Defined in Math.Matrix.SIMD type Optimized (Vector2 Double) = SIMDVec 2 Double
data Fold (Vector2 a) b Source #
Instance details Defined in Math.Matrix.Vector2 data Fold (Vector2 a) b = Vector2Fold (a -> a -> b)
type Scalar ((Vector1 :*: Vector2) a) Source #
Instance details Defined in Math.Matrix.Vector2 type Scalar ((Vector1 :*: Vector2) a) = a
type Scalar ((Vector2 :*: Vector1) a) Source #
Instance details Defined in Math.Matrix.Vector2 type Scalar ((Vector2 :*: Vector1) a) = a
type Scalar ((Vector2 :*: Vector2) a) Source #
Instance details Defined in Math.Matrix.Vector2 type Scalar ((Vector2 :*: Vector2) a) = a
type Scalar ((Vector2 :*: Vector3) a) Source #
Instance details Defined in Math.Matrix.Vector3 type Scalar ((Vector2 :*: Vector3) a) = a
type Scalar ((Vector2 :*: Vector4) a) Source #
Instance details Defined in Math.Matrix.Vector4 type Scalar ((Vector2 :*: Vector4) a) = a
type Scalar ((Vector2 :*: (->) col) a) Source #
Instance details Defined in Math.Matrix.Simple type Scalar ((Vector2 :*: (->) col) a) = a
type Scalar ((Vector3 :*: Vector2) a) Source #
Instance details Defined in Math.Matrix.Vector3 type Scalar ((Vector3 :*: Vector2) a) = a
type Scalar ((Vector4 :*: Vector2) a) Source #
Instance details Defined in Math.Matrix.Vector4 type Scalar ((Vector4 :*: Vector2) a) = a
type Scalar (((->) row :*: Vector2) a) Source #
Instance details Defined in Math.Matrix.Simple type Scalar (((->) row :*: Vector2) a) = a
type Optimized ((Vector2 :*: Vector2) Int32) Source #
Instance details Defined in Math.Matrix.SIMD type Optimized ((Vector2 :*: Vector2) Int32) = SIMDVec 4 Int32
type Optimized ((Vector2 :*: Vector2) Float) Source #
Instance details Defined in Math.Matrix.SIMD type Optimized ((Vector2 :*: Vector2) Float) = SIMDVec 4 Float
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

setx2 :: s -> Vector2 s -> Vector2 s Source #

sety2 :: s -> Vector2 s -> Vector2 s Source #

updateRow2 :: g a -> Vector2 ((Vector2 :*: g) a -> (Vector2 :*: g) a) Source #

updateColumn2 :: Applicative f => f a -> Vector2 ((f :*: Vector2) a -> (f :*: Vector2) a) Source #

type ComplexVector2 a = (Vector2 :*: Complex) a Source #

i2 :: Num a => Vector2 a Source #

j2 :: Num a => Vector2 a Source #

vector2Iso :: Vector2 a :==: Complex a Source #

matrixRoot :: (Diagonalizable m a, ProjectionSpace m Vector1) => (m :*: m) a -> a Source #

type Matrix2 a = (Vector2 :*: Vector2) a Source #

zero_codiagonal2 :: Num a => Codiagonal Vector2 a Source #

constant2 :: a -> Vector2 a Source #

complexMatrix :: Num a => Complex a -> (Vector2 :*: Vector2) a Source #

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

codiagonal2 :: Matrix2 a -> Codiagonal Vector2 a Source #

delPartial2 :: DifferentiallyClosed a => (Vector2 a -> a) -> Vector2 a -> Vector2 a Source #

diagonalMatrix2 :: Num a => Vector2 a -> (Vector2 :*: Vector2) a Source #

sumCoordinates2 :: Num a => Vector2 a -> a Source #

productCoordinates2 :: Num a => Vector2 a -> a Source #

mat2 :: Vector2 a -> Codiagonal Vector2 a -> (Vector2 :*: Vector2) a Source #

matrix2 :: Vector2 a -> Codiagonal Vector2 a -> (Vector2 :*: Vector2) a Source #

vec2 :: (a, a) -> Vector2 a Source #

su2_matrix :: (Eq a, RealFloat a) => Complex a -> Complex a -> Matrix2 (Complex a) Source #

splitMatrix :: (Functor f, SplittableVector f f, SplittableVector m m) => ((f :+: f) :*: (m :+: m)) a -> (Vector2 :*: Vector2) ((f :*: m) a) Source #

removex2 :: Vector2 a -> Vector1 a Source #

removey2 :: Vector2 a -> Vector1 a Source #

remove2 :: Vector2 (Vector2 a -> Vector1 a) Source #

remove_index2 :: Matrix2 a -> Matrix2 (Matrix1 a) Source #

cofactor2 :: Num a => Matrix2 a -> Matrix2 a Source #

adjucate2 :: Num a => Matrix2 a -> Matrix2 a Source #

inverse2 :: Fractional a => Matrix2 a -> Matrix2 a Source #

vector_indices2 :: Vector2 Integer Source #

matrix_indices2 :: (Vector2 :*: Vector2) (Integer, Integer) Source #

signs2 :: (Vector2 :*: Vector2) Integer Source #

vector_vector2 :: [a] -> Vector2 a Source #

diagonal2 :: Num a => Matrix2 a -> Vector2 a Source #

composeIndex :: (m (n a) :==: I (n a)) -> (n a :==: I a) -> (m :*: n) a :==: (I :*: I) a Source #

diagonalProjections2 :: Num a => Vector2 (Index Vector2 a) Source #

transpose2 :: Num a => Matrix2 a -> Matrix2 a Source #

transpose2Impl :: Matrix2 a -> Matrix2 a Source #

rotate2 :: Vector2 a -> Vector2 a Source #

bindDiagonal2 :: Vector2 a -> (a -> Vector2 b) -> Vector2 b Source #

bindCodiagonal2 :: Vector2 a -> (a -> Vector2 b) -> Vector2 b Source #

crossProductScalar2 :: Num a => Vector2 a -> Vector2 a -> a Source #

orthogonalVector2 :: Num a => Vector2 a -> Vector2 a Source #

crossProduct2 :: Num a => (Vector1 :*: Vector2) a -> Vector2 a Source #

leftMultiply2Gen :: (Functor f, Num a, ConjugateSymmetric a) => Vector2 a -> (f :*: Vector2) a -> f a Source #

rightMultiply2Gen :: (VectorSpace (f a), ConjugateSymmetric a, Scalar (f a) ~ a) => (Vector2 :*: f) a -> Vector2 a -> f a Source #

leftMultiply1_2 :: (Num a, ConjugateSymmetric a) => Vector2 a -> (Vector1 :*: Vector2) a -> Vector1 a Source #

leftMultiply2_1 :: (Num a, ConjugateSymmetric a) => Vector1 a -> (Vector2 :*: Vector1) a -> Vector2 a Source #

leftMultiply2 :: (Num a, ConjugateSymmetric a) => Vector2 a -> Matrix2 a -> Vector2 a Source #

rightMultiply2 :: (Num a, ConjugateSymmetric a) => Matrix2 a -> Vector2 a -> Vector2 a Source #

rightMultiply2_1 :: (ConjugateSymmetric a, Num a) => (Vector2 :*: Vector1) a -> Vector2 a -> Vector1 a Source #

rightMultiply1_2 :: (ConjugateSymmetric a, Num a) => (Vector1 :*: Vector2) a -> Vector1 a -> Vector2 a Source #

trace2 :: Num a => Matrix2 a -> a Source #

diagonal2x :: Num a => Matrix2 a -> Vector2 a Source #

diagonal2y :: Num a => Matrix2 a -> Vector2 a Source #

identity2 :: Num a => Matrix2 a Source #

determinant2 :: Num a => Matrix2 a -> a Source #

index_vector2 :: Int -> Vector2 a -> a Source #

rotateMatrix2 :: Floating a => a -> Matrix2 a Source #

eigenvalue2 :: Floating a => (Vector2 :*: Vector2) a -> Vector2 a Source #

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

leviCivita2 :: Num a => (Vector2 :*: Vector2) a Source #

https://en.wikipedia.org/wiki/Levi-Civita_symbol

Orphan instances

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